《金融学》计算习题讲课稿
金融学计算题及答案演示文稿
• 3．某债券面额100元，利息率6％，购进日2001年8月10日， 到期2005年1月1日，发行期限7年，买入价112．4元，到期还 本付息，计算直接收益率和到期收益率。
年利息收益 解：（1）直接收益率= —————— ×100% 买入价格
＝100×6％÷112.4×100％＝5.34％ （2）到期收益率＝到期本息和－买入价格/ 未到期偿还期限×发 行价格×100% ＝(142－112.4)÷(3+140/360)×112.4×100％
计算题三：
3-1．某商业银行吸收原始存款100亿元，其存款准备率 为10％，客户提取现金率为10％，不考虑其他因素， 该商业银行能创造多少派生存款? 解：存款总额（D ）＝R／(R1+R2)
=100／(10％+10％)
＝ 100／20％ ＝500亿元 500－100＝400亿元 所以该商业银行能创造400亿元的派生存款。
3-4．某银行对某企业贷款年利率为5．4％， 某企业某年6月30日向银行借款30000元， 同年9月10日归还，求利息额及本利和。 解：利息额＝30000*70*5.4％÷360＝315(元)
本利和＝30000+315＝30 315(元)
4-1．假定商业银行系统吸收存款150亿元，法定存款
准备率r＝10％，当r上升至15％或下降至5％时，最 终货币供给量有何变化?
Re=1000/5000=20％
存款总额＝5000*/（20%+20%）＝12500(万元)
派生存款总额＝12500—5000＝7500(万元)
所以银行最大可能派生的派生存款总额为7500万元。
计算题五：
1.某国2007年的名义利率为8.5%，通货膨胀率为 6.5%，请分别以粗略的方法和精确的方法求 实际利率。
《金融学》 教案大纲及习题解答(姜法芹 )
《金融学》教案大纲及习题解答第一章：金融学导论1.1 金融学的定义与意义金融学的概念金融学的研究对象与内容金融学的重要性1.2 金融市场与金融体系金融市场的概念与类型金融体系的组织结构金融市场与金融体系的关系1.3 金融学的应用领域企业金融个人金融宏观金融第二章：金融市场与金融工具2.1 金融市场的概念与类型金融市场的定义金融市场的类型与特点金融市场的作用与功能2.2 金融工具与金融产品金融工具的定义与分类金融产品的特点与功能金融工具与金融产品的选择与运用2.3 金融市场的参与者金融市场的主体与客体金融市场的投资者与融资者金融市场的服务机构第三章：金融市场的基本原理3.1 供求关系与价格机制金融市场的供求关系价格机制的作用与影响市场均衡与市场失灵3.2 金融市场的基本原理与应用金融市场的效率与有效性金融市场的风险与收益金融市场的信息与信号传递3.3 金融市场的微观结构金融市场的交易机制金融市场的信息不对称问题金融市场的交易成本与效率第四章：金融机构与金融体系4.1 金融机构的概念与类型金融机构的定义与特点商业银行与其他金融机构的比较金融机构的职能与作用4.2 金融体系的组织结构金融体系的构成要素金融体系的层次结构金融体系的监管与调控机制4.3 金融体系的功能与目标金融体系的基本功能金融体系的宏观调控目标金融体系的微观审慎监管目标第五章：金融市场与宏观经济5.1 金融市场与经济增长金融市场对经济增长的影响金融市场的规模与经济增长的关系金融市场的结构与经济增长的关系5.2 金融市场与货币政策货币政策的概念与目标金融市场在货币政策传导中的作用货币政策对金融市场的影响5.3 金融市场与金融稳定性金融稳定性的概念与意义金融市场在金融稳定性维护中的作用金融市场风险管理与监管的策略与措施《金融学》教案大纲及习题解答第六章：商业银行与存款货币银行6.1 商业银行的组织结构与运营模式商业银行的定义与特点商业银行的组织结构与管理体系商业银行的运营模式与业务流程6.2 存款货币银行的存款创造与信贷扩张存款创造的概念与机制信贷扩张的过程与影响存款货币银行的风险管理与信贷政策6.3 商业银行的金融服务与产品商业银行的存款与贷款产品商业银行的支付结算服务商业银行的金融服务创新第七章：资本市场与证券交易7.1 资本市场的概念与类型资本市场的定义与特点股票市场与债券市场的比较资本市场的功能与作用7.2 证券交易与投资分析证券交易的基本流程投资分析的方法与工具投资者偏好与投资组合的选择7.3 资本市场的效率与有效性资本市场效率的定义与衡量资本市场的有效性假说资本市场效率与有效性的实证研究第八章：金融衍生品市场8.1 金融衍生品的概念与类型金融衍生品的定义与特点期货、期权和掉期的比较金融衍生品市场的功能与作用8.2 金融衍生品的定价与风险管理金融衍生品的定价原理金融衍生品的风险类型与风险管理策略金融衍生品市场的风险监管与调控8.3 金融衍生品市场的应用与影响金融衍生品在企业金融中的应用金融衍生品在个人理财中的应用金融衍生品市场对金融体系的影响第九章：国际金融与外汇市场9.1 国际金融市场的概念与类型国际金融市场的定义与特点国际资本市场与国际外汇市场的比较国际金融市场的作用与影响9.2 外汇市场的运行机制与交易策略外汇市场的组织结构与交易机制外汇市场的汇率决定与变动外汇市场的交易策略与风险管理9.3 国际金融市场的关系与影响国际金融市场之间的联系与互动国际金融市场对国内经济的影响国际金融市场风险的识别与应对第十章：金融监管与金融政策10.1 金融监管的概念与目标金融监管的定义与意义金融监管的目标与原则金融监管的机构与体系10.2 金融政策的概念与工具金融政策的定义与类型货币政策与财政政策的比较金融政策的工具与传导机制10.3 金融政策的效应与评估金融政策的宏观经济效应金融政策的微观经济效应金融政策的评估方法与指标《金融学》教案大纲及习题解答第十一章：金融创新与金融科技11.1 金融创新的定义与类型金融创新的含义与动力金融创新的产品与服务金融创新的风险与监管11.2 金融科技的发展与应用金融科技的概念与特点数字货币与区块链技术金融科技在金融服务中的应用11.3 金融创新与金融监管的关系金融监管对金融创新的影响金融创新对金融监管的挑战金融监管与金融创新的平衡策略第十二章：金融风险与管理12.1 金融风险的定义与类型金融风险的概念与特征市场风险、信用风险和流动性风险的比较金融风险的管理与控制12.2 金融风险评估与度量金融风险评估的方法与模型金融风险度量的指标与工具金融风险评估的实践应用12.3 金融风险管理的策略与工具金融风险管理的框架与程序金融风险规避、分散与转移金融风险管理的创新与挑战第十三章：企业金融与公司财务13.1 企业金融的概念与功能企业金融的定义与目标企业金融的资本结构与投资决策企业金融的融资与理财策略13.2 公司财务的理论与实践公司财务的基本原则与目标公司财务的财务报表分析与估值公司财务的资本预算与资本结构13.3 企业金融与公司财务的挑战与趋势企业金融与公司财务的国际化企业金融与公司财务的可持续发展企业金融与公司财务的创新与发展第十四章：个人金融与理财规划14.1 个人金融的概念与内容个人金融的定义与意义个人资产与个人负债的管理个人金融产品的选择与运用14.2 理财规划的理论与方法理财规划的基本原则与步骤理财规划的工具与技术理财规划的实际操作与案例分析14.3 个人金融与理财规划的挑战与趋势个人金融市场的变化与趋势理财规划在个人金融中的应用个人金融与理财规划的创新与发展第十五章：金融伦理与职业道德15.1 金融伦理的概念与重要性金融伦理的定义与特点金融伦理在金融行业中的重要性金融伦理的挑战与问题15.2 职业道德的标准与原则职业道德的内涵与要求职业道德的实践与遵守职业道德的监督与教育15.3 金融伦理与职业道德的发展趋势金融伦理与职业道德的改进与完善金融行业职业道德建设的措施与方法金融伦理与职业道德的未来发展重点和难点解析本文档详细地编写了《金融学》教案大纲及习题解答，涵盖了金融学的基本概念、原理和应用。
黄达《金融学》讲义：第二章 利息和利率
第二章利息和利率2.1 利息2.2 利率概述2.3 利息的复利计算（货币的时间价值）2.4 利率决定2.5 利率的风险结构和期限结构第一节利息一、利息的来源（利息的来源与本质是研究利率理论的出发点）利息报酬说（威廉.配第（1633-1687）和约翰.洛克）利息是暂时放弃货币的使用权而获得的报酬(配第)，利息是贷款人因承担了风险而得到的报酬（洛克）资本租金论（达德利.诺思（1641-1649)）资本所有者出借它们的资金，像出租土地一样，从中得到的东西就是利息，利息是资本的租金。
节欲论（西尼尔）利息是借贷资本家节欲的结果人性不耐说（欧文.费雪）人性具有偏好现在就可提供收入的资本财富，而不耐心地等待将来提供收入的资本财富的心理。
利息是不耐的指标。
流动性偏好论（凯恩斯）是人们放弃流动性偏好的报酬利息来自剩余价值（马克思）：利息是职能资本家让渡给借贷资本家的一部分剩余价值，体现资本家剥削雇佣工人的关系二、利息被看作是收益的一般形态（一）利息被看作是收益的一般形态的原因：利息被看作资金所有者理所当然的收入。
在其它条件不变时，利率的大小制约企业主收入的多少(二)利息转化为收益一般形态的作用★利息转化为收益的一般形态的主要作用在于导致了可以通过收益与利率的对比倒算出它相当于多大的资本金额或价格。
）利息收益（B）=本金（P）× 利率（r）如果知道收益和利率，就可以利用这个公式套算出本金，即：P=B/r(二)利息转化为收益一般形态的作用★收益资本化在经济生活中被广泛地应用.▲例1:土地价格=土地年收益/年利率▲例2:人力资本价格=年薪/年利率▲例3:股票价格=股票收益/市场利率▲例4:债券价格=债券利息/市场利率第二节利率概述一、利率的含义：货币资金的价格二、利率的种类（一）年利率、月利率和日利率（二）名义利率和实际利率名义利率就是以名义货币表示的利率。
实际利率为名义利率与通货膨胀率之差，它是用你所能够买到的真实物品或服务来衡量的。
《金融学（第二版）》讲义大纲及课后习题答案详解十三章
《⾦融学（第⼆版）》讲义⼤纲及课后习题答案详解⼗三章CHAPTER 13THE CAPITAL ASSET PRICING MODELObjectivesExplain the theory behind the CAPM.Explain how to use the CAPM to establish benchmarks for measuring the performance of investment portfolios. Explain how to infer from the CAPM the correct risk-adjusted discount rate to use in discounted-cash-flow valuation models. Explain the APT and its relationship to the CAPM.Outline13.1 The Capital Asset Pricing Model in Brief13.2 Determinants of the Risk Premium on the Market Portfolio13.3 Beta and Risk Premiums on Individual Securities13.4 Using the CAPM in Portfolio Selection13.5 Valuation and Regulating Rates of Return13.6 Extensions, Modifications, and Alternatives to the CAPMSummaryThe CAPM has three main implications:In equilibrium, ev eryone’s relative holding of risky assets are the same as in the market portfolio.The size of the risk-premium of the market portfolio is determined by the risk-aversion of investors.The risk premium on any asset is equal to its beta times the risk premium on the market portfolio.Whether or not the CAPM is strictly true, it provides a rationale for a very simple passive portfolio strategy: Diversify your holdings of risky assets in the proportions of the market portfolio, andMix this portfolio with the risk-free asset to achieve a desired risk-reward combination.The CAPM is used in portfolio management primarily in two ways:To establish a logical and convenient starting point in asset allocation and security selectionTo establish a benchmark for evaluating portfolio management ability on a risk-adjusted basis.In corporate finance the CAPM is used to determine the appropriate risk-adjusted discount rate in valuation models of the firm and in capital budgeting decisions. The CAPM is also used to establish a “fair” rate of return on invested capital for regulated firms and in cost-plus pricing.Today few financial scholars consider the CAPM in its simplest form to be an accurate model for explaining or predicting risk premiums on risky assets. However, modified versions of the model are still a central feature of the theory and practice of finance.The APT gives a rationale for the expected return-beta relationship that relies on the condition that there be no arbitrage profit opportunities; the CAPM requires that investors be portfolio optimizers. The APT and CAPM are not incompatible; rather, they complement each other.Solutions to Problems at End of ChapterComposition of the Market Portfolio1. Capital markets in Flatland exhibit trade in four securities, the stocks X, Y and Z, and a risklessgovernment security. Evaluated at current prices in US dollars, the total market values of these assets are, respectively, $24 billion, $36 billion, $24 billion and $16 billion.a. Determine the relative proportions of each asset in the market portfolio.b. If one trader with a $100,000 portfolio holds $40,000 in the riskless security, $15,000 in X, $12,000 in Y, and$33,000 in Z, determine the holdings of the three risky assets of a second trader who invests $20, 000 of a $200, 000 portfolio in the riskless security.SOLUTION:The total value of all assets in the economy is 100 billion dollars. a. The proportions of each asset relative to the value of all assets are, respectively, .24 (X), .36 (Y),b. .24 (Z) and .16 (riskless bond.) The proportions of each risky asset to the total value of all risky assets are, respectively, (2/7) (X), (3/7) (Y) and (2/7) (Z).c. . Ignore the question as it appears in the First Edition of the textbook. Instead, the question should be: If aninvestor has $100,000 with $30,000 invested in the riskless asset, how much is invested in securities X, Y, and Z? The answer to this question is $20,000 in X and Z, and $30,000 in Y.Implications of CAPM2. The riskless rate of interest is .06 per year, and the expected rate of return on the market portfolio is .15 per year.a. According to the CAPM , what is the efficient way for an investor to achieve an expected rate of returnof .10 per year?b. If the standard deviation of the rate of return on the market portfolio is .20, what is the standarddeviation on the above portfolio?c. Draw the CML and locate the foregoing portfolio on the same graph.d. Draw the SML and locate the foregoing portfolio on the same graph.e. Estimate the value of a stock with an expected dividend per share of $5 this coming year, an expecteddividend growth rate of 4% per year forever, and a beta of .8. If its market price is less than the value you have estimated, i.e., if it is under-priced, what is true of its mean rate of return?SOLUTION: a.So one would hold a portfolio that is 4/9 invested in the market portfolio and 5/9 in the riskless asset. b.c. The formula for the CML is9415.)1(06.10.)()1()(=+-=?+-?=x xx x r E x r r E M f 08889.)20(.94==?=M x σσσσσ45.06.)()(+=-+=MfM f r r E r r Ed. The formula for the SML ise. Use constant growth rate DDM and find r using the SML relationIf the market price of the stock is less than this, then its expected return is higher than the 13.2% required rate.()ββ09.06.)()(+=-+=f M f r r E r r E 35.54$04.132.504.510=-=-=-=r g r D P 132.8.09.06.09.06.=?