金融工程Chapter2
金融工程2
案例续
长期资本管理公司以“不同市场证券间不合理价差生灭自 然性”为基础，制定了“通过电脑精密计算，发现不正常 市场价格差，资金杠杆放大，入市图利”的投资策略。 舒尔茨和默顿将金融市场历史交易资料，已有的市场理论、 学术研究报告和市场信息有机结合在一起，形成了一套较 完整的电脑数学自动投资模型。他们利用计算机处理大量 历史数据，通过连续而精密的计算得到两种不同金融工具 间的正常历史价格差，然后结合市场信息分析它们之间的 最新价格差。如果两者出现偏差，并且该偏差正在放大， 电脑立即建立起庞大的债券和衍生工具组合，大举套利入 市投资；经过市场一段时间调节，放大的偏差会自动恢复 到正常轨迹上，此时电脑指令平仓离场，获取偏差的差值。
金融工程
福建师范大学经济学院 张业圳
第一节 金融工程的作用
提供风险管理的工具与技术 投机和套利机会的发掘 公司重组安排与财务配置 避税策略和税务筹划
一、提供风险管理的工具与技术
风险管理在金融工程中居于核心地位。 风险即不确定性 1、用不确定性来代替风险； 2、替换掉与己不利的风险，保留有利风险。 3、分散风险 案例：最初出现于20世纪70年代初的美国住房 抵押贷款市场资产证券化方案的实施
案例：ESL 投资基金收购K-Mart
K-Mart经营不善债务累累﹐二十亿美金的债务 无法偿还﹐导致这个百 年老店被迫进入破产保 护。2003年5月5日是K-Mart可以走出破产法庭 最后期限﹐就在此生死存亡关头﹐当时名不见 经传的康州40岁投资人爱得华兰博(Edward Lampert) 的ESL 投资基金 公司成功地将二十 亿美金的债务折价买下(具体金额是保密的﹐ 业内灵通人士估计在二亿五至五亿之间)﹐然 后投资三亿五定向增发给ESL﹐使得他成为走 出破产后K-Mart公司的69%大股东。
第二章 金融工程基本原理《金融工程》PPT课件
相同，但它们的成本（价格）不同，这时市场存在套利机 会。 ➢ （2）如果存在两个相同成本（价格）的组合，第一个组合 在所有状态下的收益都不低于第二个组合，而且至少存在 一种状态，在此状态下第一个组合的收益大于第二个组合 ，这时市场存在套利机会。 ➢ （3）如果一个组合的构建成本为0，但在所有状态下这个 组合的收益都不小于0，而且至少存在一种状态，在此状态 下这个组合的收益大于0，则市场存在套利机会。
90
无风险资产：
1 1
1
144 108 81
1 1 1
B：
PB
128
PB1 110
PB2
101
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无套利定价原理的应用
复制策略的确定用倒推法：
（1）在t=0.5时刻：
当PA＝120时：144x y 128
x 0.5
108x y 110
y 56
PB1 120 0.5 56 116
当PA＝90时：
0 -1个B：-101
合计：
0
1/3A： 27
存款： 74
020
第二节 风险中性定价方法
一、风险中性的概念 ➢ 公平博彩 ➢ 如果一个参加者，他刚好可以接受这样一个统计意
义上的公平博彩，他就是风险中性的 ➢ 风险中性投资者投资于风险证券，不需要风险补偿
，只要收益率等于无风险利率就可以了 ➢ 如果市场上的投资者都是风险中性的，则任何一个
持有证券B空头 持有动态复制策略多头
-1个B：-128 0.5A： 72 存款： 56
卖出B： 110元 买入0.4A：-40元 存款68元：-68 合计： 2
金融工程Chapter2
2
金融远期合约（Forward Contracts）是指双方约定在未 来的某一确定时间，按确定的价格买卖一定数量的某种金 融资产的合约。在合约中，未来将买入标的物的一方称为 多方（Long Position），而在未来将卖出标的物的一方称 为空方（Short Position）。
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❖ 特定期货合约的合约规模、交割日期和交割地点等都 是标准化的，在合约上均有明确规定，无须双方再商 定，价格是期货合约的唯一变量。
❖ 一般来说，常见的标准期货合约条款包括： (1)交易单位。交易所对每个期货产品都规定了统 一的数量和数量单位，统称“交易单位”（Trade Unit）或“合约规模”（Contract Size）。不同交 易所、不同期货品种的交易单位规定各不相同。
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与远期合约的分类相似，根据标的资产不同， 常见的金融期货主要可分为股票指数期货、外汇期 货和利率期货等。 -股票指数期货是指以特定股票指数为标的资产的期 货合约，S&P500股指期货合约就是典型代表。 -外汇期货则以货币作为标的资产，如美元、德国马 克、法国法郎、英镑、日元、澳元和加元等。 -利率期货是指标的资产价格依赖于利率水平的期货 合约，如欧洲美元期货和长期国债期货等。
Copyright© Zheng Zhenlong & Chen Rong, 2008
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3．远期股票合约 远期股票合约（Equity Forwards）是指在将来某一特 定日期按特定价格交付一定数量单只股票或一揽子 股票的协议。远期股票合约在世界上出现时间不长， 总交易规模也不大。
