wk10Chap010_market risk

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投资学第10版习题答案08CHAPTER 8: INDEX MODELSPROBLEM SETS1. The advantage of the index model, compared to the Markowitzprocedure, is the vastly reduced number of estimates required. In addition, the large number of estimates required for the Markowitz procedure can result in large aggregate estimation errors whenimplementing the procedure. The disadvantage of the index modelarises from the model’s assumption that return residuals areuncorrelated. This assumption will be incorrect if the index used omits a significant risk factor.2. The trade-off entailed in departing from pure indexing in favor ofan actively managed portfolio is between the probability (or thepossibility) of superior performance against the certainty of additional management fees.3. The answer to this question can be seen from the formulas for w0(equation 8.20) and w* (equation 8.21). Other things held equal, w0 is smaller the greater the residual variance of a candidate asset for inclusion in the portfolio. Further, we see that regardless of beta, when w0 decreases, so does w*. Therefore, other things equal, the greater the residual variance of an asset, the smaller itsposition in the optimal risky portfolio. That is, increased firm- specific risk reduces the extent to which an active investor will be willing to depart from an indexed portfolio.4. The total risk premium equals: + (× Market risk premium). Wecall alpha a nonmarket return premium because it is the portion of the return premium that is independent of market performance.The Sharpe ratio indicates that a higher alpha makes a securitymore desirable. Alpha, the numerator of the Sharpe ratio, is afixed number that is not affected by the standard deviation ofreturns, the denominator of the Sharpe ratio. Hence, an increase in alpha increases the Sharpe ratio. Since the portfolio alpha is the portfolio-weighted average of the securities’ alphas, then,holding all other parameters fixed, an increase in a security’s alpha results in an increase in the portfolio Sharpe ratio.5. a. To optimize this portfolio one would need:n = 60 estimates of means n = 60 estimates of variances 770,122=-n n estimates of covariances Therefore, in total: 890,1232=+n n estimatesb.In a single index model: r i r f = α i + β i (r M – r f ) + e iEquivalently, using excess returns: R i = α i + β i R M + e i The variance of the rate of return can be decomposed into the components: (l) The variance due to the common market factor:22M i σβ (2) The variance due to firm specific unanticipated events: )(σ2i e In this model: σββ),(Cov j i j i r r = The number of parameter estimates is: n = 60 estimates of the mean E (r i ) n = 60 estimates of the sensitivity coefficient β i n = 60 estimates of the firm-specific variance σ2(e i ) 1 estimate of the market mean E (r M ) 1 estimate of the market variance 2M σ Therefore, in total, 182 estimates. The single index model reduces the total number of required estimates from 1,890 to 182. In general, the number of parameter estimates is reduced from: )23( to 232+???? ??+n n n 6. a. The standard deviation of each individual stock is given by: 2/1222)](β[σi M i i e σσ+=Since βA = 0.8, βB = 1.2, σ(e A) = 30%, σ(e B) = 40%, and σM = 22%, we get:σA = (0.82× 222 + 302 )1/2 = 34.78%σB = (1.22× 222 + 402 )1/2 = 47.93%b. The expected rate of return on a portfolio is the weighted average of the expected returns of the individual securities: E(r P ) = w A × E(r A ) + w B × E(r B ) + w f × r f E(r P )= (0.30 × 13%) + (0.45 × 18%) + (0.25 × 8%) = 14% The beta of a portfolio is similarly a weighted average of the betas of the individual securities: βP = w A × βA + w B × βB + w f × β f βP = (0.30 × 0.8) + (0.45 × 1.2) + (0.25 × 0.0) = 0.78 The variance o f this portfolio is: )(σβσ2222P M P P e +=σ where 22σβM P is the systematic component and )(2P e σis the nonsystematic component. Since the residuals (e i ) are uncorrelated, the nonsystematic variance is: 2222222()()()()P A A B B f f e w e w e w e σσσσ=?+?+? = (0.302 × 302 ) + (0.452 × 402 ) + (0.252 × 0) = 405 where σ2(e A ) and σ2(e B ) are the firm-specific (nonsystematic) variances of StocksA and B, and σ2(e f ), the nonsystematic variance of T-bills, is zero. The residual standard deviation of the po rtfolio is thus: σ(e P ) = (405)1/2 = 20.12% The total variance of the portfolio is then: 47.699405)2278.0(σ222=+?=P The total standard deviation is 26.45%.7. a.The two figures depict the stocks’ security characteri stic lines (SCL). Stock A has higher firm-specific risk because the deviations of the observations from the SCL are larger for Stock A than for Stock B. Deviations are measured by the vertical distance of each observation from the SCL.b. Beta is the slope of the SCL, which is the measure ofsystematic risk. The SCL for Stock B is steeper; hence Stock B’s systematic risk is greater.c. The R 2(or squared correlation coefficient) of the SCL is the ratio of the explained variance of the stock’s return to total variance, and the total variance is the sum of the explained variance plus the unexplained variance (the stock’s residual variance): )(σσβσβ222222i M i M i e R += Since the explained variance for Stock B is greater than for Stock A (the explained variance is 22σβM B , which is greater since its beta is higher), and its residual variance 2()B e σ is smaller, its R 2 is higher than Stock A’s.d.Alpha is the intercept of the SCL with the expected return axis. Stock A has a small positive alpha whereas Stock B has a negative alpha; hence, Stock A’s alpha is larger.e.The correlation coefficient is simply the square root of R 2,so Stock B’s correlation with the market is higher.8. a.Firm-specific risk is measured by the residual standard deviation. Thus, stock A has more firm-specific risk: 10.3% > 9.1%b.Market risk is measured by beta, the slope coefficient of the regression. A has a larger beta coefficient: 1.2 > 0.8c.R 2 measures the fraction of total variance of return explained by the market return. A’s R 2 is larger than B’s: 0.576 >0.436d.Rewriting the SCL equation in terms of total return (r ) rather than excess return (R ): ()(1)A f M f A f M r r r r r r r αβαββ-=+?-?=+?-+? The intercept is now equal to: (1)1%(1 1.2)f f r r αβ+?-=+?- Since r f = 6%, the intercept would be: 1%6%(1 1.2)1% 1.2%0.2%+-=-=-。

（完整版）投资学第10版习题答案05CHAPTER 5: RISK, RETURN, AND THE HISTORICALRECORDPROBLEM SETS1. The Fisher equation predicts that the nominal rate will equal the equilibriumreal rate plus the expected inflation rate. Hence, if the inflation rate increasesfrom 3% to 5% while there is no change in the real rate, then the nominal ratewill increase by 2%. On the other hand, it is possible that an increase in theexpected inflation rate would be accompanied by a change in the real rate ofinterest. While it is conceivable that the nominal interest rate could remainconstant as the inflation rate increased, implying that the real rate decreasedas inflation increased, this is not a likely scenario.2. If we assume that the distribution of returns remains reasonably stable overthe entire history, then a longer sample period (i.e., a larger sample) increasesthe precision of the estimate of the expected rate of return; this is aconsequence of the fact that the standard error decreases as the sample sizeincreases. However, if we assume that the mean of the distribution of returnsis changing over time but we are not in a position to determine the nature ofthis change, then the expected return must be estimated from a more recentpart of the historical period. In this scenario, we must determine how far back,historically, to go in selecting the relevant sample. Here, it is likely to bedisadvantageous to use the entire data set back to 1880.3. The true statements are (c) and (e). The explanations follow.Statement (c): Let σ = the annual standard deviation of the risky investmentsand 1σ= the standard deviation of the first investment alternative over the two-year period. Then:σσ?=21Therefore, the annualized standard deviation for the first investment alternative is equal to:σσσ<=221Statement (e): The first investment alternative is more attractive to investors with lower degrees of risk aversion. The first alternative (entailing a sequence of two identically distributed and uncorrelated risky investments) is riskierthan the second alternative (the risky investment followed by a risk-freeinvestment). Therefore, the first alternative is more attractive to investors with lower degrees of risk aversion. Notice, however, that if you mistakenlybelieved that time diversification can reduce the total risk of a sequence ofrisky investments, you would have been tempted to conclude that the firstalternative is less risky and therefore more attractive to more risk-averseinvestors. This is clearly not the case; the two-year standard deviation of thefirst alternative is greater than the two-year standard deviation of the secondalternative.4. For the money market fund, your holding-period return for the next yeardepends on the level of 30-day interest rates each month when the fund rolls over maturing securities. The one-year savings deposit offers a 7.5% holding period return for the year. If you forecast that the rate on money marketinstruments will increase significantly above the current 6% yield, then themoney market fund might result in a higher HPR than the savings deposit.The 20-year Treasury bond offers a yield to maturity of 9% per year, which is 150 basis points higher than the rate on the one-year savings deposit; however, you could earn a one-year HPR much less than 7.5% on the bond if long-term interest rates increase during the year. If Treasury bond yields rise above 9%, then the price of the bond will fall, and the resulting capital loss will wipe out some or all of the 9% return you would have earned if bond yields hadremained unchanged over the course of the year.5. a. If businesses reduce their capital spending, then they are likely todecrease their demand for funds. This will shift the demand curve inFigure 5.1 to the left and reduce the equilibrium real rate of interest.b. Increased household saving will shift the supply of funds curve to theright and cause real interest rates to fall.c. Open market purchases of U.S. Treasury securities by the FederalReserve Board are equivalent to an increase in the supply of funds (ashift of the supply curve to the right). The FED buys treasuries withcash from its own account or it issues certificates which trade likecash. As a result, there is an increase in the money supply, and theequilibrium real rate of interest will fall.6. a. The “Inflation-Plus” CD is the safer investment because it guarantees thepurchasing power of the investment. Using the approximation that the realrate equals the nominal rate minus the inflation rate, the CD provides a realrate of 1.5% regardless of the inflation rate.b. The expected return depends on the expected rate of inflation over the nextyear. If the expected rate of inflation is less than 3.5% then the conventionalCD offers a higher real return than the inflation-plus CD; if the expected rateof inflation is greater than 3.5%, then the opposite is true.c. If you expect the rate of inflation to be 3% over the next year, then theconventional CD offers you an expected real rate of return of 2%, which is0.5% higher than the real rate on the inflation-protected CD. But unless youknow that inflation will be 3% with certainty, the conventional CD is alsoriskier. The question of which is the better investment then depends on yourattitude towards risk versus return. You might choose to diversify and investpart of your funds in each.d. No. We cannot assume that the entire difference between the risk-freenominal rate (on conventional CDs) of 5% and the real risk-free rate (oninflation-protected CDs) of 1.5% is the expected rate of inflation. Part of thedifference is probably a risk premium associated with the uncertaintysurrounding the real rate of return on the conventional CDs. This impliesthat the expected rate of inflation is less than 3.5% per year.7. E(r) = [0.35 × 44.5%] + [0.30 × 14.0%] + [0.35 × (–16.5%)] = 14%σ2 = [0.35 × (44.5 – 14)2] + [0.30 × (14 – 14)2] + [0.35 × (–16.5 – 14)2] = 651.175 σ = 25.52%The mean is unchanged, but the standard deviation has increased, as theprobabilities of the high and low returns have increased.8. Probability distribution of price and one-year holding period return for a 30-year U.S. Treasury bond (which will have 29 years to maturity at year-end):Economy Probability YTM Price CapitalGainCouponInterest HPRBoom 0.20 11.0% $ 74.05 -$25.95 $8.00 -17.95% Normal growth 0.50 8.0 100.00 0.00 8.00 8.00 Recession 0.30 7.0 112.28 12.28 8.00 20.289. E(q) = (0 × 0.25) + (1 × 0.25) + (2 × 0.50) = 1.25σq = [0.25 × (0 – 1.25)2 + 0.25 × (1 – 1.25)2 + 0.50 × (2 – 1.25)2]1/2 = 0.8292 10. (a) With probability 0.9544, the value of a normally distributedvariable will fall within 2 standard deviations of the mean; that is,between –40% and 80%. Simply add and subtract 2 standarddeviations to and from the mean.11. From Table 5.4, the average risk premium for the period 7/1926-9/2012 was:12.34% per year.Adding 12.34% to the 3% risk-free interest rate, the expected annual HPR for the Big/Value portfolio is: 3.00% + 12.34% = 15.34%.No. The distributions from (01/1928–06/1970) and (07/1970–12/2012) periods have distinct characteristics due to systematic shocks to the economy and subsequent government intervention. While the returns from the two periods do not differ greatly, their respective distributions tell a different story. The standard deviation for all six portfolios is larger in the first period. Skew is also positive, but negative in the second, showing a greater likelihood of higher-than-normal returns in the right tail.Kurtosis is also markedly larger in the first period.13. a%88.5,0588.070.170.080.01111or i i rn i rn rr =-=+-=-++=b. rr ≈ rn - i = 80% - 70% = 10%Clearly, the approximation gives a real HPR that is too high.14. From Table 5.2, the average real rate on T-bills has been 0.52%.a. T-bills: 0.52% real rate + 3% inflation = 3.52%b. Expected return on Big/Value:3.52% T-bill rate + 12.34% historical risk premium = 15.86%c. The risk premium on stocks remains unchanged. A premium, thedifference between two rates, is a real value, unaffected by inflation.15. Real interest rates are expected to rise. The investment activity will shiftthe demand for funds curve (in Figure 5.1) to the right. Therefore theequilibrium real interest rate will increase.16. a. Probability distribution of the HPR on the stock market and put:STOCK PUT State of theEconomyProbability Ending Price + Dividend HPR Ending Value HPR Excellent0.25 $ 131.00 31.00% $ 0.00 -100% Good0.45 114.00 14.00 $ 0.00 -100 Poor0.25 93.25 ?6.75 $ 20.25 68.75 Crash 0.05 48.00 -52.00 $ 64.00 433.33Remember that the cost of the index fund is $100 per share, and the costof the put option is $12.b. The cost of one share of the index fund plus a put option is $112. Theprobability distribution of the HPR on the portfolio is:State of the Economy Probability Ending Price + Put + DividendHPRExcellent 0.25 $ 131.00 17.0%= (131 - 112)/112 Good 0.45 114.00 1.8= (114 - 112)/112 Poor 0.25 113.50 1.3= (113.50 - 112)/112 Crash0.05 112.00 0.0 = (112 - 112)/112 c. Buying the put option guarantees the investor a minimum HPR of 0.0% regardless of what happens to the stock's price. Thus, it offers insuranceagainst a price decline.17. The probability distribution of the dollar return on CD plus call option is:State of theEconomy Probability Ending Valueof CDEnding Valueof CallCombinedValueExcellent 0.25 $ 114.00 $16.50 $130.50Good 0.45 114.00 0.00 114.00Poor 0.25 114.00 0.00 114.00Crash 0.05 114.00 0.00 114.0018.a.Total return of the bond is (100/84.49)-1 = 0.1836. With t = 10, the annualrate on the real bond is (1 + EAR) = = 1.69%.b.With a per quarter yield of 2%, the annual yield is = 1.0824, or8.24%. The equivalent continuously compounding (cc) rate is ln(1+.0824)= .0792, or 7.92%. The risk-free rate is 3.55% with a cc rate of ln(1+.0355)= .0349, or 3.49%. The cc risk premium will equal .0792 - .0349 = .0443, or4.433%.c.The appropriate formula is ,where . Using solver or goal seek, setting thetarget cell to the known effective cc rate by changing the unknown variance(cc) rate, the equivalent standard deviation (cc) is 18.03% (excel mayyield slightly different solutions).d.The expected value of the excess return will grow by 120 months (12months over a 10-year horizon). Therefore the excess return will be 120 ×4.433% = 531.9%. The expected SD grows by the square root of timeresulting in 18.03% × = 197.5%. The resulting Sharpe ratio is531.9/197.5 = 2.6929. Normsdist (-2.6929) = .0035, or a .35% probabilityof shortfall over a 10-year horizon.CFA PROBLEMS1. The expected dollar return on the investment in equities is $18,000 (0.6 × $50,000 + 0.4×?$30,000) compared to the $5,000 expected return for T-bills. Therefore, the expected risk premium is $13,000.2. E(r) = [0.2 × (?25%)] + [0.3 × 10%] + [0.5 × 24%] =10%3. E(r X) = [0.2 × (?20%)] + [0.5 × 18%] + [0.3 × 50%] =20%E(r Y) = [0.2 × (?15%)] + [0.5 × 20%] + [0.3 × 10%] =10%4. σX2 = [0.2 × (– 20 – 20)2] + [0.5 × (18 – 20)2] + [0.3 × (50 – 20)2] = 592σX = 24.33%σY2 = [0.2 × (– 15 – 10)2] + [0.5 × (20 – 10)2] + [0.3 × (10 – 10)2] = 175σY = 13.23%5. E(r) = (0.9 × 20%) + (0.1 × 10%) =19% $1,900 in returns6. The probability that the economy will be neutral is 0.50, or 50%. Given aneutral economy, the stock will experience poor performance 30% of thetime. The probability of both poor stock performance and a neutral economy is therefore: 0.30 × 0.50 = 0.15 = 15%7. E(r) = (0.1 × 15%) + (0.6 × 13%) + (0.3 × 7%) = 11.4%。