+=+=βr3. If the CAPM is valid, which of the following situations is possible? Explain. Consider each situation independently. a.PortfolioExpected ReturnBeta A 0.20 1.4B 0.25 1.2b.PortfolioExpected ReturnStandard DeviationA 0.300.35B 0.400.25c.Portfolio Expected ReturnStandard DeviationRisk-free 0.100Market 0.180.24A 0.160.12d.Portfolio Expected ReturnStandard DeviationRisk-free 0.100Market 0.180.24A0.200.22SOLUTION:a. Impossible. Since the risk premium on the market portfolio is positive, a security with a higher beta must have ahigher expected return.b. Possible. Since portfolios A & B are not necessarily efficient, A can have a higher standard deviation and alower expected return than B.c. Impossible. Portfolio A lies above the CML, implying that the CML is not efficient. If the standard deviation ofA is .12, then according to the CML its expected return cannot be greater than .14.d. Impossible. Portfolio A has a lower standard deviation and a higher mean return than the market portfolio,implying that the market portfolio is not efficient.4. If the Treasury bill rate is currently 4% and the expected return to the market portfolio over the same period is 12%, determine the risk premium on the market. If the standard deviation of the return on the market is .20, what is the equation of the Capital Market Line?SOLUTION: The risk premium on the market portfolio is .08. The slope of the CML is .08/.2 = .4. Thus, the equation of the CML is:Determinants of the Market Risk Premium5. Consider an economy in which the expected return on the market portfolio over a particular period is .25, the standard deviation of the return to the market portfolio over this same period is .25, and the averagedegree of risk aversion among traders is 3. If the government wishes to issue risk-free zero-coupon bonds with a term to maturity of one period and a face value per bond of $100,000, how much can the government expect to receive per bond? []σσσ4.04.)()(+=++=MfMf r rE r r ESOLUTION:According to the CAPM, E(r M) - r f = Aσ2, so that r f = E(r M) - Aσ2.Substituting into this formula we find: r f = .25 – 3 x .252 = .0625Therefore the revenue raised by the government per bond issued is $100,000 = $94,117.651.06256. . Norma Swanson has invested 40% of her wealth in MGM stock and 60% in Industrial Light and Magic stock. Norma believes the returns to these stocks have a correlation of .06 and that their respective means and standard deviations are: MGM ILMExpected Return (%) 10 15Standard Deviation (%) 15 25a.Determine the expected value and standard deviation of the return on Norma’s portfolio.b.Would a risk-averse investor such as Norma prefer a portfolio composed entirely of only MGM stock? Ofonly ILM stock? Why or why not?SOLUTION:a.The expected return is .13, and the standard deviation is .1649.b. A risk averse investor will not want to hold a portfolio composed entirely of MGM or of ILM stock, becauseone can, in general, achieve the same expected return with a lower standard deviation by combining a portfolio of MGM and ILM with the risk-free asset.7. Consider a portfolio exhibiting an expected return of 20% in an economy in which the riskless interest rate is 8%, the expected return to the market portfolio is thirteen percent, and the standard deviation of the return to the market portfolio is .25. Assuming this portfolio is efficient, determine:a.its beta.b.the standard deviation of its return.c.its correlation with the market return.SOLUTION:/doc/ad5801fd700abb68a982fb59.html e the security market line to infer that the beta of this portfolio is 2.4:.20 = .08 + β(.13 - .08)β = (.20 - .08)/(.13 - .08) = .12/.05 = 2.4/doc/ad5801fd700abb68a982fb59.html e the capital market line to infer that the standard deviation of the yield to this portfolio is .6:.20 = .08+ (.13 - .08) σ = .08+ .2 σ.25σ = .12/.2 = .6c.By definition the following relationships hold:β = cov/σ2Mρ = covσiσMwhere ρ denotes the correlation coefficient. We know that β = 2.4, σM = .25, and σi = .6.So from the definition of β, we get that the cov is 2.4 x .252 = .15. Substituting this into the definition of ρ: ρ = cov = .15 __ = 1σiσM .6 x .25Application of CAPM to Corporate Finance8. . The Suzuki Motor Company is contemplating issuing stock to finance investment in producing a new sports-utility vehicle, the Seppuku. Financial analysts within Suzuki forecast that this investment will have precisely the same risk as the market portfolio, where the annual return to the market portfolio is expected to be 15% and the current risk-free interest rate is 5%. The analysts further believe that the expected return to the Seppuku project will be 20% annually. Derive the maximal beta value that would induce Suzuki to issue the stock.SOLUTION:The project would be on the borderline if its required return were 20% per year. Since the risk-free rate is 5% and the risk premium on the market portfolio is 10%, the required return would be 20% if the beta were 1.5.9. . Roobel and Associates, a firm of financial analysts specializing in Russian financial markets, forecasts that the stock of the Yablonsky Toy Company will be worth 1,000 roubles per share one year from today. If the riskless interest rate on Russian government securities is 10% and the expected return to the market portfolio is 18% determine how much you would pay for a share of Yablonsky stock today if:a.the beta of Yablonsky is 3.b.the beta of Yablonsky is 0.5.SOLUTION:Use the security market line in each case to determine a required rate of return, then infer the current price from the forecasted price of 1,000 roubles and the required rate of return you have determined.a.If beta is 3, the required return is .10+ 3x.08 = .34. You would pay 1,000/1.34 = 746.27 roubles;b.If beta is .5, the required return is .10+ .5x.08 = .14. You would pay 1,000/1.14 = 877.19 roubles.Application of CAPM to Portfolio Management10. Suppose that the stock of the new cologne manufacturer, Eau de Rodman, Inc., has been forecast to havea return with standard deviation .30 and a correlation with the market portfolio of .9. If the standard deviation of the yield on the market is .20, determine the relative holdings of the market portfolio and Eau de Rodman stock to form a portfolio with a beta of 1.8.SOLUTION: By definition:β = cov/σ2Mρ = covσrσMTherefore, β = ρσr/σM. The beta of Rodman stock is therefore .9x.3/.2 = 1.35.The beta of a portfolio is a weighted average of the betas of the component securities. Let A be a fraction of the portfolio invested in Rodman stock to produce a beta of 1.8. Then we have:1.35A + (1-A) = 1.8.35A = .8A = 2.286So the portfolio would have to have 228.6% invested in Rodman stock and a short position in the market portfolio equal to 128.6%.11. The current price of a share of stock in the Vo Giap Clothing Company of Vietnam is 50 dong and its expected yield over the year is 14%. The market risk premium in Vietnam is 8% and the riskless interest rate 6%. What would happen to the stock’s current price if its expected future payout remains co nstant while the covariance of its rate of return with the market portfolio falls by 50%?SOLUTION:Deduce that the expected future price of a share of Vo Giap is 57 dong, so that a reduction in this stock’s beta of 50% implies, by the security market relation, that the required yield on Vo Giap is now 10%, so that its current share price rises by 3.64% toa new value of 51.82 dong.12. Suppose that you believe that the price of a share of IBM stock a year from today will be equal to the sumof the price of a share of General Motors stock plus the price of a share of Exxon, and further you believethat the price of a share of IBM stock in one year will be $100 whereas the price of a share of General Motors today is $30. If the annualized yield on 91-day T-bills (the riskless rate you use) is 5%, the expected yield on the market is 15%, the variance of the market portfolio is 1, and the beta of IBM is 2, what price would you be willing to pay for one share of Exxon stock today?SOLUTION:Expected return = .05 + 2(.15 - .05) = 25%; (100 - x)/x = .25 → x = $80Deduce that the current price of a share of IBM stock is $80, so that the upper bound on the price of a share of Exxon is ($80 -$30 = $50).13. Ascertain whether the following quotation is true or false, and state why:“When arbitrage is absent from financial markets, and investors are each concerned with only the risk and return to their portfolios, then each investor can eliminate all the riskiness of his investments through diversification, and as a consequence the expected yield on each available asset will depend only on the covariance of its yield with the covariance of the yield on the diversified portfolio of risky assets each investor holds.”SOLUTION:False. You cannot eliminate all risk through diversification, only the unsystematic risk.Application of CAPM to Measuring Portfolio Performance14. During the most recent 5-year period, the Pizzaro mutual fund earned an average annualized rate of return of 12% and had an annualized standard deviation of 30%. The average risk-free rate was 5% per year. The average rate of return in the market index over that same period was 10% per year and the standard deviation was 20%. How well did Pizzaro perform on a risk-adjusted basis?SOLUTION:Compute the ratio of average excess return to standard deviation for Pizzaro and compare it to that of the market portfolio: Pizzaro risk-adjusted