Copyright© Zheng Zhenlong & Chen Rong, 2008
金融工程2(金融市场)共36页
缅甸玉石的启示：新信息
在缅甸开采玉石矿的市场上，摆放着各种未 经过任何雕琢的矿石。这些矿石中有可能包 含有大量的翡翠，也可能只有很少一点翡翠。 买卖双方其实都不知道这些矿石中究竟含有 玉多 以 现石便 玉少？请使 石翡得大之 有翠到家露可。新讨出能买信论更含主息：多有可你之有高以是后关成选否，成色择有对色的打必你的翡磨要有信 翠和去好息 ，擦打处， 那拭磨吗一 么玉一？旦 卖石块发 方， 就会相应提高价格，反之降价。从这个例子 中，我们可以得出两点重要的发现：(1) 信 息越多的地方，不确定性就越少，越容易形 成双方都接受的稳定价格。(2) 市场价格的 变动是由新出现的信息推动的，因为新信息 改变了人们对某资产未来价值的预期。
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第二章 金融市场 -Financial Market
我们需要了解金融市场的目的
金融市场提供什么样的信息？ 如何利用金融市场的信息作正确的决定？ 资本性资产定价如何在金融市场上定价？ 企业和金融市场之间存在什么关系？ 市场对于金融三要素的反应。
课堂讨论—《黑天鹅》作者名言选读
例2-1:第四个和尚买水喝 例2-3:经济大萧条时期为什么会有人销毁高炉? 例2-4:安然公司垄断现货市场为什么还会破产? 例2-5:国家储备局的失误
思考:是什么促成了金融市场价格波动?
有效金融市场假设
什么是有效金融市场呢？
一个简单的定义就是：在一个有效金融市场 上，以当时的市场价格简单地买入或者卖出 一项金融资产，并不能够使投资人实现任何 套利的利润（该定义引自Richard A. Brealey和
金融工程学：Chapter 2 Mechanics of Futures Markets
94.72 95.01 93.60 89.62
Dec 2015 86.99 87.33 86.94 86.99 86.94
Change Volume
−0.45 −0.42 −0.29 −0.09 −0.05
162,901 37,830 27,179 9,606 2,181
Options, Futures, and Other Derivatives, 9th Edition,
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
13
Collateralization in OTC Markets continued
If A defaults, B is entitled to take possession of the collateral
10
Key Points About Futures
They are settled daily Closing out a futures position involves entering into an offsetting trade Most contracts are closed out before maturity
Options, Futures, and Other Derivatives, 9th Edition,
金融工程-chapter2共46页
2.1.2 主要金融远期合约种类
• 根据标的资产不同，常见的金融远期合约 包括 1.远期利率协议 2.远期外汇协议 3.远期股票合约
2.1.2 主要金融远期合约种类
• 1．远期利率协议
远期利率协议是买卖双方同意从未来某一商定 的时期开始在某一特定时期内按协议利率借贷一 笔数额确定、以具体货币表示的名义本金的协议。 之所以称为“名义”，是因为借贷双方不必交换 本金，只是在结算日根据协议利率和参考利率之 间的差额以及名义本金额，由交易一方付给另一 方结算金。
• 远期合约并不能保证其投资者未来一定盈 利，但投资者可以通过远期合约获得确定 的未来买卖价格，从而消除了价格风险。
2.1.1 金远期合约的定义
盈亏
盈亏
K 标的资产价 格
K 标的资产价 格
(a) 远期多头的 到期盈亏
(b) 远期空头的 到期盈亏
如果到期标的资产的市场价格高于交割价格K，远期多头就 盈利而空头就会亏损;反之，远期多头就亏损而空头就会盈 利。
远期利率是指现在时刻的将来一定期限的利率。 如14远期利率，即表示1个月之后开始的期限3 个月的远期利率。
2.1.2 主要金融远期合约种类
• 2．远期外汇合约
远期外汇合约是指双方约定在将来某一时间按 约定的远期汇率买卖一定金额的某种外汇的合约。
按照远期的开始时期划分，远期外汇合约又分 为直接远期外汇合约和远期外汇综合协议。
第二章 远期与期货概述
2.1.1 金融远期合约的定义
• 金融远期合约（Forward Contracts）是指 双方约定在未来的某一确定时间，按确定 的价格买卖一定数量的某种金融资产的合 约。在合约中,未来将买入标的物的一方称 为多方（Long Position），而在未来将卖 出标的物的一方称为空方（Short Position）。
第二章 金融工程基本理论 《金融工程》ppt课件
二、有效市场假说的定义
