博迪《投资学》(第10版)笔记和课后习题详解 第四部分 固定收益证券【圣才出品】
博迪《投资学》笔记和课后习题详解(指数模型)【圣才出品】
第10章指数模型10.1 复习笔记1．单指数证券市场(1)单指数模型①单指数模型的定义式马科维茨模型在实际操作中存在两个问题，一是需要估计大量的数据；二是该模型应用中相关系数确定或者估计中的误差会导致结果无效。
单指数模型大降低了马科维茨资产组合选择程序的数据数量，它把精力放在了对证券的专门分析中。
因为不同企业对宏观经济事件有不同的敏感度。
所以，如果记宏观因素的非预测成分为F，记证券i对宏观经济事件的敏感度为βi；则证券i的宏观成分为，则股票收益的单因素模型为：②单指数模型收益率的构成因为指数模型可以把实际的或已实现的证券收益率区分成宏观(系统)的与微观(公司特有)的两部分。
每个证券的收益率是三个部分的总和：如果记市场超额收益R M的方差为σ2M，则可以把每个股票收益率的方差拆分成两部分：（2）指数模型的估计单指数模型表明，股票GM的超额收益与标准普尔500指数的超额收益之间的关系由下式给定：R i=αi+βi R M+e i该式通过βi来测度股票i对市场的敏感度，βi是回归直线的斜率。
回归直线的截距是αi，它代表了平均的公司特有收益。
在任一时期里，回归直线的特定观测偏差记为e i，称为残值。
每一个残值都是实际股票收益与由描述股票同市场之间的一般关系的回归方程所预测出的股票收益之间的差异。
这些量可以用标准回归技术来估计。
（3）指数模型与分散化资产组合的方差为其中定义资产组合方差的系统风险成分为依赖于市场运动的部分为它也依赖于单个证券的敏感度系数。
这部分风险依赖于资产组合的贝塔和σ2M，不管资产组合分散化程度如何都不会改变。
相比较，资产组合方差的非系统成分是σ2(e P)，它来源于公司特有成分e i。
因为这些e i 是独立的，都具有零期望值，所以可以得出这样的结论：随着越来越多的股票加入到资产组合中，公司特有风险倾向于被消除掉，非市场风险越来越小。
当各资产为等权重，且e i不相关时，有。
式中，为公司特有方差的均值。
博迪《投资学》笔记和课后习题详解(投资环境)【圣才出品】
第1章投资环境1.1 复习笔记1.金融资产与实物资产（1）概念实物资产指经济生活中所创造的用于生产商品和提供服务的资产。
实物资产包括：土地、建筑物、知识、机械设备以及劳动力。
实物资产和“人力”资产是构成整个社会的产出和消费的主要内容。
金融资产是实物资产所创造的利润或政府的收入的要求权。
金融资产主要指股票或债券等有价证券。
金融资产是投资者财富的一部分，但不是社会财富的组成部分。
（2）两种资产的区分①实物资产能够创造财富和收入，而金融资产却只是收入或财富在投资者之间的配置的一种手段。
②实物资产通常只在资产负债表的资产一侧出现，而金融资产却可以作为资产或负债在资产负债表的两侧都出现。
对企业的金融要求权是一种资产，但是，企业发行的这种金融要求权则是企业的负债。
③金融资产的产生和消除一般要通过一定的商务过程。
例如，当贷款被支付后，债权人的索偿权(一种金融资产)和债务人的债务(一种金融负债)就都消失了。
而实物资产只能通过偶然事故或逐渐磨损来消除。
2．金融市场（1）金融市场与经济①金融市场的概念金融市场是指以金融资产为交易对象而形成的供求关系及其机制的总和。
它包括三层含义，一是它是金融资产进行交易的一个有形和无形的场所；二是它反映了金融资产的供应者和需求者之间所形成的供求关系；三是它包含了金融资产交易过程中所产生的运行机制。
②金融市场的作用a.金融市场允许人们通过金融资产储蓄财富，使人们消费与收入在时间上分离。
人们可以通过调整消费期获得最满意的消费。
b.金融市场使人们可以通过金融资产的买卖来分配实物资产的风险。
c.金融市场保证了公司经营权和所有权的分离。
③代理问题代理问题是指公司的管理者追求自己的利益而非公司的利益所产生的管理者与股东潜在的利益冲突。
解决代理问题的管理机制有：期权等激励机制、通过董事会解雇管理者以及雇佣独立人士监控管理者。
绩效差的公司通常面临着被收购的危机，这是一种外部的激励。
公司治理危机包括会计丑闻、分析师丑闻和首次公开发行中的问题。
博迪《投资学》(第10版)配套题库【章节题库】-第14~28章【圣才出品】
第四部分 固定收益证券第14章 债券的价格与收益一、选择题1．一只支付年利率的债券的面值是1000美元，8年到期，到期收益是10.5%，息票率是9%。
这只债券的现在收益是（ ）。
A ．6.32% B ．7.44% C ．8.65%D ．9.77%【答案】D【解析】现期收益（CY ）是年利息除以现期价格。
根据附息债券现值的计算公式：()()()()23111111t t C C C C C D PV r r r r r -+=++++++++++L 其中，C 为附息债券每年支付的利息；D 为附息债券的面值；r 为到期收益率，即贴现率；t 为到期期限。
因此，给定：C ＝1000×9%＝90美元，D ＝1000，t ＝8，r ＝10.5%，将数据代入公式得到：()()()()()237890909090901000921.41110.5%110.5%110.5%110.5%110.5%PV +=+++++=+++++L 美元所以CY ＝90/921.41＝9.77%。
2．一只息票债券的卖出价在《华尔街日报》上显示为1080（也就是面值1000美元的108%）。
如果最后一次的利息支付是两个月以前，息票率为12%，那么这只债券的发票价格是（）美元。
A．1080B．1100C．1120D．1210【答案】B【解析】债券的价格是108%×1000＝1080美元，债券产生的利息：（0.12/12）×1000＝10（美元/月）。
因为最后一次的利息支付在2个月以前，那么付息后的这两个月所产生的利息就是2×10＝20美元。
因此，债券的发票价格＝市场价格＋产生的利息＝1080美元＋20美元＝1100美元。
3．票面利率为10%的附息债券其到期收益率为8%，如果到期收益率不变，则一年以后债券价格（）。
A．上升B．下降C．不变D．无法判断【答案】B【解析】当票面利率高于市场到期收益率时，债券是溢价的。
投资学第10版课后习题答案
CHAPTER 7: OPTIMAL RISKY PORTFOLIOSPROBLEM SETS1. (a) and (e). Short-term rates and labor issues are factors thatare 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 arefour 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 the correlation between real estatereturns 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 theminimum variance portfolio.4. The parameters of the opportunity set are:E (r S ) = 20%, E (r B ) = 12%, σS = 30%, σB = 15%, ρ =From the standard deviations and the correlation coefficient we generate the covariance matrix [note that (,)S B S B Cov r r ρσσ=⨯⨯]: Bonds Stocks Bonds 225 45 Stocks 45 900The 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 σσσ w Min (B ) = 1 =The minimum variance portfolio mean and standard deviation are:E (r Min ) = × .20) + × .12) = .1339 = %σMin = 2/12222)],(Cov 2[B S B S B B S Sr r