performance ratio = (.12-.05)/.30 = .233Market portfolio risk-adjusted performance ratio = (.1-.05)/.2 = .250So, on a risk-adjusted basis, Pizzaro did worse than the market index.Challenge ProblemCAPM with only 2 Risky Assets15. There are only two risky assets in the economy: stocks and real estate and their relative supplies are 50% stocks and 50% real estate. Thus, the market portfolio will be half stocks and half real estate. The standard deviations are .20 for stocks, .20 for real estate, and the correlation between them is 0. The coefficient of relative risk aversion of the average market participant (A) is 3. r f is .08 per year.a.According to the CAPM what must be the equilibrium risk premium on the market portfolio, on stocks,and on real estate?b.Draw the Capital Market Line. What is its slope? Where is the point representing stocks located relativeto the CML?c.Draw the SML. What is its formula? Where is the point representing stocks located relative to the SML? SOLUTION: a.The market portfolio consists of half stocks and half real estate. It has a standard deviation of .1414, computedas follows:σ2M = w2σ2s + (1-w)2σ2r+ 2 w(1-w) cov s,rσ2M = 2 x (1/2)2 .22 = .02σM = .1414The equilibrium risk premium on the market portfolio is E(r M)-r f = Aσ2M = 3x.02 = .06.The market portfolio’s expected rate of return is also a weighted average of the expected rates of return on stocks and real estate, where the weights are each 1/2. Stocks and real estate must have the same risk premiumbecause they have the same standard deviation and correlation with the market. Therefore the risk premium on stocks and real estate must be .06, the same as the market portfolio’s risk premium.b.The slope of the CML is .06/.1414 = .424. The point representing stocks is M, it is to the right of the CML.equaling to 1.The formula is: E(r) = r f + (E(r M) –r f).。
《金融学(第二版)》讲义大纲及课后习题答案详解 第五章
CHAPTER 5LIFE-CYCLE FINANCIAL PLANNINGObjectivesIn this chapter you will learn how to analyze:•How much to save for retirement.•Whether to defer taxes or pay them now.•Whether to get a professional degree.•Whether to buy or rent an apartment.•How to minimize estate taxes.Outline5.1 A Life-Cycle Model of Saving5.2 Taking Account of Social Security5.3 Deferring Taxes Through Voluntary Retirement Plans5.4 Should You Invest in a Professional Degree?5.5 Should You Buy or Rent?Summary•In making lifetime saving/consumption decisions:(1) Do the analysis in real terms (constant dollars) to simplify the calculations and to avoid having toforecast inflation.(2) Start by computing the present value of your lifetime resources. The present value of your lifetimespending cannot exceed this amount.•Social security or any other forced saving program will offset voluntary saving. It may have a positive or a negative effect on the present value of your total lifetime resources.•Tax-deferred retirement accounts are advantageous because they allow you to earn a before-tax rate of return until money is withdrawn from the account. They are advantageous if you are in the same tax bracket before and after you retire, and even more so if your tax bracket is lower after you retire. •Getting a professional degree can be evaluated as an investment in human capital. As such, it should be undertaken if the present value of the benefits (such as increase in your earnings) exceeds the present value of the costs (such as tuition and forgone salary.)•In deciding whether to buy or rent an apartment or a consumer durable, choose the alternative with the lower present value of costsSolutions to Problems at End of ChapterSaving for Retirement1. Assume that you are 40 years old and wish to retire at age 65. You expect to be able to average a 6% annual rate of interest on your savings over your lifetime (both prior to retirement and after retirement). You would like to save enough money to provide $8,000 per year beginning at age 66 in retirement income to supplement other sources (social security, pension plans, etc.). Suppose you decide that the extra income needs to be provided for only 15 years (up to age 80). Assume that your first contribution to the savings plan will take place one year from NOW.a.How much must you save each year between now and retirement to achieve your goal?b.If the rate of inflation turns out to be 6% per year between now and retirement, how much willyour first $8000 withdrawal be worth in terms of today’s purchasing power?SOLUTION:a. Age 40 41 65 66 80Time 0 1 25 26 40. . . .X X 8,000 8,000It is a 2 part computation. First compute the amount needed at age 65 to finance the $8,000 per year annuityin terms of today’s purchasing power.2. You are saving for retirement and you come across the following table. It shows the percentage of your current salary that you should save for your retirement in order to retire with an annuity equal to 70% of your salary if you have not yet saved anything. It assumes that your annual salary will remain constant in real terms until retirement, and that you will live for 25 years after retiring. For instance, if you have 35 years left before you retire and earn3.5% per year on your investments, then you should save 17.3% of your current salary.a. Fill in the missing number in Table A.SOLUTION:The method for computing how much saving is needed to reach the desired target (70%) consists of two steps:First compute the amount you need to have accumulated in your personal retirement account when you reach the retirement age. (We’ll do the calculations as percentages of real salary)Then compute the annual amount of saving needed to reach that future value59.79% if you have 15 years to retire29.62% if you have 25 years to retire17.30% if you have 35 years to retireb. Now fill in Table B. It assumes that instead of targeting a 70% replacement rate of preretirement income, your goal is to maintain the same level of consumption spending both before and after retirement.First compute the amount you need to have accumulated in your personal retirement account when you reach the retirement age. (We’ll do the calculations as percentages of real salary)Then compute the annual amount of saving needed to reach that future value85.41% if you have 15 years to retire42.31% if you have 25 years to retire24.72% if you have 35 years to retire3. You are saving for retirement and you come across the following the table. It shows the increase in the annual benefit you can receive in retirement per dollar that you increase your annual retirement saving in the years before retirement. It assumes that you will live for 20 years after retiring. For instance, if you have 30 years left before you retire and earn an interest rate of 3% per year, then you will obtain an increase of $3.20 in your annual retirement benefit for every $1 per year increase in annual saving. Fill in the missing table values.4. George Thriftless is 45 years old, earns $50,000 per year, and expects that his future earnings will keep pace with inflation, but will not exceed inflation. He has not yet saved anything towards his retirement. His company does not offer any pension plan. George pays Social Security taxes equal to 7.5% of his salary, and he assumes that when he retires at age 65, he will receive $12,000 per year in inflation-adjusted Social Security benefits for the rest of his life. His life expectancy is age 85.George buys a book on retirement planning that recommends saving enough so that when private savings and Social Security are combined, he can replace 80% of his preretirement salary. George buys a financial calculator and goes through the following calculations:First, he computes the amount he will need to receive in each year of retirement to replace 80% of his salary: .8 x $50,000 = $40,000.Since he expects to receive $12,000 per year in Social Security benefits, he calculates that he will have to provide the other $28,000 per year from his own retirement fund.Using the 8% interest rate on long-term default-free bonds, George computes the amount he will need to have at age 65 as $274,908 (the present value of $28,000 for 20 years at 8% per year). Then he computes the amount he will have to save in each of the next 20 years to reach that future accumulation as $6,007 (the annual payment that will produce a future value of $274,908 at an interest rate of 8% per year). George feels pretty confident that he can save 12% of his salary (i.e., $6,007/$50,000) in order to insure a comfortable retirement.a.If the expected long-term real interest rate is 3% per year, approximately what is the long-term expected rate of inflation?b.Has George correctly taken account of inflation in his calculations? If not, how would youcorrect him?c.How much should George save in each of the next 20 years (until age 65) if he wants tomaintain a constant level of consumption over the remaining 40 years of his life (from age 45 to age 85)?Ignore income taxes.SOLUTION:a. The long-term expected rate of inflation can be approximated by subtracting the expected real rate ofinterest (3% per year) from the long-term nominal interest rate (8% per year). The expected rate of inflation is therefore approximately 5% per year.The exact value can be calculated using:1+nom= (1+real)(1+inf)hence, the inflation rate is 4.854% per year.b. George has used the nominal interest rate to discount real cash flows. As a result, he has seriouslyunderestimated