法玛基于价格与信息的关系，对资本市场有效 性给出了一个颇有影响的描述性定义：如果证券价 格充分反映了可得信息，每种证券的价格都永远等 于其投资价值，则该证券市场是有效的。
金融工程
金融工程基本 理论
投资组合 资本资产
理论
定价模型
套利定价 理论
有效市场 无套利均衡
理论
分析方法
一、投资组合理论的起源
1952年，美国经济学家哈里·马柯维茨发表的 《投资组合选择》（Portfolio Selection）的论文标 志着现代投资组合理论的开端。
投资者在寻求预期收益最大化的同时，也在寻求收 益不确定性的最小化。在此基础上，马柯维茨建立了著 名的“均值—方差模型”来分析投资者的资产选择行为。 这一模型后来成为现代投资组合理论的核心与基石。
APT模型是CAPM模型的一个推广。但与 CAPM模型不同的是，该模型表明资产的期望收益 率受一组公共风险因子影响，市场组合可能只是其 中的一个风险因子，其他风险因子（诸如利率、通 货膨胀率、GDP增长率等）也可能包括在内。简单 地说，市场组合在套利定价理论中并没有特殊作用， 它只是可能影响资产收益的因素之一。
二、多因素套利定价模型
设市场上风险资产的收益一共受到k个风险因 素的影响，可表示如下：
k
ri Eri ij Fj ei j 1
其中，ri是任意一种风险资产的收益，E(ri)是该风险 资产的预期收益，Fj（j=1，2，…，k）是影响风险资产收 益的公共风险因子，βij （j=1，2，…，k）是第i个风险资 产的收益与第j个影响因素之间的协方差，表示风险资产对 不同公共风险因子的敏感度，ei是残差项。
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 arb itrageurs’ 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 $45.50 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 Standard & 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 financialintermediaries.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 received a dividend of $0.50 per share. Immediately after that he sold the shares at $28 per share. He paid commissions of $10 on the purchaseand $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, isa(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 arenumber of shares in hundredsA new buy limit order is placed for 300 shares at ¥123.40. This limit order is said 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 selllimit 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. Yourtechnical 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 the support 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 market more 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 bya 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 ,which of 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 optimalportfolios 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。
(金融工程)Chapter 2 The structure of options market
Advantages of the OTC options market
• Terms and conditions can be tailored to the specific needs of two parties
• It is a private market, no others can know the transaction
Exercise price
• The exchange prescribes the exercise prices.
• FLEX option can have any exercise price • The exchange elected not to adjust the
exercise price when a cash dividend was paid.