的计算：主要用于期权市场保值与投机 办法的比较。如将来的即期汇率降至$1.4000/ ￡ 以下，公司就行使卖权，以期权交易价 140 卖出 英镑，净收入为 $1.3730/ ￡（ $1.4000/ ￡ － $0.0270/ ￡）。因此， $1.3730/ ￡为低临界点。 如将来即期汇率降至$1.3730/ ￡以下，行使期权 的净收入大于投机；反之，如将来即期汇率高于 $1.3730/ ￡，投资办法的收入比期权市场保值高。
6.交叉套期保值(Cross hedge)
• 当公司收取的外汇不在外汇交易所交易货币品种 之列，则公司可以利用某一在交易所交易并与公 司的外汇高度相关的外汇对公司的交易风险进行 套期保值，这就是交叉套期保值。 • 例如，假设（1）一家美国公司有一笔三个月期的 港币应收款；（2）港币预期将对美元贬值；（3） 远期合约或其他的套期保值工具中没有港币的交 易；（4）英镑对美元的波动与港币对美元的波动 高度相关。此时，美国公司可以利用英镑作为港 币的代理货币有效的对交易风险进行套期保值。
4.期权市场套期保值
1）计算期权交易成本；
每个期权的交易费用（0.025 × ￡12500) 每个期权的经纪费用 每个期权的总成本 每镑期权成本（$337.50/ ￡12500) 所需购买的期权数(￡375000/ ￡12500) 总成本(30 × $337.50) $312.50 25.00 $337.50 $0.0270 30 $10125
第十章 外汇风险管理
第二节 交易风险管理
管理办法：
• • • • • 投机（不从事套期保值）； 利用远期外汇市场进行套期保值； 利用货币市场进行套期保值； 利用期权市场进行套期保值； 互换协议套期保值
• 例：假定1月份一家美国公司向一家英国客户出口 一批产品。产品的交易金额为￡375000，信用期 为三个月（公司可望在4月份收到货款）。外汇市 场和货币市场的相关资料如下： • 即期汇率： $1.4000/ ￡； • 3个月远期汇率： $1.4175/ ￡； • 美国3个月期国库券利率： 9.05%； • 英国3个月期国库券利率： 4%； • 4月份到期的英镑期权交易价为 140，每个期权 的经纪费用为25美元，期权交易费为每镑2.5美分。 每一英镑期权的标准合同数为￡12500。

