金融工程答案翻译
金融工程答案翻译
第一章1.4 仔细解释卖出一个看涨期权与买入一个看跌期权的差异卖出一个看涨期权涉及到给他人一个买入你某项财产的权利，它将给你带来的收益为-max 〔st-k，0〕=min〔k-st，0〕买入一个看跌期权涉及到从他人手里买入一个期权，带来的收益为max〔k-st，0〕他们都有一个可能性的收入k-st，当你卖出看涨期权，收入为负值或0，这是因为交易对手可以选择是否执行。
当你买入一个看跌期权，你的收入为0或正直，这是因为你选择执行与否1.5 你认为某股票价格将要上升，股票当前价格为29美元，三个月期限，执行价格为30美元的看涨期权价格为2.9美元，你共有美金5800元，说明两种投资模式，并简单说明一下两种模式的优缺点有两种方案，即买入200股股票或买入2000份看涨期权，当股票价格上涨航行好，第二种方案将得到更高的回报。
举例来说，当股价上涨为40元，此时收益为2000〔40-30〕-5800=14200 而第一种反感只有200〔40-29〕=2200元收益，但当股价下跌，第二种方案将有更大的损失。
当股票价格下跌至25元，第一种方案损失为200〔29-25〕=800元，第二种方案则带来5800元的损失，这个例子证明了期权有一定的杠杆效率这个套利者可以借入资金买入100盎司黄金现货和卖出一个100盎司于一年后交割的期货合约，这就意味着黄金以600美元每盎司买入以800美元每盎司卖出，收益率约为33.3%，远高于10%的接入率，这是一个很好的盈利时机，套利者应尽可能多的买入黄金现货及预期数量相匹配的期货合约1.27 股票当前价格为94美金，同时，三个月期，执行价格为95美元的欧式期权价格为4.7美元，一个投资者认为股价会上涨，但他并不知道应该买入100股股票或买入2000个〔20份〕期权，这两种投资所需资金均为9400美元，此时你会给出什么建议？股价涨到什么样的水平会使得期权投资盈利更好？投资于看涨期权会带来高收益但是会有高风险，如果股价停止在94美元，买入看涨期权的投资者损失9400美元，儿买入股票的投资者什么也没有损失，如果股价上涨到120美元，买入期权的投资者会得到2000〔120-95〕-9400=40600美元的收益，而买入股票的投资者会得到100〔120-94〕-9400=2600元，当股价为s时，这两种投资的收益相等，100〔s-94〕=2000〔s-95〕，s-100。
《金融工程学》习题及参考答案
《金融工程学》习题及参考答案《金融工程学》习题及参考答案无套利定价和风险中性定价练习1、假定外汇市场美元兑换马克的即期汇率是1美元换1.8马克，美元利率是8%，马克利率是4%，试问一年后远期无套利的均衡利率是多少？2、银行希望在6个月后对客户提供一笔6个月的远期贷款。
银行发现金融市场上即期利率水平是：6个月利率为9.5%，12个月利率为9.875%，按照无套利定价思想，银行为这笔远期贷款索要的利率是多少？3、假如英镑与美元的即期汇率是1英镑=1.6650美元，远期汇率是1英镑=1.6600美元，6个月期美远与英镑的无风险年利率分别是6%和8%，问是否存在无风险套利机会？如存在，如何套利？4、一只股票现在价格是40元，该股票一个月后价格将是42元或者38元。
假如无风险利率是8%，用无风险套利原则说明，执行价格为39元的一个月期欧式看涨期权的价值是多少？5、条件同题4，试用风险中性定价法计算题4中看涨期权的价值，并比较两种计算结果。
6、一只股票现在的价格是50元，预计6个月后涨到55元或是下降到45元。
运用无套利定价原理，求执行价格为50元的欧式看跌期权的价值。
7、一只股票现在价格是100元。
有连续两个时间步，每个步长6个月，每个单步二叉树预期上涨10%，或下跌10%，无风险利率8%（连续复利），运用无套利原则求执行价格为100元的看涨期权的价值。
8、假设市场上股票价格S=20元，执行价格X=18元，r=10%,T=1年。
如果市场报价欧式看涨期权的价格是3元，试问存在无风险的套利机会吗？如果有，如何套利？9、股票当前的价格是100元，以该价格作为执行价格的看涨期权和看跌期权的价格分别是3元和7元。
如果买入看涨期权、卖出看跌期权，再购入到期日价值为100 的无风险债券，则我们就复制了该股票的价值特征（可以叫做合成股票）。
试问无风险债券的投资成本是多少？如果偏离了这个价格，市场会发生怎样的套利行为？参考答案1、按照式子：（1+8%）美元=1.8×（1+4%）马克，得到1美元=1.7333马克。
金融的英语课后翻译题答案详解
中译英：一.1.金融管理是商业管理的重要方面之一,没有合适的金融计划企业是不可能成功的;Finance is one of the most important aspects of business management. Without proper financial planning a new enterprise is unlikely to be successful.2.金融中介机构的基本宗旨是把不受公众欢迎的金融资产转变为他们能够接受的金融资产;Financial intermediaries play the basic role of transforming financial assets that less desirable for a large part of the public into other financial assets-their own liabilities-which are more widely preferred by the public.3.企业经营是有风险的,因而,财务经理必须对风险进行评估和管理;Businesses are inherently risky, so the financial manager has to identify risks and make sure they are managed properly.4.投资决策首先是指投资机会,常常指资本投资项目;The investment decision stars with the identification of investment opportunities, often referred to as capital investment projects.5.现金预算常常被用来评估企业是否有足够的现金来维持企业的日常经营运转和或是否有太多现金富裕;Cash budgets are often used to assess whether the entity has sufficient cash to fulfill regular operations and/or whether too much cash is being left in unproductive capacities.6.按照金融学的观点,资本就是企业购买商品以生产其它商品或提供服务的货币资金;Capital, in the financial sense, is the money that gives the business the power to buy goods to be used in the production of other goods or the offering of a service.四.1.商业银行应积极开展银行转账功能风险评估和分类,依据收款账户的潜在风险高低,相应设置不同的转账额度和次数限制;A commercial bank shall actively conduct the risk assessment and classification of the telephone banking transfer functions, and set different limits on the transfer amount and times according to the degree of potential risks on the recipient account.2.商业银行相对其他行业属于信息化程度较高的行业,银行数据库里积累了海量的客户信息Commercial banks have gained more information and have large scale of data.3.商业银行的管理人员在分析客户的贷款申请时必须考虑许多因素;Managers in Commercial banks have to consider many factors in analyzinga customer's loan request.4.除中国银行外,交通银行、农业银行、工商银行、建设银行在城乡也都设立了许多的机构,便于你获得金融服务;Besides the Bank of China, the Communication Bank, Agricultural Bank, Industrial and Commercial Bank, Construction Bank also have created many branches in a city or town, and that makes easier for you to get financialservices.5.定期存款也叫CD,是存款证书的一种类型;A certificate of deposit, also called a CD, is a type of savings certificate.6.商业银行作为一家金融机构,其业务范围包括：从个人和公司吸收存款；通过提供贷款和其他对客户的财务或生意的运转很重要的金融业务来建立信贷,包括资金转账、支票兑现、银行保管箱等;A commercial bank is an financial institution established to: accept deposits from individuals and businesses; originate credit by providing loans and offering other financial services essential to the running of a customer's financial or business affairs, including fund transfers, check cashing, safe deposit boxes, etc.六.1.外汇交易市场,也称为"Forex"或"FX"市场,是世界上最大的金融市场,平均每天超过1兆美元的资金在当中周转 -- 相当于美国所有证券市场交易总和的30倍;The Foreign Exchange Market, called by "Forex" market or FX market, is the biggest financial market in the world with trading volumes surpassing USD1 trillion average one-day, it is as big as 30 times of stock market.2."外汇交易"是同时买入一对货币组合中的一种货币而卖出另外一种货币;外汇是以货币对形式交易,例如欧元/美元EUR/USD或美元/日元USD/JPY;“Foreign exchange” is to buy one currency and sell another in currency pair at the same time. The trading form of foreign currency is the currency pair, for example EUR/USD OR USD/JPY.3.外汇交易市场是一个24 小时全球交易市场,市场交易每天从悉尼开始,并且随着地球的转动,全球每个金融中心的营业日将依次开始 , 首先是东京,然后伦敦,和纽约;Foreign exchange market is worldwide market where operating 24 hours a day, the market trading starts from Sydney, turning around the earth , the business day of every financial center in the world will star to trade in turn, then is Tokyo, next is London, and New York.4.外汇交易投资者可以对无论是白天或者晚上发生的经济,社会和政治事件而导致的外汇波动而随时反应;Investors of FX may make decisions base on the fluctuation of foreign currency price leaded by economics, society and political events no matter happens in day time or night.5.外汇交易市场是一个超柜台 OTC 或“ 银行内部”交易市场,因为事实上外汇交易是交易双方通过或者一个电子交易网络而达成的,外汇交易不象股票和期货交易市场那样,不是集中在某一个交易所里进行的;The foreign exchange market is Over the Counter OTC or interbank market because foreign currency is traded through phone or electronic trading net in fact, the trading of foreign currency does not like stock trade, it is not intensive trading in exchange center.6.在外汇交易中,您会看到一个两边的报价,由买价与卖价组成,买价是在此价格上您拟卖掉基础货币同时买进相反货币;卖价是这个价格,在此价格上您可以买进基准货币时卖掉相反货币;You will see the price board consisted of bid price and ask price in trading of foreign currency, bid price is the price you sell your base currency at the same time buy reverse currency. Ask price is the price you buy base currency and sell reverse currency.七.1.企业融资是指企业在发展扩张中筹集所需资金的行为;Business financing is an action of raising money when firms extend business and development2.企业融资是为了满足企业战略调整、产业扩张、现金周转等方面的需要; Business financing is to meet the requirement of strategy adjustment, industry extending, and turnover of cash and so on.3.企业通过融资行为改变资本结构,使资金得以形成、集中、积累、组合,同时形成相应的产权关系和权利、责任、利益格局;The capital structure of the firm will be changed through raising money, the capital will be formed in the form of centralization, accumulation, combination, and at the same time relative property right relations and pattern of benefit, duty and right will be formed.4.内部融资的来源公司的自有资金,以及在生产经营过程中的资金积累部分,在公司内部通过计提折旧而形成现金,或通过留用利润等增加公司资本;The resource of internal financing comes from company’s internal fund, the part of fund accumulation of producing and operating, cash from depreciation, or capital from remaining earning.5.债权性融资主要有向金融机构贷款和发行企业债券两种形式;The two majority forms about debit financing are lending money from financial institutes and issuing company bond.6.目前国内企业在进行投资时采用的融资方式有股权性融资、债权性融资等; Presently financing methods used by domestic enterprises when investing are equity financing and debit financing, etc.九.1.组合投资原则,即将风险资金按一定比例投向不同行业、不同企业项目,或联合几个风险投资公司共同向一家企业投资;The principle of portfolio investment is that the venture capital is invested into different industries and different projects, or make a cooperation with other investing companies to invest a company. 2.风险投资主体多元化原则,在美国,风险资金来源相当广泛,既有政府、财团法人的资金,也有来自大众游资、民间企业和海外的投资,还有养老保险基金的积极参与;The principle of diversification of venture capital, in American, the resource of venture capital is quite widespread, it comes from government, financial institutes, and it can come from privates, private firms and oversea investment, and pension fund joint venture capital too.3.创业投资是由专业投资者投入到新兴的、迅速发展的、有巨大竞争潜力的企业中的一种股权性资本;Venture investment is an equity capital which professional investors invest to a new, developing rapidly and more competitive firm.4.随着社会经济的快速发展,如何投资、如何理财已经成为商业人士关注的焦点;With society economy high-speed development, how to invest and finance is the focal point which business men focus on.5.创业投资以其谋求长期资本收益、分散投资及专业化管理的特点适应了高新技术产业的资金需求,以其特别的投资方式、合同方式和组织架构部分地解决了信息不对称和激励约束不当所带来的问题.Venture capital is looking for long term capital return, the characteristic of diversification of investment and professional management adapts capital requirements of high-new technical industry, special investing model of venture capital, contract model and frame of organization solve problems of information asymmetry and incentive and restraint mechanisms flaw in partly.6.投资者可把目光聚焦到正在发售的银行保本基金上,这种在国际市场上大受欢迎的新型理财品种不但能够提供银行储蓄般的安全感,而且可以利用此次利率上升的机会创造更高的收益；同时,加息导致债券价格下跌,实际上提高了即将入市的银行保本基金的债券投资收益率;Investors may focus on guaranteed fund issued by bank, it is new style of financing product which is welcomed in the international market, it is not only shows the safety like bank deposit, but also make higher return with the interest rate arise, at the same time, rising interest rates will lead to fall of the bond price, and make higher return of guaranteed fund which will be issued by banks.十.1.债券买卖是指交易双方以约定的价格买卖一定金额的债券并在规定的清算时间内办理债券款交割的交易方式;Security trading is a trading model that both of seller and buyer sign a contract with the confirmed bond price and number, during settlement both of seller and buyer make a delivery.2.债券回购是指交易双方进行的以债券为权利质押的一种短期资金融通业务;资金融入方正回购方在将债券卖给资金融出方逆回购方以融入资金的同时,双方约定在将来某一日期由正回购方按约定回购利率计算的金额向逆回购方买回相等数量的同品种债券的交易行为;Redeem of security is a short term financing business that both of issuer and holder of bond takes bond as right pledge, when the borrower of fund positive redeemer sells bond to lender of fund negative redeemer for financing, both of them sign a contract in there positive redeemer will redeem the bond that he issued with redeem interest from negative redeemer before maturity of bond.3.所谓可转换公司债券是指由公司发行的,投资者在一定时期内可选择一定条件转换成公司股票的公司债券,通常称作可转换债券或可转债;这种债券兼具债权和股权双重属性;Convertible bond is security issued by firm which investors have option to convert bond into firm’s stock during holding period, the convertible bond consists of two characters of bond and stock.4.证券交易必需受SEC及证券交易所自我约束机制的监管;Security trading must be managed by SEC and self-regulating mechanism of the stock exchange.5.场外交易市场不是一个正式的证券交易所,而是由经纪人和交易商组成的一个非正式的网络,他们通过这一网络协商证券的交易;The over-the-counter market is not official security exchange market, itis unofficial network grouped by dealers and brokers, dealers and brokers exchange securities through the network.6.一级市场上的发行方式也分为两种,公募和私募;The issue model of stock in the primary market can be classified into: public offering and private offering.十二.1.新股的发行价总是超过面值的,记录在公司帐上的这个差叫附加实缴资本,也叫资本公积;The price at which new shares are sold to inverstors almost always exceeds par value,the difference is entered the company’s accounts as additional paid-in capital, or capital surplus.2.尽管股票这个名字很大众化,但是,大部分人都不是充分了解它;Despite their popularity, however, most people don't fully understand stocks.3.公司的管理层的主要任务是增加公司股票持有人所持有公司资产的价值; The management of the company is supposed to increase the value of the firm for shareholders.4.有限责任是股票的一个十分重要的特征,这意味着公司在不能支付它的债务时股票持有者没有负债责任;An extremely important feature of stock is its limited liability, which means that, as an owner of a stock, you are not personally liable if the company is not able to pay its debts.5.理解股票供求关系是容易的,但是理解人们喜欢哪些股票不喜欢哪些股票是苦难的;Understanding supply and demand is easy, What is difficult to comprehend is what makes people like a particular stock and dislike another stock. 6.一些人人为预测股票价格变化是不可能的,而一些人认为通过画图和分析以前的价格变化就能决定买卖时间;Some believe that it isn't possible to predict how stock prices will change, while others think that by drawing charts and looking at past price movements, you can determine when to buy and sell.英译中：一.1. A cash budget is extremely important, especially for small businesses, because it allows a company to determine how much credit it can extend to customers before it begins to have liquidity problems.现金预算是十分重要的,特别是对小企业,这是因为它决定了企业可以使用多大的赊销份额而不发生现金困难;2. Financial intermediaries include depository institutions commercial banks and credit union who acquired the bulk of their funds by offering their liabilities to the public mostly form of deposit. 金融中介机构包括：存款性机构商业银行和信用合作社主要通过存款的形式向公众借款,从而获得大部分资金;3. A corporation is a legally distinct from its owners, who are called shareholders or stockholders. 公司在法律上独立于其所有者,即股东;financial planning focus on the firm’s goals, the investment that will be needed to meet those goals, and the financing that must be raised. 长期财务计划是关于企业的长期目标、为实现目标所需要的投资以及因此必须筹集的资金的计划;are classified into nonfinancial and financial businesses. These entities borrow funds in the debt market and raise funds in the equity market. 企业可被分成金融企业和非金融企业两类;这些企业在债务市场借款和在权益市场融资;6. Finance is the set of activities dealing with the management of funds. More specifically, it is the decision of collection and use of funds. It is a branch of economics that studies the management of money and other assets.金融是涉及到一系列有关资金管理的活动;特别的,它是有关资金使用和筹集的决策;它是经济学的一个研究货币和其它资产管理的分枝;四. risk-based capital requirements imposed on commercial bank and saving and loan associations.对商业银行和存贷款协会实施以风险为基础的资本金要求;regulates commercial banks and thrifts and types of regulations imposed. 谁来监管商业银行与储蓄机构以及何种方式来进行;3. Banks generate income in three ways: 1the bid-ask spread;2capital gains on the securities or foreign currency used in transactions, and 3in the case of securities, the spread between interest income earned by holding the security and cost of funding the purchase of security.银行可以从三个方面产生收入：1买卖差价；2证券或外汇交易的资本利益；3证券的利息收入和购买证券资金成本之间的价格差异;4. Several types of deposit accounts are available. Checking accounts pay no interest and can be withdrawn upon demand.存款帐户有好几种,支票帐户不支付利息可以随时提取;certificate of deposit can take a wide variety of forms which are negotiable with the issuing bank. 定期存单可以采取多种多样的形式是可转让的发卡银行;that raise most of their funds from the domestic and international money markets, relying less on depositors for funds, are called money center banks.货币中心银行是指较少依赖存款,并在国内或国外货币市场筹集资金的银行;六.1,The foreign exchange market is a place to trade foreign exchange currency, or it is also a place for the transaction of all foreign currency. 外汇市场是交易外国货币或各国货币的场所.foreign exchange rate is the relative value between two currencies. In particular, it is the quantity of one currency required to buy or sell one unit of the other currency.汇率是两种货币间的相对价值, 特别是, 它是买卖一个其它货币单位所代表的本币量值.. dollars are not used to express an exchange rate, the term "cross rate" is usually used to express the relative values between two currencies.在美元被用来表示汇率的地方,套汇汇率就被用来表示两种货币间的相对价值.an online currency trader wants to survive in the business, he must learn to limit his losses. This is one of the keys to smart money management. 如果一个网络货币交易者要持续他的交易他必须学习限制损失,这是货币管理的关键点.is safer to get into a currency position in multiple lots than to do it all at once.在多个地点持有外汇头寸比同时持有多个头寸安全.Forex market itself consists of a worldwide network of primarily interbank traders connected by telephone lines and computers. FX traders constantly negotiate prices between one another and the resulting market bid/ask price for a particular currency is then fed into computers and displayed on official quote screens.外汇市场本身含有提供给银行交易者通过线和计算机连接的全球范围的网络,外汇交易者讨论的汇率价格产生了市场上某种货币的报价和询价并通过计算机系统显示在交易屏幕上.七. you have too much debt, your business may be considered overextended and risky and an unsafe investment.如果你的企业负债比重过高,投资者则会认为企业是扩张过度,对投资者来说是不安全和高风险的;financing is attractive because you do not have to sacrifice any ownership interests in your business, interest on the loan is deductible, and the financing cost is a relatively fixed expense.债务融资对企业权益者是有吸引力的因为债务融资不会牺牲权益者的利益,借款利息可在收益中扣减,财务成本是相对固定费用.corporation is a separate legal entity that can be created only by compliance with state statutes.公司是一个其所有权与经营权相分离的经济实体即法人组织,公司的成立要遵守洲法.partners raise equity funds through their own capital contributions, by adding a new partner, or by restructuring the relative ownership interests of the existing partners to reflect new contributions.合伙人企业可通过出让合伙人自己的资本份额,或增加合伙人的方式来增加企业资本,或采用对原有合伙人所拥有的相对资本份额进行重组的方式来反映新的资本.financing requires that you sell an ownership interest in the business in exchange for capital.权益融资需要企业所有者出让企业的所有权利益来换取资本.major disadvantage to equity financing is the dilution of your ownership interests and the possible loss of control that may accompany a sharingof ownership with additional investors.权益融资的主要缺点是稀释了所有者的利益,随着其他投资者所占权益份额的扩大企业控制权也可能失去.九. is when everything in the economy is great, people are finding jobs, is growing, and are rising. Things are just plain rosy during a bull market is easier because everything is going up.