Assignment for Chapter 2宋逢明金融工程习题
Lesson7_Martingale宋逢明金融工程习题
Lesson7_Martingale宋逢明金融工程习题Harrison and Kreps: Martingales and Arbitrage in Multiperiod Securities MktsJ. of Econ Theory 20(1979)Contingent claim valuation1.single period economy with uncertainty-The dates t=0,T; and consumption bundle (r,x)with x defined below-probability space(PF,,Ω)-M: a Subspace of x-Price system (M,∏); ∏is linear functional on M, in unit of consumption good in period 0.Def:A Price system (M,∏) is viable if ?an agent (represented by)and a bundle(r*,m*)R M∈?such that r*+∏(m*)≤0 and (r*,m*)(r, m) for all (r,m)R M∈?.S.t. r+∏(m)≤0Given viable price system(M, ∏)and contingent claim x∈X, what should be x’s price p in unit of time 0 consumption?-Ans: the extended price system on (M,x)should be viable, i.e., consistent with(M,∏).Theorem 1: A price system (M,∏)is viable iff ?an extension of ∏to all x that is strictly positive linear functional on X,call it ψ.Separating hyperplane theorem: suppose A and B are convexdisjoint subsets of R n There is some nonzero linear fanctional F s.t. F(x)≤F(y) for each x∈A and y∈B. Key steps of proof.Step 1: (if part) identifyon R Xas ≥:(r,x)(r′, x′) if r+ψ(x) ≥r′+ψ(x′) with this choice, (r*,m*)=(0,0)Step 2: only if part. Support (M,∏) is viable .Define two sets in R X ?:{}(,):(,)(0,0)G r x R X r x =∈?and {}(,):()0H r m R M r m =∈?+∏≤These two sets are disjoint and convex. Use separating Hyperplane theorem, ?continuous linear functional on R X φ?s.t.φ(r,x) ≥0 for G and H or x r 0),(≤φStep 3: choose φ(r,x)=r+ψ(x)Verify ①positive strictly is x )(ψ② m ψ=∏Corollary 1: If a price system(M,∏) is viable then for all ,x X ∈?some price that is consistent to (M,∏).Arbitrage price of x X ∈: the unique price for claim x that is consistent to (M,∏).Corolloary 2: If a price system (M,∏)is viable, then the price of x X ∈is determined by arbitrage iff the set {():x ψpositive linear functional ,and M ψ=∏} is unique. And this unique ():x ψis the arbitrage value of x.2. Multiperiod security market and SF simple trading strategy .Intertemperal information structure.-The economy spans: T periods: t=0,1,…T.-State of the economy: a set of possible paths of theeconomy from 0 to T, denoted by w. {}w Ω the set of all possible states-Event:-a subset of Ω-Two events are disjoint if 21E E φ?=-A partition of Ω is a collection of event {}n E E ,1, s.t.(),()i j i i i E E i jii E φ?=?≠?=Ω-The information about the state of economy at time t is represented by a partition of Ω:{},1,,:t t t t n E E σ= F -Information structure or Event treeThe true state of economy is gradually revealed over time: 二叉树2223()()S E S E =?recombined binomial.11123{,,}E w w w ={}0E =Ω1245{,}E w w =0E 11E12E21E 22E 23E24E{}0E =Ω11232342122334{{,,},{,,}}{{,},{,},{,}}E w w w w w w E w w w w w w ==-{},1,,:t t t t n E E σ= F then 1t t s for s +?