w w w w ++σσ = [ 900) + 225) + (2 45)]1/2= %5.Proportion in Stock Fund Proportionin Bond Fund ExpectedReturnStandard Deviation% % % %minimumtangencyGraph shown below.0.005.0010.0015.0020.0025.000.00 5.00 10.00 15.00 20.00 25.00 30.00Tangency PortfolioMinimum Variance PortfolioEfficient frontier of risky assetsCMLINVESTMENT OPPORTUNITY SETr f = 8.006. The above graph indicates that the optimal portfolio is thetangency portfolio with expected return approximately % andstandard deviation approximately %.7. The proportion of the optimal risky portfolio invested in the stockfund is given by:222[()][()](,)[()][()][()()](,)S f B B f S B S S f B B f SS 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 ) = × .20) + × .12) = .1561 = % σp = [ 900) +225) + (2× 45)]1/2= %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 of14%, then you can find the corresponding standard deviation from the optimal CAL. The equation for this CAL is:()().080.4601p fC f C C PE r r E r r σσσ-=+=+If E (r C ) is equal to 14%, then the standard deviation of the portfolio is %.b. To find the proportion invested in the T-bill fund, rememberthat the mean of the complete portfolio ., 14%) is an average of the T-bill rate and the optimal 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 = and (1 − y ) = (the proportion invested in the T-bill fund).To find the proportions invested in each of the funds, multiply times the respective proportions of stocks and bonds in the optimal risky portfolio:Proportion of stocks in complete portfolio = =Proportion of bonds in complete portfolio = =10. Using only the stock and bond funds to achieve a portfolio expectedreturn 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:= × w S + × (1 −w S) = + × w S w S =So the proportions are 25% invested in the stock fund and 75% inthe bond fund. The standard deviation of this portfolio will be:σP = [ 900) + 225) + (2 45)]1/2 = %This is considerably greater than the standard deviation of %achieved using T-bills and the optimal portfolio.11. a.Even though it seems that gold is dominated by stocks, gold mightstill be an attractive asset to hold as a part of a portfolio. Ifthe correlation between gold and stocks is sufficiently low, goldwill be held as a component in a portfolio, specifically, theoptimal tangency portfolio.b.If the correlation between gold and stocks equals +1, then no onewould hold gold. The optimal CAL would be composed of bills andstocks only. Since the set of risk/return combinations of stocksand gold would plot as a straight line with a negative slope (seethe following graph), these combinations would be dominated bythe stock portfolio. Of course, this situation could not persist.If no one desired gold, its price would fall and its expectedrate of return would increase until it became sufficientlyattractive to include in a portfolio.12. Since Stock A and Stock B are perfectly negatively correlated, arisk-free portfolio can be created and the rate of return for thisportfolio, in equilibrium, will be the risk-free rate. To find theproportions of this portfolio [with the proportion w A invested inStock A and w B = (1 –w A) invested in Stock B], set the standarddeviation equal to zero. With perfect negative correlation, theportfolio standard deviation is:σP = Absolute value [w AσA w BσB]0 = 5 × w A− [10 (1 –w A)] w A =The expected rate of return for this risk-free portfolio is:E(r) = × 10) + × 15) = %Therefore, the risk-free rate is: %13. False. If the borrowing and lending rates are