牛市意味着经济发展强劲,工作岗位多,GDP 增长,股票价格上升.前景变得光明.在牛市期间投资股票将有丰厚收益因为所有物品的价格都将上升.markets cannot last forever though, and sometimes they can lead to dangerous situations if stocks become overvalued.牛市不可能永远持续,如果股票价格被高估则牛市就将导致崩盘.a person is optimistic, believing that stocks will go up, he or she is called a "bull" and said to have a "bullish outlook."如果一个人乐观的认为股票价格将上升,他或她被称做”多头”和有一个行情看涨的形象.investments it is critical to distinguish between an expected return the anticipated return for some future period and a realized return the actual return over some past period. Investors invest for the future—for the return they expect to earn—but when the investing period is over, they are left with their realized returns.投资学对期望收益预测的将来某时间段的收益和已实现收益过去某时段的实际收到的收益有严格的区分.投资者投资为将来-他们希望获取的收益-但是在投资周期结束后,他们只得到实际的收益.investors actually earn from their holdings may turn out to be more or less than what they expected to earn when they initiated the investment. This point is the essence of the investments process: investors must always consider the risk involved in investing.投资者在投资期间实际得到的收益与他们初始投资所预想的收益或多或少有差异.投资过程的关键点是:投资者在投资时必须牢记风险的成在.are three important factors you need to consider before buying a bond. The first is the person issuing the bond. The second is the interest or coupon you will receive. The third is the maturity date, the day when the borrower must pay back the principal to the lender.在投资债券前你要考虑三个重要因素:第一是债券发行人;第二是你将得到的利息或折扣;第三是到期时间, 在到期日债券发行人必须将本金退给债券持有人.十. higher rate of return the bond offers, the more risky the investment. There have been instances of companies failing to pay back the bond default, so, to entice investors, most corporate bonds will offer a higher return than a government bond.债券收益率越高投资风险越大,已有公司不能在到期日偿还债券本金违约的先例,所以, 为了诱使投资者购买公司债券大多数公司都发行高于政府债券利率的债券.is important for investors to research a bond just as they would a stock or mutual fund. The bond rating will help in deciphering the default risk.象研究股票和共同基金样研究债券对投资者来说是必要的, 辨别债券等级将有助于识别违约风险.interest is added to the contract price of a bond transaction.应计利息要加到债券交易合同价格中.Gain. An increase in the value of a investment or real estate that gives it a higher worth than the purchase price. The gain is not realized until the asset is sold. A may be short term one year or less or long term more than one year and must be claimed on income taxes.资本利得是资本价值投资或不动产的增加,也就是高于购买价格的增值部分,利得只有在这些资产出售后才能实现, 资本利得可以是短期一年以内或长期一年以上, 资本利得必须征税.any other type of investment vehicle, fixed-income securities should be viewed in terms of their risk and return. Generally speaking, bonds are exposed to five major types of risks: interest rate risk, purchasing power risk, business/financial risk, liquidity risk, and call risk.象任何其它投资工具一样,固定收益证券也应该按照它们的风险和收益来进行评价. 一般看来, 证券有五种主要的风险:利率风险,购买力风险,商业风险,流动性风险和回购风险.far we've discussed the factors of face value, coupon, maturity, issuers and yield. All of these characteristics of a bond play a role in its price.到目前我们已经讨论了债券的面值,利息率,到期日,发行人和收益,全部这些特征都会影响到债券的价格.十二. splits,like stock dividents, do not increase the assets or earning capacity of the firm,the split does decrease the price of the stock and thereby may increase its marketability.股票拆分与股票股利一样,并不能增加公司的资产或者提高公司的盈利能力,拆分降低了股票的价格,从而增加了股票的流动性;may repurchase shares to reduce the chance of an unwanted takeover attempt.管理层可以回购股票来避免公司被收购;two most important characteristics of common stock as an investment are its residual claim and limited liability features.作为投资的普通股的两个最重要的特征是剩余索取权和有限责任;stocks are traded on exchanges, which are places where buyers and sellers meet and decide on a price.大部分股票都是在证券交易所交易,买卖双方在那儿搓合股票价格;5. The most important factor that affects the value of a company is its earnings. Earnings are the profit a company makes, and in the long run no company can survive without them.6. Stock prices change every day as a result of market forces. By this we mean that share prices change because of supply and demand. If more people want to buy a stock demand than sell it supply, then the price moves up.由于市场的原因股票价格每天都在变化,股票价格是由于供求关系的原因而变化的,如果买的人比卖的人多则股票价格上升;。
金融学14章金融答案翻译
CHAPTER 14FORWARD AND FUTURES PRICESObjectives∙ To explain the economic role of futures markets∙ To show what information can and cannot be inferred from forward and futures prices.∙Outline14.1 Distinctions Between Forward and Futures Contracts14.2 The Economic Function of Futures Markets14.3 The Role of Speculators14.4 Relation Between Commodity Spot and Futures Prices14.5 Extracting Information from Commodity Futures Prices14.6 Spot-Futures Price Parity for Gold14.7 Financial Futures14.8 The Implied Risk-Free Rate14.9 The Forward Price Is Not a Forecast of the Spot Price14.10 Forward-Spot Parity with Cash Payouts14.11 Implied Dividends14.12 The Foreign-Exchange Parity Relation14.13 The Role of Expectations in Determining Exchange RatesSummary∙ Futures contracts make it possible to separate the decision of whether to physically store a commodity from thedecision to have financial exposure to its price changes.∙ Speculators in futures markets improve the informational content of futures prices and make futures marketsmore liquid than they would otherwise be.∙ The futures price of wheat cannot exceed the spot price by more than the cost of carry:∙ The forward-spot price parity relation for gold is that the forward price equals the spot price times the cost ofcarry:This relation is maintained by the force of arbitrage . ∙One can infer the implied cost of carry and the implied storage costs from the observed spot and forward prices and the risk-free interest rate. ∙ The forward-spot parity relation for stocks is that the forward price equals the spot price times 1 plus the risk-free rate less the expected cash dividend.This relation can therefore be used to infer the implied dividend from the observed spot and forward prices and the risk-free interest rate. ∙ The forward-spot price parity relation for the dollar/yen exchange rate involves two interest rates:where F is the forward price of the yen, S is the current spot price, r Y is the yen interest rate, and r $ is the dollarinterest rate. ∙ If the forward dollar/yen exchange rate is an unbiased forecast of the future spot exchange rate, then one caninfer that forecast either from the forward rate or from the dollar-denominated and yen-denominated risk-free interest rates.F S C -≤F S r s =++()1F S r D=+-()1F r S r Y11+=+$Solutions to Problems at End of ChapterForward Contracts and Forward-Spot Parity.1. Suppose that you are planning a trip to England. The trip is a year from now, and you have reserved a hotel room in London at a price of ₤50 per day. You do not have to pay for the room in advance. The exchange rate is currently $1.50 to the pound sterling.a.Explain several possible ways that you could completely hedge theexchange rate risk in this situation.b.Suppose that r₤=.12 and r$=.08. Because S=$1.50, what must theforward price of the pound be?c.Show that if F is $0.10 higher than in your answer to part b, therewould be an arbitrage opportunity.SOLUTION:a.Ways to hedge the exchange rate risk:Pay for the room in advanceBuy the pounds you will need in the forward market.Invest the present value of the rental payments in a pound-denominated riskless asset.对冲外汇风险的几种方法：提前对这个房间付款；在期货市场购买英镑；将与现期价值的租金同等的英镑投资于无风险资产。
金融工程课后题7习题解答zhoujiaLite
CH 77.1 一位投资者购买了一个执行价格为X的看涨期权并出售了一个相同执行价格的看跌期权。
请描述他的头寸情况。
解：投资者头寸状况为：max（S T－X,0）－max（X－S T,0）此头寸相当于执行价格为X的远期合约。
当X与远期合约价格相同时，合约价值为0，此时看涨期权与看跌期权价值相等。
7.2请说明为什么欧式期权总是不如有相同标的物、相同执行价格、相同到期日的美式期权值钱。
解：美式期权持有者除具有欧式期权持有者所拥有的所有权利外，还有提早执行权。
因此，美式期权至少应与相应的欧式期权有相同的价值。
7.3请解释为什么美式期权的价值总是大于等于它的内在价值。
解：美式期权的持有者有立即执行期权，实现期权内在价值的权利，因此，美式期权的价值至少应等于其内在价值。
7.4列举影响期权价格的6个因素。
解：影响期权价格的6个因素有：标的资产价格、期权的执行价格、无风险利率、资产价格的波动率、期限以及持有期间收益。
7.5基于无红利支付股票的看涨期权，期限为4个月，执行价格为$25，股票价格为$28，无风险利率为8％。
该看涨期权价格下限为多少？解：该看涨期权的价格下限为：28－25×0.08*0.3333e-＝$3.667.6基于无红利支付股票的欧式看跌期权，期限为1个月，股票价格为$12，执行价格为$15，无风险年利率6％，该期权的价格下限为多少？解：该看跌期权价格下限为：15×0.06*0.083333e-－12＝$2.937.7请给出两个原因说明为什么早执行无红利支付股票的美式看涨期权不是最好的。
第一条原因应包括货币时间价值。
第二条原因在利率为零时也成立。
解：1）推迟执行可推迟支付期权的执行价格，期权持有者可赚取执行价格更长时间的时间价值；2）推迟执行可提供保值价值，避免执行日时股价低于执行价格。
假设期权购买者有现金X ，且利率为0。
提早执行会使期权购买者头寸在到期日为T S , 而推迟执行买方头寸在到期日则为max （X,T S ）7.8 “提前执行美式看跌期权是在货币的时间价值与看跌期权的保险价值之间的权衡。
【精品】金融工程第七版课后习题答案(中文
第1章导言练习题1.1请解释远期多头与远期空头的区别。
答：远期多头指交易者协定将来以某一确定价格购入某种资产；远期空头指交易者协定将来以某一确定价格售出某种资产。
1.2请详细解释套期保值、投机与套利的区别。
答：套期保值指交易者采取一定的措施补偿资产的风险暴露；投机不对风险暴露进行补偿，是一种“赌博行为”；套利是采取两种或更多方式锁定利润。
1.3请解释签订购买远期价格为$50的远期合同与持有执行价格为$50的看涨期权的区别。
答：第一种情况下交易者有义务以50$购买某项资产（交易者没有选择），第二种情况下有权利以50$购买某项资产（交易者可以不执行该权利）。
1.4一位投资者出售了一个棉花期货合约，期货价格为每磅50美分，每个合约交易量为50，000磅。
请问期货合约结束时，当合约到期时棉花价格分别为（a）每磅48.20美分；（b）每磅51.30美分时，这位投资者的收益或损失为多少？答：(a)合约到期时棉花价格为每磅$0.4820时，交易者收入：（$0.5000-$0.4820）×50，000＝$900;(b)合约到期时棉花价格为每磅$0.5130时，交易者损失:($0.5130-$0.5000)×50，000=$6501.5假设你出售了一个看跌期权，以$120执行价格出售100股IBM的股票，有效期为3个月。
IBM股票的当前价格为$121。
你是怎么考虑的？你的收益或损失如何？答：当股票价格低于$120时，该期权将不被执行。
当股票价格高于$120美元时，该期权买主执行该期权，我将损失100(st-x)。
1.6你认为某种股票的价格将要上升。
现在该股票价格为$29,3个月期的执行价格为$30的看跌期权的价格为$2.90.你有$5,800资金可以投资。
现有两种策略：直接购买股票或投资于期权，请问各自潜在的收益或损失为多少？答：股票价格低于$29时，购买股票和期权都将损失，前者损失为$5,800$29×(29-p),后者损失为$5，800;当股票价格为（29，30），购买股票收益为$5,800$29×(p-29),购买期权损失为$5,800;当股票价格高于$30时，购买股票收益为$5,800 $29×(p-29)，购买期权收益为$$5,800$29×(p-30)-5,800。
金融工程课后题13-20习题解答renzhengliang(Lite)
Ch1313.1不是可交易证券价格的变量的风险价格是如何定义的？解：不是可交换证券价格的变量的风险市场价格是通过求可交换证券的风险市场价格而来，但必须满足该可交换证券的价格与不是可交换证券价格的变量瞬态完全正相关。
13.2假设黄金的风险市场价格为零，如果贮存成本为每年1%，无风险年利率为6%，那么黄金价格的期望增长率为多少？解：由公式m-λs=r-y+u,而λ=0,r=0.06,y=0,u=0.01所以m=0.07.即期望增长率为0.07。
13.3一个证券的价格与以下两个变量正相关：铜的价格和日元兑美元的汇率，假设这两个变量的风险市场价格分别为0.5和0.1。
若铜的价格固定，则该证券的波动率为每年8%；如果日元对美元的汇率固定，则该证券的波动率为每年12%。
无风险利率为每年7%。
证券的预期回报率为多少？如果两个变量彼此之间是不相关的，该证券的波动率为多少？解：（1）令u为证券的预期收益率，已知无风险利率r=0.07，铜价和日圆兑美圆汇率的风险市场价格分别为λ1=0.5和λ2=0.1，铜价固定时汇率引起的证券波动率为σ2=0.08，汇率固定时铜价引起的证券波动率为σ1=0.12。
因此由公式u-r=λ1σ1+λ2σ2可得u=0.138即证券的预期收益率为每年0.138（2）由σ1dz1+σ2dz2=dz3代入σ1，σ2的值可得(s)*T m TS S eλ-⨯为0.144即铜价和日圆兑美圆汇率不相关时证券的波动率为0.14413.4某个石油公司只是为了开发德克萨斯一个很小区域的石油。
其价值主要依赖于如下两个随机变量：石油的价格和以探明石油的储存量。
讨论：这两个变量中的风险市场价格为正数、负数还是零？解：第二个变量的风险市场价格为0。
这是因为这种风险是非系统的，它与经济社会的其他风险完全不相关，投资者不能因为承担这种不可转换的风险而要求更高的回报。
13.5通过两个无红利支付的交易证券和两个依赖于这两个无红利支付交易证券价格的衍生工具构成一个无风险组合，推导出这个衍生工具的微分方程。
金融工程 相关习题及答案教学文案
金融工程相关习题及答案Chapter 1 Market Organization and Structure PRACTICE PROBLEMS FOR CHAPTER 11. Akihiko Takabe has designed a sophisticated forecasting model, which predicts the movements in the overall stock market, in the hope of earning a return in excess of a fair return for the risk involved. He uses the predictions of the model to decide whether to buy, hold, or sell the shares of an index fund that aims to replicate the movements of the stock market. Takabe would best be characterized as a (n):A. hedger.B. investor.C. information-motivated trader.2. James Beach is young and has substantial wealth. A significant proportion of his stock portfolio consists of emerging market stocks that offer relatively high expected returns at the cost of relatively high risk. Beach believes that investment in emerging market stocks is appropriate for him given his ability and willingness to take risk. Which of the following labels most appropriately describes Beach?A. Hedger.B. Investor.C. Information-motivated trader.3. Lisa Smith owns a manufacturing company in the United States. Her company has sold goods to a customer in Brazil and will be paid in Brazilian real (BRL) in three months. Smith is concerned about the possibility of the BRL depreciating more than expected against the U.S. dollar (USD). Therefore, she is planning to sell three-month futures contracts on the BRL. The seller of such contracts generally gains when the BRL depreciates against the USD. If Smith were to sell these future contracts, she would most appropriately be described as a (n):A. hedger.B. investor.C. information-motivated trader.4. Which of the following is not a function of the financial system?A. To regulate arbitrageurs’ profits (excess returns).B. To help the economy achieve allocational efficiency.C. To facilitate borrowing by businesses to fund current operations.5. An investor primarily invests in stocks of publicly traded companies. The investor wants to increase the diversification of his portfolio. A friend has recommendedinvesting in real estate properties. The purchase of real estate would best be characterized as a transaction in the:A. derivative investment market.B. traditional investment market.C. alternative investment market.6. A hedge fund holds its excess cash in 90-day commercial paper and negotiable certificates of deposit. The cash management policy of the hedge fund is best described as using:A. capital market instruments.B. money market instruments.C. intermediate-term debt instruments.7. An oil and gas exploration and production company announces that it is offering 30 million shares to the public at $45.50 each. This transaction is most likely a sale in the:A. futures market.B. primary market.C. secondary market.8. Consider a mutual fund that invests primarily in fixed-income securities that have been determined to be appropriate given the fund’s investment goal. Which of the following is least likely to be a part of this fund?A. Warrants.B. Commercial paper.C. Repurchase agreements.9. A friend has asked you to explain the differences between open-end and closed-end funds. Which of the following will you most likely include in your explanation?A. Closed-end funds are unavailable to new investors.B. When investors sell the shares of an open-end fund, they can receive a discount or a premium to the fund’s net asset value.C. When selling shares, investors in an open-end fund sell the shares back to the fund whereas investors in a closed-end fund sell the shares to others in the secondary market.10. The usefulness of a forward contract is limited by some problems. Which of the following is most likely one of those problems?A. Once you have entered into a forward contract, it is difficult to exit from the contract.B. Entering into a forward contract requires the long party to deposit an initial amount with the short party.C. If the price of the underlying asset moves adversely from the perspective of the long party, periodic payments must be made to the short party.11. Tony Harris is planning to start trading in commodities. He has heard about the use of futures contracts on commodities and is learning more about them. Which of the following is Harris least likely to find associated with a futures contract?A. Existence of counterparty risk.B. Standardized contractual terms.C. Payment of an initial margin to enter into a contract.12. A German company that exports machinery is expecting to receive $10 million in three months. The firm converts all its foreign currency receipts into euros. The chief financial officer of the company wishes to lock in a minimum fixed rate for converting the $10 million to euro but also wants to keep the flexibility to use the future spot rate if it is favorable. What hedging transaction is most likely to achieve this objective?A. Selling dollars forward.B. Buying put options on the dollar.C. Selling futures contracts on dollars.13. A book publisher requires substantial quantities of paper. The publisher and a paper producer have entered into an agreement for the publisher to buy and the producer to supply a given quantity of paper four months later at a price agreed upon today. This agreement is a:A. futures contract.B. forward contract.C. commodity swap.14. The Stand ard & Poor’s Depositary Receipts (SPDRs) is an investment that tracks the S&P 500 stock market index. Purchases and sales of SPDRs during an average trading day are best described as:A. primary market transactions in a pooled investment.B. secondary market transactions in a pooled investment.C. secondary market transactions in an actively managed investment.15. The Standard & Poor’s Depositary Receipts (SPDRs) is an exchange-traded fund in the United States that is designed to track the S&P 500 stock market index. The current price of a share of SPDRs is $113. A trader has just bought call options on shares of SPDRs for a premium of $3 per share. The call options expire in five months and have an exercise price of $120 per share. On the expiration date, the trader will exercise the call options (ignore any transaction costs) if and only if the shares of SPDRs are trading:A. below $120 per share.B. above $120 per share.C. above $123 per share.16. Which of the following statements about exchange-traded funds is most correct?A. Exchange-traded funds are not backed by any assets.B. The investment companies that create exchange-traded funds are financial intermediaries.C. The transaction costs of trading shares of exchange-traded funds are substantially greater than the combined costs of trading the underlying assets of the fund.17. Jason Schmidt works