赫尔期权、期货及其他衍生产品第10版框架知识点及课后习题解析背景介绍赫尔期权、期货及其他衍生产品是一本经典的金融学教材，已经出版了多个版本。

本文将对第10版的框架知识点进行详细介绍，并对课后习题进行解析。

框架知识点第1章期权与期权市场本章主要介绍了期权的基本概念和期权市场的基本特点。

其中包括期权的定义、期权的基本特征、期权的交易方式、期权市场的参与者和期权市场的发展趋势等内容。

第2章期权定价基础本章介绍了期权定价的基本理论。

其中包括无套利定价原理、布莱克-舒尔斯期权定价模型、期权的几何布朗运动模型和完全市场假设等内容。

此外，还介绍了期权定价模型的应用和限制。

第3章期权策略与风险管理本章介绍了期权策略的基本概念和常见的期权策略类型。

其中包括购买期权、卖出期权、期权组合策略和套利策略等内容。

此外，还介绍了期权风险管理的基本方法和相关的风险指标。

第4章期货市场与期货定价本章介绍了期货市场的基本原理和期货合约的定价方法。

其中包括期货市场的特点、期货合约的基本要素、期货定价的原理和期货定价模型等内容。

此外，还介绍了期货市场的参与者和期货交易的风险管理。

第5章期货交易策略与风险管理本章介绍了期货交易策略的基本原理和常用的期货交易策略类型。

其中包括多头策略、空头策略、套利策略和市场中性策略等内容。

此外，还介绍了期货交易的风险管理方法和基本的交易技巧。

第6章期货市场的运行与监管本章介绍了期货市场的运行机制和监管体系。

其中包括期货市场的交易流程、交易所的角色和功能、期货市场的风险管理和期货市场的监管机构等内容。

此外，还介绍了期货市场的监管规则和期货市场的发展趋势。

课后习题解析第1章期权与期权市场习题1：期权是一种金融衍生品，它的特点是什么？答：期权有两个基本特点，即灵活性和杠杆效应。

灵活性指的是期权可以灵活选择行权，可以在未来的某个时间点以特定的价格购买或者卖出标的资产。

杠杆效应指的是期权的价格相对于标的资产的价格波动比较大，可以获得倍数的投资回报。

CHAPTER 7: OPTIMAL RISKY PORTFOLIOSPROBLEM SETS1.(a) and (e). Short-term rates and labor issues are factors that are common to all firms and therefore must be considered as market risk factors. The remaining three factors are unique to this corporation and are not a part of market risk.2.(a) and (c). After real estate is added to the portfolio, there are four asset classes in the portfolio: stocks, bonds, cash, and real estate. Portfolio variance now includes a variance term for real estate returns and a covariance term for real estate returns with returns for each of the other three asset classes. Therefore, portfolio risk is affected by the variance (or standard deviation) of real estate returns and thecorrelation between real estate returns and returns for each of the other asset classes. (Note that the correlation between real estate returns and returns for cash is most likely zero.)3.(a) Answer (a) is valid because it provides the definition of the minimum variance portfolio.4.The parameters of the opportunity set are:E (r S ) = 20%, E (r B ) = 12%, σS = 30%, σB = 15%, ρ = 0.10From the standard deviations and the correlation coefficient we generate the covariance matrix [note that ]:(,)S B S B Cov r r ρσσ=⨯⨯Bonds StocksBonds 22545Stocks45900The minimum-variance portfolio is computed as follows:w Min (S ) =1739.0)452(22590045225)(Cov 2)(Cov 222=⨯-+-=-+-B S B S B S B ,r r ,r r σσσw Min (B ) = 1 - 0.1739 = 0.8261The minimum variance portfolio mean and standard deviation are:E (r Min ) = (0.1739 × .20) + (0.8261 × .12) = .1339 = 13.39%σMin = 2/12222)],(Cov 2[B S B S B B S S r r w w w w ++σσ= [(0.17392 ⨯ 900) + (0.82612 ⨯ 225) + (2 ⨯ 0.1739 ⨯ 0.8261 ⨯ 45)]1/2= 13.92%5.Proportion in Stock Fund Proportion in Bond FundExpectedReturn Standard Deviation 0.00%100.00%12.00%15.00%17.3982.6113.3913.92minimum variance 20.0080.0013.6013.9440.0060.0015.2015.7045.1654.8415.6116.54tangency portfolio60.0040.0016.8019.5380.0020.0018.4024.48100.000.0020.0030.00Graph shown below.6.The above graph indicates that the optimal portfolio is the tangency portfolio with expected return approximately 15.6% and standard deviation approximately 16.5%.7.The proportion of the optimal risky portfolio invested in the stock fund is given by:222[()][()](,)[()][()][()()](,)S f B B f S B S S f B B f S S f B f S B E r r E r r Cov r r w E r r E r r E r r E r r Cov r r σσσ-⨯--⨯=-⨯+-⨯--+-⨯ [(.20.08)225][(.12.08)45]0.4516[(.20.08)225][(.12.08)900][(.20.08.12.08)45]-⨯--⨯==-⨯+-⨯--+-⨯10.45160.5484B w =-=The mean and standard deviation of the optimal risky portfolio are:E (r P ) = (0.4516 × .20) + (0.5484 × .12) = .1561 = 15.61% σp = [(0.45162 ⨯ 900) + (0.54842 ⨯ 225) + (2 ⨯ 0.4516 ⨯ 0.5484 × 45)]1/2= 16.54%8.The reward-to-volatility ratio of the optimal CAL is:().1561.080.4601.1654p fpE r r σ--==9.a.If you require that your portfolio yield an expected return of 14%, then you can find the corresponding standard deviation from the optimal CAL. The equation for this CAL is:()().080.4601p fC f C CPE r r E r r σσσ-=+=+If E (r C ) is equal to 14%, then the standard deviation of the portfolio is 13.04%.b.To find the proportion invested in the T-bill fund, remember that the mean of the complete portfolio (i.e., 14%) is an average of the T-bill rate and theoptimal combination of stocks and bonds (P ). Let y be the proportion invested in the portfolio P . The mean of any portfolio along the optimal CAL is:()(1)()[()].08(.1561.08)C f P f P f E r y r y E r r y E r r y =-⨯+⨯=+⨯-=+⨯-Setting E (r C ) = 14% we find: y = 0.7884 and (1 − y ) = 0.2119 (the proportion invested in the T-bill fund).To find the proportions invested in each of the funds, multiply 0.7884 times the respective proportions of stocks and bonds in the optimal risky portfolio:Proportion of stocks in complete portfolio = 0.7884 ⨯ 0.4516 = 0.3560Proportion of bonds in complete portfolio = 0.7884 ⨯ 0.5484 = 0.4323ing only the stock and bond funds to achieve a portfolio expected return of 14%, we must find the appropriate proportion in the stock fund (w S ) and the appropriate proportion in the bond fund (w B = 1 − w S ) as follows:0.14 = 0.20 × w S + 0.12 × (1 − w S ) = 0.12 + 0.08 × w S ⇒ w S = 0.25So the proportions are 25% invested in the stock fund and 75% in the bond fund. The standard deviation of this portfolio will be:σP = [(0.252 ⨯ 900) + (0.752 ⨯ 225) + (2 ⨯ 0.25 ⨯ 0.75 ⨯ 45)]1/2 = 14.13%This is considerably greater than the standard deviation of 13.04% achieved using T-bills and the optimal portfolio.11.a.Standard Deviation(%)0.005.0010.0015.0020.0025.00010203040Even though it seems that gold is dominated by stocks, gold might still be an attractive asset to hold as a part of a portfolio. If the correlation between gold and stocks is sufficiently low, gold will be held as a component in a portfolio, specifically, the optimal tangency portfolio.b.If the correlation between gold and stocks equals +1, then no one would holdgold. The optimal CAL would be composed of bills and stocks only. Since theset of risk/return combinations of stocks and gold would plot as a straight linewith a negative slope (see the following graph), these combinations would bedominated by the stock portfolio. Of course, this situation could not persist. If noone desired gold, its price would fall and its expected rate of return wouldincrease until it became sufficiently attractive to include in a portfolio.ll12.Since Stock A and Stock B are perfectly negatively correlated, a risk-free portfoliocan be created and the rate of return for this portfolio, in equilibrium, will be therisk-free rate. To find the proportions of this portfolio [with the proportion w Ainvested in Stock A and w B = (1 – w A) invested in Stock B], set the standarddeviation equal to zero. With perfect negative correlation, the portfolio standarddeviation is:σP = Absolute value [w AσA-w BσB]0 = 5 × w A− [10 ⨯ (1 – w A)] ⇒w A = 0.6667The expected rate of return for this risk-free portfolio is:E(r) = (0.6667 × 10) + (0.3333 × 15) = 11.667%Therefore, the risk-free rate is: 11.667%13.False. If the borrowing and lending rates are not identical, then, depending on the tastes of the individuals (that is, the shape of their indifference curves), borrowers and lenders could have different optimal risky portfolios.14.False. The portfolio standard deviation equals the weighted average of the component-asset standard deviations only in the special case that all assets are perfectly positively correlated. Otherwise, as the formula for portfolio standard deviation shows, the portfolio standard deviation is less than the weighted average of the component-asset standard deviations. The portfolio variance is a weighted sum of the elements in the covariance matrix, with the products of the portfolio proportions as weights.15.The probability distribution is:ProbabilityRate of Return0.7100%0.3−50Mean = [0.7 × 100%] + [0.3 × (-50%)] = 55%Variance = [0.7 × (100 − 55)2] + [0.3 × (-50 − 55)2] = 4725Standard deviation = 47251/2 = 68.74%16.σP = 30 = y × σ = 40 × y ⇒ y = 0.75E (r P ) = 12 + 0.75(30 − 12) = 25.5%17.The correct choice is (c). Intuitively, we note that since all stocks have the same expected rate of return and standard deviation, we choose the stock that will result in lowest risk. This is the stock that has the lowest correlation with Stock A.More formally, we note that when all stocks have the same expected rate of return, the optimal portfolio for any risk-averse investor is the global minimum variance portfolio (G). When the portfolio is restricted to Stock A and one additional stock, the objective is to find G for any pair that includes Stock A, and then select the combination with the lowest variance. With two stocks, I and J, the formula for the weights in G is:)(1)(),(Cov 2),(Cov )(222I w J w r r r r I w Min Min J I J I J I J Min -=-+-=σσσSince all standard deviations are equal to 20%:(,)400and ()()0.5I J I J Min Min Cov r r w I w J ρσσρ====This intuitive result is an implication of a property of any efficient frontier, namely, that the covariances of the global minimum variance portfolio with all other assets on the frontier are identical and equal to its own variance. (Otherwise, additional diversification would further reduce the variance.) In this case, the standard deviation of G(I, J) reduces to:1/2()[200(1)]Min IJ G σρ=⨯+This leads to the intuitive result that the desired addition would be the stock with the lowest correlation with Stock A, which is Stock D. The optimal portfolio is equally invested in Stock A and Stock D, and the standard deviation is 17.03%.18.No, the answer to Problem 17 would not change, at least as long as investors are not risk lovers. Risk neutral investors would not care which portfolio they held since all portfolios have an expected return of 8%.19.Yes, the answers to Problems 17 and 18 would change. The efficient frontier of risky assets is horizontal at 8%, so the optimal CAL runs from the risk-free rate through G. This implies risk-averse investors will just hold Treasury bills.20.Rearrange the table (converting rows to columns) and compute serial correlation results in the following table:Nominal RatesFor example: to compute serial correlation in decade nominal returns for large-company stocks, we set up the following two columns in an Excel spreadsheet. Then, use the Excel function “CORREL” to calculate the correlation for the data.Decade Previous 1930s -1.25%18.36%1940s 9.11%-1.25%1950s 19.41%9.11%1960s7.84%19.41%f 1970s 5.90%7.84%1980s 17.60% 5.90%1990s 18.20%17.60%Note that each correlation is based on only seven observations, so we cannot arrive at any statistically significant conclusions. Looking at the results, however, it appears that, with the exception of large-company stocks, there is persistent serial correlation. (This conclusion changes when we turn to real rates in the next problem.)21.The table for real rates (using the approximation of subtracting a decade’s average inflation from the decade’s average nominal return) is:Real RatesWhile the serial correlation in decade nominal returns seems