how much saving he must do to achieve an 80% replacement rate. The time line for this problem is:Age 45 46 65 66 85Time 0 1 20 21 40. . . .X X 28,000 28,000Using the real rate of 3% per year in the calculations results in a needed accumulation at age 65 of $416,569.30:The annual saving needed to achieve this accumulation at a 3% real rate is $15,502.92:So instead of $6,007 per year, George must save $15,502.92 per year. This is 31% of his salary rather than 12%.c. The time line for this problem is:Age 45 46 65 66 85Time 0 1 20 21 40. . . .Inflows 46,250 46,250 12,000 12,000Outflows C CIf George wants to maintain a constant level of consumption both before and after retirement, he must find C , where C is the solution to the following equation:∑∑∑===+=40140212010310001203125046031t t tt t t .,.,.C Equation 1 says that the present value of consumption spending over the next 40 years equals the present value of labor income over the next 20 years (after paying Social Security taxes) plus the present value of Social Security benefits received after retirement.First we find the value on the right side of the equation, the PV of George’s lifetime resources:Step 4: Find PV of lifetime resources as of age 45:688,083.21 + 98,847.56 = 786,930.78So each year between the ages of 46 and 65 George must save $12,205.50, the difference between his income after SS tax ($46,250) and his consumption spending ($34,044.50).Now let us check to make sure that by saving this amount George will indeed have enough to provide the same constant level of consumption spending after retirement as before.Thus, by saving $12,205.50 per year for 20 years earning a real rate of 3% per year, he will have at age 65 an accumulation of $327,966.36.Adding this annuity to the SS benefit we get:$22,044.50 + $12,000 = $34,044.505. George’s company has a defined-benefit pension plan. Suppose the plan pays a benefit equal to 1% of final salary per year of service. George is 40 years old and has worked for the company for 15 years. His last year’s salary was $50,000 and is expected to remain so in real terms until retirement. The expected rate of inflation is 4%.a.If normal retirement age is 65, the interest rate is 8%, and Geor ge’s life expectancy is 80, what isthe present value of his accrued pension benefit?b.What effect should his pension benefit have on George’s planned saving assuming he has a 75%target replacement rate?SOLUTION:a.George’s last year salary $50,000 has a r eal growth rate of 0%, hence it will keep up with inflation untilretirement but not beat it. At retirement, he would have worked for the company for a total of forty years. Hence his annual pension benefit will be equal to 1% x (50,000x 1.0425) x 40 = $53,316.73. We must first find the value of those annual payments in the year when he retires, then discount that back to today.PV65 = $456,363.4140b.For a 75% replacement rate, George expects to have an annual income of 0.75 x 50,000 =$37,500 inreal terms after retirement. Since his pension benefit is providing him with part of his financial needs after retirement, he would only need to worry about the difference between his target income and what the pension is providing him, hence decreasing his planned savings before retirement.6.Analyze the “expert’s” responses to the following questions:Question: How early do you recommend people begin saving for retirement? Would it be too early for my 14-year-old to start saving?Expert: It’s never too early.Question: For a college student , what would you suggest for a savings plan?Expert: I’d suggest deciding on a specific a mount to set aside each month, then making sure you do it, no matter the temptations not to.SOLUTION:a.Because of the time value of money, obviously, the earlier you start saving for retirement the morevalue you’ll have for each dollar saved.Suppose you save $1 at age 15 and you expect to retire at age 65, this dollar will be worth at 8% interest rate $46.9. Of course there’s a trade-off because you’ll also be postponing your spending (enjoying life) to your retirement.b.Again, because of the time value of money, each dollar you save as a college student will earn youmore than a dollar saved later on in your life. That’s why, you must decide on a certain amount you can afford to save and stick with it.Investing in Human Capital7. You are 30 years old and are considering full-time study for an MBA degree. Tuition and other direct costs will be $15,000 per year for two years. In addition you will have to give up a job with a salary of $30,000 per year. Assume tuition is paid and salary received at the end of the year. By how much does your salary have to increase (in real terms) as a result of getting your MBA degree to justify the investment? Assume a real interest rate of 3% per year and ignore taxes. Also assume that the salary increase is a constant real amount that starts after you complete your degree (at the end of the year following graduation) and lasts until retirement at age 65.SOLUTION:Buy or Rent?8. Suppose you currently rent an apartment and have an option to buy it for $200,000. Property taxes are $2,000 per year and are deductible for income tax purposes. Annual maintenance costs on the property are $1,500 per year and are not tax deductible. You expect property taxes and maintenance costs to increase at the rate of inflation. Your income tax rate is 40%, you can earn an after-tax real interest rate of 2% per year, and you plan to keep the apartment forever. What is the “break-even” annual rent such that you would buy it if the rent exceeds this amount? SOLUTION:The after-tax annual outlay if you buy is:$1,500 + .6 x $2,000 = $2,700The PV of this is $2700/.02 = $135,000.The PV of the costs of owning are $135,000 + $200,000 = $335,000.The break-even rent is .02 x $335,000 = $6,700 per year.Buy or lease a car9. You have decided to acquire a new car which costs $30,000. You are considering whether to lease it for 3 years or to purchase it and finance the purchase with a 3-year installment loan. The lease requires no down payment and lasts for 3 years. Lease payments are $400 monthly starting immediately, whereas the installment loan will require monthly payments starting a month from now at an annual percentage rate (APR) of 8%.a.If you expect the resale value of the car to be $20,000 3 years from now, should you buy or leaseit?b.What is the break-even resale price of the car 3 years from now, such that you would beindifferent between buying and leasing it?SOLUTION:a.We have to compare the NPVs of the two alternatives:Since in this case, the car is costing me more, I should choose the first alternative of leasing the car.b. In order to be indifferent among the two alternatives, their respective NPV must be equal, i.e. –12,850.Hence, the PV of the resale price is 30,000-12,850=17,15010. Analyze the following newspaper column:“Many of us who started families late share a nightmare image: having to pay huge college bills just as we’re giving up paychecks and shouldering the ste ep costs of retirement. In fact, the double whammy might not be so bad, assuming the parents have prepared properly. On the plus side, older parents are likely to have enjoyed their best earnings years before the college costs begin, allowing them to put a side more than younger parents can. They’ve also had more years for investments to compound. In the ideal situation, older parents can avoid borrowing to meet college costs, taking the preferred route of earning interest on investments rather than paying i t on student loans.” (Excerpted from Jeff Brown’s Personal Finance column in the Philadelphia Inquirer, May 11, 1998.) SOLUTION:As it is mentioned in the newspaper column, ideally older parents can avoid borrowing to meet college costs provided that they had prepared properly and started saving early in their lives.However, one can argue that with no children in the household, parents have less incentive to save (and enjoy their younger years) and might in fact be faced with this nightmare image of having to pay huge college bills just as they are giving up paychecks.11. Analyze the following newspaper column:“What’s the best age for a person to start collecting Social Security benefits? According to conventional wisdom, retirement starts at age 65. I t’s true that full benefits don’t start until age 65, but 62 year olds can retire and collect 80% of their benefits.Take the hypothetical cases of John and Mary, who have the same birthday and who are both slated to start drawing $1,000 a month in Social Security benefits at age 65. On his 62nd birthday, John decides to go ahead and start claiming his benefits of $800 a month (80% of $1000). Mary decides to wait until she’s 65, when she can claim the full $1000. Three years later, Mary turns 65 and begins receiving $1,000 a month from the Social Security Administration. John continues to receive $800 a month. But he has already been paid $28,800 while Mary received nothing.Five years go by, with Mary drawing $1,000 a month and John $800 a month. At 70, John has received $76,800, compared to Mary’s $60,000. When they reach 77, Mary will pull ahead. So, it seems if a person doesn’t live past 76, it would better to start collecting Social Security benefits at 62. For those who reach their upper 70’s, it pays to wait until they are 65 to collect Social Security. (adapted