for a hedge fund and he specializes in finding profit opportunities that are the result of inefficiencies in the market for convertible bonds—bonds that can be converted into a predetermined amount of a company’s common stock. Schmidt tries to find convertibles that are priced inefficiently relative to the underlying stock. The trading strategy involves the simultaneous purchase of the convertible bond and the short sale of the underlying common stock. The above process could best be described as:A. hedging.B. arbitrage.C. securitization.18. Pierre-Louis Robert just purchased a call option on shares of the Michelin Group.A few days ago he wrote a put option on Michelin shares. The call and put options have the same exercise price, expiration date, and number of shares underlying. Considering both positions, Robert’s exposure to the risk of the stock of the Michelin Group is:A. long.B. short.C. neutral.19. An online brokerage firm has set the minimum margin requirement at 55 percent. What is the maximum leverage ratio associated with a position financed by this minimum margin requirement?A. 1.55.B. 1.82.C. 2.22.20. A trader has purchased 200 shares of a non-dividend-paying firm on margin at a price of $50 per share. The leverage ratio is 2.5. Six months later, the trader sells these shares at $60 per share. Ignoring the interest paid on the borrowed amount and the transaction costs, what was the return to the trader during the six-month period?A. 20 percent.B. 33.33 percent.C. 50 percent.21. Jason Williams purchased 500 shares of a company at $32 per share. The stock was bought on 75 percent margin. One month later, Williams had to pay interest on the amount borrowed at a rate of 2 percent per month. At that time, Williams receiveda dividend of $0.50 per share. Immediately after that he sold the shares at $28 per share. He paid commissions of $10 on the purchase and $10 on the sale of the stock. What was the rate of return on this investment for the one-month period?A. −12.5 percent.B. –15.4 percent.C. –50.1 percent.22. Caroline Rogers believes the price of Gamma Corp. stock will go down in the near future. She has decided to sell short 200 shares of Gamma Corp. at the current market price of €47. The initial margin requirement is 40 percent. Which of the following is an appropriate statement regarding the margin requirement that Rogers is subject to on this short sale?A. She will need to contribute €3,760 as margin.B. She will need to contribute €5,640 as margin.C. She will only need to leave the proceeds from the short sale as deposit and does not need to contribute any additional funds.23. The current price of a stock is $25 per share. You have $10,000 to invest. You borrow an additional $10,000 from your broker and invest $20,000 in the stock. If the maintenance margin is 30 percent, at what price will a margin call first occur?A. $9.62.B. $17.86.C. $19.71.24. You have placed a sell market-on-open order—a market order that would automatically be submitted at the market’s open tomorrow and would fill at the market price. Your instruction, to sell the shares at the market open, is a(n):A. execution instruction.B. validity instruction.C. clearing instruction.25. A market has the following limit orders standing on its book for a particular stock. The bid and ask sizes are number of shares in hundreds.What is the market?A. 9.73 bid, offered at 10.14.B. 9.81 bid, offered at 10.10.C. 9.95 bid, offered at 10.02.26. Consider the following limit order book for a stock. The bid and ask sizes are number of shares in hundredsA new buy limit order is placed for 300 shares at ¥123.40. This limit order issaid to:A. take the market.B. make the market.C. make a new market.27. Currently, the market in a stock is "$54.62 bid, offered at $54.71." A new sell limit order is placed at $54.62. This limit order is said to:A. take the market.B. make the market.C. make a new market.28. Jim White has sold short 100 shares of Super Stores at a price of$42 per share. He has also simultaneously placed a "good-till-cancelled, stop 50, limit 55 buy" order. Assume that if the stop condition specified by White is satisfied and the order becomes valid, it will get executed. Excluding transaction costs, what is the maximum possible loss that White can have?A. $800.B. $1,300.C. Unlimited.29. You own shares of a company that are currently trading at $30 a share. Your technical analysis of the shares indicates a support level of $27.50. That is, if the price of the shares is going down, it is more likely to stay above this level rather than fall below it. If the price does fall below this level, however, you believe that the price may continue to decline. You have no immediate intent to sell the shares but are concerned about the possibility of a huge loss if the share price declines below thesupport level. Which of the following types of orders could you place to most appropriately address your concern?A. Short sell order.B. Good-till-cancelled stop sell order.C. Good-till-cancelled stop buy order.30. In an underwritten offering, the risk that the entire issue may not be sold to the public at the stipulated offering price is borne by the:A. issuer.B. investment bank.C. buyers of the part of the issue that is sold.31 . A British company listed on the Alternative Investment Market of the London Stock Exchange, announced the sale of 6,686,665 shares to a small group of qualified investors at £0.025 per share. Which of the following best describesthis sale?A. Shelf registration.B. Private placement.C. Initial public offering.32. A German publicly traded company, to raise new capital, gave its existing shareholders the opportunity to subscribe for new shares. The existing shareholders could purchase two new shares at a subscription price of €4.58 per share for every 15 shares held. This is an example of a(n):A. rights offering.B. private placement.C. initial public offering.33. Consider an order-driven system that allows hidden orders. The following four sell orders on a particular stock are currently in the system's limit order book. Based on the commonly used order precedence hierarchy, which of these orders will have precedence over others?A. Order I (time of arrival of 9:52:01 ).B. Order II (time of arrival of 9:52:08).C. Order III (time of arrival of 9:53:04)34. Zhenhu Li has submitted an immediate-or-cancel buy order for 500 shares of a company at a limit price of CNY 74.25. There are two sell limit orders standing in that stock's order book at that time. One is for 300 shares at a limit price of CNY 74.30 and the other is for 400 shares at a limit price of CNY 74.35. How many shares in Li's order would get cancelled?A. None (the order would remain open but unfilled).B. 200 (300 shares would get filled).C. 500 (there would be no fill).35. A market has the following limit orders standing on its book for a particular stock:Ian submits a day order to sell 1,000 shares, limit £19.83. Assuming that no more buy orders are submitted on that day after Ian submits his order, what would be Ian's average trade price?A. £19.70.B. £19.92.C. £20.05.36. A financial analyst is examining whether a country's financial market is well functioning. She finds that the transaction costs in this market are low and trading volumes are high. She concludes that the market is quite liquid. In such a market:A. traders will find it hard to make use of their information.B. traders will find it easy to trade and their trading will make the market less informationally efficient.C. traders will find it easy to trade and their trading will make the marketmore informationally efficient.37. The government of a country whose financial markets are in an early stage of development has hired you as a consultant on financial market regulation. Your first task is to prepare a list of the objectives of market regulation. Which of the following is least likely to be included in this list of objectives?A. Minimize agency problems in the financial markets.B. Ensure that financial markets are fair and orderly.C. Ensure that investors in the stock market achieve a rate of return that is at least equal to the risk-free rate of return.Chapter 2 Portfolio Management: An Overview PRACTICE PROBLEMS FOR CHAPTER 21. Investors should use a portfolio approach to:A. reduce risk.B. monitor risk.C. eliminate risk.2. Which of the following is the best reason for an investor to be concerned with the composition of a portfolio?A. Risk reduction.B. Downside risk protection.C. Avoidance of investment disasters.3. With respect to the formation of portfolios, which of the following statements is most accurate?A. Portfolios affect risk less than returns.B. Portfolios affect risk more than returns.C. Portfolios affect risk and returns equally.4. Which of the following institutions will on average have the greatest need for liquidity?A. Banks.B. Investment companies.C. Non-life insurance companies.5. Which of the following institutional investors will most likely have the longest time horizon?A. Defined benefit plan.B. University endowment.C. Life insurance company.6. A defined benefit plan with a large number of retirees is likely to have a high need forA. income.B. liquidity.C. insurance.7. Which of the following institutional investors is most likely to manage investments in mutual funds?A. Insurance companies.B. Investment companies.C. University endowments.8. With respect to the portfolio management process, the asset allocation is determined in the:A. planning step.B. feedback step.C. execution step9. The planning step of the portfolio management process is least likely to include an assessment of the client'sA. securities.B. constraints.C. risk tolerance.10. With respect to the portfolio management process, the rebalancing of a portfolio's composition is most likely to occur in the:A. planning step.B. feedback step.C. execution step.11. An analyst gathers the following information for the asset allocations of three portfolios:Which of the portfolios is most likely appropriate for a client who has a high degree of risk tolerance?A. Portfolio 1.B. Portfolio 2.C. Portfolio 3.12. Which of the following investment products is most likely to trade at their net asset value per share?A. Exchange traded funds.B. Open-end mutual funds.C. Closed-end mutual funds.13. Which of the following financial products is least likely to have a capital gain distribution?A. Exchange traded funds.B. Open-end mutual funds.C. Closed-end mutual funds.14. Which of the following forms of pooled investments is subject to the least amount of regulation?A. Hedge funds.B. Exchange traded funds.C. Closed-end mutual funds.15. Which of the following pooled investments is most likely characterized by a few large investments?A. Hedge funds.B. Buyout funds.C. Venture capital funds.Chapter 3 Portfolio Risk and Return: Part I PRACTICE PROBLEMS FOR CHAPTER 31. An investor purchased 100 shares of a stock for $34.50 per share at the beginning of the quarter. If the investor sold all of the shares for $30.50 per share after receiving a $51.55 dividend payment at the end of the quarter, the holding period return is closest to:A. - 13.0%.B. - 11.6%.C. - 10.1%.2. An analyst obtains the following annual rates of return for a mutual fund:The fund's holding period return over the three-year period is closest to:A. 0.18%.B. 0.55%.C. 0.67%.3. An analyst observes the following annual rates of return for a hedge fund:The hedge fund's annual geometric mean return is closest to:A. 0.52%.B. 1.02%.C. 2.67%.4. Which of the following return calculating methods is best for evaluating the annualized returns of a buy-and-hold strategy of an investor who has made annual deposits to an account for each of the last five years?A. Geometric mean return.B. Arithmetic mean return.C. Money-weighted return.5. An investor evaluating the returns of three recently formed exchange-traded funds gathers the following information:The ETF with the highest annualized rate of return is:A. ETF 1.B. ETF 2.C. ETF 3.6. With respect to capital market theory, which of the following asset characteristics is least likely to impact the variance of an investor's equally weighted portfolio?A. Return on the asset.B. Standard deviation of the asset.C. Covariances of the asset with the other assets in the portfolio.7. A portfolio manager creates the following portfolio:If the correlation of returns between the two securities is 0.40, the expected standard deviation of the portfolio is closest to:A. 10.7%.B. 11.3%.C. 12.1%.8. A portfolio manager creates the following portfolio:If the covariance of returns between the two securities is - 0.0240, the expected standard deviation of the portfolio is closest to:A. 2.4%.B. 7.5%.C. 9.2%.The following information relates to Questions 9-10A portfolio manager creates the following portfolio:9. If the standard deviation of the portfolio is 14.40%, the correlation between the two securities is equal to:A. - 1.0.B. 0.0.C. 1.0.10. If the standard deviation of the portfolio is 14.40%, the covariance between the two securities is equal to:A. 0.0006.B. 0.0240.C. 1.0000.The following information relates to Questions 11-14An analyst observes the following historic geometric returns:11 . The real rate of return for equities is closest to:A. 5.4%.B. 5.8%.C. 5.9%.12. The real rate of return for corporate bonds is closest to:A. 4.3%.B. 4.4%.C. 4.5%.13. The risk premium for equities is closest to:A. 5.4%.B. 5.5%.C. 5.6%.14. The risk premium for corporate bonds is closest to:A. 3.5%.B. 3.9%.C. 4.0%.15. With respect to trading costs, liquidity is least likely to impact the:A. stock price.B. bid-ask spreads.C. brokerage commissions.16. Evidence of risk aversion is best illustrated by a risk-return relationship that is:A. negative.B. neutral.C. positive.17. With respect to risk-averse investors, a risk-free asset will generate a numerical utility that is:A. the same for all individuals.B. positive for risk-averse investors.C. equal to zero for risk seeking investors18. With respect to utility theory, the most risk-averse investor will have an indifference curve with the:A. most convexity.B. smallest intercept value.C. greatest slope coefficient.19. With respect to an investor's utility function expressed as:21=E(r)-2u A , whichof the following values for the measure for risk aversion has the least amount of risk aversion?A. - 4.B. 0.C. 4.The following information relates to Questions 20-23A financial planner has created the following data to illustrate the application of utility theory to portfolio selection:20. A risk-neutral investor is most likely to choose:A. Investment 1.B. Investment 2.C. Investment 3.ExpectedStandard Deviation (% )28153021. If an investor's utility function is expressed as U = E(r) ~A& and the measure for risk aversion has a value of- 2, the risk-seeking investor is most likely to choose:A. Investment 2.B. Investment 3.C. Investment 4.22. If an investor's utility function is expressed as U = E(r) - ~A& and the measure for risk aversion has a value of2, the risk-averse investor is most likely to choose:A. Investment 1.B. Investment 2.C. Investment 3.23. If an investor's utility function is expressed as U =E(r) - ~A& and the measure for risk aversion has a value of4, the risk-averse investor is most likely to choose:A. Investment 1.B. Investment 2.C. Investment 3.24. With respect to the mean-variance portfolio theory, the capital allocation line, CAL, is the combination of the risk-free asset and a portfolio of all:A. risky assets.B. equity securities.C. feasible investments.25. Two individual investors with different levels of risk aversion will have optimal portfolios that are:A. below the capital allocation line.B. on the capital allocation line.C. above the capital allocation line.The following information relates to Questions 26-28A portfolio manager creates the following portfolio:26. If the portfolio of the two securities has an expected return of15%, the proportion invested in Security 1 is:A. 25%.B. 50%.C. 75%.27. If the correlation of returns between the two securities is - 0.15, the expected standard deviation of an equal-weighted portfolio is closest to:A. 13.04%.B. 13.60%.C. 13.87%.28. If the two securities are uncorrelated, the expected standard deviation of an equal-weighted portfolio is closest to:A. 14.00%.B. 14.14%.C. 20.00%.29. As the number of assets in an equally-weighted portfolio increases, the contribution of each individual asset's variance to the volatility of the portfolio:A. increases.B. decreases.C. remains the same.30. With respect to an equally-weighted portfolio made up of a large number of assets, which of the following contributes the most to the volatility of the portfolio?A. Average variance