not identical, then,depending on the tastes of the individuals (that is, the shape oftheir indifference curves), borrowers and lenders could havedifferent optimal risky portfolios.14. False. The portfolio standard deviation equals the weighted averageof 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 portfoliostandard deviation is less than the weighted average of thecomponent-asset standard deviations. The portfolio variance is aweighted sum of the elements in the covariance matrix, with theproducts of the portfolio proportions as weights.15. The probability distribution is:Probability Rate ofReturn100%−50Mean = [ × 100%] + [ × (-50%)] = 55%Variance = [ × (100 − 55)2] + [ × (-50 − 55)2] = 4725Standard deviation = 47251/2 = %16. σP = 30 = y× σ = 40 × y y =E(r P) = 12 + (30 − 12) = %17. The correct choice is (c). Intuitively, we note that since allstocks have the same expected rate of return and standard deviation, we choose the stock that will result in lowest risk. This is thestock 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 thecombination with the lowest variance. With two stocks, I and J, theformula 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 %.18. No, the answer to Problem 17 would not change, at least as long asinvestors 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 efficientfrontier 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 serialcorrelation results in the following table:Nominal RatesFor example: to compute serial correlation in decade nominalreturns for large-company stocks, we set up the following twocolumns in an Excel spreadsheet. Then, use the Excel function“CORREL” to calculate the correlation for the data.Decade Previous1930s%%1940s%%1950s%%1960s%%1970s%%1980s%%1990s%%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 theexception of large-company stocks, there is persistent serialcorrelation. (This conclusion changes when we turn to real rates in the next problem.)21. The table for real rates (using the approximation of subtracting adecade’s average inflation from the decade’s average nominalreturn) is:Real RatesSmall Company StocksLarge Company StocksLong-TermGovernmentBondsIntermed-TermGovernmentBondsTreasuryBills 1920s1930s1940s1950s1960s1970s1980s1990sSerialCorrelationWhile 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 definitiveconclusions) 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 thehedge fund portfolio is S&P 3-year standard deviation is 0. The hedge fund 3-year standard deviation is 0. S&P Sharpe ratio is = , and the hedge fund Sharpe ratio is = .23. With a ρ = 0, the optimal asset allocation is,.With these weights,EThe resulting Sharpe ratio is = . 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: = % and Hedge: = %. The remaining 26% will be invested in the risk-free asset.24. With ρ = , the annual covariance is .25. S&P 3-year standard deviation is . The hedge fund 3-year standard deviation is . Therefore, the 3-year covariance is 0.26. With a ρ=.3, the optimal asset allocation is, .With these weights,E. The resulting Sharpe ratio is = . 