≥F F-probability measure defined on the state space {}:w Ω∏=∏For any event E,w E w E ∏∑=∏∈Security price process and simple trading strategy -A security is a claim that pays ()t t d E at time t in the event Et t t E ∈F i.e. t d is a stochastic process that is measurable w.r.t. t F .-A basic security: pays $1 only at t in an event t t E ∈F .-Assume N+1 securities traded in security market. Let ,i t S be the price of security i att. ,i t S is a function of t E , i.e., ,i t S is measurable w.r.t. t F t 1,t n,t S =(S ,S ) , N dimension.-Simple trading strategy t θ: an (N ×1)-dimensional process that is adapted to t F , 0E 11E12E 22E23E 311E w =322E w = 333E w =344E w = 21Ei.e., t θ only depends on time t information.M-payoff generated by simple trading strategy-Self-financing simple trading strategy:11()Nt t t t t PL S S d θ+==-+∑ Let t d =0, in continuous time ()t o PL S dS θ=? in ito ’s sense.No arbitrage2.3.1 Definition: Arbitrage or free lunch: If ? SF t θ, let t t P S θ≡? ,① P 0≤0 and P T ≥0,with prob(P T >0)＞0,or ②P 0＜0 and P T ≥0.000()S θθ?∏=? linear, positive.2.3.2 Dynamic completeness: For any payoff x T , ? a simple trading strategy,000..()T T s t x S S dS θθ=?+??3. Equivalent martingale measure3.1 Def: On a probability space (,F Ω), define two measures P and Q. If for any F E ∈, ()0()0P E Q E >?>, then Q is equivalent to P.3.2 Def: Martingale: On a filtered probability space (P F t ,,Ω), S t is an adaptive stochastic process w.r.t. F t . If for any 0≤s ≤t, we have ()()p s E S t S s ??=??F , then S(t) is a martingale. P is the martingale measure4. Foundamental theorem4.1 Theorem 1: In the security market defined above, there exists no arbitrage iff there exists an equivalent martingale measure.4.2 Theorem 2: The market is dynamically complete iff there exists a unique equivalent martingale measure. (M=X) Sketch of proof: 4.1 M: the set of payoff genated by SF simple trading strategyStep 1: no arbitrage ∏? is positive linear functional on M.Step 2: Use theorem 1 from previous section (,)(,)M viable X ψ∏? extensionSuppose :s F R R →is linear. Then ?a unique ρ in s R s.t. for s x R ∈, we have F(x)=E(ρx). 2211()...(,,),()s s s sE x Px P x R LF p x R E x =++=Ω∈<∞. Step 3: Riesz representation Theorem: 220()()(,,)*.0*()[]0Tx y t t t t t x t x E x L F P E dP define dPstrctly positive P and P equivalent M E X E S dS S E dS ψρρρρψρψθθθθ=∈Ω<∞=?>?=∏?=+?== S is martingale under P*. Example: f r =010 10 1/3 1/3 1/3 11 9 11 10 8 111/4 1/5 11/20 1/4 1/2 1/2 1/5 1/5 3/5 14,9 w110,13 w210,8 w314,9 w410,13 w510,9 w612,10 w77,15 w87,10 w911234567892{{,,},{,,},{,,}}()F w w w w w w w w w F F σσ==。
金融工程习题及答案
金融工程习题及答案《金融工程学》思考与练习题第一章金融工程概述1.金融工程的含义是什么？2.金融工程中的市场如何分类？3.金融工程中的无套利分析方法？举例说明。
4.金融工程中的组合分解技术的含义是什么？举例说明。
5.远期利率与即期利率的关系如何确定。
推导远期利率与即期利率的关系。
6.假定在外汇市场和货币市场有如下行情，分析市场是否存在套利机会。
如何套利？如何消除套利？第二章现货工具及其应用1.举例说明商品市场与货币市场如何配置？2.商品市场与外汇市场的现货工具如何配置？举例说明。
3.举一个同一个金融市场中现货工具配置的例子。
4.举例说明多重现货市场之间的工具配置。
第三章远期工具及其应用1.什么是远期交易？远期交易的基本要素有哪些？2.多头与空头交易策略的含义是什么？3.什么是远期利率？4.举例说明“借入长期，贷出短期”与“借入短期，贷出长期”策略的含义。
5.何谓远期利率协议？其主要功能是什么？描述其交易时间流程。