of the individual assets.B. Standard deviation of the individual assets.C. Average covariance between all pairs of assets.31. The correlation between assets in a two-asset portfolio increases during a market decline. If there is no change in the proportion of each asset held in the portfolio or the expected standard deviation of the individual assets, the volatility of the portfolio is most likely to:A. increase.B. decrease.C. remain the same.The following information relates to Questions 32-34An analyst has made the following return projections for each of three possible outcomes with an equal likelihood of occurrence:32. Which pair of assets is perfectly negatively correlated?A. Asset 1 and Asset 2.B. Asset 1 and Asset 3.C. Asset 2 and Asset 3.33. If the analyst constructs two-asset portfolios that are equally-weighted, which pair of assets has the lowest expected standard deviation?A. Asset 1 and Asset 2.B. Asset 1 and Asset 3.C. Asset 2 and Asset 3.34. If the analyst constructs two-asset portfolios that are equally weighted, which pair of assets provides the least amount of risk reduction?A. Asset 1 and Asset 2.B. Asset 1 and Asset 3.C. Asset 2 and Asset 3.35. Which of the following statements is least accurate? The efficient frontier is the set of all attainable risky assets with the:A. highest expected return for a given level of risk.B. lowest amount of risk for a given level of return.C. highest expected return relative to the risk-free rate.36. The portfolio on the minimum-variance frontier with the lowest standard deviation is:A. unattainable.B. the optimal risky portfolio.C. the global minimum-variance portfolio.37. The set of portfolios on the minimum-variance frontier that dominates all sets of portfolios below the global minimum-variance portfolio is the:A. capital allocation line.B. Markowitz efficient frontier.C. set of optimal risky portfolios.38. The dominant capital allocation line is the combination of the risk-free asset and the:A. optimal risky portfolio.B. levered portfolio of risky assets.C. global minimum-variance portfolio.39. Compared to the efficient frontier of risky assets, the dominant capital allocation line has higher rates of return for levels of risk greater than the optimal risky portfolio because of the investor's ability to:A. lend at the risk-free rate.B. borrow at the risk-free rate.C. purchase the risk-free asset.40. With respect to the mean-variance theory, the optimal portfolio is determined by each individual investor's:A. risk-free rate.B. borrowing rate.C. risk preference.Chapter 4 Portfolio Risk and Return: Part II PRACTICE PROBLEMS FOR CHAPTER 41. The line depicting the risk and return of portfolio combinations of a risk-free asset and any risky asset is the:A. security market line.B. capital allocation line.C. security characteristic line.2. The portfolio of a risk-free asset and a risky asset has a better risk-return tradeoff than investing in only one asset type because the correlation between the risk-free asset and the risky asset is equal to:A. - 1.0.B. 0.0.C. 1.0.3. With respect to capital market theory, an investor's optimal portfolio is the combination of a risk-free asset and a risky asset with the highest:A. expected return.B. indifference curve.C. capital allocation line slope.4. Highly risk-averse investors will most likely invest the majority of their wealth in:A. risky assets.B. risk-free assets.C. the optimal risky portfolio.5. The capital market line, CML, is the graph of the risk and return of portfolio combinations consisting of the risk-free asset and:A. any risky portfolio.B. the market portfolio.C. the leveraged portfolio.6. Which of the following statements most accurately defines the market portfolio in capital market theory? The market portfolio consists of all:A. risky assets.B. tradable assets.C. investable assets.7. With respect to capital market theory, the optimal risky portfolio:。
金融工程相关习题及答案
⾦融⼯程相关习题及答案Chapter 1 Market Organization and Structure PRACTICE PROBLEMS FOR CHAPTER 11. Akihiko Takabe has designed a sophisticated forecasting model, which predicts the movements in the overall stock market, in the hope of earning a return in excess of a fair return for the risk involved. He uses the predictions of the model to decide whether to buy, hold, or sell the shares of an index fund that aims to replicate the movements of the stock market. Takabe would best be characterized as a (n):A. hedger.B. investor.C. information-motivated trader.2. James Beach is young and has substantial wealth. A significant proportion of his stock portfolio consists of emerging market stocks that offer relatively high expected returns at the cost of relatively high risk. Beach believes that investment in emerging market stocks is appropriate for him given his ability and willingness to take risk. Which of the following labels most appropriately describes Beach?A. Hedger.B. Investor.C. Information-motivated trader.3. Lisa Smith owns a manufacturing company in the United States. Her company has sold goods to a customer in Brazil and will be paid in Brazilian real (BRL) in three months. Smith is concerned about the possibility of the BRL depreciating more than expected against the U.S. dollar (USD). Therefore, she is planning to sell three-month futures contracts on the BRL. The seller of such contracts generally gains when the BRL depreciates against the USD. If Smith were to sell these future contracts, she would most appropriately be described as a (n):A. hedger.B. investor.C. information-motivated trader.4. Which of the following is not a function of the financial system?A. To regulate arbitrageurs’ profits (excess returns).B. To help the economy achieve allocational efficiency.C. To facilitate borrowing by businesses to fund current operations.5. An investor primarily invests in stocks of publicly traded companies. The investor wants to increase the diversification of his portfolio. A friend has recommended investing in real estate properties. The purchase of real estate would best be characterized as a transaction in the:A. derivative investment market.B. traditional investment market.C. alternative investment market.6. A hedge fund holds its excess cash in 90-day commercial paper and negotiable certificates of deposit. The cash management policy of the hedge fund is best described as using:A. capital market instruments.B. money market instruments.C. intermediate-term debt instruments.7. An oil and gas exploration and production company announces that it is offering 30 million shares to the public at $45.50each. This transaction is most likely a sale in the:A. futures market.B. primary market.C. secondary market.8. Consider a mutual fund that invests primarily in fixed-income securities that have been determined to be appropriate given the fund’s investment goal. Which of the following is least likely to be a part of this fund?A. Warrants.B. Commercial paper.C. Repurchase agreements.9. A friend has asked you to explain the differences between open-end and closed-end funds. Which of the following will you most likely include in your explanation?A. Closed-end funds are unavailable to new investors.B. When investors sell the shares of an open-end fund, they can receive a discount or a premium to the fund’s net asset value.C. When selling shares, investors in an open-end fund sell the shares back to the fund whereas investors in a closed-end fund sell the shares to others in the secondary market.10. The usefulness of a forward contract is limited by some problems. Which of the following is most likely one of those problems?A. Once you have entered into a forward contract, it is difficult to exit from the contract.B. Entering into a forward contract requires the long party to deposit an initial amount with the short party.C. If the price of the underlying asset moves adversely from the perspective of the long party, periodic payments must be made to the short party.11. Tony Harris is planning to start trading in commodities. He has heard about the use of futures contracts on commodities and is learning more about them. Which of the following is Harris least likely to find associated with a futures contract?A. Existence of counterparty risk.B. Standardized contractual terms.C. Payment of an initial margin to enter into a contract.12. A German company that exports machinery is expecting to receive $10 million in three months. The firm converts all its foreign currency receipts into euros. The chief financial officer of the company wishes to lock in a minimum fixed rate for converting the $10 million to euro but also wants to keep the flexibility to use the future spot rate if it is favorable. What hedging transaction is most likely to achieve this objective?A. Selling dollars forward.B. Buying put options on the dollar.C. Selling futures contracts on dollars.13. A book publisher requires substantial quantities of paper. The publisher and a paper producer have entered into an agreement for the publisher to buy and the producer to supply a given quantity of paper four months later at a price agreed upon today. This agreement is a:A. futures contract.B. forward contract.C. commodity swap.14. The Standard & Poor’s Depos itary Receipts (SPDRs) is an investment that tracks the S&P 500 stock market index. Purchases and sales of SPDRs during an average trading day are best described as:A. primary market transactions in a pooled investment.B. secondary market transactions in a pooled investment.C. secondary market transactions in an actively managed investment.15. The Standard & Poor’s Depositary Receipts (SPDRs) is an exchange-traded fund in the United States that is designed to track the S&P 500 stock market index. The current price of a share of SPDRs is $113. A trader has just bought call options on shares of SPDRs for a premium of $3 per share. The call options expire in five months and have an exercise price of $120 per share. On the expiration date, the trader will exercise the call options (ignore any transaction costs) if and only if the shares of SPDRs are trading:A. below $120 per share.B. above $120 per share.C. above $123 per share.16. Which of the following statements about exchange-traded funds is most correct?A. Exchange-traded funds are not backed by any assets.B. The investment companies that create exchange-traded funds are financial intermediaries.C. The transaction costs of trading shares of exchange-traded funds are substantially greater than the combined costs of trading the underlying assets of the fund.17. Jason Schmidt works for a hedge fund and he specializes in finding profit opportunities that are the result of inefficiencies in the market for convertible bonds—bonds that can be conver ted into a predetermined amount of a company’s common stock. Schmidt tries to find convertibles that are priced inefficiently relative to the underlying stock. The trading strategy involves the simultaneous purchase of the convertible bond and the short sale of the underlying common stock. The above process could best be described as:A. hedging.B. arbitrage.C. securitization.18. Pierre-Louis Robert just purchased a call option on shares of the Michelin Group.A few days ago he wrote a put option on Michelin shares. The call and put options have the same exercise price, expiration date, and number of shares underlying. Considering both positions, Robert’s exposure to the risk of the stock of the Michelin Group is:A. long.B. short.C. neutral.19. An online brokerage firm has set the minimum margin requirement at 55 percent. What is the maximum leverage ratio associated with a position financed by this minimum margin requirement?A. 1.55.B. 1.82.C. 2.22.20. A trader has purchased 200 shares of a non-dividend-paying firm on margin at a price of $50 per share. The leverage ratio is 2.5. Six months later, the trader sells these shares at $60 per share. Ignoring the interest paid on the borrowed amount and the transaction costs, what was the return to the trader during the six-month period?A. 20 percent.B. 33.33 percent.C. 50 percent.21. Jason Williams purchased 500 shares of a company at $32 per share. The stock was bought on 75 percent margin. One month later, Williams had to pay interest on the amount borrowed at a rate of 2 percent per month. At that time, Williams receiveda dividend of $0.50 per share. Immediately after that he sold the shares at $28 per share. He paid commissions of $10 on the purchase and $10 on the sale of the stock. What was the rate of return on this investment for the one-month period?A. ?12.5 percent.B. –15.4 percent.C. –50.1 percent.22. Caroline Rogers believes the price of Gamma Corp. stock will go down in the near future. She has decided to sell short 200 shares of Gamma Corp. at the current market price of €47. The initial margin requirement is 40 percent. Which of the following is an appropriate statement regarding the margin requirement that Rogers is subject to on this short sale?A. She will need to c ontribute €3,760 as margin.B. She will need to contribute €5,640 as margin.C. She will only need to leave the proceeds from the short sale as deposit and does not need to contribute any additional funds.23. The current price of a stock is $25 per share. You have $10,000 to invest. You borrow an additional $10,000 from your broker and invest $20,000 in the stock. If the maintenance margin is 30 percent, at what price will a margin call first occur?A. $9.62.B. $17.86.C. $19.71.24. You have placed a sell market-on-open order—a market order that would automatically be submitted at the market’s open tomorrow and would fill at the market price. Your instruction, to sell the shares at the market open, is a(n):A. execution instruction.B. validity instruction.C. clearing instruction.25. A market has the following limit orders standing on its book for a particular stock. The bid and ask sizes are number of shares in hundreds.What is the market?A. 9.73 bid, offered at 10.14.B. 9.81 bid, offered at 10.10.C. 9.95 bid, offered at 10.02.26. Consider the following limit order book for a stock. The bid and ask sizes are number of shares in hundredsA new buy limit order is placed for 300 shares at ￥123.40. This limit order issaid to:A. take the market.B. make the market.C. make a new market.27. Currently, the market in a stock is "$54.62 bid, offered at $54.71." A new sell limit order is placed at $54.62. This limit order is said to:A. take the market.B. make the market.C. make a new market.28. Jim White has sold short 100 shares of Super Stores at a price of$42 per share. He has also simultaneously placed a "good-till-cancelled, stop 50, limit 55 buy" order. Assume that if the stop condition specified by White is satisfied and the order becomes valid, it will get executed. Excluding transaction costs, what is the maximum possible loss that White can have?A. $800.B. $1,300.C. Unlimited.29. You own shares of a company that are currently trading at $30 a share. Your technical analysis of the shares indicates a support level of $27.50. That is, if the price of the shares is going down, it is more likely to stay above this level rather than fall below it. If the price does fall below this level, however, you believe that the price may continue to decline. You have no immediate intent to sell the shares but are concerned about the possibility of a huge loss if the share price declines below thesupport level. Which of the following types of orders could you place to most appropriately address your concern?A. Short sell order.B. Good-till-cancelled stop sell order.C. Good-till-cancelled stop buy order.30. In an underwritten offering, the risk that the entire issue may not be sold to the public at the stipulated offering price is borne by the:A. issuer.B. investment bank.C. buyers of the part of the issue that is sold.31 . A British company listed on the Alternative Investment Market of the London Stock Exchange, announced the sale of 6,686,665 shares to a small group of qualified investors at ￡0.025 per share. Which of the following best describesA. Shelf registration.B. Private placement.C. Initial public offering.32. A German publicly traded company, to raise new capital, gave its existing shareholders the opportunity to subscribe for new shares. The existing shareholders could purchase two new shares at a subscription price of €4.58 per share for every 15 shares held. This is an example of a(n):A. rights offering.B. private placement.C. initial public offering.33. Consider an order-driven system that allows hidden orders. The following four sell orders on a particular stock are currently in the system's limit order book. Based on the commonly used order precedence hierarchy, which of these orders will have precedence over