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: =% and hedge: = %. The remaining % will be invested in the risk-free asset.CFA PROBLEMS1. a. Restricting the portfolio to 20 stocks, rather than 40 to 50stocks, will increase the risk of the portfolio, but it ispossible that the increase in risk will be minimal. Suppose that, for instance, the 50 stocks in a universe have the same standard deviation () and the correlations between each pair areidentical, 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 theright-hand side would be relatively small (since 49/50 is close to 19/20 and ρσ2 is smaller than σ2), but thedenominator of the first term would be 20 instead of 50. For example, if σ = 45% and ρ = , then the standard deviation with 50 stocks would be %, and would rise to % 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 thathe 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 = , the increase in portfolio risk was minimal. As a practical matter, this means that Hennessy would have to spread his portfolio 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 linearfunction of the number of issues in the portfolio. Rather, the incremental benefits from additional diversification are mostimportant 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 theportfolio from 30 to 20 stocks. In our example, restricting the number of stocks to 10 will increase the standard deviation to %. The % increase in standard deviation resulting from giving up 10 of20 stocks is greater than the % increase that results from givingup 30 of 50 stocks.3. The point is well taken because the committee should be concernedwith the volatility of the entire portfolio. Since Hennessy’sportfolio is only one of six well-diversified portfolios and issmaller than the average, the concentration in fewer issues mighthave 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 byanother portfolio. For example, Portfolio X has both higherexpected return and lower standard deviation.5. c.6. d.7. b.8. a.9. c.10. Since we do not have any information about expected returns, wefocus exclusively on reducing variability. Stocks A and C have equal standard deviations, but the correlation of Stock B with Stock C is less than that of Stock A with Stock B . Therefore, a portfoliocomposed of Stocks B and C will have lower total risk than aportfolio composed of Stocks A and B.11. Fund D represents the single best addition to complementStephenson's current portfolio, given his selection criteria. Fund D’s expected return percent) has the potential to increase theportfolio’s return somewhat. Fund D’s relatively low correlation with his current portfolio (+ indicates that Fund D will providegreater diversification benefits than any of the other alternativesexcept 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 for increasing the portfolio’s return but is too highly correlated to provide substantial volatility reduction benefits through diversification. Fund B provides substantial volatility reduction through diversification benefits but is expected to generate a return 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 thenew stock, and NP to the new portfolio.i. E(r NP) = w OP E(r OP) + w ABC E(r ABC) = + = %ii. Cov = ρOP ABC = =iii. NP = [w OP2OP2 + w ABC2ABC2 + 2 w OP w ABC(Cov OP , ABC)]1/2= [ 2 + + (2 ]1/2= % %b. Subscript OP refers to the original portfolio, GS to governmentsecurities, and NP to the new portfolio.i. E(r NP) = w OP E(r OP) + w GS E(r GS) = + = %ii. Cov = ρOP GS = 0 0 = 0iii. NP = [w OP2OP2 + w GS2GS2 + 2 w OP w GS (Cov OP , GS)]1/2= [ + 0) + (2 0)]1/2= % %c. Adding the risk-free government securities would result in alower beta for the new portfolio. The new portfolio beta will bea weighted average of the individual security betas in theportfolio; the presence of the risk-free securities would lowerthat weighted average.d. The comment is not correct. Although