The difference between offsetting in the OTC market and offsetting in the exchange market is that in the latter the contracts cancel any obligation of the writer. In the former, both contracts remain on the books, so they are both subject to default risk.
The order book official
• Obo is also called board broker, an employee of the exchange.
The mechanics of trading
• Placing an opening order • The role of the clearinghouse • Placing an offsetting order • Exercising an option
优选金融工程学远期利率和演示ppt
上升。希望用FRA进行保值。于是，该公
司向银行买了一份3×9FRA，ic=6.25%
。3个月后，市场利率ir=7%。则该公司 在结算日是收到还是支付多少结算金？其
综合借款成本是多少？
第29页，共44页。
第30页，共44页。
该公司综合借款成本i：
3623.19×(1+7%×1/2)=3750
第18页，共44页。
图中涉及的各个日期的含义分别如下：
交易日（dealing day）（签约日）——FRA
交易合约达成或签定日；
起算日（spot day）（起息日 value day）---
----递延期限开始日；
确定日（fixing day）（基准日）--------- 确 定FRA的市场参考利率日；
（6.65%）
第10页，共44页。
根据以上两例，可以得出以下普通公式：
P（1+rl×tl）=P(1+rs×ts) ×(1+rf×tf)
式中：P——本金 is——短期利率
il——长期利率
if——远期利率
ts——短期期限（以年表示）
tl——长期期限（以年表示）
tf——远期期限（以年表示）
结算日（settlement day）（交割日）—— FRA合约开始执行日；FRA结算金支付日。
第19页，共44页。
到期日（maturity day）-------FRA合约 终结日；
合约期（contract period）--------从 FRA结算日至到期日的时间；
递延期（deferred period）--------从 FRA起算日至结算日的时间；
第23页，共44页。
金融工程第2章
17
问题
一项新完成的交易对未平仓数量有什么样 的影响？ 一天的交易数量能否比未平仓数量更大？
期权、期货及其他衍生产品（第八版） Copyright © John C. Hull 2012
18
交易指令类型
期权、期货及其他衍生产品（第八版） Copyright © John C. Hull 2012 14
结算中心和场外市场
场外市场交易的传统结算方法是双边结算。 自2007~2009年金融危机以后，世界各国纷纷要 求标准化的场外衍生品交易通过中心结算机制来 进行结算。
期权、期货及其他衍生产品（第八版） Copyright © John C. Hull 2012
7
期货交易例子 (P20-21)
某投资者于6月5日持有两份12月份到期的 黄金期货多头合约
合约规模为100盎司黄金 期货价格为1250美元 初始保证金为每份合约6000美元（总计 12000美元） 维持保证金为每份合约4500美元（总计 9000美元）
期权、期货及其他衍生产品（第八版） Copyright © John C. Hull 2012
期权、期货及其他衍生产品（第八版） Copyright © John C. Hull 2012
20
表2-3 远期合约与期货合约的比较
远期合约 交易双方间的私下合约 非标准化 通常只有单一交割日 在合约到期时结算 通常会发生实物或现金交割
有信用风险
期货合约 交易所内的标准合约 标准化 有一系列的交割日 每日结算 合约通常在到期前会被平仓
变化量
2.76 2.44 2.19 2.00 1.86
金融工程学第二章
对未来金融工程技术的展望
大数据与人工智能的融合应用
随着大数据和人工智能技术的不断发展，未来金融工程技术将更加注重数据驱动和智能化决策，提高金融服务的精准 度和个性化水平。
区块链技术的广泛应用
区块链技术具有去中心化、安全性高、可追溯等特点，将在金融工程领域发挥重要作用，如智能合约、数字货币等创 新应用。
05
案例分析与实践应用
案例分析：金融工程技术在风险管理中的应用
信用风险管理
通过金融工程技术，如信用评分 模型、信用违约互换等，对信用 风险进行量化评估和管理，降低