others?A. Order I (time of arrival of 9:52:01 ).B. Order II (time of arrival of 9:52:08).C. Order III (time of arrival of 9:53:04)34. Zhenhu Li has submitted an immediate-or-cancel buy order for 500 shares of a company at a limit price of CNY 74.25. There are two sell limit orders standing in that stock's order book at that time. One is for 300 shares at a limit price of CNY74.30 and the other is for 400 shares at a limit price of CNY 74.35. How many shares in Li's order would get cancelled?A. None (the order would remain open but unfilled).B. 200 (300 shares would get filled).C. 500 (there would be no fill).35. A market has the following limit orders standing on its book for a particular stock:Ian submits a day order to sell 1,000 shares, limit ￡19.83. Assuming that no more buy orders are submitted on that day after Ian submits his order, what would be Ian's average trade price?A. ￡19.70.36. A financial analyst is examining whether a country's financial market is well functioning. She finds that the transaction costs in this market are low and trading volumes are high. She concludes that the market is quite liquid. In such a market:A. traders will find it hard to make use of their information.B. traders will find it easy to trade and their trading will make the market less informationally efficient.C. traders will find it easy to trade and their trading will make the marketmore informationally efficient.37. The government of a country whose financial markets are in an early stage of development has hired you as a consultant on financial market regulation. Your first task is to prepare a list of the objectives of market regulation. Which of the following is least likely to be included in this list of objectives?A. Minimize agency problems in the financial markets.B. Ensure that financial markets are fair and orderly.C. Ensure that investors in the stock market achieve a rate of return that is at least equal to the risk-free rate of return. Chapter 2 Portfolio Management: An Overview PRACTICE PROBLEMS FOR CHAPTER 21. Investors should use a portfolio approach to:A. reduce risk.B. monitor risk.C. eliminate risk.2. Which of the following is the best reason for an investor to be concerned with the composition of a portfolio?A. Risk reduction.B. Downside risk protection.C. Avoidance of investment disasters.3. With respect to the formation of portfolios, which of the following statements is most accurate?A. Portfolios affect risk less than returns.B. Portfolios affect risk more than returns.C. Portfolios affect risk and returns equally.4. Which of the following institutions will on average have the greatest need for liquidity?A. Banks.B. Investment companies.C. Non-life insurance companies.5. Which of the following institutional investors will most likely have the longest time horizon?A. Defined benefit plan.B. University endowment.C. Life insurance company.6. A defined benefit plan with a large number of retirees is likely to have a high need forA. income.7. Which of the following institutional investors is most likely to manage investmentsin mutual funds?A. Insurance companies.B. Investment companies.C. University endowments.8. With respect to the portfolio management process, the asset allocation is determined in the:A. planning step.B. feedback step.C. execution step9. The planning step of the portfolio management process is least likely to include an assessment of the client'sA. securities.B. constraints.C. risk tolerance.10. With respect to the portfolio management process, the rebalancing of a portfolio's composition is most likely to occur in the:A. planning step.B. feedback step.C. execution step.11. An analyst gathers the following information for the asset allocations of three portfolios:Which of the portfolios is most likely appropriate for a client who has a high degree of risk tolerance?A. Portfolio 1.B. Portfolio 2.C. Portfolio 3.12. Which of the following investment products is most likely to trade at their net asset value per share?A. Exchange traded funds.B. Open-end mutual funds.C. Closed-end mutual funds.13. Which of the following financial products is least likely to have a capital gain distribution?A. Exchange traded funds.B. Open-end mutual funds.C. Closed-end mutual funds.14. Which of the following forms of pooled investments is subject to the least amount of regulation?A. Hedge funds.B. Exchange traded funds.C. Closed-end mutual funds.15. Which of the following pooled investments is most likely characterized by a few large investments?A. Hedge funds.B. Buyout funds.C. Venture capital funds.Chapter 3 Portfolio Risk and Return: Part I PRACTICE PROBLEMS FOR CHAPTER 31. An investor purchased 100 shares of a stock for $34.50 per share at the beginning of the quarter. If the investor sold all of the shares for $30.50 per share after receiving a $51.55 dividend payment at the end of the quarter, the holding period return is closest to:A. - 13.0%.B. - 11.6%.C. - 10.1%.2. An analyst obtains the following annual rates of return for a mutual fund:The fund's holding period return over the three-year period is closest to:A. 0.18%.B. 0.55%.C. 0.67%.3. An analyst observes the following annual rates of return for a hedge fund:The hedge fund's annual geometric mean return is closest to:A. 0.52%.B. 1.02%.C. 2.67%.4. Which of the following return calculating methods is best for evaluating the annualized returns of a buy-and-hold strategy of an investor who has made annual deposits to an account for each of the last five years?A. Geometric mean return.B. Arithmetic mean return.C. Money-weighted return.5. An investor evaluating the returns of three recently formed exchange-traded funds gathers the following information:The ETF with the highest annualized rate of return is:A. ETF 1.B. ETF 2.C. ETF 3.6. With respect to capital market theory, which of the following asset characteristics is least likely to impact the variance of an investor's equally weighted portfolio?A. Return on the asset.B. Standard deviation of the asset.C. Covariances of the asset with the other assets in the portfolio.7. A portfolio manager creates the following portfolio:If the correlation of returns between the two securities is 0.40, the expected standard deviation of the portfolio is closest to:A. 10.7%.B. 11.3%.C. 12.1%.8. A portfolio manager creates the following portfolio:If the covariance of returns between the two securities is - 0.0240, the expectedstandard deviation of the portfolio is closest to:A. 2.4%.B. 7.5%.C. 9.2%.The following information relates to Questions 9-10A portfolio manager creates the following portfolio:9. If the standard deviation of the portfolio is 14.40%, the correlation between the two securities is equal to:A. - 1.0.B. 0.0.C. 1.0.10. If the standard deviation of the portfolio is 14.40%, the covariance between the two securities is equal to:A. 0.0006.B. 0.0240.C. 1.0000.The following information relates to Questions 11-14An analyst observes the following historic geometric returns:11 . The real rate of return for equities is closest to:A. 5.4%.B. 5.8%.C. 5.9%.12. The real rate of return for corporate bonds is closest to:A. 4.3%.B. 4.4%.C. 4.5%.13. The risk premium for equities is closest to:A. 5.4%.B. 5.5%.C. 5.6%.14. The risk premium for corporate bonds is closest to:A. 3.5%.B. 3.9%.C. 4.0%.15. With respect to trading costs, liquidity is least likely to impact the:A. stock price.B. bid-ask spreads.C. brokerage commissions.16. Evidence of risk aversion is best illustrated by a risk-return relationship that is:A. negative.B. neutral.C. positive.17. With respect to risk-averse investors, a risk-free asset will generate a numerical utility that is:A. the same for all individuals.B. positive for risk-averse investors.C. equal to zero for risk seeking investors18. With respect to utility theory, the most risk-averse investor will have an indifference curve with the:A. most convexity.B. smallest intercept value.C. greatest slope coefficient.19. With respect to an investor's utility function expressed as:21=E(r)-2u A , whichof the following values for the measure for risk aversion has the least amount of risk aversion?A. - 4.B. 0.C. 4.The following information relates to Questions 20-23A financial planner has created the following data to illustrate the application of utility theory to portfolio selection:20. A risk-neutral investor is most likely to choose:A. Investment 1.B. Investment 2.C. Investment 3.ExpectedStandard Deviation (% )28153021. If an investor's utility function is expressed as U = E(r) ~A& and the measure for risk aversion has a value of- 2, the risk-seeking investor is most likely to choose:A. Investment 2.B. Investment 3.C. Investment 4.22. If an investor's utility function is expressed as U = E(r) - ~A& and the measure for risk aversion has a value of2, the risk-averse investor is most likely to choose:A. Investment 1.B. Investment 2.C. Investment 3.23. If an investor's utility function is expressed as U =E(r) - ~A& and the measure for risk aversion has a value of4, the risk-averse investor is most likely to choose:A. Investment 1.B. Investment 2.C. Investment 3.24. With respect to the mean-variance portfolio theory, the capital allocation line, CAL, is the combination of the risk-free asset and a portfolio of all:A. risky assets.B. equity securities.C. feasible investments.25. Two individual investors with different levels of risk aversion will have optimal portfolios that are:A. below the capital allocation line.B. on the capital allocation line.C. above the capital allocation line.The following information relates to Questions 26-28A portfolio manager creates the following portfolio:26. If the portfolio of the two securities has an expected return of15%, the proportion invested in Security 1 is:A. 25%.B. 50%.C. 75%.27. If the correlation of returns between the two securities is - 0.15, the expected standard deviation of an equal-weighted portfolio is closest to:A. 13.04%.B. 13.60%.C. 13.87%.28. If the two securities are uncorrelated, the expected standard deviation of anequal-weighted portfolio is closest to:A. 14.00%.B. 14.14%.C. 20.00%.29. As the number of assets in an equally-weighted portfolio increases, the contribution of each individual asset's variance to the volatility of the portfolio:A. increases.B. decreases.C. remains the same.30. With respect to an equally-weighted portfolio made up of a large number of assets, which of the following contributes the most to the volatility of the portfolio?A. Average variance of the individual assets.B. Standard deviation of the individual assets.C. Average covariance between all pairs of assets.31. The correlation between assets in a two-asset portfolio increases during a market decline. If there is no change in the proportion of each asset held in the portfolio or the expected standard deviation of the individual assets, the volatility of the portfolio is most likely to:A. increase.B. decrease.C. remain the same.The following information relates to Questions 32-34An analyst has made the following return projections for each of three possible outcomes with an equal likelihood of occurrence:32. Which pair of assets is perfectly negatively correlated?A. Asset 1 and Asset 2.B. Asset 1 and Asset 3.C. Asset 2 and Asset 3.33. If the analyst constructs two-asset portfolios that are equally-weighted, which pair of assets has the lowest expected standard deviation?A. Asset 1 and Asset 2.B. Asset 1 and Asset 3.C. Asset 2 and Asset 3.34. If the analyst constructs two-asset portfolios that are equally weighted, which pair of assets provides the least amount of risk reduction?A. Asset 1 and Asset 2.B. Asset 1 and Asset 3.C. Asset 2 and Asset 3.35. Which of the following statements is least accurate? The efficient frontier is the set of all attainable risky assets with the:A. highest expected return for a given level of risk.B. lowest amount of risk for a given level of return.C. highest expected return relative to the risk-free rate.36. The portfolio on the minimum-variance frontier with the lowest standard deviation is:A. unattainable.。
金融工程教材英文版课后习题
END-OF-CHAPTER QUESTIONS AND PROBLEMSChapter 11. Business risk is the risk associated with a particular line of business, whereas financial risk is the risk associated with stock prices, exchange rates, interest rates and commodity prices. An example would be that a firm might be in the business of manufacturing furniture. Business risk would reflect the uncertainty of the furniture market, whereas financial risk would reflect the risk associated with the interest rates that would impact their borrowing costs. In addition a business might also be affected by exchange rates. Some of the financial risks can also be business risks. The business risk of a bank, for example, is highly affected by interest rate and exchange rate risk.2. Real assets consist of the tangible assets of the economy; however, for our purposes we also define them to include such intangible assets as management talent, ideas, brand names, etc. They are distinguished from financial assets, which are securities. These securities represent claims on business firms, which own the real assets, or on governments.3. An investor who is risk averse does not like risk and will not take on additional risk without the expectation of higher return. Such an individual will try to get the highest return for a given amount of risk or the lowest risk for a given amount of return. An individual who is risk neutral will simply seek the highest return without regard to risk.4. Financial markets distinguish the qualities of stocks and bonds by their prices. The markets set the price so that the return expected by investors is appropriate for the level of risk. In competitive and efficient markets, the expected return will vary directly with the level of risk. If one wishes to earn a higher return, it is necessary to assume more risk. This is the risk-return trade-off. Investors trade off risk against return.The risk-return trade-off will also hold in derivative markets. The risk-return trade-off is a fundamental result of the nature of competition in the marketplace. Attractive, low-risk investments will have their prices driven up and this will lower the expected returns. High-risk investments will have their prices driven down and this will result in higher expected returns.5. The expected return consists of the risk-free rate and a risk premium. The risk-free rate is the return one expects from investing money today and, thereby, foregoing the consumption that could be obtained. A risk premium is the additional return that one expects to receive by virtue of assuming risk.6. An efficient market is one in which prices reflect the true economic values of the assets trading therein. Inefficient markets, no one can earn returns that are more than commensurate with the level of risk. Efficient markets are characterized by low transaction costs and by the rapid rate at which new information is incorporated into prices.7. Arbitrage is a type of investment transaction that seeks to profit when identical goods are priced differently. Buying an item at one price and immediately selling it at another is a type of arbitrage. Because of the combined activities of arbitrageurs, identical goods, primarily financial assets, cannot sell for different prices for long. This is the law of one price. Arbitrage helps make our markets efficient by assuring that prices are in line with what they are supposed to be. In short, we cannot get something for nothing. A situation involving two identical goods or portfolios that are not priced equivalently would be exploited by arbitrageurs until their prices were equal. The "one price" that an asset must be is called the "theoretical fair value."11. Derivative markets provide a means of adjusting the risk of spot market investments to a more acceptable level and identifying the consensus market beliefs. They make trading easier and less costly and spot markets more efficient. These markets also provide a means of speculating.Chapter 33. European call: We know that its price cannot exceed S0 but must exceed Max(0, S0 - X(1+r)-T). With an infinite time to expiration, the present value of X is zero so the lower bound is S0 and, since the upper bound is S0, the call price must be S0. American call: We know that its price cannot exceed S0 but it must be at least as valuable as a European call. Thus its value must also be S0. Note that if exercised early it would be worth only S0 - X so it will never be exercised early.4. Ordinarily the option with the longer time to expiration would sell for more. If both options were deep out of-the-money, however, they could both sell for essentially nothing. The market would be