6.在远期利率协议的结算中，利率上涨或下跌对借款方和贷款方的影响如何？7.什么情况下利用购入远期利率协议进行保值？什么情况下利用卖出远期利率协议进行保值？8.远期合约的价格与远期价格的含义是什么？如果远期价格偏高或偏低，市场会出现什么情况？9.远期价格和未来即期价格的关系是什么？10.在下列三种情况下如何计算远期价格？11.合约期间无现金流的投资类资产12.合约期间有固定现金流的投资类资产13.合约期间按固定收益率发生现金流的投资类资产14.一客户要求银行提供500万元的贷款，期限半年，并且从第6个月之后开始执行，该客户要求银行确定这笔贷款的固定利率，银行应如何操作？目前银行的4月期贷款利率为9.50%，12月期贷款利率为9.80%。
15.假设某投资者现在以20美元的现价购买某只股票，同时签订一个半年后出售该股票的远期合约，在该期间不分红利，试确定该远期合约的价格。
假定无风险利率为7.5%。
金融工程练习题二 (答案)
金融工程练习题二一、计算题1.设一份标的证券为一年期贴现债券、剩余期限为6个月的远期合约多头，其交割价格为$930，6个月期的无风险年利率（连续复利）为6%，该债券的现价为$910，求远期合约多头的价值。
解: 由题意有910S =, 930K = , 0.06r = , 0.5T t -=,所以远期合约多头价值为 ()(0.060.5)9109307.49r T t f S Ke e ---⨯=-=-⨯≈2.假设6个月期和12个月期的无风险年利率分别为5%和6%，而一种十年期债券现货价格为800元，该证券一年期远期合约的交割价格为900元，该债券在6个月和12个月后都将收到$50的利息，且第二次付息日在远期合约交割日之前，求该合约的价值。
解: 收益的现金贴现 (0.050.5)(0.065050I e e -⨯-⨯=+远期合约的价值 0.061(800)900f I e -⨯=-- PS:构建两个组合,组合A:(一单位的远期合约多头,加上现金贴现值为()r T t Xe --),组合B:(一单位的标的资产,和刚好与利息现金流相反的负债I),在到期时间T 的时候,组合A 的价值刚好为购买一单位的标的资产,组合B 的价值为一单位的标的资产,产生的利息刚好用于负债的偿还,那么在时间t 的时候,两个组合的价值也应该相等,即合约的价值加上现金应该等于资产的价值加上负债.3.股票价格为50美元，无风险年利率为10%，一个基于这个股票、执行价格都为40美元的欧式看涨和欧式看跌期权价格相差7美元，都将于6个月后到期。
这其中是否存在套利机会？如果有，应该如何进行套利？解:根据无收益资产欧式看涨期权和看跌期权之间的平价公式()r T t c Xe p S --+=+, 代入数据进行计算可以得到()0.10.05504010.1997r T t c p S Xe e ---⨯-=-=-=>, 所以题目不满足平价公式,其中存在了套利机会.套利的方法:卖出股票,同时买入看涨期权和卖出看跌期权(使得参与者到期只能按执行价格买入),利用所得的现金收益进行无风险投资买入看涨期权,卖空看跌期权,将净现金收入43元(50元-7元)进行6个月的无风险投资,到期获得45.2元.如果到期时股票价格高于40元,执行看涨期权,如果低于40元,看跌期权被执行,因此无论如何到期时股票价格都以40元购买股票用于平仓卖空的股票,净收益5.2元.PS:当看涨期权和看跌期权之间不满足期权 的平价公式的时候,市场就存在无风险的套利机会4.假设一份5年期附息票债券，价格为900元。
CHAPTER2宋逢明金融工程
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金融工程 第二版 课后习题 完整答案
第1章7、讨论以下观点是否正确：看涨期权空头可以被视为其他条件都相同的看跌期权空头与标的资产现货空头（其出售价格等于期权执行价格）的组合。
(1)9、如果连续复利年利率为5%，10000元现值在4.82年后的终值是多少？ (1)10、每季度记一次复利年利率为14%，请计算与之等价的每年记一年复利的年利率和连续复利年利率。
(1)11、每月记一次复利的年利率为15%，请计算与之等价的连续复利年利率。
(1)12、某笔存款的连续复利年利率为12%，但实际上利息是每季度支付一次。
请问1万元存款每季度能得到多少利息？ (1)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.()5%4.821000012725.21e ××=元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=4ln(1+0.14/4)=13.76%。
11.连续复利年利率=12ln(1+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（e 0.03-1）=12.18%。
因此每个季度可得的利息=10000×12.8%/4=304.55元。
第2章1、2007年4月16日，中国某公司签订了一份跨国订单，预计半年后将支付1000000美元，为规避汇率风险，该公司于当天向中国工商银行买入了半年期的10000000美元远期，起息日为2007年10月8日，工商银行的实际美元现汇买入价与卖出价分别为749.63和752.63。
请问该公司在远期合同上的盈亏如何？ (1)2、设投资者在2007年9月25日以1530点（每点250美元）的价格买入一笔2007年12月到期的S^P500指数期货，按CME 的规定，S^P500指数期货的初始保证金为19688美元，维持保证金为15750美元。
金融工程-习题-第二部分-答案
《金融工程与风险管理》习题第二部分1． 假设某不付红利股票价格遵循几何布朗运动，其预期年收益率16%，年波动率30%，该股票当天收盘价为50元，求：①第二天收盘时的预期价格，②第二天收盘时股价的标准差，③在量信度为95%情况下，该股票第二天收盘时的价格范围。
1、 由于),(~t t SS∆∆∆σμφ 在本题中，S ＝50，μ＝0.16,σ=0.30,∆t=1/365=0.00274.因此，∆S/50~φ(0.16⨯0.00274,0.3⨯0.002740.5)=φ(0.0004,0.0157) ∆S ~φ(0.022,0.785)因此，第二天预期股价为50.022元，标准差为0.785元，在95％的置信水平上第2天股价会落在50.022-1.96⨯0.785至50.022+1.96⨯0.785,即48.48元至51.56元之间。
2.变量X 1和X 2遵循普通布朗运动，漂移率分别为μ1和μ2，方差率分别为σ12和σ22。
请问在下列两种情况下，X 1+X 2分别遵循什么样的过程？（1）在任何短时间间隔中X 1和X 2的变动都不相关； （2）在任何短时间间隔中X 1和X 2变动的相关系数为ρ。
2、 （1）假设X 1和X 2的初始值分别为a 1和a 2。