to be positive, it appears that real rates are serially uncorrelated. The decade time series (although again too short for any definitive conclusions) suggest that real rates of return are independent from decade to decade.22. The 3-year risk premium for the S&P portfolio is, the 3-year risk premium for the hedge fund(1+.05)3‒1=0.1576 or 15.76%portfolio is S&P 3-year standard deviation is 0(1+.1)3‒1=0.3310 or 33.10%. . The hedge fund 3-year standard deviation is 0. S&P Sharpe ratio is 15.76/34.64 = 0.4550, and thehedge fund Sharpe ratio is 33.10/60.62 = 0.5460.23.With a ρ = 0, the optimal asset allocation isW S &P =,15.76×60.622‒33.10×(0×34.64×60.62)15.76×60.622+33.10×34.642‒[15.76+33.10]×(0×34.64×60.62)=0.5932.W Hedge =1‒0.5932=0.4068With these weights,ne iEσp=.59322×34.642+.40682×60.622+2×.5932×.4068×(0×=0.3210 or 32.10%The resulting Sharpe ratio is 22.81/32.10 = 0.7108. Greta has a risk aversion of A=3, Therefore, she will investyof her wealth in this risky portfolio. The resulting investment composition will be S&P: 0.7138 59.32 = 43.78% and Hedge: 0.7138 40.68 = 30.02%. The remaining 26% will be invested in the risk-free asset.24. With ρ = 0.3, the annual covariance is .25. S&P 3-year standard deviation is . The hedge fund 3-year standard deviation is . Therefore, the 3-yearcovariance is 0.26. With a ρ=.3, the optimal asset allocation isW S &P =,15.76×60.622‒33.10×(.3×34.64×60.62)15.76×60.622+33.10×34.642‒[15.76+33.10]×(.3×34.64×60.62)=0.5545.W Hedge =1‒0.5545=0.4455With these weights,Eσp=.55452×34.642+.44552×60.622+2×.5545×.4455×(.3×=0.3755 or 37.55%The resulting Sharpe ratio is 23.49/37.55 = 0.6256. Notice that the higher covariance results in a poorer Sharpe ratio. Greta will investyof her wealth in this risky portfolio. The resulting investment composition will be S&P: 0.5554 55.45 =30.79% and hedge: 0.5554 44.55= 24.74%. The remaining 44.46% will be invested in the risk-free asset.CFA PROBLEMS 1.a.Restricting the portfolio to 20 stocks, rather than 40 to 50 stocks, will increase the risk of the portfolio, but it is possible that the increase in risk will beminimal. Suppose that, for instance, the 50 stocks in a universe have the same standard deviation (σ) and the correlations between each pair are identical, with correlation coefficient ρ. Then, the covariance between each pair of stocks would be ρσ2, and the variance of an equally weighted portfolio would be:222ρσ1σ1σnn n P -+=The effect of the reduction in n on the second term on the right-hand side would be relatively small (since 49/50 is close to 19/20 and ρσ2 is smaller than σ2), but the denominator of the first term would be 20 instead of 50. For example, if σ = 45% and ρ = 0.2, then the standard deviation with 50 stocks would be 20.91%, and would rise to 22.05% when only 20 stocks are held. Such an increase might be acceptable if the expected return is increased sufficiently.b.Hennessy could contain the increase in risk by making sure that he maintains reasonable diversification among the 20 stocks that remain in his portfolio. This entails maintaining a low correlation among the remaining stocks. For example, in part (a), with ρ = 0.2, the increase in portfolio risk was minimal. As a practical matter, this means that Hennessy would have to spread hisportfolio among many industries; concentrating on just a few industries would result in higher correlations among the included stocks.2.Risk reduction benefits from diversification are not a linear function of the number of issues in the portfolio. Rather, the incremental benefits from additional diversification are most important when you are least diversified. Restricting Hennessy to 10 instead of 20 issues would increase the risk of his portfolio by a greater amount than would a reduction in the size of the portfolio from 30 to 20 stocks. In our example, restricting the number of stocks to 10 will increase the standard deviation to 23.81%. The 1.76% increase in standard deviation resulting from giving up 10 of 20 stocks is greater than the 1.14% increase that results from giving up 30 of 50 stocks.3.The point is well taken because the committee should be concerned with thevolatility of the entire portfolio. Since Hennessy’s portfolio is only one of six well-diversified portfolios and is smaller than the average, the concentration in fewer issues might have a minimal effect on the diversification of the total fund. Hence, unleashing Hennessy to do stock picking may be advantageous.4. d.Portfolio Y cannot be efficient because it is dominated by another portfolio.For example, Portfolio X has both higher expected return and lower standarddeviation.5. c.6. d.7. b.8. a.9. c.10.Since we do not have any information about expected returns, we focus exclusivelyon reducing variability. Stocks A and C have equal standard deviations, but thecorrelation of Stock B with Stock C (0.10) is less than that of Stock A with Stock B(0.90). Therefore, a portfolio composed of Stocks B and C will have lower total riskthan a portfolio composed of Stocks A and B.11.Fund D represents the single best addition to complement Stephenson's currentportfolio, given his selection criteria. Fund D’s expected return (14.0 percent) has the potential to increase the portfolio’s return somewhat. Fund D’s relatively lowcorrelation with his current portfolio (+0.65) indicates that Fund D will providegreater diversification benefits than any of the other alternatives except Fund B. The result of adding Fund D should be a portfolio with approximately the same expected return and somewhat lower volatility compared to the original portfolio.The other three funds have shortcomings in terms of expected return enhancement or volatility reduction through diversification. Fund A offers the potential forincreasing the portfolio’s return but is too highly correlated to provide substantialvolatility reduction benefits through diversification. Fund B provides substantialvolatility reduction through diversification benefits but is expected to generate areturn well below the current portfolio’s return. Fund C has the greatest potential to increase the portfolio’s return but is too highly correlated with the current portfolio to provide substantial volatility reduction benefits through diversification.12. a.Subscript OP refers to the original portfolio, ABC to the new stock, and NPto the new portfolio.i.E(r NP) = w OP E(r OP) + w ABC E(r ABC) = (0.9 ⨯ 0.67) + (0.1 ⨯ 1.25) = 0.728%ii.Cov = ρ⨯σOP⨯σABC = 0.40 ⨯ 2.37 ⨯ 2.95 = 2.7966 ≅ 2.80iii.σNP = [w OP2σOP2 + w ABC2σABC2 + 2 w OP w ABC(Cov OP , ABC)]1/2= [(0.9 2⨯ 2.372) + (0.12⨯ 2.952) + (2 ⨯ 0.9 ⨯ 0.1 ⨯ 2.80)]1/2= 2.2673% ≅ 2.27%b.Subscript OP refers to the original portfolio, GS to government securities, andNP to the new portfolio.i.E(r NP) = w OP E(r OP) + w GS E(r GS) = (0.9 ⨯ 0.67) + (0.1 ⨯ 0.42) = 0.645%ii.Cov = ρ⨯σOP⨯σGS = 0 ⨯ 2.37 ⨯ 0 = 0iii.σNP = [w OP2σOP2 + w GS2σGS2 + 2 w OP w GS (Cov OP , GS)]1/2= [(0.92⨯ 2.372) + (0.12⨯ 0) + (2 ⨯ 0.9 ⨯ 0.1 ⨯ 0)]1/2= 2.133% ≅ 2.13%c.Adding the risk-free government securities would result in a lower beta for thenew portfolio. The new portfolio beta will be a weighted average of theindividual security betas in the portfolio; the presence of the risk-free securitieswould lower that weighted average.d.The comment is not correct. Although the respective standard deviations andexpected returns for the two securities under consideration are equal, thecovariances between each security and the original portfolio are unknown, makingit impossible to draw the conclusion stated. For instance, if the covariances aredifferent, selecting one security over the other may result in a lower standarddeviation for the portfolio as a whole. In such a case, that security would be thepreferred investment, assuming all other factors are equal.e.i. Grace clearly expressed the sentiment that the risk of loss was more importantto her than the opportunity for return. Using variance (or standard deviation) as ameasure of risk in her case has a serious limitation because standard deviationdoes not distinguish between positive and negative price movements.ii. Two alternative risk measures that could be used instead of variance are:Range of returns, which considers the highest and lowest expected returns inthe future period, with a larger range being a sign of greater variability andtherefore of greater risk.Semivariance can be used to measure expected deviations of returns below themean, or some other benchmark, such as zero.Either of these measures would potentially be superior to variance for Grace.Range of returns would help to highlight the full spectrum of risk she isassuming, especially the downside portion of the range about which she is soconcerned. Semivariance would also be effective, because it implicitlyassumes that the investor wants to minimize the likelihood of returns fallingbelow some target rate; in Grace’s case, the target rate would be set at zero (toprotect against negative returns).13. a.Systematic risk refers to fluctuations in asset prices caused by macroeconomicfactors that are common to all risky assets; hence systematic risk is oftenreferred to as market risk. Examples of systematic risk factors include thebusiness cycle, inflation, monetary policy, fiscal policy, and technologicalchanges.Firm-specific risk refers to fluctuations in asset prices caused by factors thatare independent of the market, such as industry characteristics or firmcharacteristics. Examples of firm-specific risk factors include litigation,patents, management, operating cash flow changes, and financial leverage.b.Trudy should explain to the client that picking only the top five best ideaswould most likely result in the client holding a much more risky portfolio. Thetotal risk of a portfolio, or portfolio variance, is the combination of systematicrisk and firm-specific risk.The systematic component depends on the sensitivity of the individual assetsto market movements as measured by beta. Assuming the portfolio is welldiversified, the number of assets will not affect the systematic risk componentof portfolio variance. The portfolio beta depends on the individual securitybetas and the portfolio weights of those securities.On the other hand, the components of firm-specific risk (sometimes callednonsystematic risk) are not perfectly positively correlated with each other and,as more assets are added to the portfolio, those additional assets tend to reduceportfolio risk. Hence, increasing the number of securities in a portfolioreduces firm-specific risk. For example, a patent expiration for one companywould not affect the other securities in the portfolio. An increase in oil pricesis likely to cause a drop in the price of an airline stock but will likely result inan increase in the price of an energy stock. As the number of randomlyselected securities increases, the total risk (variance) of the portfolioapproaches its systematic variance.。