expecting that both the shorter- and longer-lived options will expire out-of-the-money.5. If both options were deep out-of-the-money, they might have prices of zero. As in the previous question, the two options are expected to expire out-of-the-money.6. The call is underpriced, so buy the call, sell short the stock, and buy risk-free bonds with face value of X. The cash received from the stock is greater than the cost of the call and bonds. Thus, there is a positive cash flow up front. The payoffs from the portfolio at expiration are as follows:If S T < X,- S T (from the stock)X (from the bonds)the total, X - S T, is positive3-2If S T ≥ XS T - X (from the call)- S T (from the stock)X (from the bonds)the total is zero.The portfolio generates a positive cash flow up front and there is no cash outflow at expiration.7. Time value is a measure of the amount of uncertainty in an option. Uncertainty relates to whether the option will expire in- or out-of-the-money. When the option is deep in-the-money, there is little uncertainty about the fact that the option will expire in-the-money. The option will then begin to behave about like the stock. Then the option is deep-out-the-money, there is also little uncertainty since it is likely to finish out-of-the money. When the option is at-the-money there is considerable uncertainty about how it will finish.8. Assuming the stock pays no dividends, there is no reason to exercise a call early (this obviously presumes the call is American). The tendency to believe that exercising an option because the stock can go up no further ignores the fact that an option can generally be sold. Exercising an option throws away any chance that the stock can go up further. If the stock falls, the option holder would be hurt, but if the option holder exercised and became a stock holder, he would also be hurt by a falling stock price. There is simply no reason to give away the time value that arises because of the possibility that the stock can always go further upward. In simple, mathematical terms, exercising captures only the intrinsic value S0 - X. The call can always be sold for at least S0 - X (1 + r) -T.9. The paradox is resolved by recalling that if the option expires out-of-the-money, it does not matter how far out-of-the-money it is. The loss to the option holder is limited to the premium paid. For example, suppose the stock price is $24, the exercise price is $20, and the call price is $6. Higher volatility increases the chance of greater gains to the holder of the call. It also increases the chance of a larger stock price decrease. If, however, the stock price does end up below $20, the investor's loss is the same regardless of whether the stock price at expiration is $19 or $1. If the stock were purchased instead of the call, the loss would obviously be greater if the stock price went to $1 than if it went to $19. For this reason, holders of stocks dislike volatility, while holders of calls like volatility. A similar argument applies to puts.10. The minimum value of an American put is Max(0, X - S0). This is always higher than the lower bound of a European put, X (1 + r) -T - S0, except at expiration when the two are equal.11. When buying a call option, one hopes to exercise it at a later date. Thus, the exercise price will be paid out later. If interest rates are higher, additional interest can be earned on the money that will eventually be paid out as the exercise price. When buying a put option, one hopes to exercise it later, thus receiving the exercise price. If interest rates are higher, the put is less valuable because the holder is foregoing interest by having to wait to exercise the put. Higher interest rates make the present value of the exercise price be lower. In the case of the call, this is good because the call holder anticipates having to pay out the exercise price. For the put holder this is bad because the put holder anticipates receiving the exercise price.12. If the put price is higher than predicted by the model, the put is overpriced. Then the put should be sold. The funds should be used to construct a portfolio consisting of a long call and risk-free bonds with face value of X, and a short position in the stock. You can (and should) verify that this portfolio has a payoff at expiration that is the same as that of the put. Thus, if you sell the put for more than it costs to construct this portfolio, you can create a portfolio that offsets your put and have some money left over.13. An American call is exercised early only to capture a dividend. When a stock goes ex-dividend, the call will lose value as the stock drops. This will cause a loss in value to the holder of the call. The call holder knows this loss will be incurred as soon as the stock goes ex-dividend. If the call were exercised just before the stock goes ex-dividend, however, the call holder would capture the stock and the dividend, which might be enough to offset the otherwise loss in the value of the call. For a put, however, dividends are not necessary to make the argument that it might be optimal to exercise early. The holder of an American put faces a situation in which the gains are limited to the exercise price. Since the stock price can go down only to zero, early exercise of a put on a bankrupt firm would obviously be advisable. But the firm does not have to go bankrupt. If the stock price is low enough, the gains from waiting for it to go lower are not worth the wait. If dividends were added to the picture, however, they would discourage early exercise. The more dividends paid, the lower the stock price is driven and the more valuable it is to hold on to the put.Chapter 41. When we price an option according to its boundary conditions, we do not find an exact price for the option. We provide only limits on the maximum and minimum price of an option or group of options. In the case of options differing by exercise prices or in the case of put-call parity, we can price only the relationship or difference between the option prices. We cannot price each option individually without an option pricing odel; however, an option pricing model must provide prices that conform to the boundary conditions. Because boundary condition rules require fewer assumptions, we can say that they are more generally applicable and are more likely to hold in practice. They are incomplete, however, in the sense that they do not tell us exactly what the option price should be, which is what an option pricing model does tell us.2. A binomial option pricing model enables us to see the relationship between the stock price and the call price. The model shows, in a simple framework, how to construct a riskless portfolio by appropriately weighting the stock against the option. By noting that the riskless portfolio should return the risk-free rate, we can see what the call price must be. We can also understand the forces that bring the call option price in line if it is not priced according to the model. In addition, the model illustrates the importance of revising the hedge ratio. Finally, the model is probably the best way to handle the problem of pricing an American option.3. For a call, a hedge portfolio will consist of n shares of stock and one short call. The shares of stock, n, will be a long position that will reflect the next two possible values of the call and stock. The call is short because the call and stock move opposite each other, so a short position in the call is needed to offset a long position in the stock. If the option is a put, a long position in n shares will be hedged by a long position in one put. The number of shares, n, is also a reflection of the next two possible option and stock values. The put is long because it already moves opposite to the stock.4. This means that the option is trading in the market for a price that is lower than its theoretical fair value. Consequently, the option is underpriced. An underpriced option should be bought. To hedge the position, one should sell n shares of stock, where n is the hedge ratio as defined in the chapter.5. At each point in the binomial tree, the option price is computed based on the next two possible prices, weighted by the appropriate probability values and discounted back one period. If the option can be exercised early, we determine its intrinsic value, i.e., the value it would have if it were exercised at that point. If the intrinsic value is greater, it replaces the computed value. This is done at all nodes. Note that it is quite possible that the option will be exercised at many different nodes.6. A path independent problem is one in which the only values that matter in determining the current price are the values at expiration. A particular expiration value is the same regardless of the sequence of up and down moves the stock took to get to that point. A path dependent model is one in which the sequence of up and down moves does matter. For example, suppose the stock goes down, up and then up. Contrast that with up, up and down. If the option is a European put, it does not matter which sequence the stock followed. Where it is at expiration is the only thing that matters. If the option is, however, an American put, the down, up, up sequence could lead to early exercise when it makes that first move down, whereas the up, up, down sequence is unlikely to lead to early exercise.Chapter 51. In a discrete time model, the stock price can make a jump to only one of two possible values. The length of time over which the move can be made is finite. In a continuous time model, the stock price can jump to an infinite number of possibilities. The length of time over which the move can be made is infinitesimal (very, very small). The difference between the two models is perhaps best described as in the text as the difference between still photos and a movie.2. The familiar normal or bell-shaped distribution is a symmetric probability distribution that depends only on the mean and variance. A lognormal distribution is skewed, having more extreme right values. A lognormal distribution, however, is normal in the logarithm. Thus, if x is lognormally distributed, its logarithm, lnx, is normally distributed. With respect to stock prices, the logarithm is of the rate of return. That is, let (S1 –S0)/S0 be defined as the return over period 0 to period 1. Then if it is lognormally distributed, ln(S1/S0) is normally distributed. Note what appears to be slight inconsistency: (S1 – S0)/S0 is a percentage return whereas S1/S0 is 1.0 plus the percentage return. That does not matter as we can always shift a normal distribution by adding a constant such as 1.0 and it does not affect the fact that it is normally distributed. It just slides it over.3. The Black-Scholes model assumes no dividends, but actually this was just for convenience to allow us to start at the simplest level. If the dividends are appropriately modeled, the Black-Scholes model handles stocks with dividends with only the minor adjustment that we must remove the present value of the dividends from the stock price before using it in the model. We can do this by subtracting the present value of the stream of discrete dividends over the life of the model or by discounting the stock price by the dividend yield rate over the life of the model.4. The variables in the binomial model are S0 (the stock price), X (the exercise price), r (the discrete risk-free rate), u (one plus the return on the stock if it goes up), d (one plus the return on the stock if it goes down) and n, the number of time periods. The variables in the Black-Scholes model are S0 (the stock price), X (the exercise price), r c (the continuously compounded risk-free rate), ó (the standard deviation of the continuously compounded return on the stock) and T (the time to expiration). The variables S0 and X are the same in both models. In the binomial model, r is the discrete interest rate per period. In the Black-Scholes model, the interest rate must be expressed in continuously compounded form. The annual discrete interest rate (r) is related to the annual continuously compounded rate (r c) by the formula, r c = ln(1 + r). Then the binomial rate per period is found as (1 + r)T/n - 1. The up and down factors in the binomial model are directly related to ó in the Black-Scholes model by the formula u = T/n ó e – 1 and d = (1/(1+u)) – 1. The time to expiration (T) in the Black-Scholes model is related to the length of each binomial period by the relationship T/n where n is the number of periods. Thus, all of the Black-Scholes variables are either equal to or directly convertible to binomial variables.Chapter6Chapter7Chapter 8Chapter9Chapter 10。
金融工程教材英文版课后习题
END-OF-CHAPTER QUESTIONS AND PROBLEMSChapter 11. Business risk is the risk associated with a particular line of business, whereas financial risk is the risk associated with stock prices, exchange rates, interest rates and commodity prices. An example would be that a firm might be in the business of manufacturing furniture. Business risk would reflect the uncertainty of the furniture market, whereas financial risk would reflect the risk associated with the interest rates that would impact their borrowing costs. In addition a business might also be affected by exchange rates. Some of the financial risks can also be business risks. The business risk of a bank, for example, is highly affected by interest rate and exchange rate risk.2. Real assets consist of the tangible assets of the economy; however, for our purposes we also define them to include such intangible assets as management talent, ideas, brand names, etc. They are distinguished from financial assets, which are securities. These securities represent claims on business firms, which own the real assets, or on governments.3. An investor who is risk averse does not like risk and will not take on additional risk without the expectation of higher return. Such an individual will try to get the highest return for a given amount of risk or the lowest risk for a given amount of return. An individual who is risk neutral will simply seek the highest return without regard to risk.4. Financial markets distinguish the qualities of stocks and bonds by their prices. The markets set the price so that the return expected by investors is appropriate for the level of risk. In competitive and efficient markets, the expected return will vary directly with the level of risk. If one wishes to earn a higher return, it is necessary to assume more risk. This is the risk-return trade-off. Investors trade off risk against return.The risk-return trade-off will also hold in derivative markets. The risk-return trade-off is a fundamental result of the nature of competition in the marketplace. Attractive, low-risk investments will have their prices driven up and this will lower the expected returns. High-risk investments will have their prices driven down and this will result in higher expected returns.5. The expected return consists of the risk-free rate and a risk premium. The risk-free rate is the return one expects from investing money today and, thereby, foregoing the consumption that could be obtained. A risk premium is the additional return that one expects to receive by virtue of assuming risk.6. An efficient market is one in which prices reflect the true economic values of the assets trading therein. Inefficient markets, no one can earn returns that are more than commensurate with the level of risk. Efficient markets are characterized by low transaction costs and by the rapid rate at which new information is incorporated into prices.7. Arbitrage is a type of investment transaction that seeks to profit when identical goods are priced differently. Buying an item at one price and immediately selling it at another is a type of arbitrage. Because of the combined activities of arbitrageurs, identical goods, primarily financial assets, cannot sell for different prices for long. This is the law of one price. Arbitrage helps make our markets efficient by assuring that prices are in line with what they are supposed to be. In short, we cannot get something for nothing. A situation involving two identical goods or portfolios that are not priced equivalently would be exploited by arbitrageurs until their prices were equal. The "one price" that an asset must be is called the "theoretical fair value."11. Derivative markets provide a means of adjusting the risk of spot market investments to a more acceptable level and identifying the consensus market beliefs. They make trading easier and less costly and spot markets more efficient. These markets also provide a means of speculating.Chapter 33. European call: We know that its price cannot exceed S0 but