经过一段时间T 后，X 1的概率分布为：11,a T φμσ+（X 2的概率分布为：22,a T φμσ+（根据独立的正态分布变量之和的性质，可求X 1和X 2的概率分布为：11221212()a T a T a a T φμμφμμ+++=+++（（这表明，X 1和X 2遵循漂移率为12μμ+，方差率为2212σσ+的普通布朗运动。
（2）在这种情况下，X 1和X 2在短时间间隔Δt 之内的变化的概率分布为：12[()t φμμ+∆如果1212μμσσρ、、、和都是常数，则X 1和X 2在较长时间间隔T 之内的变化的概率分布为：12[()T φμμ+这表明，X 1和X 2遵循漂移率为12μμ+，方差率为2212σσ++ 122ρσσ的普通布朗运动。
金融工程试题及答案
金融工程试题及答案【篇一：金融工程期末练习题答案】2、与n个未来状态相对应，若市场存在n个收益线性无关的资产，则市场具有完全性。
（√）3、根据风险中性定价原理，某项资产当前时刻的价值等于根据其未来风险中性概率计算的4、如果套利组合含有衍生产品，则组合中通常包含对应的基础资产。
（√）5、在套期保值中，若保值工具与保值对象的价格负相关，则一般可利用相反的头寸进行套二、单选题1、下列哪项不属于未来确定现金流和未来浮动现金流之间的现金流交换？（b）a、利率互换b、股票c、远期d、期货2、关于套利组合的特征，下列说法错误的是（a）。
a.套利组合中通常只包含风险资产b.套利组合中任何资产的购买都是通过其他资产的卖空来融资c.若套利组合含有衍生产品，则组合通常包含对应的基础资产d．套利组合是无风险的3、买入一单位远期，且买入一单位看跌期权（标的资产相同、到期日相同）等同于（c）a、卖出一单位看涨期权b、买入标的资产c、买入一单位看涨期权d、卖出标的资产4、假设一种不支付红利股票目前的市价为10元，我们知道在3个月后，该股票价格要么是11元，要么是9元。
假设现在的无风险年利率等于10%，该股票3个月期的欧式看涨期权协议价格为10.5元。
则（d）a. 一单位股票多头与4单位该看涨期权空头构成了无风险组合b. 一单位该看涨期权空头与0.25单位股票多头构成了无风险组合c. 当前市值为9的无风险证券多头和4单位该看涨期权多头复制了该股票多头d．以上说法都对三、名词解释1、套利答：套利是在某项金融资产的交易过程中，交易者可以在不需要期初投资支出的条件下获取无风险报酬。
2、阿罗-德不鲁证券答：阿罗-德不鲁证券指的是在特定的状态发生时回报为1，否则回报为0的资产。
3、等价鞅测度答：资产价格st是一个随机过程，假定资产价格的实际概率分布为p，若存在另一种概率分布p使得以p计算的未来期望风险价格经无风险利率贴现后的价格序列是一个鞅，即**ste?rt?et(st??e?r(t??))，则称p*为p的等价鞅测度。
金融工程学各章习题及答案
金融工程学各章习题及答案第一章综合远期外汇协议（SAFE交易）1.请简述金融衍生产品的功能。
2.金融工程的应用领域。
3.金融远期合约有哪些优点？又有哪些缺点？4.请简述远期外汇市场的卖出者包括那些人。
5.请简述远期外汇市场的买入者包括那些人。
6.常见的远期合约有哪几种?7.远期交易主要应用在哪些领域?8.某交易商拥有1亿日元远期空头,远期汇率为0.008美元/日元.如果合约到期时汇率分别为0.0074美元/日元和0.0090美元/日元,请计算该交易商的盈亏状况。
9.某日美元对瑞郎即期汇率为USD/CHF1.2200－1.2210，若l个月美元对瑞郎远期汇率点数为20－30，l个月美元对瑞郎远期汇率点数为45－40，分别求l 个月和3个月美元对瑞郎远期汇率。
10．有些学者认为，远期汇率是对未来汇率的无偏预测。
请问在什么情况下这种观点是正确的？11.请简述影响期货汇率波动的主要因素。
12.请简述有效的外汇风险管理步骤。
第一章答案1.答：1.规避市场风险2.套利3.投机4.提高效率5.促进金融市场的完善2.答：1.公司理财方面2.金融工具及其交易策略3.投资与货币管理方面4.风险管理技术与手段3.答：优点主要是具有较大的灵活性；缺点是市场效率较低、流动性较差、违约风险较高。
4.答：1.有远期外汇收入的出口商2.持有未到期外汇的债权人3.输出短期资本的牟利者4.对远期外汇看跌的投机者5.答：1.有远期外汇支出的进口商2.负有未到期外汇的债务人3.输入短期资本的牟利者4.对远期外汇看涨的投机者6.常见的远期合约主要包括远期利率协议和远期外汇协议。
7.主要应用于利率风险和外汇风险防范。
8.若合约到期时汇率为0.0075美元/日元，则他赢利1亿（0.008-0.0074）=6万美元。
若合约到期时汇率为0.0090美元/日元，则他赢利1亿（0.008-0.009）=-10万美元。
9. l个月美元对瑞郎远期汇率为USD/CHF：（1.2200+0.0020）－（1.2210+30）=1.2220－1.2240。
金融工程课后练习(doc 6页)
8.8 仔细分析由看跌期权构造的牛式价差期权和由看涨期权构造的牛市价差期权之间的不同点。
解：由看跌期权构造的牛市价差期权和由看涨期权构造的牛市价差期权的损益图大致相同。
令11,P C 分别为执行价格为1X 的看跌期权与看涨期权，22,P C 分别为执行价格为2X 的看跌期权与看涨期权，由期权平价公式可得：111rT P S C X e -+=+，222rT P S C X e -+=+则：121221()rT P P C C X X e --=---，这表明，由看跌期权构造的牛市价差期权的初始投资小于由看涨期权构造的牛市价差期权初始投资数额为21()rT X X e --。
实际上，看跌期权构造的牛市价差期权的初始投资为负值，而看涨期权构造的牛市价差期权的初始投资为正值。
看涨期权构造的牛市价差收益高于看跌期权21()rT X X e --。
这反映了看涨策略较看跌策略多了额外无风险投资21()rT X X e --，并获取21()(1)rT X X e ---的利息。
8.9解释如何使用看跌期权怎样构造进取型的熊市价差期权？解：进取型的熊市价差期权可由虚值看跌期权（均有相对低的执行价格），因为两份看涨期权价值接近于0，价差期权仅需很少成本构造。
在大多数情形下，价差期权的价值为0。
然而，为使期权在到期日处于实值状态，股价仅有很小机会快速下降。
那么价差期权的价值即两执行价格之差21X X -。
8.10假设执行价格为$30和$35的看跌期权成本分别为$4和$7，怎样用期权构造（a ）牛市价差期权；(b)熊市价差期权？做出表格说明这两个期权的收益与报酬状况。
解：a)牛市价差期权可通过买入执行价格为$30的看跌期权同时卖空执行价格为$35的看涨期权。
此策略将有$3期初现金流入，其损益状况如下：股价T S 价差期权损益 利润T S >=35 0 －330<＝T S <35 T S －35 T S －32T S <30 －5 －2b)熊市价差期权可通过卖空执行价格为$30的看跌期权同时买入执行价格为$35的看跌期权构造。