赫尔期权、期货及其他衍生产品第10版框架知识点及课后习题解析一、简介本文为赫尔期权、期货及其他衍生产品第10版的框架知识点及课后习题解析文档。

旨在帮助读者全面理解并掌握本教材中涉及的重要知识点，并通过课后习题的解析巩固所学内容。

二、框架知识点1. 期权•期权基本概念•期权合约要素•期权价格与影响因素•期权交易与结算•期权交易策略与风险管理2. 期货•期货市场与交易所•期货合约与交易机制1•期货价格与影响因素•期货交易策略与风险管理3. 其他衍生产品•互换（Swap）市场与交易•互换合约与交易机制•互换价格与影响因素•互换交易策略与风险管理4. 衍生产品交易策略•覆写（Covered Call）策略•裸写（Naked Writing）策略•敞口套利（Arbitrage）策略•期权组合策略•期货交易策略5. 风险管理•期权风险管理•期货风险管理•风险度量与序列风险三、课后习题解析1. 期权习题解析•习题1：某期权的看涨期权合约标的资产价格为$50，执行价为$55，期权价格为$3，到期日为3个月。

计算看涨期权合约是否处于实值、虚值或平值状态。

•习题2：假设某期权的看涨期权合约标的资产价格为$100，执行价为$90，到期日为6个月。

如果该看涨期权合约的价格为$8，在到期日当天标的资产价格为$110，计算期权的收益情况。

2. 期货习题解析•习题3：某期货合约的标的资产价格为$80，合约单位为100股，头寸为多头。

当期货价格上涨10%时，计算头寸的盈亏情况。

•习题4：某期货合约的标的资产价格为$100，合约单位为100股，头寸为空头。

当期货价格下跌5%时，计算头寸的盈亏情况。

3. 其他衍生产品习题解析•习题5：某互换合约的固定利率为5%，标的资产为未来6个月的黄金价格。

当前6个月黄金期货价格为$1500/盎司。

计算该互换合约的价格。

•习题6：某互换合约的固定利率为4%，标的资产为未来9个月的原油价格。

当前9个月原油期货价格为$70/桶。

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CHAPTER 10: ARBITRAGE PRICING THEORY ANDMULTIFACTOR MODELS OF RISK AND RETURN PROBLEM SETS1. The revised estimate of the expected rate of return on the stock would be the oldestimate plus the sum of the products of the unexpected change in each factor times the respective sensitivity coefficient:Revised estimate = 12% + [(1 × 2%) + (0.5 × 3%)] = 15.5%Note that the IP estimate is computed as: 1 × (5% - 3%), and the IR estimate iscomputed as: 0.5 × (8% - 5%).2. The APT factors must correlate with major sources of uncertainty, i.e., sources ofuncertainty that are of concern to many investors. Researchers should investigatefactors that correlate with uncertainty in consumption and investment opportunities.GDP, the inflation rate, and interest rates are among the factors that can be expected to determine risk premiums. In particular, industrial production (IP) is a goodindicator of changes in the business cycle. Thus, IP is a candidate for a factor that is highly correlated with uncertainties that have to do with investment andconsumption opportunities in the economy.3. Any pattern of returns can be explained if we are free to choose an indefinitelylarge number of explanatory factors. If a theory of asset pricing is to have value, itmust explain returns using a reasonably limited number of explanatory variables(i.e., systematic factors such as unemployment levels, GDP, and oil prices).4. Equation 10.11 applies here:E(r p) = r f + βP1 [E(r1 ) −r f ] + βP2 [E(r2 ) – r f]We need to find the risk premium (RP) for each of the two factors:RP1 = [E(r1 ) −r f] and RP2 = [E(r2 ) −r f]In order to do so, we solve the following system of two equations with two unknowns: .31 = .06 + (1.5 ×RP1 ) + (2.0 ×RP2 ).27 = .06 + (2.2 ×RP1 ) + [(–0.2) ×RP2 ]The solution to this set of equations isRP1 = 10% and RP2 = 5%Thus, the expected return-beta relationship isE(r P) = 6% + (βP1× 10%) + (βP2× 5%)5. The expected return for portfolio F equals the risk-free rate since its beta equals 0.For portfolio A, the ratio of risk premium to beta is (12 − 6)/1.2 = 5For portfolio E, the ratio is lower at (8 – 6)/0.6 = 3.33This implies that an arbitrage opportunity exists. For instance, you can create aportfolio G with beta equal to 0.6 (the same as E’s) by combining portfolio A and portfolio F in equal weights. The expected return and beta for portfolio G are then: E(r G) = (0.5 × 12%) + (0.5 × 6%) = 9%βG = (0.5 × 1.2) + (0.5 × 0%) = 0.6Comparing portfolio G to portfolio E, G has the same beta and higher return.Therefore, an arbitrage opportunity exists by buying portfolio G and selling anequal amount of portfolio E. The profit for this arbitrage will ber G – r E =[9% + (0.6 ×F)] − [8% + (0.6 ×F)] = 1%That is, 1% of the funds (long or short) in each portfolio.6. Substituting the portfolio returns and betas in the expected return-beta relationship,we obtain two equations with two unknowns, the risk-free rate (r f) and the factor risk premium (RP):12% = r f + (1.2 ×RP)9% = r f + (0.8 ×RP)Solving these equations, we obtainr f = 3% and RP = 7.5%7. a. Shorting an equally weighted portfolio of the ten negative-alpha stocks andinvesting the proceeds in an equally-weighted portfolio of the 10 positive-alpha stocks eliminates the market exposure and creates a zero-investmentportfolio. Denoting the systematic market factor as R M, the expected dollarreturn is (noting that the expectation of nonsystematic risk, e, is zero):$1,000,000 × [0.02 + (1.0 ×R M)] − $1,000,000 × [(–0.02) + (1.0 ×R M)]= $1,000,000 × 0.04 = $40,000The sensitivity of the payoff of this portfolio to the market factor is zerobecause the exposures of the positive alpha and negative alpha stocks cancelout. (Notice that the terms involving R M sum to zero.) Thus, the systematiccomponent of total risk is also zero. The variance of the analyst’s profit is notzero, however, since this portfolio is not well diversified.For n = 20 stocks (i.e., long 10 stocks and short 10 stocks) the investor willhave a $100,000 position (either long or short) in each stock. Net marketexposure is zero, but firm-specific risk has not been fully diversified. Thevariance of dollar returns from the positions in the 20 stocks is20 × [(100,000 × 0.30)2] = 18,000,000,000The standard deviation of dollar returns is $134,164.b. If n = 50 stocks (25 stocks long and 25 stocks short), the investor will have a$40,000 position in each stock, and the variance of dollar returns is50 × [(40,000 × 0.30)2] = 7,200,000,000The standard deviation of dollar returns is $84,853.Similarly, if n = 100 stocks (50 stocks long and 50 stocks short), the investorwill have a $20,000 position in each stock, and the variance of dollar returns is100 × [(20,000 × 0.30)2] = 3,600,000,000The standard deviation of dollar returns is $60,000.Notice that, when the number of stocks increases by a factor of 5 (i.e., from 20 to 100), standard deviation decreases by a factor of 5= 2.23607 (from$134,164 to $60,000).8. a. )(σσβσ2222e M +=88125)208.0(σ2222=+×=A50010)200.1(σ2222=+×=B97620)202.1(σ2222=+×=Cb. If there are an infinite number of assets with identical characteristics, then awell-diversified portfolio of each type will have only systematic risk since thenonsystematic risk will approach zero with large n. Each variance is simply β2 × market variance:222Well-diversified σ256Well-diversified σ400Well-diversified σ576A B C;;;The mean will equal that of the individual (identical) stocks.c. There is no arbitrage opportunity because the well-diversified portfolios allplot on the security market line (SML). Because they are fairly priced, there isno arbitrage.9. a. A long position in a portfolio (P) composed of portfolios A and B will offer anexpected return-beta trade-off lying on a straight line between points A and B.Therefore, we can choose weights such that βP = βC but with expected returnhigher than that of portfolio C. Hence, combining P with a short position in Cwill create an arbitrage portfolio with zero investment, zero beta, and positiverate of return.b. The argument in part (a) leads to the proposition that the coefficient of β2must be zero in order to preclude arbitrage opportunities.10. a. E(r) = 6% + (1.2 × 6%) + (0.5 × 8%) + (0.3 × 3%) = 18.1%b.Surprises in the macroeconomic factors will result in surprises in the return ofthe stock:Unexpected return from macro factors =[1.2 × (4% – 5%)] + [0.5 × (6% – 3%)] + [0.3 × (0% – 2%)] = –0.3%E(r) =18.1% − 0.3% = 17.8%11. The APT required (i.e., equilibrium) rate of return on the stock based on r f and thefactor betas isRequired E(r) = 6% + (1 × 6%) + (0.5 × 2%) + (0.75 × 4%) = 16% According to the equation for the return on the stock, the actually expected return on the stock is 15% (because the expected surprises on all factors are zero bydefinition). Because the actually expected return based on risk is less than theequilibrium return, we conclude that the stock is overpriced.12. The first two factors seem promising with respect to the likely impact on the firm’scost of capital. Both are macro factors that would elicit hedging demands acrossbroad sectors of investors. The third factor, while important to Pork Products, is a poor choice for a multifactor SML because the price of hogs is of minor importance to most investors and is therefore highly unlikely to be a priced risk factor. Betterchoices would focus on variables that investors in aggregate might find moreimportant to their welfare. Examples include: inflation uncertainty, short-terminterest-rate risk, energy price risk, or exchange rate risk. The important point here is that, in specifying a multifactor SML, we not confuse risk factors that are important toa particular investor with factors that are important to investors in general; only the latter are likely to command a risk premium in the capital markets.13. The formula is ()0.04 1.250.08 1.50.02.1717%E r =+×+×==14. If 4%f r = and based on the sensitivities to real GDP (0.75) and inflation (1.25),McCracken would calculate the expected return for the Orb Large Cap Fund to be:()0.040.750.08 1.250.02.040.0858.5% above the risk free rate E r =+×+×=+=Therefore, Kwon’s fundamental analysis estimate is congruent with McCracken’sAPT estimate. If we assume that both Kwon and McCracken’s estimates on the return of Orb’s Large Cap Fund are accurate, then no arbitrage profit is possible.15. In order to eliminate inflation, the following three equations must be solvedsimultaneously, where the GDP sensitivity will equal 1 in the first equation,inflation sensitivity will equal 0 in the second equation and the sum of the weights must equal 1 in the third equation.1.1.250.75 1.012.1.5 1.25 2.003.1wx wy wz wz wy wz wx wy wz ++=++=++=Here, x represents Orb’s High Growth Fund, y represents Large Cap Fund and z represents Utility Fund. Using algebraic manipulation will yield wx = wy = 1.6 and wz = -2.2.16. Since retirees living off a steady income would be hurt by inflation, this portfoliowould not be appropriate for them. Retirees would want a portfolio with a return positively correlated with inflation to preserve value, and less correlated with the variable growth of GDP. Thus, Stiles is wrong. McCracken is correct in that supply side macroeconomic policies are generally designed to increase output at aminimum of inflationary pressure. Increased output would mean higher GDP, which in turn would increase returns of a fund positively correlated with GDP.17. The maximum residual variance is tied to the number of securities (n ) in theportfolio because, as we increase the number of securities, we are more likely to encounter securities with larger residual variances. The starting point is todetermine the practical limit on the portfolio residual standard deviation, σ(e P ), that still qualifies as a well-diversified portfolio. A reasonable approach is to compareσ2(e P) to the market variance, or equivalently, to compare σ(e P) to the market standard deviation. Suppose we do not allow σ(e P) to exceed pσM, where p is a small decimal fraction, for example, 0.05; then, the smaller the value we choose for p, the more stringent our criterion for defining how diversified a well-diversified portfolio must be.Now construct a portfolio of n securities with weights w1, w2,…,w n, so that Σw i =1. The portfolio residual variance is σ2(e P) = Σw12σ2(e i)To meet our practical definition of sufficiently diversified, we require this residual variance to be less than (pσM)2. A sure and simple way to proceed is to assume the worst, that is, assume that the residual variance of each security is the highest possible value allowed under the assumptions of the problem: σ2(e i) = nσ2MIn that case σ2(e P) = Σw i2 nσM2Now apply the constraint: Σw i2 nσM2 ≤ (pσM)2This requires that: nΣw i2 ≤ p2Or, equivalently, that: Σw i2 ≤ p2/nA relatively easy way to generate a set of well-diversified portfolios is to use portfolio weights that follow a geometric progression, since the computations then become relatively straightforward. Choose w1 and a common factor q for the geometric progression such that q < 1. Therefore, the weight on each stock is a fraction q of the weight on the previous stock in the series. Then the sum of n terms is:Σw i= w1(1– q n)/(1– q) = 1or: w1 = (1– q)/(1– q n)The sum of the n squared weights is similarly obtained from w12 and a common geometric progression factor of q2. ThereforeΣw i2 = w12(1– q2n)/(1– q 2)Substituting for w1 from above, we obtainΣw i2 = [(1– q)2/(1– q n)2] × [(1– q2n)/(1– q 2)]For sufficient diversification, we choose q so that Σw i2 ≤ p2/nFor example, continue to assume that p = 0.05 and n = 1,000. If we chooseq = 0.9973, then we will satisfy the required condition. At this value for q w1 = 0.0029 and w n = 0.0029 × 0.99731,000In this case, w1 is about 15 times w n. Despite this significant departure from equal weighting, this portfolio is nevertheless well diversified. Any value of q between0.9973 and 1.0 results in a well-diversified portfolio. As q gets closer to 1, theportfolio approaches equal weighting.18. a. Assume a single-factor economy, with a factor risk premium E M and a (large)set of well-diversified portfolios with beta βP. Suppose we create a portfolio Zby allocating the portion w to portfolio P and (1 – w) to the market portfolioM. The rate of return on portfolio Z is:R Z = (w × R P) + [(1 – w) × R M]Portfolio Z is riskless if we choose w so that βZ = 0. This requires that:βZ = (w × βP) + [(1 – w) × 1] = 0 ⇒w = 1/(1 – βP) and (1 – w) = –βP/(1 – βP)Substitute this value for w in the expression for R Z:R Z = {[1/(1 – βP)] × R P} – {[βP/(1 – βP)] × R M}Since βZ = 0, then, in order to avoid arbitrage, R Z must be zero.This implies that: R P = βP × R MTaking expectations we have:E P = βP × E MThis is the SML for well-diversified portfolios.b. The same argument can be used to show that, in a three-factor model withfactor risk premiums E M, E1 and E2, in order to avoid arbitrage, we must have:E P = (βPM × E M) + (βP1 × E1) + (βP2 × E2)This is the SML for a three-factor economy.19. a. The Fama-French (FF) three-factor model holds that one of the factors drivingreturns is firm size. An index with returns highly correlated with firm size (i.e.,firm capitalization) that captures this factor is SMB (small minus big), thereturn for a portfolio of small stocks in excess of the return for a portfolio oflarge stocks. The returns for a small firm will be positively correlated withSMB. Moreover, the smaller the firm, the greater its residual from the othertwo factors, the market portfolio and the HML portfolio, which is the returnfor a portfolio of high book-to-market stocks in excess of the return for aportfolio of low book-to-market stocks. Hence, the ratio of the variance of thisresidual to the variance of the return on SMB will be larger and, together withthe higher correlation, results in a high beta on the SMB factor.b.This question appears to point to a flaw in the FF model. The model predictsthat firm size affects average returns so that, if two firms merge into a largerfirm, then the FF model predicts lower average returns for the merged firm.However, there seems to be no reason for the merged firm to underperformthe returns of the component companies, assuming that the component firmswere unrelated and that they will now be operated independently. We mighttherefore expect that the performance of the merged firm would be the sameas the performance of a portfolio of the originally independent firms, but theFF model predicts that the increased firm size will result in lower averagereturns. Therefore, the question revolves around the behavior of returns for aportfolio of small firms, compared to the return for larger firms that resultfrom merging those small firms into larger ones. Had past mergers of smallfirms into larger firms resulted, on average, in no change in the resultantlarger firms’ stock return characteristics (compared to the portfolio of stocksof the merged firms), the size factor in the FF model would have failed.Perhaps the reason the size factor seems to help explain stock returns is that,when small firms become large, the characteristics of their fortunes (andhence their stock returns) change in a significant way. Put differently, stocksof large firms that result from a merger of smaller firms appear empirically tobehave differently from portfolios of the smaller component firms.Specifically, the FF model predicts that the large firm will have a smaller riskpremium. Notice that this development is not necessarily a bad thing for thestockholders of the smaller firms that merge. The lower risk premium may bedue, in part, to the increase in value of the larger firm relative to the mergedfirms.CFA PROBLEMS1. a. This statement is incorrect. The CAPM requires a mean-variance efficientmarket portfolio, but APT does not.b.This statement is incorrect. The CAPM assumes normally distributed securityreturns, but APT does not.c. This statement is correct.2. b. Since portfolio X has β = 1.0, then X is the market portfolio and E(R M) =16%.Using E(R M ) = 16% and r f = 8%, the expected return for portfolio Y is notconsistent.3. d.4. c.5. d.6. c. Investors will take on as large a position as possible only if the mispricingopportunity is an arbitrage. Otherwise, considerations of risk anddiversification will limit the position they attempt to take in the mispricedsecurity.7. d.8. d.。

2 2 var = a 2 σ2 x + 2ab cov(x, x) + b σ x
The long position means 100% in X and the short position means –100% in X. Therefore, a=1 b = –1 Therefore, the variance is
Thus, x and y are perfectly negatively correlated. 3. (a) Table S5.1 Prob. .15 .10 .30 .20 .25 ri –.30 –.16 0 .10 .20 piri –.045 –.016 0 .020 .050 ∑ = .009 where
49
(c) The minimum variance portfolio is given by equation 5.21. a* = σ2 y − rxy σ x σ y
Chapter 5
Objects of Choice: Mean-Variance Portfolio Theory
47
5. Let σ2 x be the variance of the stock. The variance of a perfectly hedged portfolio is
σp 6.905 5.292 4.298 4.370 5.466 7.127 9.048
The opportunity set is shown in Figure S5.2 on the following page.
Chapter 5
Objects of Choice: Mean-Variance Portfolio Theory