from 1998, Atlanta Business Chronicle, Gary Summer Contributing writer, June 29, 1998.) SOLUTION:The analysis in this newspaper column ignores the time value of money. The best way to look at this situation is to assume an interest rate, say 5%.The FV at age 65 of the $800 payments that John was taking is:At age 65, when Mary decides to start receiving the benefits from SSA, John has been paid $31,003. Not $28,800 as mentioned in the article.Now, in order to see when Mary will pull ahead, we have to see how many $200 payments (=1000-800) are the $31,003 worth.After 250 month, i.e. at age 85 and 10 months, Mary will eventually pull ahead.Personal Balance Sheets12. Using the finance concepts presented in this chapter, construct a personal balance sheet showing your assets, liabilities and net worth.a.Did you value your assets at cost or at current market value? Why?b.Did you include your human capital as an asset? Why?c.Did you include deferred taxes as a liability? Why?a.I valued my assets at current market value because their cost is irrelevant to me.b.Even though human capital is probably anyone’s biggest asset, I didn’t include it in the balance sheetbecause it’s uncert ain, hard to quantify and I will need to make too many assumptions concerning the PV of my future earnings.c.Once again, I haven’t.Home ownership Over the Life Cycle13. Suppose you buy a house for $200,000 when you are 35 years old. You make a 20% down payment and borrow the other 80% from a mortgage lender. The mortgage loan is at a fixed interest rate of 8% per year for 30 years and requires level annual payments. At age 65, you plan to take out a “reverse-mortgage” loan which will allow you to borrow a constant annual amount for the rest of your life to be paid off by the sale of your house when you die. Your life expectancy is age 85. The interest rate on both the original mortgage loan and the reverse mortgage will be 8% per year.a.Suppose that you expect the inflation rate to be 3% per year and you can rent an equivalenthouse for $10,000 per year. Is it worth buying the house?b.Show how buying the house will affect your assets, liabilities and cash flow over the next 50 years.c.In Making the Most of your money, JB Quinn has written: “ Over the long run, the value ofhomes should follow the inflation rate. But over the time that you won your particular house, its value might rise or fall or stall. You can’t predict. But there are reasons other than profit for owning a house.•Mortgage payments force to save, while rental payments don’t.•You get tax deductions, and can tax-shelter your capital gains.•You’re landlord free.•You know the deep contentment of holding a spot of ground that others can enter by invitation only.•You won’t lose your lease.•You can renovate to suit.• A house is collateral for a loan.Comment.SOLUTION:a.In order to compare the two alternatives, we have to compare their NPVs.Buy Alternative:Basically, this alternative consists of buying the house now at $200,000 and selling it 50 years from now at its market value, accounting for inflation:The FV of the house is:The house will be worth : $876,781 when you are 85.Now, to calculate the NPV of this alternative, we have to discount at 8% to account for the mortgage and the reverse mortgage.Hence the NPV of this option is: -200,000 + 18,694 = -181,306Rent Alternative:We assume that rent will be $10,000 in real terms and hence must be discounted at the real interest rate = 4.854%Hence, it is more economical to buy the house.c. Most of the points mentioned by JB Quinn were discussed in this exercise, namely the fact thatmortgage payments force you to save and that a house can serve as collateral for a loan. She also presents in his discussion some “intangible” benefits from owning a house such as not having a landlord and renovating to suit.。
《金融学》 教案大纲及习题解答(姜法芹 )
《金融学》教案大纲及习题解答第一章：金融学导论1.1 金融学的定义和研究对象1.2 金融市场的基本概念和分类1.3 金融市场的参与者：投资者、金融机构、监管机构1.4 金融学的主要学科领域和应用范围习题解答：1.1 金融学是研究金融市场、金融机构以及金融政策的学科。
它的研究对象包括金融市场的运作机制、金融产品的定价和交易、金融机构的经营管理和监管政策等方面。
1.2 金融市场是指资金供应者和资金需求者通过金融工具进行交易的场所。
金融市场可以分为货币市场、资本市场、金融衍生品市场和外汇市场等。
1.3 金融市场的参与者包括投资者、金融机构和监管机构。
投资者包括个人投资者和机构投资者，金融机构包括银行、证券公司、保险公司等，监管机构负责对金融市场进行监管和调控。
1.4 金融学的主要学科领域包括金融市场、金融机构、金融衍生品、金融政策和金融监管等。
金融学广泛应用于金融行业、企业管理和政府监管等领域。
第二章：金融市场的基本原理2.1 金融市场的供求关系和价格机制2.2 金融市场的效率和稳定性2.3 金融市场的风险和收益2.4 金融市场的信息不对称和信息不对称问题习题解答：2.1 金融市场的供求关系是指资金供应者和资金需求者之间的相互作用。
价格机制是指金融市场的价格由市场供求关系决定，反映了资金的稀缺程度。
2.2 金融市场的效率是指市场能够迅速、准确地反映信息的能力。
金融市场的稳定性是指市场能够保持稳定的运行，不发生大规模的波动。
2.3 金融市场的风险是指投资者在投资过程中可能遭受的损失。
收益是指投资者从投资中获得的回报。
投资者在选择金融产品时需要权衡风险和收益。
2.4 信息不对称是指市场参与者之间信息的不平衡。
信息不对称问题可能导致市场失灵和资源配置效率低下，需要通过监管和制度建设来解决。
第三章：金融市场的主要金融产品3.1 货币市场的金融产品：短期债券、商业票据等3.2 资本市场的主要金融产品：股票、债券、基金等3.3 金融衍生品市场的主要产品：期货、期权、掉期等3.4 其他金融产品：外汇、黄金、大宗商品等习题解答：3.1 货币市场的金融产品是指在货币市场上交易的金融工具。
《金融学（第二版）》讲义大纲及课后习题答案详解十二章
《⾦融学（第⼆版）》讲义⼤纲及课后习题答案详解⼗⼆章CHAPTER 12CHOOSING AN INVESTMENT PORTFOLIOObjectivesTo understand the process of personal investing in theory and in practice.To build a quantitative model of the tradeoff between risk and reward.Outline12.1 The Process of Personal Portfolio Selection12.2 The Trade-off between Expected Return and Risk12.3 Efficient Diversification with Many Risky AssetsSummaryThere is no single portfolio selection strategy that is best for all people.Stage in the life cycle is an imp ortant determinant of the optimal composition of a person’s optimal portfolio of assets and liabilities.Time horizons are important in portfolio selection. We distinguish among three time horizons: the planning horizon, the decision horizon, and the trading horizon.In making portfolio selection decisions, people can in general achieve a higher expected rate of return only by exposing themselves to greater risk.One can sometimes reduce risk without lowering expected return by diversifying more completely either withina given asset class or across asset classes.The power of diversification to reduce the riskiness of an investor’s portfolio depends on the correlations among the assets that make up the portfolio. In practice, the vast majority of assets are positively correlated with each other because they are all affected by common economic factors. Consequently, one’s ability to reduce risk through diversification among risky assets without lowering expected return is limited.Although in principle people have thousands of assets to choose from, in practice they make their choices from a menu of a few final products offered by financial intermediaries such as bank accounts, stock and bond mutual funds, and real estate. In designing and producing the menu of assets to offer to their customers theseintermediaries make use of the latest advances in financial technology.Solutions to Problems at End of Chapter1. Suppose that your 58-year-old father works for the Ruffy Stuffed Toy Company and has contributed regularly to his company-matched savings plan for the past 15 years. Ruffy contributes $0.50 for every $1.00 your father puts into the savings plan, up to the first 6% of his salary. Participants in the savings plan can allocate their contributions among four different investment choices: a fixed-income bond fund, a “blend” option that invests in large companies, small companies, and the fixed-income bond fund, a growth-income mutual fund whose investments do not include other toy companies, and a fund whose sole investment is stock in the Ruffy Stuffed Toy Company. Over Thanksgiving vacation, Dad realizes that you have been majoring in finance and decides to reap some early returns on that tuition money he’s been investing in your education. He shows you the most recent quarterly statement for his savings plan, and you see that 98% of its current value is in the fourth investment option, that of the Ruffy Company stock..a.Assume that your Dad is a typical risk-averse person who is considering retirement in five years. Whenyou ask him why he has made the allocation in this way, he responds that the company stock has continually performed quite well, except for a few declines that were caused by problems in a division that the company has long since sold off. Inaddition, he says, many of his friends at work have done the same. What advice would you give your dad about adjustments to his plan allocations? Why?b.If you consider the fact that your dad works for Ruffy in addition to his 98% allocation to the Ruffy stockfund, does this make his situation more risky, less risky, or does it make no difference? Why? SOLUTION:a.Dad has exposed himself to risk by concentrating almost all of his plan money in the Ruffy Stock fund. This is analogous to taking 100% of the money a family has put aside for investment and investing it in a single stock.First, Dad needs to be shown that just because the company stock has continually performed quite well is no guarantee that it will do so indefinitely. The company may have sold off the divisions which produced price declines in the past, but future problems are unpredictable, and so is the movement of the stock price. “Past performance is no guarantee of future results” is the lesson.Second, Dad needs to hear about diversification. He needs to be counseled that he can reduce his risk by allocating his money among several of the options available to him. Indeed, he can reduce his risk considerably merely by moving all of his money into the “blend” fund because it is diversifi ed by design: it has a fixed-income