金融工程练习题及答案解析
一、 单项选择1、下列关于远期价格和远期价值的说法中，不正确的是：（B ）B ．远期价格等于远期合约在实际交易中形成的交割价格2.在衍生证券定价中，用风险中性定价法，是假定所有投资者都是( 风险无所谓的3.金融工具合成是指通过构建一个金融工具组合使之与被模仿的金融工具具有(相同价值4.远期价格是( 使得远期合约价值为零的交割价格5.无收益资产的美式期权和欧式期权比较( 美式期权价格大于欧式期权价格6.无收益资产欧式看跌期权的价格上限公式是( )(t T r Xe p --≤7.在期货交易中，基差是指（B.现货价格与期货价格之差8.无风险套利活动在开始时不需要（任何资金） 投入。
9.金融互换具有( 降低筹资成本 )功能。
10.对利率互换定价可以运用(债券组合定价 )方法。
11.期货价格和远期价格的关系（ 期货价格和远期价格具有趋同性 )。
12.对于期权的买者来说，期权合约赋予他的（ 只有权利而没有义务13.期权价格即为( 内在价值加上时间价值14.下面哪一因素将直接影响股票期权价格( 股票价格的波动率15.无收益资产的欧式看涨期权与看跌期权之间的平价关系为( s p Xe c t T r +=+--)(16、假设有两家公司A 和B ，资产性质完全一样，但资本结构不同，在MM 条件下，它们每年创造的息税前收益都是1000万元。
A 的资本全部由股本组成，共100万股（设公司不用缴税），预期收益率为10%。
B 公司资本中有4000万企业债券，股本6000万，年利率为8%，则B 公司的股票价格是（100）元17、表示资金时间价值的利息率是（社会资金平均利润率18.金融工程的复制技术是（一组证券复制另一组证券19、金融互换的条件之一是( 比较优势20、期权的内在价值加上时间价值即为( 期权价值21、对于期权的卖者来说，期权合约赋予他的（ 只有义务而没有权利22、无收益资产的美式看跌期权和欧式看跌期权比较( 美式期权价格大于欧式期权价格二、多项选择1、下列因素中，与股票欧式看涨期权价格呈负相关的是：（期权执行价格/期权有效期内标的股票发放的红利2、以下关于实值期权和虚值期权的说法中，不正确的是：（ ABCD ）A ．当标的资产价格高于期权执行价格时，我们将其称为实值期权B ．当标的资产价格低于期权执行价格时，我们将其称为虚值期权C ．当标的资产价格低于期权执行价格时，我们将其称为实值期权D．当标的资产价格高于期权执行价格时，我们将其称为虚值期权3、下列关于有收益资产的美式看跌期权的说法中，不正确的是：（AC ）A．对于有收益资产的美式看涨期权，提前执行期权意味着放弃收益权，因此不应提前执行C．对于有收益资产的美式看跌期权，提前执行期权可以获得利息收入，应该提前执行4. 以下的那些参数与股票欧式看涨期权的价格总是正相关？（股票价格/波动率5. 以下哪个说法是不正确的：（ AC ）A. 期货合约到期时间几乎总是长于远期合约。
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。
金融工程_宋逢明_资产负债管理
这些手段在功能上与互换是等价的，从这 种意义上可以说互换是一种合成投资
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金融工程案例分析
银行管理利率风险暴露的方法
Banc One管理利率风险的投资
1981，增加平衡性资产,比如美国中短期国债 和高等级市政债券 1983，利率互换(Swaps) 1986，住房抵押贷款证券(MBSs) 1983，担保抵押贷款证券(CMO) 80年代末，分期偿付利率互换(AIRS)
2012-5-11 金融工程案例分析 3
1、问题是什么?
Banc One公司背景介绍 股价下跌对Banc One的影响 股价为什么下跌
2012-5-11 4
金融工程案例分析
Banc One公司背景
总部位于俄亥俄州哥伦比亚，总资产765 亿美元，是俄亥俄州最大和美国第八大 银行持股公司，共有78家银行子公司 业务战略：
2012-5-11 金融工程案例分析 29
3、什么是AIRS？
什么是AIRS 为什么运用它来控制风险
2012-5-11
金融工程案例分析
30
什么是AIRS？
分期偿还利率互换，Amortizing Interest Rate Swap 利率下降时名义本金额将进行摊销
2012-5-11
金融工程案例分析
第一银行公司资产负债管理
2012-5-11
金融工程案例分析
1
案例回顾
Banc One，全美最大的超级区域性银行之一， 其股票价格在1993年内大幅下跌，由$48.75 （1993年4月时）下跌至$36.75（现在，1993年 11月14日） 尽管无法确定股价下跌的具体原因，一些分析 家对银行持有的大量金融衍生品进行了批评。 这些衍生品用于进行利率风险管理并且是一种 组合投资的手段。银行的高级管理层被迫重新 回顾其管理过程，并且将决定如何对分析家的 关注和问题进行回复。
金融工程 练习题
金融工程练习题金融工程-练习题chap1－2练习单选题1、如果一年期的即期利率为10%，二年期的即期利率为10.5%，那么其暗含的一年至二年的远期利率就相当于（）。
a.0.1b.0.105c.0.11d.0.122、6个月期和1年期即期年利率分别就是10%和12%，问6个月至一年期的远期利率就是多少a.0.11b.0.14c.0.125d.0.133、证券市场上有一种证券a，a的价格是100元，无风险利率r=5%(连续复利)，一年后a可能为110元，也可能为90元.证券b在a为90元时价值1元，在a为110元时价值0元，问b现在的价格是多少?（）a.0.4563b.0.3219c.0.2318d.0.19824、证券市场上有一种证券a,a的价格是100元,无风险利率r=5%(连续复利),一年后a可能为110元,也可能为90元.证券b在a为110元时价值1元,在a为90元时价值0元,问b现在的价格是多少?（）a.0.3279b.0.6588c.0.7982d.0.71955、金融市场在一年后可能出现两种价格状态，有价证券a的两种基本证券的价格分别是0.523和0.465，现在有一种证券b，它在两种价格状态下的价格分别是109和92，问b的当前价格是多少？（）a.99.787b.101.324c.98.567d.102.3496、金融市场在一年后存有两种状态,第一种状态证券a价值120元,第二种状态a价值80元,a的现值就是100元,无风险利率r=5%(已连续乘数),问a的两种基本证券的价格就是多少?（）a.0.5975和0.3537b.0.6139和0.4362c.0.6139和0.3537d.0.5975和0.43627、x国证券市场在一年后可能出现两种状态,出现第一种时证券a价值115元,出现第二种时证券a价值95元,a的现值是100元,无风险利率r=8%(连续复利),问a的两种基本证券的价格是多少?（）a.0.6532和0.3079b.0.6152和0.3079c.0.6532和0.3378d.0.6152和0.33788、下面哪个组合可以构造卖出远期？（）a.买进看跌期权+买进看涨期权b.买进看跌期权+买进看涨期权c.买进看跌期权+买进看涨期权d.买进看跌期权+买进看涨期权9、某投资者持有一份看涨期权空头，他预期资产价格可能会上升给他带来损失，问下面哪种方法可以帮这位资者规避风险？（）a.卖空一份资产b.买进一份看涨期权1c.买进一份看涨期权d.买进一份资产10、下面哪项是错误的?（）a.汇率风险可以用对冲交易去避免b.信用风险可以用对冲交易去避免c.利率风险可以用对冲交易去避免d.市场风险可以用对冲交易去避免判断题1、复制组合的多头（空头）与被复制组合的空头（多头）互相之间应该完全实现头寸对冲2、并无套利定价建议套利活动在无风险的状态下展开3、无套利定价从即时现金流看是零投资组合4、金融工程的产生在本质上充分反映了市场崇尚效率的内在建议。