CHAPTER 3: HOW SECURITIES ARE TRADEDPROBLEM SETS1.Stop-loss order: allows a stock to be sold if the price falls below a predeterminedlevel. Stop-loss orders often accompany short sales. Limit sell order: sells stockwhen the price rises above a predetermined level. Market order: either a buy or sellorder that is executed immediately at the current market price2. In response to the potential negative reaction to large [block] trades, trades will be splitup into many small trades, effectively hiding the total number of shares bought or sold.3. The use of leverage necessarily magnifies returns to investors. Leveragingborrowed money allows for greater return on investment if the stock price increases.However, if the stock price declines, the investor must repay the loan, regardless ofhow far the stock price drops, and incur a negative rate of return. For example, if aninvestor buys an asset at $100 and the price rises to $110, the investor earns 10%.If an investor takes out a $40 loan at 5% and buys the same stock, the return will be13.3%, computed as follows: $10 capital gain minus $2 interest expense divided bythe $60 original investment. Of course, if the stock price falls below $100, thenegative return will be greater for the leveraged account.4. (a) A market order is an order to execute the trade immediately at the bestpossible price. The emphasis in a market order is the speed of execution (thereduction of execution uncertainty). The disadvantage of a market order is thatthe price at which it will be executed is not known ahead of time; it thus hasprice uncertainty.5. (a) A broker market consists of intermediaries who have the discretion to tradefor their clients. A large block trade in an illiquid security would most likelytrade in this market as the brokers would have the best access to clientsinterested in this type of security.The advantage of an electronic communication network (ECN) is that it canexecute large block orders without affecting the public quote. Since thissecurity is illiquid, large block orders are less likely to occur and thus it wouldnot likely trade through an ECN.Electronic limit-order markets (ELOM) transact securities with high tradingvolume. This illiquid security is unlikely to be traded on an ELOM.6. a. The stock is purchased for: 300 ⨯ $40 = $12,000The amount borrowed is $4,000. Therefore, the investor put up equity, ormargin, of $8,000.b.If the share price falls to $30, then the value of the stock falls to $9,000. Bythe end of the year, the amount of the loan owed to the broker grows to:$4,000 ⨯ 1.08 = $4,320Therefore, the remaining margin in the investor’s account is:$9,000 - $4,320 = $4,680The percentage margin is now: $4,680/$9,000 = 0.52, or 52%Therefore, the investor will not receive a margin call.c.The rate of return on the investment over the year is:(Ending equity in the account - Initial equity)/Initial equity= ($4,680 - $8,000)/$8,000 = -0.415, or -41.5%Alternatively, divide the initial equity investments into the change in valueplus the interest payment:($3,000 loss + $320 interest)/$8,000 = -0.415.7. a. The initial margin was: 0.50 ⨯ 1,000 ⨯ $40 = $20,000As a result of the increase in the stock price Old Economy Traders loses: $10 ⨯ 1,000 = $10,000Therefore, margin decreases by $10,000. Moreover, Old Economy Tradersmust pay the dividend of $2 per share to the lender of the shares, so that themargin in the account decreases by an additional $2,000. Therefore, theremaining margin is:$20,000 – $10,000 – $2,000 = $8,000b. The percentage margin is: $8,000/$50,000 = 0.16, or 16%So there will be a margin call.c. The equity in the account decreased from $20,000 to $8,000 in one year, for arate of return of: (-$12,000/$20,000) = -0.60, or -60%8.a. The buy order will be filled at the best limit-sell order price: $50.25b.The next market buy order will be filled at the next-best limit-sell order price: $51.50 c. You would want to increase your inventory. There is considerable buyingdemand at prices just below $50, indicating that downside risk is limited. Incontrast, limit sell orders are sparse, indicating that a moderate buy order could result in a substantial price increase.9. a.You buy 200 shares of Telecom for $10,000. These shares increase in value by 10%, or $1,000. You pay interest of: 0.08 ⨯ $5,000 = $400The rate of return will be: $1,000$4000.1212%$5,000-==b. The value of the 200 shares is 200P . Equity is (200P – $5,000). You will receive a margin call when:PP 200000,5$200-= 0.30 ⇒ when P = $35.71 or lower10. a.Initial margin is 50% of $5,000, or $2,500.b. Total assets are $7,500 ($5,000 from the sale of the stock and $2,500 put up formargin). Liabilities are 100P . Therefore, equity is ($7,500 – 100P ). A margin call will be issued when:PP 100100500,7$-= 0.30 ⇒ when P = $57.69 or higher11. The total cost of the purchase is: $20 ⨯ 1,000 = $20,000You borrow $5,000 from your broker and invest $15,000 of your own funds.Your margin account starts out with equity of $15,000.a. (i) Equity increases to: ($22 ⨯ 1,000) – $5,000 = $17,000Percentage gain = $2,000/$15,000 = 0.1333, or 13.33%(ii) With price unchanged, equity is unchanged.Percentage gain = zero(iii) Equity falls to ($18 ⨯ 1,000) – $5,000 = $13,000Percentage gain = (–$2,000/$15,000) = –0.1333, or –13.33%The relationship between the percentage return and the percentage change inthe price of the stock is given by:% return = % change in price ⨯ equityinitial s Investor'investment T otal = % change in price ⨯ 1.333 For example, when the stock price rises from $20 to $22, the percentage change in price is 10%, while the percentage gain for the investor is:% return = 10% ⨯000,15$000,20$= 13.33%b. The value of the 1,000 shares is 1,000P . Equity is (1,000P – $5,000). You will receive a margin call when:P P 000,1000,5$000,1-= 0.25 ⇒ when P = $6.67 or lowerc. The value of the 1,000 shares is 1,000P . But now you have borrowed $10,000instead of $5,000. Therefore, equity is (1,000P – $10,000). You will receive a margin call when:PP 000,1000,10$000,1-= 0.25 ⇒ when P = $13.33 or lower With less equity in the account, you are far more vulnerable to a margin call.d. By the end of the year, the amount of the loan owed to the broker grows to:$5,000 ⨯ 1.08 = $5,400The equity in your account is (1,000P – $5,400). Initial equity was $15,000.Therefore, your rate of return after one year is as follows: (i)000,15$000,15$400,5$)22$000,1(--⨯= 0.1067, or 10.67% (ii)000,15$000,15$400,5$)20$000,1(--⨯= –0.0267, or –2.67% (iii)000,15$000,15$400,5$)18$000,1(--⨯= –0.1600, or –16.00% The relationship between the percentage return and the percentage change inthe price of Intel is given by: % return = ⎪⎪⎭⎫ ⎝⎛⨯equity initial s Investor'investment Total price in change %⎪⎪⎭⎫ ⎝⎛⨯-equity initial s Investor'borrowed Funds %8For example, when the stock price rises from $40 to $44, the percentage change in price is 10%, while the percentage gain for the investor is:⎪⎭⎫ ⎝⎛⨯000,15$000,20$%10⎪⎭⎫ ⎝⎛⨯-000,15$000,5$%8=10.67%e. The value of the 1000 shares is 1,000P . Equity is (1,000P – $5,400). You will receive a margin call when:PP 000,1400,5$000,1-= 0.25 ⇒ when P = $7.20 or lower12. a. The gain or loss on the short position is: (–1,000 ⨯ ΔP )Invested funds = $15,000Therefore: rate of return = (–1,000 ⨯ ΔP )/15,000The rate of return in each of the three scenarios is:(i) Rate of return = (–1,000 ⨯ $2)/$15,000 = –0.1333, or –13.33%(ii) Rate of return = (–1,000 ⨯ $0)/$15,000 = 0%(iii) Rate of return = [–1,000 ⨯ (–$2)]/$15,000 = +0.1333, or+13.33%b. Total assets in the margin account equal:$20,000 (from the sale of the stock) + $15,000 (the initial margin) = $35,000Liabilities are 500P . You will receive a margin call when:PP 000,1000,1000,35$-= 0.25 ⇒ when P = $28 or higherc. With a $1 dividend, the short position must now pay on the borrowed shares:($1/share ⨯ 1000 shares) = $1000. Rate of return is now:[(–1,000 ⨯ ΔP ) – 1,000]/15,000(i) Rate of return = [(–1,000 ⨯ $2) – $1,000]/$15,000 = –0.2000, or –20.00%(ii) Rate of return = [(–1,000 ⨯ $0) – $1,000]/$15,000 = –0.0667, or –6.67% (iii) Rate of return = [(–1,000) ⨯ (–$2) – $1,000]/$15,000 = +0.067, or+6.67%Total assets are $35,000, and liabilities are (1,000P + 1,000). A margin call will be issued when:PP 000,1000,1000,1000,35--= 0.25 ⇒ when P = $27.2 or higher13. The broker is instructed to attempt to sell your Marriott stock as soon as theMarriott stock trades at a bid price of $40 or less. Here, the broker will attempt to execute but may not be able to sell at $40, since the bid price is now $39.95. The price at which you sell may be more or less than $40 because the stop-loss becomes a market order to sell at current market prices.14. a. $55.50b. $55.25c. The trade will not be executed because the bid price is lower than the pricespecified in the limit-sell order.d. The trade will not be executed because the asked price is greater than the pricespecified in the limit-buy order.15. a. You will not receive a margin call. You borrowed $20,000 and with another$20,000 of your own equity you bought 1,000 shares of Disney at $40 pershare. At $35 per share, the market value of the stock is $35,000, your equityis $15,000, and the percentage margin is: $15,000/$35,000 = 42.9%Your percentage margin exceeds the required maintenance margin.b. You will receive a margin call when:PP 000,1000,20$000,1-= 0.35 ⇒ when P = $30.77 or lower16. The proceeds from the short sale (net of commission) were: ($21 ⨯ 100) – $50 = $2,050A dividend payment of $200 was withdrawn from the account.Covering the short sale at $15 per share costs (with commission): $1,500 + $50 = $1,550Therefore, the value of your account is equal to the net profit on the transaction:$2,050 – $200 – $1,550 = $300Note that your profit ($300) equals (100 shares ⨯ profit per share of $3). Your net proceeds per share were:$21selling price of stock –$15 repurchase price of stock–$ 2 dividend per share–$ 1 2 trades $0.50 commission per share$ 3CFA PROBLEMS1. a. In addition to the explicit fees of $70,000, FBN appears to have paid animplicit price in underpricing of the IPO. The underpricing is $3 per share, ora total of $300,000, implying total costs of $370,000.b. No. The underwriters do not capture the part of the costs correspondingto the underpricing. The underpricing may be a rational marketingstrategy. Without it, the underwriters would need to spend more resourcesin order to place the issue with the public. The underwriters would thenneed to charge higher explicit fees to the issuing firm. The issuing firmmay be just as well off paying the implicit issuance cost represented bythe underpricing.2. (d) The broker will sell, at current market price, after the first transaction at$55 or less.3. (d)。

CHAPTER 2: ASSET CLASSES AND FINANCIALINSTRUMENTSPROBLEM SETS1. Preferred stock is like long-term debt in that it typically promises a fixed paymenteach year. In this way, it is a perpetuity. Preferred stock is also like long-term debt in that it does not give the holder voting rights in the firm.Preferred stock is like equity in that the firm is under no contractual obligation tomake the preferred stock dividend payments. Failure to make payments does not set off corporate bankruptcy. With respect to the priority of claims to the assets of thefirm in the event of corporate bankruptcy, preferred stock has a higher priority than common equity but a lower priority than bonds.2. Money market securities are called cash equivalents because of their high levelof liquidity. The prices of money market securities are very stable, and they canbe converted to cash (i.e., sold) on very short notice and with very lowtransaction costs. Examples of money market securities include Treasury bills,commercial paper, and banker's acceptances, each of which is highly marketableand traded in the secondary market.3. (a) A repurchase agreement is an agreement whereby the seller of a securityagrees to “repurchase” it from the buyer on an agreed upon date at an agreedupon price. Repos are typically used by securities dealers as a means forobtaining funds to purchase securities.4. Spreads between risky commercial paper and risk-free government securitieswill widen. Deterioration of the economy increases the likelihood of default oncommercial paper, making them more risky. Investors will demand a greaterpremium on all risky debt securities, not just commercial paper.5.6. Municipal bond interest is tax-exempt at the federal level and possibly at thestate level as well. When facing higher marginal tax rates, a high-incomeinvestor would be more inclined to invest in tax-exempt securities.7. a. You would have to pay the ask price of:161.1875% of par value of $1,000 = $1611.875b. The coupon rate is 6.25% implying coupon payments of $62.50annually or, more precisely, $31.25 semiannually.c. The yield to maturity on a fixed income security is also known as its requiredreturn and is reported by The Wall Street Journal and others in the financialpress as the ask yield. In this case, the yield to maturity is 2.113%. An investorbuying this security today and holding it until it matures will earn an annualreturn of 2.113%. Students will learn in a later chapter how to compute boththe price and the yield to maturity with a financial calculator.8. Treasury bills are discount securities that mature for $10,000. Therefore, a specific T-bill price is simply the maturity value divided by one plus the semi-annual return:P = $10,000/1.02 = $9,803.929. The total before-tax income is $4. After the 70% exclusion for preferred stockdividends, the taxable income is: 0.30 ⨯ $4 = $1.20Therefore, taxes are: 0.30 ⨯ $1.20 = $0.36After-tax income is: $4.00 – $0.36 = $3.64Rate of return is: $3.64/$40.00 = 9.10%10. a. You could buy: $5,000/$64.69 = 77.29 shares. Since it is not possible to tradein fractions of shares, you could buy 77 shares of GD.b. Your annual dividend income would be: 77 ⨯ $2.04 = $157.08c. The price-to-earnings ratio is 9.31 and the price is $64.69. Therefore:$64.69/Earnings per share = 9.3 ⇒ Earnings per share = $6.96d. General Dynamics closed today at $64.69, which was $0.65 higher thanyesterday’s price of $64.0411. a. At t = 0, the value of the index is: (90 + 50 + 100)/3 = 80At t = 1, the value of the index is: (95 + 45 + 110)/3 = 83.333The rate of return is: (83.333/80) - 1 = 4.17%b. In the absence of a split, Stock C would sell for 110, so the value of theindex would be: 250/3 = 83.333 with a divisor of 3.After the split, stock C sells for 55. Therefore, we need to find the divisor(d) such that: 83.333 = (95 + 45 + 55)/d ⇒ d = 2.340. The divisor fell,which is always the case after one of the firms in an index splits its shares.c. The return is zero. The index remains unchanged because the return foreach stock separately equals zero.12. a. Total market value at t = 0 is: ($9,000 + $10,000 + $20,000) = $39,000Total market value at t = 1 is: ($9,500 + $9,000 + $22,000) = $40,500Rate of return = ($40,500/$39,000) – 1 = 3.85%b.The return on each stock is as follows:r A = (95/90) – 1 = 0.0556r B = (45/50) – 1 = –0.10r C = (110/100) – 1 = 0.10The equally weighted average is:[0.0556 + (-0.10) + 0.10]/3 = 0.0185 = 1.85%13. The after-tax yield on the corporate bonds is: 0.09 ⨯ (1 – 0.30) = 0.063 = 6.30%Therefore, municipals must offer a yield to maturity of at least 6.30%.14. Equation (2.2) shows that the equivalent taxable yield is: r = r m/(1 –t), so simplysubstitute each tax rate in the denominator to obtain the following:a. 4.00%b. 4.44%c. 5.00%d. 5.71%15. In an equally weighted index fund, each stock is given equal weight regardless of itsmarket capitalization. Smaller cap stocks will have the same weight as larger cap stocks.The challenges are as follows:•Given equal weights placed to smaller cap and larger cap, equal-weighted indices (EWI) will tend to be more volatile than their market-capitalization counterparts;•It follows that EWIs are not good reflectors of the broad market that they represent; EWIs underplay the economic importance of larger companies.•Turnover rates will tend to be higher, as an EWI must be rebalancedback to its original target. By design, many of the transactions would beamong the smaller, less-liquid stocks.16. a. The ten-year Treasury bond with the higher coupon rate will sell for a higherprice because its bondholder receives higher interest payments.b. The call option with the lower exercise price has more value than one with ahigher exercise price.c. The put option written on the lower priced stock has more value than onewritten on a higher priced stock.17. a. You bought the contract when the futures price was $7.8325 (see Figure2.11 and remember that the number to the right of the apostrophe represents aneighth of a cent). The contract closes at a price of $7.8725, which is $0.04 morethan the original futures price. The contract multiplier is 5000. Therefore, thegain will be: $0.04 ⨯ 5000 = $200.00b. Open interest is 135,778 contracts.18. a. Owning the call option gives you the right, but not the obligation, to buy at$180, while the stock is trading in the secondary market at $193. Since thestock price exceeds the exercise price, you exercise the call.The payoff on the option will be: $193 - $180 = $13The cost was originally $12.58, so the profit is: $13 - $12.58 = $0.42b. Since the stock price is greater than the exercise price, you will exercise the call.The payoff on the option will be: $193 - $185 = $8The option originally cost $9.75, so the profit is $8 - $9.75 = -$1.75c. Owning the put option gives you the right, but not the obligation, to sell at $185,but you could sell in the secondary market for $193, so there is no value inexercising the option. Since the stock price is greater than the exercise price,you will not exercise the put. The loss on the put will be the initial cost of$12.01.19. There is always a possibility that the option will be in-the-money at some time prior toexpiration. Investors will pay something for this possibility of a positive payoff.20.Value of Call at Expiration Initial Cost Profita. 0 4 -4b. 0 4 -4c. 0 4 -4d. 5 4 1e. 10 4 6Value of Put at Expiration Initial Cost Profita. 10 6 4b. 5 6 -1c. 0 6 -6d. 0 6 -6e. 0 6 -621. A put option conveys the right to sell the underlying asset at the exercise price. Ashort position in a futures contract carries an obligation to sell the underlying assetat the futures price. Both positions, however, benefit if the price of the underlyingasset falls.22. A call option conveys the right to buy the underlying asset at the exercise price. Along position in a futures contract carries an obligation to buy the underlying assetat the futures price. Both positions, however, benefit if the price of the underlyingasset rises.CFA PROBLEMS1.(d) There are tax advantages for corporations that own preferred shares.2. The equivalent taxable yield is: 6.75%/(1 0.34) = 10.23%3. (a) Writing a call entails unlimited potential losses as the stock price rises.4. a. The taxable bond. With a zero tax bracket, the after-tax yield for thetaxable bond is the same as the before-tax yield (5%), which is greater thanthe yield on the municipal bond.b. The taxable bond. The after-tax yield for the taxable bond is:0.05⨯ (1 – 0.10) = 4.5%c. You are indifferent. The after-tax yield for the taxable bond is:0.05 ⨯ (1 – 0.20) = 4.0%The after-tax yield is the same as that of the municipal bond.d. The municipal bond offers the higher after-tax yield for investors in taxbrackets above 20%.5.If the after-tax yields are equal, then: 0.056 = 0.08 × (1 –t)This implies that t = 0.30 =30%.。