must exceed Max(0, S0 - X(1+r)-T). With an infinite time to expiration, the present value of X is zero so the lower bound is S0 and, since the upper bound is S0, the call price must be S0. American call: We know that its price cannot exceed S0 but it must be at least as valuable as a European call. Thus its value must also be S0. Note that if exercised early it would be worth only S0 - X so it will never be exercised early.4. Ordinarily the option with the longer time to expiration would sell for more. If both options were deep out of-the-money, however, they could both sell for essentially nothing. The market would be expecting that both the shorter- and longer-lived options will expire out-of-the-money.5. If both options were deep out-of-the-money, they might have prices of zero. As in the previous question, the two options are expected to expire out-of-the-money.6. The call is underpriced, so buy the call, sell short the stock, and buy risk-free bonds with face value of X. The cash received from the stock is greater than the cost of the call and bonds. Thus, there is a positive cash flow up front. The payoffs from the portfolio at expiration are as follows:If S T < X,- S T (from the stock)X (from the bonds)the total, X - S T, is positive3-2If S T ≥ XS T - X (from the call)- S T (from the stock)X (from the bonds)the total is zero.The portfolio generates a positive cash flow up front and there is no cash outflow at expiration.7. Time value is a measure of the amount of uncertainty in an option. Uncertainty relates to whether the option will expire in- or out-of-the-money. When the option is deep in-the-money, there is little uncertainty about the fact that the option will expire in-the-money. The option will then begin to behave about like the stock. Then the option is deep-out-the-money, there is also little uncertainty since it is likely to finish out-of-the money. When the option is at-the-money there is considerable uncertainty about how it will finish.8. Assuming the stock pays no dividends, there is no reason to exercise a call early (this obviously presumes the call is American). The tendency to believe that exercising an option because the stock can go up no further ignores the fact that an option can generally be sold. Exercising an option throws away any chance that the stock can go up further. If the stock falls, the option holder would be hurt, but if the option holder exercised and became a stock holder, he would also be hurt by a falling stock price. There is simply no reason to give away the time value that arises because of the possibility that the stock can always go further upward. In simple, mathematical terms, exercising captures only the intrinsic value S0 - X. The call can always be sold for at least S0 - X (1 + r) -T.9. The paradox is resolved by recalling that if the option expires out-of-the-money, it does not matter how far out-of-the-money it is. The loss to the option holder is limited to the premium paid. For example, suppose the stock price is $24, the exercise price is $20, and the call price is $6. Higher volatility increases the chance of greater gains to the holder of the call. It also increases the chance of a larger stock price decrease. If, however, the stock price does end up below $20, the investor's loss is the same regardless of whether the stock price at expiration is $19 or $1. If the stock were purchased instead of the call, the loss would obviously be greater if the stock price went to $1 than if it went to $19. For this reason, holders of stocks dislike volatility, while holders of calls like volatility. A similar argument applies to puts.10. The minimum value of an American put is Max(0, X - S0). This is always higher than the lower bound of a European put, X (1 + r) -T - S0, except at expiration when the two are equal.11. When buying a call option, one hopes to exercise it at a later date. Thus, the exercise price will be paid out later. If interest rates are higher, additional interest can be earned on the money that will eventually be paid out as the exercise price. When buying a put option, one hopes to exercise it later, thus receiving the exercise price. If interest rates are higher, the put is less valuable because the holder is foregoing interest by having to wait to exercise the put. Higher interest rates make the present value of the exercise price be lower. In the case of the call, this is good because the call holder anticipates having to pay out the exercise price. For the put holder this is bad because the put holder anticipates receiving the exercise price.12. If the put price is higher than predicted by the model, the put is overpriced. Then the put should be sold. The funds should be used to construct a portfolio consisting of a long call and risk-free bonds with face value of X, and a short position in the stock. You can (and should) verify that this portfolio has a payoff at expiration that is the same as that of the put. Thus, if you sell the put for more than it costs to construct this portfolio, you can create a portfolio that offsets your put and have some money left over.13. An American call is exercised early only to capture a dividend. When a stock goes ex-dividend, the call will lose value as the stock drops. This will cause a loss in value to the holder of the call. The call holder knows this loss will be incurred as soon as the stock goes ex-dividend. If the call were exercised just before the stock goes ex-dividend, however, the call holder would capture the stock and the dividend, which might be enough to offset the otherwise loss in the value of the call. For a put, however, dividends are not necessary to make the argument that it might be optimal to exercise early. The holder of an American put faces a situation in which the gains are limited to the exercise price. Since the stock price can go down only to zero, early exercise of a put on a bankrupt firm would obviously be advisable. But the firm does not have to go bankrupt. If the stock price is low enough, the gains from waiting for it to go lower are not worth the wait. If dividends were added to the picture, however, they would discourage early exercise. The more dividends paid, the lower the stock price is driven and the more valuable it is to hold on to the put.Chapter 41. When we price an option according to its boundary conditions, we do not find an exact price for the option. We provide only limits on the maximum and minimum price of an option or group of options. In the case of options differing by exercise prices or in the case of put-call parity, we can price only the relationship or difference between the option prices. We cannot price each option individually without an option pricing odel; however, an option pricing model must provide prices that conform to the boundary conditions. Because boundary condition rules require fewer assumptions, we can say that they are more generally applicable and are more likely to hold in practice. They are incomplete, however, in the sense that they do not tell us exactly what the option price should be, which is what an option pricing model does tell us.2. A binomial option pricing model enables us to see the relationship between the stock price and the call price. The model shows, in a simple framework, how to construct a riskless portfolio by appropriately weighting the stock against the option. By noting that the riskless portfolio should return the risk-free rate, we can see what the call price must be. We can also understand the forces that bring the call option price in line if it is not priced according to the model. In addition, the model illustrates the importance of revising the hedge ratio. Finally, the model is probably the best way to handle the problem of pricing an American option.3. For a call, a hedge portfolio will consist of n shares of stock and one short call. The shares of stock, n, will be a long position that will reflect the next two possible values of the call and stock. The call is short because the call and stock move opposite each other, so a short position in the call is needed to offset a long position in the stock. If the option is a put, a long position in n shares will be hedged by a long position in one put. The number of shares, n, is also a reflection of the next two possible option and stock values. The put is long because it already moves opposite to the stock.4. This means that the option is trading in the market for a price that is lower than its theoretical fair value. Consequently, the option is underpriced. An underpriced option should be bought. To hedge the position, one should sell n shares of stock, where n is the hedge ratio as defined in the chapter.5. At each point in the binomial tree, the option price is computed based on the next two possible prices, weighted by the appropriate probability values and discounted back one period. If the option can be exercised early, we determine its intrinsic value, i.e., the value it would have if it were exercised at that point. If the intrinsic value is greater, it replaces the computed value. This is done at all nodes. Note that it is quite possible that the option will be exercised at many different nodes.6. A path independent problem is one in which the only values that matter in determining the current price are the values at expiration. A particular expiration value is the same regardless of the sequence of up and down moves the stock took to get to that point. A path dependent model is one in which the sequence of up and down moves does matter. For example, suppose the stock goes down, up and then up. Contrast that with up, up and down. If the option is a European put, it does not matter which sequence the stock followed. Where it is at expiration is the only thing that matters. If the option is, however, an American put, the down, up, up sequence could lead to early exercise when it makes that first move down, whereas the up, up, down sequence is unlikely to lead to early exercise.Chapter 51. In a discrete time model, the stock price can make a jump to only one of two possible values. The length of time over which the move can be made is finite. In a continuous time model, the stock price can jump to an infinite number of possibilities. The length of time over which the move can be made is infinitesimal (very, very small). The difference between the two models is perhaps best described as in the text as the difference between still photos and a movie.2. The familiar normal or bell-shaped distribution is a symmetric probability distribution that depends only on the mean and variance. A lognormal distribution is skewed, having more extreme right values. A lognormal distribution, however, is normal in the logarithm. Thus, if x is lognormally distributed, its logarithm, lnx, is normally distributed. With respect to stock prices, the logarithm is of the rate of return. That is, let (S1 –S0)/S0 be defined as the return over period 0 to period 1. Then if it is lognormally distributed, ln(S1/S0) is normally distributed. Note what appears to be slight inconsistency: (S1 – S0)/S0 is a percentage return whereas S1/S0 is 1.0 plus the percentage return. That does not matter as we can always shift a normal distribution by adding a constant such as 1.0 and it does not affect the fact that it is normally distributed. It just slides it over.3. The Black-Scholes model assumes no dividends, but actually this was just for convenience to allow us to start at the simplest level. If the dividends are appropriately modeled, the Black-Scholes model handles stocks with dividends with only the minor adjustment that we must remove the present value of the dividends from the stock price before using it in the model. We can do this by subtracting the present value of the stream of discrete dividends over the life of the model or by discounting the stock price by the dividend yield rate over the life of the model.4. The variables in the binomial model are S0 (the stock price), X (the exercise price), r (the discrete risk-free rate), u (one plus the return on the stock if it goes up), d (one plus the return on the stock if it goes down) and n, the number of time periods. The variables in the Black-Scholes model are S0 (the stock price), X (the exercise price), r c (the continuously compounded risk-free rate), ó (the standard deviation of the continuously compounded return on the stock) and T (the time to expiration). The variables S0 and X are the same in both models. In the binomial model, r is the discrete interest rate per period. In the Black-Scholes model, the interest rate must be expressed in continuously compounded form. The annual discrete interest rate (r) is related to the annual continuously compounded rate (r c) by the formula, r c = ln(1 + r). Then the binomial rate per period is found as (1 + r)T/n - 1. The up and down factors in the binomial model are directly related to ó in the Black-Scholes model by the formula u = T/n ó e – 1 and d = (1/(1+u)) – 1. The time to expiration (T) in the Black-Scholes model is related to the length of each binomial period by the relationship T/n where n is the number of periods. Thus, all of the Black-Scholes variables are either equal to or directly convertible to binomial variables.Chapter6Chapter7Chapter 8Chapter9Chapter 10。
《金融工程》(第三版)课后习题参考答案.doc
《金融工程》高等教育出版社郑振龙陈蓉主编(第三版)课后习题参考答案《金融工程》高等教育出版社(郑振龙、陈蓉主编/第三版)课后习题参考答案第1章金融工程概述7.该说法是正确的。
从图1.3中可以看出，如果将等式左边的标的资产多头移至等式右边，整个等式左边就是看涨期权空头，右边则是看跌期权空头和标的资产空头的组合。
9. lOOOOe 5% 4.u82元M2725.21 10.每年计一次复利的年利率=(1+0.14/4) 4-1=14.75% 连续复利年利率= 41n(l+0.14/4)=13.76%o 11,连续复利年利率=121n(l+0.15/12)=14.91%。
12. 12%连续复利利率等价的每季度支付一次利息的年利率=4 (0.03e-l) =12.18%。
因此每个季度可得的利息=10000xl2.8%/4=304.55元。
第2章远期与期货概述1.2007年4月16日，该公司向工行买入半年期美元远期，意味着其将以764.21人民币/100美元的价格在2007年10月18日向工行买入美元。
合约到期后，该公司在远期合约多头上的盈亏=10000 (71)52。
,637 64 .21)11 5,8 0 0 2,收盘时，该投资者的盈亏= (1528.9 —1530.0)x250=-275美元；保证金账户余额=19,688-275 = 19,413美元。
若结算后保证金账户的金额低于所需的维持保证金，即19,688 (S &P时5(即S&0P5000指数指期货结算价数＜1514.3期时)，货结算价1 530 )250 lv5,750交易商会收到追缴保证金通知，而必须将保证金账户余额补足至19,688美元。
3.他的说法是不对的。
首先应该明确，期货(或远期)合约并不能保证其投资者未来一定盈利，但投资者通过期货(或远期)合约获得了确定的未来买卖价格，消除了因价格波动带来的风险。
本例中，汇率的变动是影响公司跨国贸易成本的重要因素，是跨国贸易所面临的主要风险之一，汇率的频繁变动显然不利于公司的长期稳定运营(即使汇率上升与下降的概率相等)；而通过买卖外汇远期(期货)，跨国公司就可以消除因汇率波动而带来的风险，锁定了成本，从而稳定了公司的经营。
最新金融工程答案翻译
第一章1.4 仔细解释卖出一个看涨期权与买入一个看跌期权的差别卖出一个看涨期权涉及到给他人一个买入你某项财产的权利，它将给你带来的收益为-max （st-k，0）=min（k-st，0）买入一个看跌期权涉及到从他人手里买入一个期权，带来的收益为max（k-st，0）他们都有一个可能性的收入k-st，当你卖出看涨期权，收入为负值或0，这是因为交易对手可以选择是否执行。
当你买入一个看跌期权，你的收入为0或正直，这是因为你选择执行与否1.5 你认为某股票价格将要上升，股票当前价格为29美元，三个月期限，执行价格为30美元的看涨期权价格为2.9美元，你共有美金5800元，说明两种投资模式，并简单说明一下两种模式的优缺点有两种方案，即买入200股股票或买入2000份看涨期权，当股票价格上涨航行好，第二种方案将得到更高的回报。
举例来说，当股价上涨为40元，此时收益为2000（40-30）-5800=14200 而第一种反感只有200（40-29）=2200元收益，但当股价下跌，第二种方案将有更大的损失。
当股票价格下跌至25元，第一种方案损失为200（29-25）=800元，第二种方案则带来5800元的损失，这个例子证明了期权有一定的杠杆效率1.26当前黄金市价为每盎司600美元，一个一年期远期合约的执行价格为800美元，一个套利者能以每年10%的利率借入资金，套利者应如何做才能达到套利目的？这里我们假设黄金存储费用为0.同时黄金不会带来任何利息收入这个套利者可以借入资金买入100盎司黄金现货和卖出一个100盎司于一年后交割的期货合约，这就意味着黄金以600美元每盎司买入以800美元每盎司卖出，收益率约为33.3%，远高于10%的接入率，这是一个很好的盈利机会，套利者应尽可能多的买入黄金现货及预期数量相匹配的期货合约1.27 股票当前价格为94美金，同时，三个月期，执行价格为95美元的欧式期权价格为4.7美元，一个投资者认为股价会上涨，但他并不知道应该买入100股股票或买入2000个（20份）期权，这两种投资所需资金均为9400美元，此时你会给出什么建议？股价涨到什么样的水平会使得期权投资盈利更好？投资于看涨期权会带来高收益但是会有高风险，如果股价停止在94美元，买入看涨期权的投资者损失9400美元，儿买入股票的投资者什么也没有损失，如果股价上涨到120美元，买入期权的投资者会得到2000（120-95）-9400=40600美元的收益，而买入股票的投资者会得到100（120-94）-9400=2600元，当股价为s时，这两种投资的收益相等，100（s-94）=2000（s-95），s-100。
国际金融中英文版答案解析)