金融工程练习题及解析
一、单项选择1、以下对于远期价钱和远期价值的说法中，不正确的选项是：（B）B．远期价钱等于远期合约在本质交易中形成的交割价钱2. 在衍生证券订价中，用风险中性订价法，是假定所有投资者都是(风险无所谓的3. 金融工具合成是指经过建立一个金融工具组合使之与被模拟的金融工具拥有( 相同价值4.远期价钱是 ( 使得远期合约价值为零的交割价钱5.无利润财产的美式期权和欧式期权比较( 美式期权价钱大于欧式期权价钱6. 无利润财产欧式看跌期权的价钱上限公式是(p Xe r (T t )7.在期货交易中，基差是指（ B. 现货价钱与期货价钱之差8.无风险套利活动在开始时不需要（任何资本）投入。
9.金融交换拥有 ( 降低筹资成本) 功能。
10.对利率交换订价能够运用 ( 债券组合订价) 方法。
11.期货价钱和远期价钱的关系（期货价钱和远期价钱拥有趋同性) 。
12.对于期权的买者来说，期权合约给予他的（只有权益而没有义务13.期权价钱即为 (内在价值加上时间价值14.下边哪一要素将直接影响股票期权价钱(股票价钱的颠簸率15.无利润财产的欧式看涨期权与看跌期权之间的平价关系为(cXe r (T t )p s16、假定有两家公司 A 和 B，财产性质完整相同，但资本结构不一样，在MM条件下，它们每年创建的息税前利润都是1000 万元。
A 的资本所有由股本构成，共100 万股（设公司不用缴税），预期利润率为10%。
B 公司资本中有4000万公司债券，股本6000万，年利率为8%，则 B 公司的股票价钱是（100）元17、表示资本时间价值的利息率是（社会资本均匀利润率18.金融工程的复制技术是（一组证券复制另一组证券19、金融交换的条件之一是(比较优势20、期权的内在价值加上时间价值即为(期权价值21、对于期权的卖者来说，期权合约给予他的（只有义务而没有权益22、无利润财产的美式看跌期权和欧式看跌期权比较(美式期权价钱大于欧式期权价钱二、多项选择1、以下要素中，与股票欧式看涨期权价钱呈负有关的是：（期权履行价钱/ 期权有效期内标的股票发放的盈余2、以下对于实值期权和虚值期权的说法中，不正确的选项是：（ABCD）A．当标的财产价钱高于期权履行价钱时，我们将其称为实值期权B．当标的财产价钱低于期权履行价钱时，我们将其称为虚值期权C．当标的财产价钱低于期权履行价钱时，我们将其称为实值期权D．当标的财产价钱高于期权履行价钱时，我们将其称为虚值期权3、以下对于有益润财产的美式看跌期权的说法中，不正确的选项是：（AC）A．对于有益润财产的美式看涨期权，提早履行期权意味着放弃利润权，所以不该提早履行C．对于有益润财产的美式看跌期权，提早履行期权能够获取利息收入，应当提早履行4.以下的那些参数与股票欧式看涨期权的价钱老是正有关（股票价钱/ 颠簸率5.以下哪个说法是不正确的：（AC ）A.期货合约到期时间几乎老是擅长远期合约。
《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。
《金融工程学》题库及答案
《金融工程学》题库及答案一、选择题1.证券投资收益最大化和风险最小化这两个目标（）.A.可以同时实现；B.是一致的；C.是相互冲突的；D.大多数情况下可以同时实现.2.金融工程中，通常用（）来衡量风险.A．收益率； B.收益率的标准差； C.到期收益率； D.市场风险.3. 系数表示的是（）.A.市场收益率的单位变化引起证券收益率的预期变化幅度；B.市场收益率的单位变化引起无风险利率的预期变化幅度；C.无风险利率的单位变化引起证券收益率的预期变化幅度；D.无风险利率的单位变化引起市场收益率的预期变化幅度.4.下列哪个不是远期合约的特点( ).A.非标准化；B.实物交割；C.流动性好；D.信用分险大.5.下列哪项不属于金融期货（）.A.外汇期货；B.利率期货；C.股票指数期货；D.商品期货.6.下列不属于资本资产定价模型的前提假设条件（）.A.证券交易是在一个无摩擦的、完备的竞争性市场中进行的；B.所有投资者都是理性的；C.每个投资者对预期收益率及其标准差、证券之间的协方差有不同的预期；D.资产能够被无限细分，拥有充分的流动性.7.相对于基础证券，下列不属于金融衍生工具的特点是（）.A.高收益和高风险并存；B.交易金额的不确定性；C.具有一定的技术性和复杂性；D.对投资者的要求不高.8.由于中央政府予以税收、货币发行等特权，通常情况下，中央政府证券不存在违约风险，因此，这一类证券被视为（）.A.低风险证券；B.无风险证券；C.风险证券；D.高风险证券.9.债券价格受市场利率的影响，若市场利率上升，则（）.A.债券价格下降；B.债券价格上升；C.不变；D.难以确定.10.在2007年以来发生的全球性金融危机中，导致大量金融机构陷入危机的最重要一类衍生金融产品的是（）.A.货币互换；B.信用违约互换；C.利率互换；D.股权互换.11.某投资者投资10000元于一项期限为3年、年息8%的债券，按年计息，按复利计算该投资的终值为（）.A.12597.12元；B.12400元；C.10800元；D.13310元.12.股权类产品的衍生工具是指以（）为基础的金融衍生工具.A.各种货币；B.股票或股票指数；C.利率或利率的载体；D.以基础产品所蕴含的信用风险或违约风险.二、填空题1.按金融工具的风险是否能被分散和规避，将其风险可分为个别风险和 .2.按照交易的金融工具的期限的长短，可将金融市场分为和货币市场.3.一个在小麦期货中做_______头寸的交易者希望小麦价格将来上涨.4.在资本资产定价模型中，投资者分别用资产未来预期收益率的期望和方差来评价某一资产的收益率水平和水平.5.股票指数期货是以为买卖标的物的期货.6.根据合约履约时间的不同，期权可以分为欧式期权和 .7.金融工程学有三个基本要素：不确定性、和能力.8.在有效金融市场上，一个公司的价值是由其资产负债表的资产一栏里面的盈利能力所决定的，而与该公司的负债一栏里面的以及股本结构无关.9.