the respective standarddeviations and expected returns for the two securities underconsideration are equal, the covariances between each security andthe original portfolio are unknown, making it impossible to drawthe conclusion stated. For instance, if the covariances aredifferent, selecting one security over the other may result in alower standard deviation for the portfolio as a whole. In such acase, that security would be the preferred investment, assumingall other factors are equal.e. i. Grace clearly expressed the sentiment that the risk of losswas more important to her than the opportunity for return. Usingvariance (or standard deviation) as a measure of risk in her casehas a serious limitation because standard deviation does notdistinguish between positive and negative price movements.ii. Two alternative risk measures that could be used instead ofvariance are:Range of returns, which considers the highest and lowestexpected returns in the future period, with a larger rangebeing a sign of greater variability and therefore of greaterrisk.Semivariance can be used to measure expected deviations ofreturns below the mean, or some other benchmark, such as zero.Either of these measures would potentially be superior tovariance for Grace. Range of returns would help to highlightthe full spectrum of risk she is assuming, especially thedownside portion of the range about which she is so concerned.Semivariance would also be effective, because it implicitlyassumes that the investor wants to minimize the likelihood ofreturns falling below some target rate; in Grace’s case, thetarget rate would be set at zero (to protect against negativereturns).13. a. Systematic risk refers to fluctuations in asset prices causedby macroeconomic factors that are common to all risky assets;hence systematic risk is often referred to as market risk.Examples of systematic risk factors include the business cycle,inflation, monetary policy, fiscal policy, and technologicalchanges.Firm-specific risk refers to fluctuations in asset pricescaused by factors that are independent of the market, such asindustry characteristics or firm characteristics. Examples offirm-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 topfive best ideas would most likely result in the client holdinga much more risky portfolio. The total risk of a portfolio, orportfolio variance, is the combination of systematic risk andfirm-specific risk.The systematic component depends on the sensitivity of theindividual assets to market movements as measured by beta.Assuming the portfolio is well diversified, the number ofassets will not affect the systematic risk component ofportfolio variance. The portfolio beta depends on theindividual security betas and the portfolio weights of those securities.On the other hand, the components of firm-specific risk (sometimes called nonsystematic risk) are not perfectly positively correlated with each other and, as more assets are added to the portfolio, those additional assets tend to reduce portfolio risk. Hence, increasing the number of securities in a portfolio reduces firm-specific risk. For example, a patent expiration for one company would not affect the othersecurities in the portfolio. An increase in oil prices islikely to cause a drop in the price of an airline stock butwill likely result in an increase in the price of an energy stock. As the number of randomly selected securities increases, the total risk (variance) of the portfolio approaches its systematic variance.。