国际金融中英文版Chapter 2:Payments among NationsSingle-Choice Questions1.A country’s balance of payments records:一个国家的国际收支平衡记录了 Ba.The value of all exports of goods and services from thatcountry for a period of time.b.All flows of value between that c ountry’s residentsand residents of the rest of the world during a periodof time. 在一定时间段里, 一个国家居民的资产和其它世界居民资产的流动c.All flows of financial assets that cross thatcountry’s borders during a period of time.d.All flows of goods into that country during a periodof time.2.A credit item in the balance of payments is: 在国际收支平衡里的贷项是 Aa.An item for which the country must be paid. 一个国家必须收取的条款b.An item for which the country must pay.c.Any imported item.d.An item that creates a monetary claim owed to aforeigner.3.Every international exchange of value is entered into thebalance-of-payments accounts __________ time(s). 每一次国际等价交换都记进国际收支帐户２次 Ba.1b.2c.3d.44.A debit item in the balance of payments is: 在国际收支平衡中的借项是 Ba.An item for which the country must be paid.b.An item for which the country must pay. 一个国家必须支付的条款c.Any exported item.d.An item that creates a monetary claim on a foreigner.5.In a nation's balance of payments, which one of the followingitems is always recorded as a positive entry? D 在国际收支中, 下列哪个项目总被视为有利条项a.Changes in foreign currency reserves.b.Imports of goods and services.itary foreign aid supplied to allied nations.d.Purchases by foreign travelers visiting the country.国外游客在本国发生的购买6.The sum of all of the debit items in the balance of payments:在收支平衡中,所有贷项的总和 Ba.Equals the overall balance.b.Equals the sum of all credit items.等于所有借项的总和c.Equals ‘compensating’ transactions.d.Equals the sum of credit items minus errors andomissions.7.Which of the following capital transactions are entered asdebits in the U.S. balance of payments? 下列哪个资本交易在美国的收支平衡中当作借项？Ba.A U.S. resident transfers $100 from his account atCredit Suisse in Basel (Switzerland) to his account ata San Francisco branch of Wells Fargo Bank.b.A French resident transfers $100 from his account atWells Fargo Bank in San Francisco to his Credit Suisseaccount in Basel. 一个法国居民在旧金山的Fargo Bank用其帐户转帐１００美金到位于巴塞尔的瑞士信贷户口c.A U.S. resident sells his IBM stock to a Frenchresident.d.A U.S. resident sells his Credit Suisse stock to aFrench resident.8.An increase in a nation's financial liabilities to foreignresidents is a: 一个国家对另一个国家金融负债的增加是一种Ca.Reserve inflow.b.Reserve outflow.c.Capital inflow.资本流入d.Capital outflow.9.___A_______ are money-like assets that are held bygovernments and that are recognized by governments as fully acceptable for payments between them. 官方国际储备资产是一种类似于钱的资产，这种资产由政府掌握并作为政府间的一种支付手段得到充分认可.a.Official international reserve assets 官方国际储备资产b.Unofficial international reserve assetsc.Official domestic reserve assetsd.Unofficial domestic reserve assets10.Which of the following is considered a capital inflow?下列哪项被视为资本流入 Aa.A sale of U.S. financial assets to a foreign buyer.美国一金融资产卖给一外国买家b.A loan from a U.S. bank to a foreign borrower.c.A purchase of foreign financial assets by a U.S. buyer.d.A U.S. citizen’s repayment of a loan from a foreignbank.11.In a country’s balance of payments, which of thefollowing transactions are debits?一个国家的收支平衡表中,哪个交易属于借项？ Aa.Domestic bank balances owned by foreigners aredecreased. 外国人拥有的国内银行资产的下降b.Foreign bank balances owned by domestic residents aredecreased.c.Assets owned by domestic residents are sold tononresidents.d.Securities are sold by domestic residents tononresidents.12.The role of ___D_______ is to direct one nation’ssavings into another nation’s investments: 资金流的作用是指导一个国家的储蓄进入到另一个国家的投资a.Merchandise trade flowsb.Services flowsc.Current account flowsd.Capital flows 资金流13.The net value of flows of goods, services, income, andunilateral transfers is called the: 商品,服务,收入和单方面转让等现金流的净收益叫经常账目（户）Ba.Capital account.b.Current account.经常账目（户）c.Trade balance.d.Official reserve balance.14.The net value of flows of financial assets and similarclaims (excluding official international reserve asset flows) is called the: 金融资产和类似的资产（官方国际储备资产流除外）的净值流叫 Aa.Financial account.金融帐b.Current account.c.Trade balance.d.Official reserve balance.15.The financial account in the U.S. balance of paymentsincludes: 美国国家收支表中的金融帐包括： Ba.Everything in the current account.b.U.S. government payments to other countries for the useof military bases.美政府采用其它国家军事基地所需支付款项c.Profits that Nissan of America sends back to Japan.d.New U.S. investments in foreign countries.16.Ａ U.S. resident increasing her holdings of a foreignfinancial asset causes a: 一个美国居民增持一外国金融资产会引起Da.Credit in the U.S. current account.b.Debit in the U.S. current account.c.Credit in the U.S. capital account.d.Debit in the U.S. capital account. 美国资本帐的借帐17. A foreign resident increasing her holdings of a U.S.financial asset causes a: 一个美国居民增持本国一金融资产会引起 Ca.Credit in the U.S. current account.b.Debit in the U.S. current account.c.Credit in the U.S. capital account.美国资本帐的贷帐d.Debit in the U.S. capital account.18. A deficit in the current account: 经常帐户中的赤字 Aa.Tends to cause a surplus in the financial account.会导致金融帐中的盈余b.Tends to cause a deficit in the financial account.c.Has no relationship to the financial account.d.Is the result of increasing exports and decreasingimports.19.In September, 2005, exports of goods from the U.S.decreased $3.3 billion to $73.4 billion, and imports of goods increased $3.8 billion to $144.5 billion. Thisincreased the deficit in:2005年8月,美国商品出口降低了33亿美元,共734亿美元；商品进口上升到1145亿美元,上长了38亿.这样增加了哪个方面的赤字？Ca.The balance of payments.b.The financial account.c.The current account. 经常帐户d.Unilateral transfers.20.Which of the following would contribute to a U.S. currentaccount surplus? 以下哪项有助于美国现金帐的盈余？ Ba.The United States makes a unilateral tariff reductionon imported goods.b.The United States cuts back on American militarypersonnel stationed in Japan.美国削减在日本的军事人员c.U.S. tourists travel in large numbers to Asia.d.Russian vodka becomes increasingly popular in theUnited States.21.Which of the following transactions is recorded in thefinancial account?以下哪个交易会被当作金融帐Aa.Ford motor company builds a new plant in China 福特摩托公司在中国设立车间b.A Chinese businessman imports Ford automobiles from theUnited States.c.A U.S. tourist spends money on a trip to China.d.The New York Yankees are paid $10 million by the Chineseto play an exhibition game in Beijing, China.22.If a British business buys U.S. government securities,how will this be entered in the balance of payments? 如果一英国商人购买了美国政府的债券,那么这个交易在收支平衡表中会被当作是？ Ca.It will appear in the trade account as an import.b.It will appear in the trade account as an export.c.It will appear in the financial account as an increasein U.S. assets held by foreigners.会被当作是外国人所有的美国资产增长d.It will appear in the financial account as a decreasein U.S. assets held by foreigners.23.In the balance of payments, the statistical discrepancyor error term is used to: 在收支平衡表中, 统计差异与错误项目会用来确保借帐总和跟贷帐总和一致 Aa.Ensure that the sum of all debits matches the sum ofall credits.b.Ensure that imports equal the value of exports.c.Obtain an accurate account of a balance-of-paymentsdeficit.d.Obtain an accurate account of a balance-of-paymentssurplus.24.Official reserve assets are: 官方储备资产是Ba.The gold holdings in the nation’s central bank.b.Money like assets that are held by governments and thatare recognized by governments as fully acceptable forpayments between them. 官方国际储备资产是一种类似于钱的资产，这种资产由政府掌握并作为政府间的一种支付手段得到充分认可ernment T-bills and T-bonds.ernment holdings of SDR’s25.Which of the following constitutes the largest componentof the world’s international reserve assets?下列哪项构成了世界国际储备资产的大部份？ Da.Gold.b.Special Drawing Rights.c.IMF Reserve Positions.d.Foreign Currencies. 外汇（币）26.The net accumulation of foreign assets minus foreignliabilities is: 海外净资产的积累减去外债等于C official reserves. domestic investment. foreign investment. 国外投资净值 foreign deficit.27. A country experiencing a current account surplus: 一个国家经历经常帐户的盈余 Ba.Needs to borrow internationally.b.Is able to lend internationally.就有能力向外放贷c.Must also have had a surplus in its "overall" balance.d.Spent more than it earned on its merchandise and servicetrade, international income payments and receipts andinternational transfers.28.The ___C_______ measures the sum of the current accountbalance plus the private capital account balance. 官方结算差额是指经常帐户余额的总和加上私人资本帐（B=CA+FA,FA:为非官方投资和储备）a.Official capital balanceb.Unofficial capital balancec.Official settlements balance官方结算差额d.Unofficial settlements balance29.If the overall balance is in __A________, there is anaccumulation of official reserve assets by the country ora decrease in foreign official reserve holdings of thecountry's assets. 如果综合差额处于盈余，那么会出现本国官方储备资产的积累或者国外官方储备的减少（B=CA+FA,B+OR=0，OR:官方储备金额）a.Surplus盈余b.Deficitc.Balanced.Foreign hands30.Which of the following is the current account balance NOTequal to? 以下哪项不等同于现金帐 Da.The difference between domestic product and domesticexpenditure.b.The difference between national saving and domesticinvestment. foreign investment.d.The difference between government saving andgovernment investment. 政府储蓄与政府投资的差值True/False Questions31.Capital inflows are debits and capital outflows arecredits. 资金流入是借项，资金外流是贷项32.The net value of the flow of goods, services, income, andgifts is the current account balance. (T) 商品,服务,收入和单方面转让等现金流的净收益叫经常账目余额33.The net flow of financial assets and similar claims isthe private current account balance. 金融资产和类似的资产的净值叫经常帐目余额34.The majority of countries' official reserves assets arenow foreign exchange assets, financial assets denominated in a foreign currency that is readily acceptable ininternational transactions. (T) 大部份官方储备资产作为以外汇资产和金融资产为命名的外币在世界上交易与流通.35. A country's financial account balance equals thecountry's net foreign investment.一个国家的金融帐差额相当于一个国家的净国外投资36. A country has a current account deficit if it is savingmore than it is investing domestically.一个国家如果在国内的储蓄比投资要大,那么会出现经常账目赤字37.The official settlements balance measures the sum of thecapital account balance plus the public current account balance. 官方结算差额是资金帐户余额的总额加上公共经常帐户余额38. A nation's international investment position shows itsstock of international assets and liabilities at a moment in time. (T) 一个国家的国际投资状况反映出它在特定时间里的国际资产股份以及债务情况.39. A nation is a borrower if its current account is indeficit during a time period. (T)在一段时间内,如果一个国家的经常帐出现赤字,那么它就是借方.40. A nation is a debtor if its net stock of foreign assetsis positive. 如果一个国家的国外资产净储备是正数,那么它是借方（债务方）41. A transaction leading to a foreign resident increasingher holdings of a U.S. financial asset will be recorded asa debit on the U.S. financial account. 如果一项交易引起一外国居民增持美国金融资产的股份,那么这项交易在美国金融帐中会被当作借项42. A credit item is an item for which a country must pay.贷项是指一个国家必须还款的条项43.Gold is a major reserve asset that is currently often usedin official reserve transactions. 黄金作为主要的储备资产,常被用在官方储备交易当中.44.The current account balance is equal to the differencebetween domestic product and national expenditure.(T) 经常项目余额等于国民生产与国民支出的差额45.In 2007 U.S. households, businesses and government werebuying more goods and services than they were producing.(T)２００７年,美国家庭,商业,政府购买的商品和服务比他们生产（商品和服务）的要多.46。
金融工程课后题8习题解答zhoujia(Lite)
金融工程课后题8习题解答z h o u j i a(L i t e)-标准化文件发布号：（9456-EUATWK-MWUB-WUNN-INNUL-DDQTY-KIICH8什么是有保护的看跌期权看涨期权的什么头寸等价于有保护的看跌期权解：有保护的看跌期权由看跌期权多头与标的资产多头组成，由期权平价公式可知，其等价于看涨期权多头与一笔固定收入的组合。
解释构造熊市价差期权的两种方法。
解：1）熊市价差期权可由2份相同期限、不同执行价格的看涨期权构成；投资者可通过卖空执行价格低的同时买入执行价格高的看涨期权构造。
2）熊市价差期权也可由2份相同期限、不同执行价格的看跌期权构成；投资者可通过卖空执行价格低的同时买入执行价格高的看跌期权构造。
对于投资者来说，什么时候购买蝶形期权是合适的解：蝶形期权涵盖了3份执行价格不同的期权，当投资者认为标的资产价格很可能位于中间执行价格附件时，则会购买蝶形期权。
有效期为一个月的股票看涨期权分别有$15、$和$20的执行价格，其期权价格分别为$4、$2和$。
解释如何应用这些期权来构造出蝶式价差期权。
做个表格说明蝶式价差期权损益如何随股票变化而变化的。
解：投资者可通过购买执行价格为$15和$20的看涨期权，同时卖空2份执行价格为$的看涨期权构造蝶式价差期权。
初始投资为4＋－2×2＝$。
T时刻损益随股价变化如下：股价T S T时蝶式价差期权损益S<15 －T15<T S< T S－<T S<20 －T SS>20 －T什么样的交易策略可构造出倒置日历价差期权解：倒置日历价差期权可通过买入1份较短期限的期权，同时卖出1份执行价格相同但期限较长的期权构造。
宽跨式期权与跨式期权之间有何不同解：宽跨式与跨式期权均是由1份看涨与1份看跌期权构成。
在跨式期权中，看涨期权与看跌期权具有相同的执行价格和到期日；而宽跨式期权中，看涨期权与看跌期权到期日相同，但执行价格不同。
金融工程课后(附答案)
金融工程老师划题目的部分答案1.1请解释远期多头与远期空头的区别。
答：远期多头指交易者协定将来以某一确定价格购入某种资产；远期空头指交易者协定将来以某一确定价格售出某种资产。
1.2请详细解释套期保值、投机与套利的区别。
答：套期保值指交易者采取一定的措施补偿资产的风险暴露；投机不对风险暴露进行补偿，是一种“赌博行为”；套利是采取两种或更多方式锁定利润。
1.8你认为某种股票的价格将要上升。
现在该股票价格为$29,3个月期的执行价格为$30的看跌期权的价格为$2.90.你有$5,800资金可以投资。
现有两种策略：直接购买股票或投资于期权，请问各自潜在的收益或损失为多少？答：股票价格低于$29时，购买股票和期权都将损失，前者损失为($5,800/$29)×(29-p),后者损失为$5，800;当股票价格为（29，30），购买股票收益为($5,800/$29)×(p-29),购买期权损失为$5,800;当股票价格高于$30时，购买股票收益为($5,800/$29)×(p-29)，购买期权收益为$($5,800/$29)×(p-30)-5,800。
2.1请说明未平仓合约数与交易量的区别。
答：未平仓合约数既可以指某一特定时间里多头合约总数，也可以指空头合约总数，而交易量是指在某一特定时间里交易的总和约数。
3.1一家银行给你的报价如下:年利率14％，按季度计复利。
问：(a)等价的连续复利利率为多少？(b)按年计复利的利率为多少？解：(a)等价的连续复利为4ln(1+0.14/4) ＝0.1376 或每年13.76％。
（b）按年计复利的利率为(1+0.14/4)^4＝0.1475 或每年14.75%。
3.4一种股票指数现为350。
无风险年利率为8％（连续复利计息）。
指数的红利收益为每年4％。
一份四个月期限的期货合约价格为多少？解：期货合约价格为350e^( 0.08-0.04 )＝$354.73.8一人现在投资$1,000，一年后收回$1,100，当按以下方式计息时，年收益为多少？(a)按年计复利(b)以半年计复利(c)以月计复利(d)连续复利解：（a）按年计复利时收益为1100/1000－1＝0.1 或每年10%的收益率。
金融学第十五章课后答案翻译
第十五章课后答案翻译1.a.如果你持有多头：价值为s的股票为基础资产发行的，执行价格为E的欧式卖出期权的收益曲线为：卖出期权的收益曲线为：2．持有一份欧式卖出期权和一份欧式买入期权的投资组合的收益图（E＝100）：3．a ．为了保证你至少能够收回你初始的一百万美元，你需要投资在till 股票上。
你可以购买的期权。
104股指的报酬线斜率是4807.69，正如图表所显示的。
B ．4．a.要复制一个面值为100美元的纯贴现债券，应买一份股票：其欧式买入期权价格和欧式卖出期权价格均为100。
b. S = $100, P = $10, and C = $15.E/(1+r) = S + P- C$100/(1+r) = $100 + $10 - $15 = $95 r = 100/95 -1 =0 .053 or 5.3%c.如果1年期无风险利率小于b 的答案，则说明纯贴现债券的价格过高，人们便会通过便宜购买综合性产品（一份其欧式买入期权价格和欧式卖出期权价格均为100的股票）来替换价格较高的纯贴现债券以从中套利。
5．用P = -S + E/(1+r)T + C 这个表达式来表示卖出期权S 是股价，P 是卖出的执行价，C 是买入期权的价格，E 是执行价格，既然政府债券是以9855日元每10000日元的价格出售，这就是计算执行价格现值的贴现率，而无须用风险利率进行折现。
用平价的替代等式来计算，我们可以得到：P = -2,400 + 500 x .9855 +2,000 = 92.75 yen6．a.根据卖出－买入平价，Gekko 投资组合中买入期权的价格： C = S - E/(1+r)T + P = $215 - $50 ×0 .9901 + $25 = $190.495b. Gekko 的投资组合的总价值：10 x $990.10 + 200 x $190.495 = $48,000，而300股股票的总价值：$64,500。
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第一章1.4 仔细解释卖出一个看涨期权与买入一个看跌期权的差别卖出一个看涨期权涉及到给他人一个买入你某项财产的权利，它将给你带来的收益为-max （st-k，0）=min（k-st，0）买入一个看跌期权涉及到从他人手里买入一个期权，带来的收益为max（k-st，0）他们都有一个可能性的收入k-st，当你卖出看涨期权，收入为负值或0，这是因为交易对手可以选择是否执行。
当你买入一个看跌期权，你的收入为0或正直，这是因为你选择执行与否1.5 你认为某股票价格将要上升，股票当前价格为29美元，三个月期限，执行价格为30美元的看涨期权价格为2.9美元，你共有美金5800元，说明两种投资模式，并简单说明一下两种模式的优缺点有两种方案，即买入200股股票或买入2000份看涨期权，当股票价格上涨航行好，第二种方案将得到更高的回报。
举例来说，当股价上涨为40元，此时收益为2000（40-30）-5800=14200 而第一种反感只有200（40-29）=2200元收益，但当股价下跌，第二种方案将有更大的损失。
当股票价格下跌至25元，第一种方案损失为200（29-25）=800元，第二种方案则带来5800元的损失，这个例子证明了期权有一定的杠杆效率1.26当前黄金市价为每盎司600美元，一个一年期远期合约的执行价格为800美元，一个套利者能以每年10%的利率借入资金，套利者应如何做才能达到套利目的？这里我们假设黄金存储费用为0.同时黄金不会带来任何利息收入这个套利者可以借入资金买入100盎司黄金现货和卖出一个100盎司于一年后交割的期货合约，这就意味着黄金以600美元每盎司买入以800美元每盎司卖出，收益率约为33.3%，远高于10%的接入率，这是一个很好的盈利机会，套利者应尽可能多的买入黄金现货及预期数量相匹配的期货合约1.27 股票当前价格为94美金，同时，三个月期，执行价格为95美元的欧式期权价格为4.7美元，一个投资者认为股价会上涨，但他并不知道应该买入100股股票或买入2000个（20份）期权，这两种投资所需资金均为9400美元，此时你会给出什么建议？股价涨到什么样的水平会使得期权投资盈利更好？投资于看涨期权会带来高收益但是会有高风险，如果股价停止在94美元，买入看涨期权的投资者损失9400美元，儿买入股票的投资者什么也没有损失，如果股价上涨到120美元，买入期权的投资者会得到2000（120-95）-9400=40600美元的收益，而买入股票的投资者会得到100（120-94）-9400=2600元，当股价为s时，这两种投资的收益相等，100（s-94）=2000（s-95），s-100。
所以当股价高于一百时，期权盈利更好2.9 设计一个新的期货合约时需要考虑那些方面？合约规模，交割安排，交割月份2.19在期货市场，投机就是纯粹的赌博，为了公众利益，不应该让投机者在交易场所交易齐国，评价这种说法投机者是期货市场重要的参与者，因为他们增加了期货市场的流动性，和投机一样合约对于对冲来说必须是有用的。
因为总的来说，和投机这类似，当合约对风险对冲者有利益时才会得到监管部门的通过2.25 现在是2008年7月，一个矿物公司刚刚发现了一个小型金矿，决定用六个月时间建矿，黄金将在今后的一年内连续被开发出，nyce有关于黄金期货的合约，从2008.8-2009.12月，每两个月有一个期货交割月，每一个合约规模为100盎司黄金，讨论矿业公司将采用何种期货产品来对冲风险。
矿业公司应该连续按月估计出黄金的产量，今儿通过卖出与黄金产量想等的期货合约来锁定近期黄金价格，比如2009年1、2月共产出黄金三千盎司，卖出30长期货合约可以锁定其价格2.26 一家公司进入一个期货短头寸，合约中，公司以每蒲式耳250美分卖出5000蒲式耳小麦，初始保证金为3000美金，维持保证金为2000美金，价格如何变化会导致保证金的催收？什么情况下，公司可以从保证金账户中提取1500美金？在期货市场损失1000美金，即小麦期货没蒲式耳上涨二十美分时，会导致保证金的催收，当小麦期货价格每蒲式耳下降30美分时，可以从保证金账户中提取1500美金。
3.7：一家公司持有价值为2000万美元，β值为1.2的股票组合，该公司想要采用S＆P500期货来对冲风险，股指期货的当前价格为1080，每一个期货是关于250美元倍的股指，什么样的对冲可以使风险极小化？公司怎么做才可以将组合的beta值降为0.6？N*=1.2*20000000/(250*1080)=88.89所以进入89份的期货短头寸。
N`=(1.2-0.6)*20000000/(250*1080)=44.4所以公司只需持有44份期货短头寸就可以将beta值降为0.6.3.17:一个玉米农场的农场主有以下观点，我们不能采用期货来对冲我面临的风险，我的真正风险并不是玉米价格的变化，而是气候原因使我颗粒无收。
讨论这一观点，这个农民是否应该对玉米的预期产量有所估计然后采用对冲策略来锁定预期价格。
由于气候原因使得玉米颗粒无收，但是气候的影响对于所有的玉米农场主来说都是一样的。
因此玉米的总产量下降，导致玉米价格会有个相当大的提高。
相对于实际的玉米产量，这个农民很有可能会过度对冲了。
这样一来农民在期货市场上的损失会增加自己整体的损失。
因此这个农场主的观点是正确的，也即是这个农民不应该对玉米预期产量有所估计然后采用对冲策略来锁定预期价格。
3.23下表关于某商品的即期以及期货每月价格变化的数据，利用这些数据来计算使方差最小化即期价格变化期货价格变化即期价格变化期货价格变化δF估计值为δS估计值为ρ估计值为最小方差为：3.25一个基金经理持有一价值为5000万美元，Beta等于0.87的股票组合。
该经理担心在今后两个月内市场的表现，因此打算采用3个月期的关于S&P500的期货合约来对冲其风险。
股指的当前水平为1250，期货合约是关于250倍的指数，无风险利率未每年6%，股息收益率为每年3%，当前3个月期的期货价格为1259.（a）基金经理应采用什么样的头寸来对冲今后两个月内的市场风险？（b）当股指在两个月后分别为1000、1100、1200、1300和1400时，你的策略对于基金经理的收益影响会如何？假定一个月期的期货价格比现在的股指水平高0.25%。
(a)...N*=0.87*50000000/(1259*250)=138.2 ...进入期货合约的短头寸，数量为138份。
（b)当股指为1000时：期货市场上投资效果=250×（1259-1000×1.0025）×138=8849250现货市场上的效果：由于股指在这两个月的亏损率=3%×2/12-{（1000-1250）/1250}-6%×2/12=0.5%-21%=-20.5%而基金经理所持有的股票组合的beta值为0.87，所以该股票组合的亏损率为20.5%×0.87=17.835%，减去其中的无风险利率1%,那么现货市场的实际亏损率为16.835%亏损价值=16.835%×5000×10000=8417500则总效果=884=431750美元其他情形雷同。
4.8从久期你能知道债券组合对于利率有什么样的敏感度？久期有什么局限性？久期提供的信息是一个小的收益率曲线的平行移动对债券投资组合价值的影响。
投资组合价值减少的百分比等于久期乘以相对应的平行移动的利率的变化。
久期的局限性是只能在利率的平行移动中适用。
4.21解释为什么一个FRA 等价于以浮动利率交换固定利率？一个FRA 是约定在将来某一段时间交易的一方将以某一个特定的利率RK 借入或者借出一个固定的资金L 的协议。
不管市场上的利率如何变化，订立FRA 协议者就有权在约定的时间以利率为RK 这一固定利率借入或者借出资金。
相当于以浮动利率交换固定利率。
4.25：6个月、12个月、18个月和24个月期限的零息利率分别为4%、4.5%、4.75%和5%，这里利率为每半年复利一次。
（a ）相应的连续复利利率为多少？（b ）在18个月开始的6个月期的远期利率为多少？（a ）R 6=2ln1.02=0.039605，R 12=2ln1.0225=0.044501，R 18=2ln1.02375=0.046945，R 24=2ln1.025=0.049385.（b ）远期利率=（4.9385*2-4.9645*1.5）/0.5=0.05670718个月开始的6个月期的远期利率=2（e 0.056707*0.5-1）=0.0575184.27下表给出了债券价格表中，每6个月支付所示利息的一半。
（a）计算对应于6个月、12个月、18个月和24个月期限的零息利率。
（b ）以下时间段的远期利率为多少？6~12个月；12~18个月；18~24个月。
（c ）对于每半年支付一次券息，期限分别为6个月、12个月、18个月和24个月的债券平价收益率为多少？（d ）估算年券息率未10%，每半年支付一次券息，2年期限债券的收益率。
（a ）零息利率：R 0.5=2ln(1+2/98)=4.0405%； R 1=ln(1+5/95)=5.1293%,；R 1.5满足3.1e -0.0405*0.5+3.1e -0.051293*1+103.1e -R*1.5=101,得出，R 1.5=5.4429%；R 2满足4-0.0405*0.5+4e -0.051293*1+4e -0.054429*1+104e -R*2=104,得出，R 1.5=5.8085%；（b ）远期利率：R 0.5=4.0405%，R 1=6.2181%，R 1.5=6.0700%，R 2=6.9054%；（c ）票面利率：R 0.5=4.0816%，R 1=5.1813%，R 1.5=5.4986%，R 2=5.8620%；（第二问和第三问的解题方式找不到，直接给出了答案。
）（d ）债券价格：债券收益率y 满足：y=0.057723，所以，收益率未5.7723%5.6 仔细解释便利收益与持有成本两个术语的含义。
期货价格、即期价格、便利收益与持有成本的关系式是什么？便利收益率反映了市场对未来商品可获得性的预期也可以说是因持有商品而带来的好处。
持有成本包括储存成本加上资产的融资利息，再减去资产的收益。
期货价格：F0. 即期价格:S0.便利收益：y持有成本：c关系式为T是期货合约到期时间5.15 白银的限价为每盎司9美元，每年储存费用为每盎司0.24美元，储存费要每季度预先支付一次。
假定所有期限的利率均为每年10%（连续复利），计算9个月后到期的期货价格。