金融工程学是帮助人们在繁杂的金融市场中找到解决金融问题的方法论，其目的是 .10. 是一种能在未来特定时间以特定价格买进或卖出一定数量的特定资产的权利.11. 是指一种可以在特定时间、按特定条件转换为普通股票的特殊企业债券.12.债券按发行主体的不同，可以分为政府债券、金融债券和 .三、判断题（T代表正确，F代表错误）1.交易所交易存在的问题之一是缺乏灵活性. （）2.大多数期货合约以现货进行交割. （）3.债券资产的价值变动应与其息票收入再投资收益率反方向变动. （）4.签订远期合约的双方最终不需要进行实物交割. （）5.如果期权是虚值，期权买方就不会行使期权，直到到期任期权失效.这样，期权买方最多损失所交的权利金. （）6.期权买方和卖方均有执行和不执行交易的权利. （）7.金融远期和约由于采用了集中交易的方式，交易事项可以协商确定，较为灵活，金融机构或大型工商企业通常利用远期交易作为风险管理的手段. ( )8.金融衍生工具的杠杆效应一定程度上决定了它的高投机性和高风险性. （）9.单因素模型假定任意风险资产收益由一个公共因素决定. ( )10.期货合约设计成标准化的合约是为了便于交易双方在合约到期前分别做一笔相反的交易进行对冲，从而避免实物交割. （）11.远期交易的原理是“借入长期，贷出短期”. （）12.远期、期货和期权的交易双方在权利和义务上都是对等的. （）四、简答题1.什么是金融工程?金融工程技术可以用来解决什么问题？2.试比较场外交易市场与交易所交易市场的利弊？3.期权的要素及功能分别是什么？4.CAPM模型的假设条件是什么？并写出CAPM模型的表达式.5、什么是债券？债券包括哪些基本要素？6、影响期权价格（期权费）的因素有哪些？7、简述期货和远期的区别？8、简述金融工程运作的六个步骤.9.简述股指期货的功能.影响股票指数期货的因素是什么？10.阐述期货与期权的区别.五、计算题1.某交易商拥有1亿日元远期多头,远期汇率为0.008美元/日元.如果合约到期时汇率分别为0.0074美元/日元和0.0090美元/日元,请计算该交易商的盈亏状况.2.某投资者在5月份以5.5美元/盎司的权利金买入一份执行价格为430美元/盎司的6月份黄金看跌期权，又以4.5美元/盎司的权利金卖出一张执行价格为430美元/盎司的6月份黄金看涨期权，再以市场价格428.5美元/盎司买进一张6月份黄金期货合约.那么当合约到期时该投机者的净收益是？3.A公司今年每股股息为0.5元，预期今后每股股息将以每年10％的速度稳定增长.当前的无风险利率为0.03，市场组合的风险溢价为0.08，A公司股票β值为1.5.那么，A公司股票当前的合理价格P是多少？4.某贴现债券面值1000元，期限180天，以10.5%的年贴现率公开发行，计算该债券的发行价格和投资者的到期收益率.5．A公司2008年每股股息为0.9元，预期今后每股股息将以每年10％的速度稳定增长.当前的无风险利率为0.04，市场组合的风险溢价为0.12，A公司股票β值为1.5.那么，A公司股票当前的合理价格P是多少？6．已知证券组合P是由证券A和B构成，证券A和B的期望收益，标准差以及相关系数如下：计算组合P的期望收益率和方差.7.甲方希望在3个月以后以6.80元人民币/美元的汇率用人民币买入10万美金，乙方愿意在三个月后以同样的汇率卖出10万美金，于是双方签订一份在3个月以后成交的远期合约.如在到期日汇率变为6.85元人民币/美元，则计算甲乙两方的损益情况及各方的损益数目?六、论述题1、请论述在看好某项资产的情况下，“多方头寸”的三种实现方式，并分析各自的收益损失特征。
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 $45.50 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 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 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 positionfinanced by this minimum margin requirement?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 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. $17.86.24. 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 particularstock. 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 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 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 ofthe 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 atleast 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 ofa 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 theannualized 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 generatea 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 expressedas:21=E(r)-2u A , which of the following values for the measure for riskaversion has the leastamount 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 areequally-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 ofa 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.。
金融经济学浅述--宋逢明(主要是金融工程)
金融经济学基本定理
金融经济学第一基本定理:
风险中性概率存在的充分必要条件是不存在无风险 套利机会。
金融经济学第二基本定理:
风险中性概率是唯一的，其充分必要条件是市场是 完全的。
金融经济学第三基本定理:
在一定的条件下，动态地修改现有证券的组合可以 复制创造出新的证券，从而有效地填补市场以增加完全 性。
F$ 1 0(1 0 1% 5$ )11? 5