CHAPTER 17Does Debt Policy Matter?Answers to Problem Sets1.Note the market value of Copperhead is far in excess of its book value:Ms. Kraft owns .625% of the firm, which proposes to increase common stock to $17 million and cut short-term debt. Ms. Kraft can offset this by (a)borrowing .00625 X 1,000,000 = $6,250, and (b) buying that much more Copperhead stock. 2. a. 55.5.⨯+E r % = 12.5%; E r = 20%b. 12.5%c. E/P = 20%; P/E = 5d. $50e..5 X E β + .5 X 0 = 1.0; E β= 2.0.3.E xpected return on assets is r A = .08 X 30/80 + .16 X 50/80 = .13. The new return on equity will be r E = .13 + (20/60)(.13 - .08) = .147.4. a.b. ⎪⎭⎫⎝⎛⨯++⎪⎭⎫⎝⎛⨯+=E D A E D E E D D βββ.8 = (.25 x 0) + (.75 x βE)βE = 1.075. a. Trueb. True (as long as the return earned by the company is greater than theinterest payment, earnings per share increase, but the PyE falls to reflectthe higher risk).c. False (the cost of equity increases with the ratio D/E).d. False (the formula r E = r A + (D/E)(r A - r D) does not require r D to beconstant).e. False (debt amplifies variations in equity income).f. False (value increases only if clientele is not satisfied).6. a. r A = .15, r E = .175b. βA= .6 (unchanged), βD= .3, βE= .9.7. See Figure 17.3.8. Currently r A = r E = .14, or 14%. From proposition 2 the leverage causes r E toincrease to r E = r A + (r A– r D)(D/E) = .14 + (.14 - .095) X (45/55) = .1768, or17.68%After-tax WACC = .095 X (1 - .40) X .45 + .1768 X .55 = .1229, or 12.29%.9. a. The two firms have equal value; let V represent the total value of the firm.Rosencrantz could buy one percent of Company B’s equity and borrow anamount equal to:0.01 ⨯ (D A - D B) = 0.002VThis investment requires a net cash outlay of (0.007V) and provides a netcash return of:(0.01 ⨯ Profits) – (0.003 ⨯ r f⨯ V)where r f is the risk-free rate of interest on debt. Thus, the two investmentsare identical.b. Guildenstern could buy two percent of Company A’s equity and lend anamount equal to:0.02 ⨯ (D A - D B) = 0.004VThis investment requires a net cash outlay of (0.018V) and provides a netcash return of:(0.02 ⨯ Profits) – (0.002 ⨯ r f⨯ V)Thus the two investments are identical.c. The expected dollar return to Rosencrantz’ original investment in A is:(0.01 ⨯ C) – (0.003 ⨯ r f⨯ V A)where C is the expected profit (cash flow) generated by the firm’s assets.Since the firms are the same except for capital structure, C must also bethe expected cash flow for Firm B. The dollar return to Rosencrantz’alternative strategy is:(0.01 ⨯ C) – (0.003 ⨯ r f⨯ V B)Also, the cost of the original strategy is (0.007V A) while the cost of thealternative strategy is (0.007V B).If V A is less than V B, then the original strategy of investing in Company Awould provide a larger dollar return at the same time that it would cost lessthan the alternative. Thus, no rational investor would invest in Company Bif the value of Company A were less than that of Company B.10. When a firm issues debt, it shifts its cash flow into two streams. MM’sProposition I states that this does not affect firm value if the investor canreconstitute a firm’s cash flow stream by creati ng personal leverage or byundoing the effect of the firm’s leverage by investing in both debt and equity.It is similar with Carruther’s cows. If the cream and skim milk go into the samepail, the cows have no special value. (If an investor holds both the debt andequity, the firm does not add value by splitting the cash flows into the twostreams.) In the same vein, the cows have no special value if a dairy cancostlessly split up whole milk into cream and skim milk. (Firm borrowing does not add value if investors can borrow on their own account.) Carruther’s cows willhave extra value if consumers want cream and skim milk and if the dairy cannot split up whole milk, or if it is costly to do so.11. a. The market price of the stock is not affected by the announcement.b. Since the market price of the shares is $10, the company can buy back:$160 million/$10 = 16 million sharesc. After the change in capital structure, the market value of the firm isunchanged:Equity + Debt = (9 million ⨯ $10) + $160 million = $250 milliond. After the change in structure, the debt ratio is:Debt/(Debt + Equity) = $160 million/$250 million = 0.64e. No one gains or loses. (See the answer to the next question.)12. a. The market value of the firm’s equity incr eases by $30 million, the amountof the decrease in the market value of the firm’s existing debt. Therefore,the price of the stock increases to:($150 million + $30 million)/15 million shares = $12b. Since the market price of the shares is $12, the company can buy back:$60 million/$12 = 5 million sharesc. After the change in capital structure, the market value of the firm isunchanged:Equity + Debt = (10 million ⨯ $12) + $130 million = $250 milliond. After the change in structure, the debt ratio is:Debt/(Debt + Equity) = $130 million/$250 million = 0.52e. The investors in the existing debt lose $30 million while the shareholdersgain this $30 million. The value of each share increases by:$30 million/15 million shares = $213. The company cost of capital is:r A = (0.8 ⨯ 0.12) + (0.2⨯ 0.06) = 0.108 = 10.8%Under Proposition I, this is unaffected by capital structure changes. With thebonds remaining at the 6% default-risk free rate, we have:Debt-Equityr E r ARatio0.00 0.108 0.1080.10 0.113 0.1080.50 0.132 0.1081.00 0.156 0.1082.00 0.204 0.1083.00 0.252 0.108See figure on next page.14. This is not a valid objection. MM’s Proposition II explicitly allows for the rates ofreturn for both debt and equity to increase as the proportion of debt in the capital structure increases. The rate for debt increases because the debt-holders aretaking on more of the risk of the firm; the rate for common stock increasesbecause of increasing financial leverage. See Figure 17.2 and theaccompanying discussion.15. a. Under Proposition I, the firm’s cost of capital (r A) is not affected by thechoice of capital structure. The reason the quoted statement seems to betrue is that it does not account for the changing proportions of the firmfinanced by debt and equity. As the debt-equity ratio increases, it is truethat both the cost of equity and the cost of debt increase, but a smallerproportion of the firm is financed by equity. The overall effect is to leavethe firm’s cost of capital unchanged.b. Moderate borrowing does not significantly affect the probability of financialdistress, but it does increase the variability (and market risk) borne bystockholders. This additional risk must be offset by a higher averagereturn to stockholders.16. a. If the opportunity were the firm’s only asset, this would be a good deal.Stockholders would put up no money and, therefore, would havenothing to lose. However, rational lenders will not advance 100% ofthe asset’s value for an 8% promised return unless other assets areput up as collateral.Sometimes firms find it convenient to borrow all the cash required for aparticular investment. Such investments do not support all of theadditional debt; lenders are p rotected by the firm’s other assets too.In any case, if firm value is independent of leverage, then any asset’scontribution to firm value must be independent of how it is financed. Notealso that the statement ignores the effect on the stockholders of anincrease in financial leverage.b. This is not an important reason for conservative debt levels. So long asMM’s Proposition I holds, the company’s overall cost of capital isunchanged despite increasing interest rates paid as the firm borrows more.(However, the increasing interest rates may signal an increasingprobability of financial distress—and that can be important.)17. Examples of such securities are given in the text and include unbundled stockunits, preferred equity redemption cumulative stock and floating-rate notes. Note that, in order to succeed, such securities must both meet regulatory requirements and appeal to an unsatisfied clientele.18. a.As leverage is increased, the cost of equity capital rises. This is the same as saying that, as leverage is increased, the ratio of the income afterinterest (which is the cash flow stockholders are entitled to) to the value of equity increases. Thus, as leverage increases, the ratio of the market value of the equity to income after interest decreases.b.(i) Assume MM are correct. The market value of the firm is determinedby the income of the firm, not how it is divided among the firm’s security holders. Also, the firm’s income before interest isindependent of the firm’s financing. Th us, both the value of the firm and the value of the firm’s income before interest remain constant as leverage is increased. Hence, the ratio is a constant. (ii) Assume the traditionalists are correct. The firm’s income beforeinterest is independent of levera ge. As leverage increases, the firm’s cost of capital first decreases and then increases; as a result, themarket value of the firm first increases and then decreases. Thus, the ratio of the market value of the firm to firm income before interest first increases and then decreases, as leverage increases.19.We begin with r E and the capital asset pricing model:r E = r f + βE (r m – r f ) = 0.10 + 1.5 (0.18 – 0.10) = 0.22 = 22.0%Similarly for debt:r D = r f + βD (r m – r f )0.12 = 0.10 + βD (0.18 – 0.10) βD = 0.25Also, we know that:17.0%0.170.22)(0.50.12)(0.5E D r E D E r E D DrA==⨯+⨯⎪⎪⎭⎫⎝⎛⎪⎪⎭⎫⎝⎛=⨯++⨯+= To solve for βA , use the following:0.8751.5)(0.50.25)(0.5β E D E β E D D βE D A =⨯+⨯=⎪⎪⎭⎫ ⎝⎛⨯++⎪⎪⎭⎫ ⎝⎛⨯+=20.We know from Proposition I that the value of the firm will not change. Also, because the expected operating income is unaffected by changes in leverage, the firm’s overall cost of capital will not change. In other words, r A remains equal to 17% and βA remains equal to 0.875. However, risk and, hence, the expected return for equity and for debt, will change. We know that r D is 11%, so that, for debt:r D = r f + βD (r m – r f )0.11 = 0.10 + βD (0.18 – 0.10) βD = 0.125For equity:⎪⎪⎭⎫⎝⎛⎪⎪⎭⎫⎝⎛⨯++⨯+=ED rE D E r E D DrA0.17 = (0.3 ⨯ 0.11) + (0.7 ⨯ r E ) r E = 0.196 = 19.6%Also:r E = r f + βE (r m – r f )0.196 = 0.10 + βE (0.18 – 0.10) βE = 1.2021.[Note: In the following solution, we have assumed that $200 million of long-term bonds have been issued.] a.E = $55 ⨯ 10 million = $550 millionV = D + E = $200 million + $550 million = $750 million0.267n$750millio n $200millio V D == 0.733n$750millio n $550millio V E == After-tax WACC = VErV D )T (1r E CD+- 10.01%0.10010.733)(0.120.2670.35)(10.07==⨯+⨯-⨯=b.The after-tax WACC would increase to the extent of the loss of the tax deductibility of the interest on debt. Therefore, the after-tax WACC would equal the opportunity cost of capital, computed from the WACC formula without the tax-deductibility of interest:10.67%0.10670.733)(0.120.267)(0.07VE r V D rWACC E D==⨯+⨯=+= 22.We make use of the basic relationship:⎪⎭⎫ ⎝⎛⎪⎭⎫ ⎝⎛⨯+-= V E r V D )T (1r r E CDASince overall beta (βA ) is not affected by capital structure or taxes, then:r A = r f + βA (r m – r f ) = 0.06 + (1.5 × 0.08) = 0.18The following table shows the value of r E for various values of D/E (and thecorresponding values of D/V), derived from the above formula. The graph is on the next page.D/E D/V r A r D r E 0.00 0.00000 0.18 0.0600 0.1800 0.05 0.04762 0.18 0.0600 0.1871 0.10 0.09091 0.18 0.0600 0.1941 0.15 0.13043 0.18 0.0600 0.2012 0.20 0.16667 0.18 0.0600 0.2082 0.25 0.20000 0.18 0.0600 0.2153 0.30 0.23077 0.18 0.0610 0.2221 0.35 0.25926 0.18 0.0620 0.2289 0.40 0.28571 0.18 0.0630 0.2356 0.45 0.31034 0.18 0.0640 0.2423 0.50 0.33333 0.18 0.0650 0.2489 0.55 0.35484 0.18 0.0660 0.2554 0.60 0.37500 0.18 0.0670 0.2619 0.65 0.39394 0.18 0.0680 0.2683 0.70 0.41176 0.18 0.0690 0.2746 0.75 0.42857 0.18 0.0690 0.2814 0.80 0.44444 0.18 0.0700 0.2876 0.85 0.45946 0.18 0.0725 0.2929 0.90 0.47368 0.18 0.0750 0.2981 0.95 0.48718 0.18 0.0775 0.3031 1.000.500000.180.08000.308023. Assume the election is near so that we can safely ignore the time value ofmoney.Because one, and only one, of three events will occur, the guaranteed payofffrom holding all three tickets is $10. Thus, the three tickets, taken together, could never sell for less than $10. This is true whether they are bundled into onecomposite security or unbundled into three separate securities.However, unbundled they may sell for more than $10. This will occur if theseparate tickets fill a need for some currently unsatisfied clientele. If this isindeed the case, then Proposition I fails. The sum of the parts is worth more than the whole.24. Some shoppers may want only the chicken drumstick. They could buy a wholechicken, cut it up, and sell off the other parts in the supermarket parking lot. This is costly. It is far more efficient for the store to cut up the chicken and sell thepieces separately. But this also has some cost, hence the observation thatsupermarkets charge more for chickens after they have been cut.The same considerations affect financial products, but:a. The proportionate costs to companies of repackaging the cash flow streamare generally small.b. Investors can also repackage cash flows cheaply for themselves. In fact,specialist financial institutions can often do so more cheaply than thecompanies can do it themselves.25. Firms that are ab le to identify an ‘unsatisfied’ clientele and then design a financialservice or instrument that satisfies the demands of this clientele can, in violationof MM’s capital-structure irrelevance theory, enhance firm value. However, if this is done successfully by one financial innovator, others will follow, eventuallyrestoring the validity of the MM irrelevance theory.If the financial innovation can be patented, the creator of the innovation can restrict the use of the innovation by other financial managers and therebycontinue to use the innovation to create value. Consequently, MM’s capital-structure irrelevance theory would potentially be violated during the life of the patent.。