component, a large companies component, and a small companies component. Diversification isachieved not only via the three differing objectives of these components, but also via the numerous stocks that comprise each of the three components.Finally, Dad’s age and his retirement plans need to be considered. People nearing retirement age typically begin to shift the value of their portfolios into safer investments. “Safer” normally connotes less variability, so that the risk of a large decline in the value of a portfolio is reduced. This decline could come at any time, and it would be very unfortunate if it were to happen the day before Dad retires. In this example, the safest option would be the fixed-income bond fund because of its diversified composition and interest-bearing design, but there is still risk exposure to inflation and the level of interest rates. Note that the tax-deferred nature of the savings plan encourages allocation to something that produces interest or dividends. As it stands now, Dad is very exposed to a large decline in the value of his savings plan because it is dependent on the value of one stock.Individual equities over time have proven to produce the most variable of returns, so Dad should definitely move some, probably at least half, of his money out of the Ruffy stock fund. In fact, a good recommendation given his retirement horizon of five years would be to re-align the portfolio so that it has 50% in the fixed- income fund and the remaining 50% split between the Ruffy stock fund (since Dad insists) and the “blend” fund.Or, maybe 40% fixed-income, 25% Ruffy, 15% growth-income fund, and 20% “blend” fund. This latterallocation has the advantage of introducing another income-producing component that can be shielded by the tax-deferred status of the plan.b.The fact that Dad is employed by the Ruffy Company makes his situation more risky. Let’s say that the companyhits a period of slowed business activities. If the stock price declines, so will th e value of Dad’s savings plan. If the company encounters enough trouble, it may consider layoffs. Dad’s job may be in jeopardy. At the same time that his savings plan may be declining in value, Dad may also need to look for a job or go onunemployment. Thus, Dad is exposed on two fronts to the same risk. He has invested both his human capital and his wealth almost exclusively in one company.2. Refer to Table 12.1.a.Perform the calculations to verify that the expected returns of each of the portfolios (F, G, H, J, S) in thetable (column 4) are correct.b.Do the same for the standard deviations in column 5 of the table.c.Assume that you have $1million to invest. Allocate the money as indicated in the table for each of the fiveportfolios and calculate the expected dollar return of each of the portfolios.d.Which of the portfolios would someone who is extremely risk tolerant be most likely to select? SOLUTION:d.An extremely risk tolerant person would select portfolio S, which has the largest standard deviation but also thelargest expected return.3. A mutual fund company offers a safe money market fund whose current rate is4.50% (.045). The same company also offers an equity fund with an aggressive growth objective which historically has exhibited an expected return of 20% (.20) and a standard deviation of .25.a.Derive the equation for the risk-reward trade-off line.b.How much extra expected return would be available to an investor for each unit of extra risk that shebears?c.What allocation should be placed in the money market fund if an investor desires an expected return of15% (.15)?SOLUTION:a.E[r] = .045 + .62b.0.62c.32.3% [.15 = w*(.045) + (1-w)*(.020) ]4. If the risk-reward trade-off line for a riskless asset and a risky asset results in a negative slope, what does that imply about the risky asset vis-a-vis the riskless asset?SOLUTION:A trade-off line wit h a negative slope indicates that the investor is “rewarded” with less expected return for taking on additional risk via allocation to the risky asset.5. Suppose that you have the opportunity to buy stock in AT&T and Microsoft.a.stocks is 0? .5? 1? -1? What do you notice about the change in the allocations between AT&T andMicrosoft as their correlation moves from -1 to 0? to .5? to +1? Why might this be?b.What is the variance of each of the minimum-variance portfolios in part a?c.What is the optimal combination of these two securities in a portfolio for each value of the correlation,assuming the existence of a money market fund that currently pays 4.5% (.045)? Do you notice any relation between these weights and the weights for the minimum variance portfolios?d.What is the variance of each of the optimal portfolios?e.What is the expected return of each of the optimal portfolios?f.Derive the risk-reward trade-off line for the optimal portfolio when the correlation is .5. How much extraexpected return can you anticipate if you take on an extra unit of risk?SOLUTION:a.Minimum risk portfolios if correlation is:-1: 62.5% AT&T, 37.5% Microsoft0: 73.5% AT&T, 26.5% Microsoft.5: 92.1% AT&T, 7.9% Microsoft1: 250% AT&T, short sell 150% MicrosoftAs the correlation moves from -1 to +1, the allocation to AT&T increases. When two stocks have negativec orrelation, standard deviation can be reduced dramatically by mixing them in a portfolio. It is to the investors’benefit to weight more heavily the stock with the higher expected return since this will produce a high portfolio expected return while the standard deviation of the portfolio is decreased. This is why the highest allocation to Microsoft is observed for a correlation of -1, and the allocation to Microsoft decreases as the correlationbecomes positive and moves to +1. With correlation of +1, the returns of the two stocks will move closely together, so you want to weight most heavily the stock with the lower individual standard deviation.b. Variances of each of the minimum variance portfolios:62.5% AT&T, 37.5% Microsoft Var = 073.5% AT&T, 26.5% Microsoft Var = .016592.1% AT&T, 7.9% Microsoft Var = .0222250% AT&T, short 150% Microsoft Var = 0c. Optimal portfolios if correlation is:-1: 62.5% AT&T, 37.5% Microsoft0: 48.1% AT&T, 51.9% Microsoft.5: 11.4% AT&T, 88.6% Microsoft1: 250% AT&T, short 150% Microsoftd. Variances of the optimal portfolios:62.5% AT&T, 37.5% Microsoft Var = 048.1% AT&T, 51.9% Microsoft Var = .022011.4% AT&T, 88.6% Microsoft Var = .0531250% AT&T, short 150% Microsoft Var = 0e. Expected returns of the optimal portfolios:62.5% AT&T, 37.5% Microsoft E[r] = 14.13%48.1% AT&T, 51.9% Microsoft E[r] = 15.71%11.4% AT&T, 88.6% Microsoft E[r] = 19.75%250% AT&T, short 150% Microsoft E[r] = -6.5%f.Risk-reward trade-off line for optimal portfolio with correlation = .5:E[r] = .045 + .66/doc/31dbf23b580216fc700afd59.html ing the optimal portfolio of AT&T and Microsoft stock when the correlation of their price movements is 0.5, along with the results in part f of question 12-5, determine:a.the expected return and standard deviation of a portfolio which invests 100% in a money market fundreturning a current rate of 4.5%. Where is this point on the risk-reward trade-off line?b.the expected return and standard deviation of a portfolio which invests 90% in the money market fundand 10% in the portfolio of AT&T and Microsoft stock.c.the expected return and standard deviation of a portfolio which invests 25% in the money market fundand 75% in the portfolio of AT&T and Microsoft stock.d.the expected return and standard deviation of a portfolio which invests 0% in the money market fundand 100% in the portfolio of AT&T and Microsoft stock. What point is this?SOLUTION:a.E[r] = 4.5%, standard deviation = 0. This point is the intercept of the y (expected return) axis by the risk-rewardtrade-off line.b.E[r] = 6.03%, standard deviation = .0231c.E[r] = 15.9%, standard deviation = .173d.E[r] = 19.75%, standard deviation = .2306. This point is the tangency between the risk-reward line from 12-5part f and the risky asset risk-reward curve (frontier) for AT&T and Microsoft.7. Again using the optimal portfolio of AT&T and Microsoft stock when the correlation of their price movements is 0.5, take $ 10,000 and determine the allocations among the riskless asset, AT&T stock, and Microsoft stock for:a. a portfolio which invests 75% in a money market fund and 25% in the portfolio of AT&T and Microsoftstock. What is this portfolio’s expected return?b. a portfolio which invests 25% in a money market fund and 75% in the portfolio of AT&T and Microsoftstock. What is this portfolio’s expect ed return?c. a portfolio which invests nothing in a money market fund and 100% in the portfolio of AT&T andMicrosoft stock. What is this portfolio’s expected return?SOLUTION:a.$7,500 in the money-market fund, $285 in AT&T (11.4% of $2500), $2215 in Microsoft. E[r] = 8.31%, $831.b.$2,500 in the money-market fund, $855 in AT&T (11.4% of $7500), $6645 in Microsoft. E[r] = 15.94%, $1,594.c.