假如股票的远期价格是F=$106/股，用远期合约和无风险证 券来复制该股票，进行如下套利分析：
4
用远期合约和无风险证券来复制该股票
持仓量（头寸）
即期现金流
价值 $100 的无风险 证券的空头
订价为 $106 的 1股股票 的远期合约空头
以 $100 的价格购买 1 份股票现货（多头）
• 套期保值功能：
期货市场如何实现套期保值功能？
6
关于股指期货
104 103 102 101 100
99 98 97 96 95
期货价格
VS
现货价格
3个月的指数期货
指数价格
平行性
收敛性
date 2001-1-3 2001-1-5 2001-1-9 2001-1-11 2001-1-15 2001-1-17 2001-1-19 2001-2-6 2001-2-8 2001-2-12 2001-2-14 2001-2-16 2001-2-20 2001-2-22 2001-2-26 2001-2-28 2001-3-2 2001-3-6 2001-3-8 2001-3-12 2001-3-14 2001-3-16 2001-3-20 2001-3-22 2001-3-26 2001-3-28
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Assignment for Chapter2:
Now given the risk-free zero coupon rate as following:
Term
1 year
2 year
3 year
4 year Risk-free rate 3.25% 3.33% 3.41% 3.60%
（1）Question: There is an interest swap: principal 1million, 4 years, fixed interest to float
interest, change the interest every year. What is the price of the swap?
（2）Question: Assume the risk-free zero coupon rate changed one year later. Show in the Risk-free rate 3.40% 3.52% 3.65% 3.74%
Currency swap has a remaining life of 15 months. It involves exchanging interest at 14% on 20 million pound for interest at 10% on $30 million once a year. The term structure of interest rates in both the UK and the US is currently flat, and if the swap were negotiated today the interest rates exchanged would be 8% in dollars and 11% in pound. All interest rates are quoted with annual compounding. The current exchange rate (dollars per pound) is 1.65. What is the value of the swap to the party paying pound sterling? What is the value of the swap to the party paying dollars?
A financial institution has entered into an interest rate swap with company X. Under the terms of the swap, it receives 10% per annum and pays six-month LIBOR on a principal of $10 million for five years. Payments are made every six months. Suppose that company X defaults on the sixth payment date (end of year three) when the interest rate (with semiannual compounding) is 8% per annum for all maturities. What is the loss to the financial institution? Assume that six-month LIBOR was 9% per annum halfway through year three.
4. The term structure is upward sloping. Put the following in order of magnitude:
(1) The five-year zero rate.
(2) The yield on a five-year coupon-bearing bond.
(3) The forward rate corresponding to the period between 5 and 4
15years in the future. What is the answer to this question when the term structure is downward sloping?
5. A $100 million interest rate swap has a remaining life of 10 months. Under the terms of the
swap, six-month LIBOR is exchanged for 12% per annum (compounded semiannually). The average of the bid-ask rate being exchanged for six-month LIBOR in swaps of all maturities is currently 10% per annum with continuous compounding. The six-month LIBOR rate was
9.6% per annum two months ago. What is the current value of the swap to the party paying floating? What is its value to the party paying fixed?。