信贷风险。
市场风险管理
运用金融工程技术，如风险价值模 型、压力测试等，对市场风险进行 度量和监控，帮助投资者在波动市 场中保持理性决策。
金融工程学的背景
随着金融市场的发展和金融创新的不断涌现，传统金融学已无法 满足日益复杂的金融需求。金融工程学的出现填补了这一空白， 为金融市场的发展注入了新的活力。
第二章内容概述
01
02
03
04
金融工程工具
介绍金融工程中常用的工具和 技术，如期权、期货、掉期等 衍生产品，以及数值计算、蒙 特卡洛模拟等计算方法。
第二章内容总结
金融工程学的基本概念和原理
介绍了金融工程学的定义、发展历程、基本原理和核心思想，以及金融工程技术在金融市 场中的应用。
金融产品的设计与定价
详细阐述了金融产品的设计流程、定价方法和风险管理策略，包括股票、债券、期货、期 权等多种金融产品。
金融工程技术的实践应用
通过案例分析，探讨了金融工程技术在企业融资、投资决策、风险管理等方面的实践应用 ，以及面临的挑战和解决方案。
金融工具的种类与特点
金融工具的定义
金融工程应用教程-答案
金融工程习题解答第二章 远期合约1、如何区分远期价值和远期价格的不同含义。
答：远期合约的价值是合同的价值，用f 表示；远期价格F 是标的资产的理论价格，是远期合约价值f 为0时的交割价。
2、FRA 协议中的几个日期之间有何关系？答：FRA 协议中的几个日期之间的关系如下图所示：其中的确定日、结算日、到期日，遇到节假日及法定休息日向前延伸或向后顺延。
3、请解释远期合约用来套期保值和来投机的方法。
答：套期保值，是签订远期合约，将未来交易的利率或汇率固定下来，避免利率或汇率波动对于负债或收益带来的风险。
投机，是建立在某种预期的基础上，以承担风险为代价获取收益的远期交易。
当投资者预期标的资产将上涨时做多头，反之做空头。
4、解释为什么外币可以被视为支付已知红利率的资产？答：由于外币的隶属国对于存入银行的外币按一定的利率支付利息，故外币可看成支付红利的资产。
5、当一种不支付红利股票的价格为$40时，签订一份1年期的基于该股票的远期合约，无风险利率为10%(连续复利)，试问：(1) 远期价格为多少？远期合约的初始价值为多少？(2) 两个月后，股票的价格为$45，远期价格和远期合约价值各为多少？解：已知：S=40，T －t =1，r =10%。
交易日 起算日确定日 结算日 到期日(1) 根据公式(2-2-2)有：F=Se r (T-t )=40e 0.1×1=44.21(美元)，初始价值：f =0。
(2) 已知：S=45，T －t =10/12，r =10%。
根据公式(2-2-2)有：F=Se r (T-t )=45e 0.1×5/6=48.91(美元)根据公式(2-2-1)有：f =45－40=5(美元)。
7、已知美元的即期利率为5%，人民币的即期利率为2%。
当前的人民币对美元的汇率是6.80:1，我国人民币计息天数为365天，问：一年之后的人民币对美元的远期汇率是多少？解：已知：S =6.80，r =0.05，r f =0.02，由公式(2-4-1)有：8、远期利率协议某交易日是2010年5月12日星期三，双方同意成交1×4金额100万美元，利率为6.25%的远期利率协议，确定日市场利率为7%。
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金融期货合约（Financial Futures Contracts） 是指在交易所交易的、协议双方约定在将来某个 日期按事先确定的条件（包括交割价格、交割地 点和交割方式等）买入或卖出一定标准数量的特 定金融工具的标准化协议。同样，我们称在合约 中未来将买入标的物的一方为多方，而在未来卖 出标的物的一方为空方。合约中规定的价格就是 期货价格。
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远期合约是适应规避现货交易风险的需要而产 生的。
远期市场的交易机制可以归纳为两大特征：分 散的场外交易和非标准化合约。
远期合约不在交易所交易，而是在金融机构之 间或金融机构与客户之间通过谈判后签署的。其交 易主要是私下进行的，基本不受监管当局监管。
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❖ 在盯市结算完成以后，如果交易者保证金账 户的余额超过初始保证金水平，交易者可随 时提取现金或用于开新仓。但交易者取出的 资金额不得使保证金账户中的余额低于初始 保证金水平。
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❖ 而当保证金账户的余额低于交易所规定的维持保证金 （Maintenance Margin）水平时（维持保证金水平通
❖通常期货合约的到期交割可能有两种方式：现 金交割与实物交割。