$1140 in AT&T, $8860 in Microsoft. E[r] = 19.75%, $1,975.8. What strategy is implied by moving further out to the right on a risk-reward trade-off line beyond the tangency point between the line and the risky asset risk-reward curve? What type of an investor would be most likely to embark on this strategy? Why?SOLUTION:This strategy calls for borrowing additional funds and investing them in the optimal portfolio of AT&T and Microsoft stock. A risk-tolerant, aggressive investor would embark on this strategy. This person would be assuming the risk of the stock portfolio with no risk-free component; the money at risk is not onl y from this person’s own wealth but also represents a sum that isowed to some creditor (such as a margin account extended by the investor’s broker).9. Determine the correlation between price movements of stock A and B using the forecasts of their rate of return and the assessments of the possible states of the world in the following table. The standard deviations for stock A and stock B are0.065 and 0.1392, respectively. Before doing the calculation, form an expectation of whether that correlation will be closer to1 or -1 by merely inspecting the numbers.SOLUTION:Expectation: correlation will be closer to +1.E[r A] = .05*(-.02) + .15*(-.01) + .60*(.15) + .20*(.15) = .1175, or, 11.75%E[r B] = .05*(-.20) + .15*(-.10) + .60*(.15) + .20*(.30) = .1250, or, 12.50%Covariance = .05*(-.02-.1175)*(-.20-.125) + .15*(-.01-.1175)*(-.10-.125) +.60*(.15-.1175)*(.15-.125) + .20*(.15-.1175)*(.30-.125) =.008163Correlation = .008163/(.065)*(.1392) = .90210.Analyze the “expert’s” answers to the following questions:a.Question:I have approx. 1/3 of my investments in stocks, and the rest in a money market. What do you suggestas a somewhat “safer” place to invest another 1/3? I like to keep 1/3 accessible for emergencies.Expert’s answer:Well, you could try 1 or 2 year Treasury bonds. You’d get a little bit more yie ld with no risk.b.Question:Where would you invest if you were to start today?Expert’s answer:That depends on your age and short-term goals. If you are very young – say under 40 –and don’tneed the money you’re investing for a home or college tuition or such, you would put it in a stockfund. Even if the market tanks, you have time to recoup. And, so far, nothing has beaten stocks overa period of 10 years or more. But if you are going to need money fairly soon, for a home or for yourretirement, you need to play it safer.SOLUTION:a.You are not getting a little bit more yield with no risk. The real value of the bond payoff is subject to inflationrisk. In addition, if you ever need to sell the Treasury bonds before expiration, you are subject to the fluctuation of selling price caused by interest risk.b.The expert is right in pointing out that your investment decision depends on your age and short-term goals. In addition, the investment decision also depends on other characteristics of the investor, such as the special character of the labor income (whether it is highly correlated with the stock market or not), and risk tolerance.Also, the fact that over any period of 10 years or more the stock beats everything else cannot be used to predict the future.。
《金融学(第二版)》讲义大纲及课后习题答案详解 第七章
《金融学〔第二版〕》讲义大纲及课后习题答案详解第七章CHAPTER 7PRINCIPLES OF ASSET VALUATIONObjectives? Understand why asset valuation is important in finance.? Explain the Law of One Price as the principle underlying all asset-valuation procedures. ? Explain the meaning and role of valuation models.? Explain how information gets reflected in security prices.Outline7.1 The Relation Between an Asset’s Value and Its Price 7.2 Value Maximization and Financial Decisions 7.3 The Law of One Price and Arbitrage7.4 Arbitrage and the Prices of Financial Assets 7.5 Exchange Rates and Triangular Arbitrage 7.6 Interest Rates and the Law of One Price 7.7 Valuation Using Comparables 7.8 Valuation Models7.9 Accounting Measures of Value7.10 How Information Gets Reflected in Security Prices 7.11 The Efficient Markets HypothesisSummary? In finance the measure of an asset’s value is the price it would fetch if it were sold in a competitive market. Theability to accurately value assets is at the heart of the discipline of finance because many personal and corporate financial decisions can be made by selecting the alternative that maximizes value.? The Law of One Price states that in a competitive market, if two assets are equivalent they will tend to have thesame price. The law is enforced by a process called arbitrage, the purchase and immediate sale of equivalent assets in order to earn a sure profit from a difference in their prices.? Even if arbitrage cannot be carried out in practice to enforce the Law of One Price, unknown asset values canstill be inferred from the prices of comparable assets whose prices are known.? The quantitative method used to infer an asset’s value from information about the prices of comparable assets iscalled a valuation model. The best valuation model to employ varies with the information available and the intended use of the estimated value. ? The book value of an asset or a liability as reported in a firm’s financial statements often differs from its currentmarket value.? In making most financial decisions, it is a good idea to start by assuming that for assets that are bought and soldin competitive markets, price is a pretty accurate reflection of fundamental value. This assumption is generally warranted precisely because there are many well-informed professionals looking for mispriced assets who profit by eliminating discrepancies between the market prices and the fundamental values of assets. The proposition that an asset’s current price fully reflects all publicly-available information about future economic fundamentals affecting the asset’s value is known as the Efficient Markets Hypothesis.? The prices of traded assets reflect information about the fundamental economic determinants of their value.Analysts are constantly searching for assets whose prices are different from their fundamental value in order to buy/sell these “bargains.〞 In deciding the best strategy for the purchase/sale of a “bargain,〞 theanalyst has to evaluate the accuracy of her information. The market price of an asset reflects the weighted average of all analysts opinions with heavier weights for analysts who control large amounts of money and for those analysts who have better than average information.Instructor’s ManualChapter 7 Page 106Solutions to Problems at End of ChapterLaw of One Price and Arbitrage1. IBX stock is trading for $35 on the NYSE and $33 on the Tokyo Stock Exchange. Assume that the costs of buying and selling the stock are negligible. a. How could you make an arbitrage profit?b. Over time what would you expect to happen to the stock prices in New York and Tokyo?c. Now assume that the cost of buying or selling shares of IBX is 1% per transaction. How does this affectyour answer?SOLUTION:a. Buy IBX stock in Tokyo and simultaneously sell them in NY. Your arbitrage profit is $2 per share.b. The prices would converge.c. Instead of the prices becoming exactly equal, there can remain a 2% discrepancy between them, roughly $.70 inthis case.2. Suppose you live in the state of Taxachusetts which has a 16% sales tax on liquor. A neighboring state called Taxfree has no tax on liquor. The price of a case of beer is $25 in Taxfree and it is $29 in Taxachusetts.a. Is this a violation of the Law of One Price?b. Are liquor stores in Taxachusetts near the border with Taxfree going to prosper?SOLUTION:a. This is not a violation of the Law of One Price because it is due to a tax imposed in one state but not in the other.Illegal arbitrage will probably occur, with lawbreakers buying large quantities of liquor in Taxfree and selling it in Taxachusetts without paying the tax.b. It is likely that liquor stores will locate in Taxfree near the border with Taxachusetts. Residents of both stateswill buy their liquor in the stores located in Taxfree, and liquor stores in Taxachusetts will go out of business.Triangular Arbitrage3. Suppose the price of gold is 155 marks per ounce.a. If the dollar price of gold is $100 per ounce, what should you expect the dollar price of a mark to be?b. If it actually only costs $0.60 to purchase one mark, how could one make arbitrage profits?SOLUTION:a. $100 buys the same amount of gold (1 ounce) as 155 DM, so 1 DM should cost 100/155 or $.645.b. The marks are “cheaper〞 than they should be, so the arbitrage transaction requires you to buy marks at thecheap price, use them to purchase gold, and sell the gold for dollars. Example:1. Start with $1 million, which you borrow for only enough time to carry out the arbitrage transaction.2. Use the million dollars to buy 1,666,667 marks (1,000,000 / 0.60)3. Buy 10,752.69 ounces of gold (1,666,667 / 155)4. Sell the gold for $1,075,269 (10752.69 x 100)Your risk-free arbitrage profit is $75,269.4. You observe that the dollar price of the Italian lira is $0.0006 and the dollar price of the yen is $0.01. What must be the exchange rate between lira and yen for there to be no arbitrage opportunity?SOLUTION:.0006$/lira?.06Yen/lira.01$/YenInstructor’s ManualChapter 7 Page 1075. Fill in the missing exchange rates in the following table: US dollar British pound German mark Yen US dollar $1 $1.50 $.5 $.01 British pound ￡0.67 German mark DM2.0 Japanese ￥100 Yen SOLUTION: US dollar British pound German mark Japanese Yen US dollar $1 $1.50 $.5 $.01 British pound ￡0.67 1 = .67 / 2 = .67 / 100 German mark DM2.0 = 2 / .67 1 = 2 / 100 Japanese ￥100 = 100 / .67 = 100 / 2 1 Yen US dollar British pound German mark Japanese Yen US dollar $1 $1.50 $.5 $.01 British pound ￡0.67 ￡1 ￡.33 ￡.0067 German mark DM2.0 DM3.0 DM1.0 DM.02 Japanese ￥100 ￥150 ￥50 ￥1 Yen Valuation Using Comparables6. Suppose