CHAPTER 1: THE INVESTMENT ENVIRONMENT PROBLEM SETS1. While it is ultimately true that real assets determine the material well-being of aneconomy, financial innovation in the form of bundling and unbundling securitiescreates opportunities for investors to form more efficient portfolios. Bothinstitutional and individual investors can benefit when financial engineering creates new products that allow them to manage their portfolios of financial assets moreefficiently. Bundling and unbundling create financial products with new properties and sensitivities to various sources of risk that allows investors to reduce volatility by hedging particular sources of risk more efficiently.2.Securitization requires access to a large number of potential investors. To attractthese investors, the capital market needs:1. a safe system of business laws and low probability of confiscatorytaxation/regulation;2. a well-developed investment banking industry;3. a well-developed system of brokerage and financial transactions; and4.well-developed media, particularly financial reporting.These characteristics are found in (indeed make for) a well-developed financialmarket.3. Securitization leads to disintermediation; that is, securitization provides a meansfor market participants to bypass intermediaries. For example, mortgage-backedsecurities channel funds to the housing market without requiring that banks orthrift institutions make loans from their own portfolios. Securitization works welland can benefit many, but only if the market for these securities is highly liquid.As securitization progresses, however, and financial intermediaries loseopportunities, they must increase other revenue-generating activities such asproviding short-term liquidity to consumers and small business and financialservices.4. The existence of efficient capital markets and the liquid trading of financial assetsmake it easy for large firms to raise the capital needed to finance their investments in real assets. If Ford, for example, could not issue stocks or bonds to the generalpublic, it would have a far more difficult time raising capital. Contraction of thesupply of financial assets would make financing more difficult, thereby increasing the cost of capital. A higher cost of capital results in less investment and lowerreal growth.5. Even if the firm does not need to issue stock in any particular year, the stock marketis still important to the financial manager. The stock price provides importantinformation about how the market values the firm's investment projects. For example, if the stock price rises considerably, managers might conclude that the marketbelieves the firm's future prospects are bright. This might be a useful signal to thefirm to proceed with an investment such as an expansion of the firm's business.In addition, shares that can be traded in the secondary market are more attractive toinitial investors since they know that they will be able to sell their shares. This inturn makes investors more willing to buy shares in a primary offering and thusimproves the terms on which firms can raise money in the equity market.Remember that stock exchanges like those in New York, London, and Paris are theheart of capitalism, in which firms can raise capital quickly in primary marketsbecause investors know there are liquid secondary markets.6. a. No. The increase in price did not add to the productive capacity of the economy.b. Yes, the value of the equity held in these assets has increased.c. Future homeowners as a whole are worse off, since mortgage liabilities havealso increased. In addition, this housing price bubble will eventually burst andsociety as a whole (and most likely taxpayers) will suffer the damage.7. a. The bank loan is a financial liability for Lanni, and a financial asset for the bank.The cash Lanni receives is a financial asset. The new financial asset created isLanni's promissory note to repay the loan.b. Lanni transfers financial assets (cash) to the software developers. In return,Lanni receives the completed software package, which is a real asset. Nofinancial assets are created or destroyed; cash is simply transferred from one partyto another.c. Lanni exchanges the real asset (the software) for a financial asset, which is 1,500shares of Microsoft stock. If Microsoft issues new shares in order to pay Lanni,then this would represent the creation of new financial assets.d. By selling its shares in Microsoft, Lanni exchanges one financial asset (1,500shares of stock) for another ($120,000 in cash). Lanni uses the financial asset of$50,000 in cash to repay the bank and retire its promissory note. The bank mustreturn its financial asset to Lanni. The loan is "destroyed" in the transaction, since it is retired when paid off and no longer exists.8. a.AssetsLiabilities & Shareholders’ EquityCash $ 70,000 Bank loan $ 50,000 Computers 30,000 Shareholders’ equity50,000 Total $100,000 Total $100,000 Ratio of real assets to total assets = $30,000/$100,000 = 0.30b.AssetsLiabilities & Shareholders’ EquitySoftware product* $ 70,000 Bank loan $ 50,000 Computers 30,000 Shareholders’ equity50,000 Total $100,000 Total $100,000 *Valued at costRatio of real assets to total assets = $100,000/$100,000 = 1.0c.AssetsLiabilities & Shareholders’ EquityMicrosoft shares $120,000 Bank loan $ 50,000Computers 30,000 Shareholders’ equity100,000Total $150,000 Total $150,000 Ratio of real assets to total assets = $30,000/$150,000 = 0.20Conclusion: when the firm starts up and raises working capital, it is characterized bya low ratio of real assets to total assets. When it is in full production, it has a highratio of real assets to total assets. When the project "shuts down" and the firm sells it off for cash, financial assets once again replace real assets.9. For commercial banks, the ratio is: $166.1/$13,926.0 = 0.0119For nonfinancial firms, the ratio is: $15,320/$30,649 = 0.4999The difference should be expected primarily because the bulk of thebusiness of financial institutions is to make loans and the bulk of non-financial corporations is to invest in equipment, manufacturing plants, andproperty. The loans are financial assets for financial institutions, but theinvestments of non-financial corporations are real assets.10. a. Primary-market transaction in which gold certificates are being offered topublic investors for the first time by an underwriting syndicate led by JW KorthCapital.b. The certificates are derivative assets because they represent an investment inphysical gold, but each investor receives a certificate and no gold. Note thatinvestors can convert the certificate into gold during the four-year period.c. Investors who wish to hold gold without the complication, risk, and cost ofphysical storage.11. a. A fixed salary means that compensation is (at least in the short run)independent of the firm's success. This salary structure does not tie the manager’simmediate compensation to the success of the firm, so a manager might not feeltoo compelled to work hard to maximize firm value. However, the managermight view this as the safest compensation structure and therefore value it morehighly.b. A salary that is paid in the form of stock in the firm means that the manager earnsthe most when the shareholders’ wealth is maximized. Five years of vesting helpsalign the interests of the employee with the long-term performance of the firm. Thisstructure is therefore most likely to align the interests of managers and shareholders.If stock compensation is overdone, however, the manager might view it as overlyrisky since the manager’s career is already linked to the firm, and this undiversifiedexposure would be exacerbated with a large stock position in the firm.c. A profit-linked salary creates great incentives for managers to contribute to thefirm’s success. However, a manager whose salary is tied to short-term profits will be risk seeking, especially if these short-term profits determine salary or if thecompensation structure does not bear the full cost of the project’s risks. Shareholders, in contrast, bear the losses as well as the gains on the project and might be lesswilling to assume that risk.12. Even if an individual shareholder could monitor and improve managers’ performanceand thereby increase the value of the firm, the payoff would be small, since theownership share in a large corporation would be very small. For example, if you own $10,000 of Ford stock and can increase the value of the firm by 5%, a very ambitious goal, you benefit by only: 0.05 $10,000 = $500. The cost, both personal andfinancial to an individual investor, is likely to be prohibitive and would typicallyeasily exceed any accrued benefits, in this case $500.In contrast, a bank that has a multimillion-dollar loan outstanding to the firm has a big stake in making sure that the firm can repay the loan. It is clearly worthwhile for thebank to spend considerable resources to monitor the firm.13. Mutual funds accept funds from small investors and invest, on behalf of theseinvestors, in the domestic and international securities markets.Pension funds accept funds and then invest in a wide range of financial securities, on behalf of current and future retirees, thereby channeling funds from one sector of theeconomy to another.Venture capital firms pool the funds of private investors and invest in start-up firms.Banks accept deposits from customers and loan those funds to businesses or use thefunds to buy securities of large corporations.14. Treasury bills serve a purpose for investors who prefer a low-risk investment.The lower average rate of return compared to stocks is the price investors payfor predictability of investment performance and portfolio value.15. With a top-down investing style, you focus on asset allocation or the broadcomposition of the entire portfolio, which is the major determinant of overallperformance. Moreover, top-down management is the natural way to establish aportfolio with a level of risk consistent with your risk tolerance. The disadvantage ofan exclusive emphasis on top-down issues is that you may forfeit the potential highreturns that could result from identifying and concentrating in undervalued securitiesor sectors of the market.With a bottom-up investing style, you try to benefit from identifying undervaluedsecurities. The disadvantage is that investors might tend to overlook the overallcomposition of your portfolio, which may result in a nondiversified portfolio or aportfolio with a risk level inconsistent with the appropriate level of risk tolerance. Inaddition, this technique tends to require more active management, thus generatingmore transaction costs. Finally, the bottom-up analysis may be incorrect, in which case there will be a fruitlessly expended effort and money attempting to beat a simple buy-and-hold strategy.16. You should be skeptical. If the author actually knows how to achieve such returns, onemust question why the author would then be so ready to sell the secret to others.Financial markets are very competitive; one of the implications of this fact is thatriches do not come easily. High expected returns require bearing some risk, andobvious bargains are few and far between. Odds are that the only one getting rich from the book is its author.17. Financial assets provide for a means to acquire real assets as well as an expansionof these real assets. Financial assets provide a measure of liquidity to real assetsand allow for investors to more effectively reduce risk through diversification.18. Allowing traders to share in the profits increases th e traders’ willingness toassume risk. Traders will share in the upside potential directly in the form ofhigher compensation but only in the downside indirectly in the form of potentialjob loss if performance is bad enough. This scenario creates a form of agencyconflict known as moral hazard, in which the owners of the financial institutionshare in both the total profits and losses, while the traders will tend to share more of the gains than the losses.19. Answers may vary, however, students should touch on the following: increasedtransparency, regulations to promote capital adequacy by increasing the frequency of gain or loss settlement, incentives to discourage excessive risk taking, and thepromotion of more accurate and unbiased risk assessment.。

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