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❖ 除了以上5个方面之外，期货合约中通常还有诸如交 易时间、产品代码、头寸限额（Position Limit）等不 太重要的或是不具有一般性的标准条款。
注意：远期交易是到期一次性结算的，所以在远 期存续期内，实际交割价格始终不变，标的资产市场价 格的变化给投资者带来的是账面浮动盈亏，到期结算时 标的资产的市场价格与交割价格的差异才是投资者的真 实盈亏。
期货则有所不同。由于期货是每日盯市结算实现 真实盈亏的，因此可以把期货看作一个每日以结算价平 仓结清并以该结算价重新开立的合约，每日结算价格就 是不断变动的期货交割价格。
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金融期货问世至今不过短短三十余年的历
史，但其发展速度却相当惊人。时至今日，金融
期货交易在许多方面都已经远远走在了商品期货
交易的前端。一些重要的期货交易甚至可以一天
24小时在世界各地不同的期货市场上连续进行。
目前全球最大的期货交易所当属2007年7月
CME（芝加哥商品交易所）与CBOT（芝加哥期
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与远期合约的分类相似，根据标的资产不同， 常见的金融期货主要可分为股票指数期货、外汇期 货和利率期货等。 -股票指数期货是指以特定股票指数为标的资产的期 货合约，S&P500股指期货合约就是典型代表。 -外汇期货则以货币作为标的资产，如美元、德国马 克、法国法郎、英镑、日元、澳元和加元等。 -利率期货是指标的资产价格依赖于利率水平的期货 合约，如欧洲美元期货和长期国债期货等。
❖ 这些标准化的期货合约条款看似对期货交易进行了高 度的限制，但实际上正是由于期货合约的高度标准化， 价格成为期货合约交易中的唯一变量，才使得期货头 寸的开立和平仓能够非常便利地进行，大大提高了期 货合约的交易效率和流动性，促进了期货交易的发展， 使其成为期货有别于远期的一个重要特征。
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案例：沪深300 股指期货合约
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❖ 在这些公司签订的远期股票合约中，约定的远期 价格通常高于签订时的股票市价。例如2000年3月礼 来公司签订远期股票合约，约定在2003年年底以前购 买本公司450万股股票时，该公司的股票市价为70美 元左右。而远期股票合约中的协议价格定在86美元到 100美元。然而到了2002年9月，礼来公司的股票市价 却跌至55美元上下，致使礼来公司面临着1.5亿美元 的潜在亏损。类似的，由于被迫购买其544万股股票， 电子资讯系统公司在2002年的短短几个月内便损失了 约1亿美元。
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3．远期股票合约 远期股票合约（Equity Forwards）是指在将来某一特 定日期按特定价格交付一定数量单只股票或一揽子 股票的协议。远期股票合约在世界上出现时间不长， 总交易规模也不大。
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2．远期外汇协议 远期外汇协议（FXA）是指双方约定在将来某 一时间按约定的汇率买卖一定金额的某种外汇的合 约。 注意，有些国家由于外汇管制，因此本金不可 交割。这种外汇远期合约称为本金不可交割远期 （Non-Deliverable Forwards, NDF）。 远期汇率协议（Exchange Rate Agreements, ERA） (远期的远期外汇协议)
货交易所）合并后形成的CME GROUP（芝加哥
交易所集团），2006年两家交易所交易的合约总
数加起来超过了22亿份，合约总名义本金超过
1000万亿美元 。
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❖ 期货交易的基本特征就是标准化和在交易所集 中交易，这两个特征及其衍生出来的一些交易 机制，成为期货有别于远期的关键。
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❖ 期货市场的第一个运行特征是在有组织的交易所内集中 进行，交易双方并不直接接触，交易所和清算机构充当 所有期货买方的卖者和所有期货卖方的买者，匹配买卖 撮合成交，集中清算。这种交易方式克服了远期交易信 息不充分和违约风险较大的缺陷，在很大程度上提高了 市场流动性和交易效率，降低了违约风险，成为远期交 易进化到期货交易的一个关键。