you own a home that you purchased four years ago for $475,000. The tax assessor’s office has just informed you that they are increasing the taxable value of your home to $525,000. a. How might you gather information to help you appeal the new assessment?b. Suppose the house next door is comparable to yours except that it has one fewer bedroom. It just sold for$490,000. How might you use that information to argue your case? What inference must you make about the value of an additional bedroom?SOLUTION:a. You should retrieve as much information as you can about recent sales of comparable homes. If you canconvince the assessor’s office that your home is comparable (and the market value of the recent sales is less than $525,000) you should have a good case. You can gather the information about home sales from a real estate broker.b. The difference between your house’s assessed value and the actual market value of the home next door is$35,000 ($525,000 - $490,000). If you can convince the tax assessor’s office that the value of a bedroom is less than $35,000, then the assessor must agree that your home is worth less than $525,000. For example, if comparable sales figures show that one additional bedroom (all else reasonably equivalent) is worth only $10,000, then you should be able to argue that your home is worth $500,000 rather than $525,000.7. The P/E ratio of ITT Corporation is currently 6 while the P/E ratio of the S&P 500 is 10. What might account for the difference? SOLUTION: There are several possible reasons:? ITT may be riskier than the S&P500 either because it is in a relatively risky industry or has a relatively higherdebt ratio.? ITT’s reported earnings may be higher than they are expected to be in the future, or they may be inflated due tospecial accounting methods used by ITT.Instructor’s ManualChapter 7 Page 1088. Suppose you are chief financial officer of a private toy company. The chief executive officer has asked you to come up with an estimate for the company’s price per share. Your company’s earnings per share were $2.00 in the year just ended. You know that you should look at public company comparables, however, they seem to fall into two camps. Those with P/E ratios of 8x earnings and those with P/E ratios of 14x earnings. You are perplexed at the difference until you notice that on average, the lower P/E companies have higher leverage than the higher P/E group. The 8x P/E group has a debt/equity ratio of 2:1. The 14x P/E group has a debt/equityratio of 1:1. If your toy company has a debt/equity ratio of 1.5:1, what might you tell the CEO about your company’s equity value per share? SOLUTION:It would be reasonable to apply a P/E of 11x earnings (= (8 + 14) / 2) because your leverage is midway between the two groups. Hence, your company’s price per share would be: 11x $2.00 = $22.00 per share.9. Assume that you have operated your business for 15 years. Sales for the most recent fiscal year were $12,000,000. Net income for the most recent fiscal year was $1,000,000. Your book value is $10,500,000. A similar company recently sold for the following statistics: Multiple of Sales: 0.8x Multiple of Net Income 12x Multiple of Book Value 0.9xa. What is an appropriate range of value for your company?b. If you know that your company has future investment opportunities that are far more profitable than thecompany above, what does that say about your company’s likely valuation? SOLUTION:a. Multiple of Sales: .8x = $12 million x .8 Multiple of Net Income 12x = $1 million x 12 Multiple of Book Value .9x = $10.5 million x .9 An appropriate range might be 9 to 12 millionb. Higher end of the range = $9.6 million = $12 million = $9.45 millionEfficient Markets Hypothesis10. The price of Fuddy Co. stock recently jumped when the sudden unexpected death of its CEO was announced. What might account for such a market reaction?SOLUTION:Investors may believe that the company’s future prospects look better(i.e., either higher earnings or less risky) without the deceased CEO.11. Your analysis leads you to believe that the price of Outel’s stock should be $25 per share. Its current market price is $30.a. If you do not believe that you have access to special information about the company, what do you do?b. If you are an analyst with much better than average information, what do you do?SOLUTION:a. If you believe that the market for Outel stock is an informationally efficient one then the $30 market price(which is a weighted average of the valuations of all analysts) is the best estimate of the stock’s true value. You should question whether your own analysis is correct.b. You sell the stock because you think you have superior information. Real Interest Rate Parity12. Assume that the world-wide risk-free real rate of interest is 3% per year. Inflation in Switzerland is 2% per year and in the United States it is 5% per year. Assuming there is no uncertainty about inflation, what are the implied nominal interest rates denominated in Swiss francs and in US dollars?SOLUTION: Switzerland: (1.03 x 1.02) =1.0506 hence nominal interest rate = 5.06% US: (1.03 x 1.05) = 1 .0815 hence nominal interest rate = 8.15%Instructor’s ManualChapter 7 Page 109Integrative Problem13. Suppose an aunt has passed away and bequeathed to you and your siblings (one brother, one sister) a variety of assets. The original cost of these assets follows:ITEM COST WHEN PURCHASEDJewelry $500 by Grandmother 75 years ago House 1,200,000 10 years ago Stocks and Bonds 1,000,000 3 years ago Vintage (used) Car 200,000 2 months ago Furniture 15,000 various dates during last 40 yearsBecause you are taking a course in finance, your siblings put you in charge of dividing the assets fairly among the three of you. Before you start, your brother approaches you and says: “I’d really like the car for myself, so when you divide up the assets, just give me the car and deduct the $200,000 from my share.〞Hearing that, your sister says: “That sounds fair, because I really like the jewelry and you can assign that to me and deduct the $500 from my share.〞You have always loved your aunt’s house and its furnishings, so you would like to keep the house and the furniture.a. How do you respond to your brother and sister’s requests? Justify your responses.b. How would you go about determining appropriate values for each asset?SOLUTION:a. Because the market price of the car is close to the what your brother is willing to give up for it, your brother’srequest is reasonable. It is, however, quite possible (even likely), that the antique jewelry is worth much more today than what your relative’s grandmother paid for it in the past. Assigning only its acquisition cost to your sister’s share is quite likely a gross miscalculation. If she wants the jewelry, she should be “charged〞 an amount equal to today’s market value. It does not matter that your sister does not want to sell the jewelry for a profit, because the jewelry has VALUE even if you do not sell it. Fairness is all about equal VALUE.b. You would probably have to hire a professional appraiser for the furniture and the jewelry. You can look up thevalue of the stocks and bonds in a financial newspaper. You can estimate the value of the house by inquiring for how much similar houses in the same neighborhood have recently been sold. The car was purchased only twomonths ago, so it is probably reasonable to assume that the current market price is very close to what your distant relative paid for the car. Instructor’s ManualChapter 7 Page 110。
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第一题：你现在有10000元资金准备存在银行5年，有三种存款方式可选择：存1 年期存款，每年到期后连本带利转存4次；存3年期存款，到期后连本带利转存1年期存款2次；存5年期存款1期。
1 年期、3年期、5 年期存款的年利率分别为2%、2.2%、3%。
请问三种方式5年后的终值各为多少？哪种方式最优？
第二题：你现在每个月存款1000元，年利率为3%，5年后你有多少钱？这5年存款的现值为多少钱？
第三题：你现在有10万美元可进行投资，美元存款年利率为3%，日元存款年利率为1%，预测未来两年日元将升值5%，哪种投资方案较优？
第四题：欧元对美元汇率，2005年12月底为1：1.1，预计2006年12月底将变为1：1.2。
（1）某欧洲企业预计2006年底有100亿美元的外汇收入。
为了控制美元汇率下跌可能带来的汇兑损失，该企业在2006年初以1：1.12的汇率出售100亿美元的1 年期远期美元外汇。
如果2006年底欧元对美元汇率实际为1：1.25，则该企业可以减少汇兑损失多少欧元？如果2006年底欧元对美元汇率实际为1：1.05呢？
（2）D企业并无外汇收入，而在2006年初购买100亿美元的1年期美元期货，价格为1：1.12，保证金比率为5%。
如果2006年底欧元对美元汇率实际为1：1.25，该企业的盈利如何？如果2006年底欧元对美元汇率实际为1：1.05呢？
第五题：C银行购买了200亿元的5年期国债，票面利率为3%，价格为面值100元。
其面临利率上升价格下跌的风险。
为了防范利率上升的风险，C银行购买了200亿元的国债看跌期权。
期权价格为1元，敲定价格为100元。
（1）如果市场利率上升，该债券的价格下跌到98元，C银行将会怎样操作？其盈利怎样？
（2）如果市场利率下降，该债券的价格上涨到105元，C银行将会怎样操作？其盈利怎样？
第六题：恒星公司发行的3年期债券票面利率为6%，到期后一次性还本付息。
请问在发行时购买一万元该债券，3年到期后可获得多少利息？其到期收益率为多少？在发行1年后银行1年期存款利率下调为3%，请问此时恒星公司的债券价值为多少？
第七题：假定你购买了一套住房，从银行得到了20万元的抵押贷款，偿还期为20年，贷款的年利率为8.4%，那么，你的月供是多少？
第八题：假设在东京、纽约的伦敦外汇市场上有如下的外汇行情：
东京市场：1美元=120.0000日元；
纽约市场：1美元=0.7500英镑；
伦敦市场：1英镑=160.0000日元。
在这三个市场上，是否存在套汇机会？
如存在套汇机会，假设你有100万英镑，如何套汇，可获利多少？
第九题：如果你购买了三只股票，总投资10万元。
这三只股票分别是A、B、C。
持仓双重为A股票20%、B股票30%、C股票50%。
即，你在三只股票上的投资分别为2万、3万和5万元。
如果A、B、C的期望收益分别为10%、30%和60%，那么，你这个投资组合的期望收益率是多少？
第十题：假设:即期美元/日元汇率为123.50，美元三个月同业拆息率为4.3125%,日元三个月同业拆息率为5.25%,请计算美元兑日元三个月远期的汇率。
第十一题：假设某银行向其客户发放了一笔金额为100万元、期限为4年、年利率为6%的贷款，请用单利和复利两种方法计算该银行发放这笔贷款可以获得的利息额。
第十二题：（1）USD1＝CNY7.0910-20 GBP1＝USD2.0140-50 GBP1＝CNY？（2）USD1=DKr5.3420/5 .3430 USD1＝SFr1.0270/1 .0280 SFr1＝DKr？
第十三题：某日，银行报出的美元和欧元的报价为：
USD1＝EUR0.6317-27
一个月掉期率为35/20
三个月掉期率为30/45
美元和欧元的一月期和三月期远期汇率分别是多少？
第十四题：假设有两只股票A和B。
投资于投票A，以60%的概率获得15%的收益，以40%的概率获得5%的收益；投资于股票B，以50%的概率获得10%的收益，以50%的概率获得8%的收益。
如果你在这两只股票上的投资金额相同，这一投资组合的期望收益率是多少？如果你只想投资于其中的一只股票，A和B的期望收益率各是多少？哪个风险更大？
第十五题：已知法定准备金率为10%，提现率为10%，超额准备金率为5%，试计算存款扩张倍数。