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但相应地，远期合约也有明显的缺点： 首先，没有固定集中的交易场所，不利于信息交流 和传递，不利于形成和发现统一的市场价格，市场 效率较低； 其次，由于非标准，每份远期合约千差万别，给远 期合约的二级流通造成较大不利，因此远期合约的 流动性较差； 最后，履约没有保证，违约风险相对较高。 这些特征，与下一节我们将要介绍的期货合约正好 相反。
如果到期标的资产的市场价格高于交割价格K，远期多头
就会盈利而空头则会亏损;反之，远期多头就会亏损而空头
则会盈利。
Copyright© Zheng Zhenlong & Chen Rong, 2008
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案例2.1 人民币即期与远期报价
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根据标的资产不同，常见的金融远期合约 包括：
1.远期利率协议 2.远期外汇协议 3.远期股票合约
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由于不在交易所集中交易而是由交易双方具 体谈判商定细节 ，双方可以就交割地点、交割 时间、交割价格、合约规模、标的物的品质等细 节进行谈判，以便尽量满足双方的需要。
总的来看，作为场外交易的非标准化合约， 远期的优势在于灵活性很大，可以根据交易双方 的具体需要签订远期合约，比较容易规避监管。
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股票指数期货、外汇期货、利率期货它们与本 章第一节中所介绍的远期利率协议、远期外汇合约 和远期股票合约的区别都主要体现在交易机制的不 同，我们将在第五章针对不同标的资产的远期和期 货产品作更深入的介绍。
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金融期货合约交易是在现代商品期货交易 的基础上发展起来的。
20世纪70年代初，世界经济环境发生巨大 变化，“布雷顿森林体系”崩溃，世界各国开始 实行浮动汇率制，金融市场上的利率、汇率和证 券价格开始发生急剧波动，整个经济体系风险增 大。人们日益增长的金融避险需求推动了金融期 货交易的产生 。
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案例2.5 欧洲美元期货交易的保证金计算与每日盯市结算
❖ 2007年9月20日，投资者A以95.2850的价位购买了一份将于 2007年12月到期的欧洲美元期货合约EDZ7.假设A的经纪人的 保证金要求与CME规定相同，此时一份欧洲美元期货的初始 保证金为743美元，维持保证金为550美元。
❖ 9月20日交易结束时EDZ7结算价为95.2650.这意味着多头A在 这一份合约上损失了2*25=50美元（合约规定0.01代表25美 元）。则A的保证金账户余额相应减少了50美元，减少至693 美元。
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金融远期合约（Forward Contracts）是指双方约定在未 来的某一确定时间，按确定的价格买卖一定数量的某种金 融资产的合约。在合约中，未来将买入标的物的一方称为 多方（Long Position），而在未来将卖出标的物的一方称 为空方（Short Position）。
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从本质上说，期货与远期是完全相同的，都 是在当前时刻约定未来的各交易要素。
期货与远期的重要区别就在于交易机制的差 异。与场外交易的非标准化远期合约相反，期货 是在交易所内交易的标准化合约。交易所同时还 规定了一些特殊的交易和交割制度，如每日盯市 结算（Market to Market and Daily Settlement）和 保证金（Margin）制度等。
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案例2.2 远期股票合约
❖ 21世纪初，一些以远期股票合约为主要交易形式 的股票回购协议使得礼来和电子资讯系统等公司面临 着巨大的财务风险。与其他许多公司一样，这些公司 通过向员工发放优先认股权作为激励，因此要从市场 上购买本公司股票以满足认股权执行时的需要。在20 世纪90年代的股票市场繁荣时期，这些公司股票价格 强劲上扬。为了控制他们的购买成本，这些公司便与 投资银行签订合同，约定将来以固定价格购买本公司 的股票，显然这就是远期股票合约。
常低于初始保证金水平），经纪公司就会通知交易者 在限期内把保证金水平补足到初始保证金水平，否则