博迪《投资学》笔记和课后习题详解(资产组合业绩评估)【圣才出品】
第24章资产组合业绩评估24.1 复习笔记1．测算投资收益（1）时间加权收益率与货币加权收益率内部收益率，又称为投资的货币加权收益率。
之所以称它是货币加权的，是因为在测算该收益率时，不同时期的持股数对平均收益率有更大的影响。
时间加权收益率忽略了不同时期所持股数的不同，只考虑了每一期的收益，而忽略了每一期股票投资额之间的不同。
一般来说，货币加权和时间加权的收益率是不同的，孰高孰低取决于收益的时间结构和资产组合的成分。
对于单个投资者来说，货币加权收益率应该更准确些；但对于资金管理行业来说，由于投资额度的不确定性通常采用时间加权收益率来评估其业绩。
（2）算术平均与几何平均时间加权收益率与货币加权收益率两种方法为算术平均收益率，另一种方法为几何平均收益率。
一般情况下，对于一个n期投资来说，其几何平均收益率如下：其中，r t(t=1，2，…，n)为每期的收益率。
几何平均收益率绝不会超过算术平均收益率，而且在几何平均收益率的算法中，较低的收益率具有更大的影响，得出几何平均收益率要比算术平均收益率低一些。
算术平均收益率是预期未来业绩的正确方法。
2．业绩评估的传统理论（1）合适的业绩评估指标①夏普测度：夏普测度是用资产组合的长期平均超额收益除以这个时期收益的标准差。
它测度了对总波动性权衡的回报，适用于该资产组合就是投资者所有投资的情况。
②特雷纳测度：与夏普测度指标相类似，特雷纳测度给出了单位风险的超额收益，但它用的是系统风险而不是全部风险。
其适用于该资产组合只是众多子资产组合中某个资产组合的情况。
③詹森测度(组合阿尔法值)：詹森测度是建立在CAPM测算基础上的资产组合的平均收益，它用到了资产组合的贝塔值和平均市场收益，其结果即为资产组合的阿尔法值。
其适用范围同特雷纳测度一致。
④信息比率(也称估价比率)：信息比率这种方法用资产组合的阿尔法值除以其非系统风险，它测算的是每单位非系统风险所带来的非常规收益，前者是指在原则上可以通过持有市场上全部资产组合而完全分散掉的那一部分风险。
投资学第10版课后习题答案
CHAPTER 4: MUTUAL FUNDS AND OTHER INVESTMENTCOMPANIESPROBLEM SETS1. The unit investment trust should have lower operating expenses.Because the investment trust portfolio is fixed once the trust isestablished, it does not have to pay portfolio managers toconstantly monitor and rebalance the portfolio as perceived needsor opportunities change. Because the portfolio is fixed, the unitinvestment trust also incurs virtually no trading costs.2. a. Unit investment trusts: Diversification from large-scaleinvesting, lower transaction costs associated with large-scaletrading, low management fees, predictable portfolio composition,guaranteed low portfolio turnover rate.b. Open-end mutual funds: Diversification from large-scaleinvesting, lower transaction costs associated with large-scaletrading, professional management that may be able to takeadvantage of buy or sell opportunities as they arise, recordkeeping.c. Individual stocks and bonds: No management fee; ability tocoordinate realization of capital gains or losses withinvestors’ personal tax situation s; capability of designingportfolio to investor’s specific risk and return profile.3. Open-end funds are obligated to redeem investor's shares at netasset value and thus must keep cash or cash-equivalent securitieson hand in order to meet potential redemptions. Closed-end funds do not need the cash reserves because there are no redemptions forclosed-end funds. Investors in closed-end funds sell their shareswhen they wish to cash out.4. Balanced funds keep relatively stable proportions of funds investedin each asset class. They are meant as convenient instruments toprovide participation in a range of asset classes. Life-cycle fundsare balanced funds whose asset mix generally depends on the age of the investor. Aggressive life-cycle funds, with larger investments in equities, are marketed to younger investors, while conservative life-cycle funds, with larger investments in fixed-income securities, are designed for older investors. Asset allocation funds, in contrast, may vary the proportions invested in each asset class by large amounts as predictions of relative performance across classes vary. Asset allocation funds therefore engage in more aggressive market timing.5. Unlike an open-end fund, in which underlying shares are redeemedwhen the fund is redeemed, a closed-end fund trades as a security in the market. Thus, their prices may differ from the NAV.6. Advantages of an ETF over a mutual fund:ETFs are continuously traded and can be sold or purchased on margin.There are no capital gains tax triggers when an ETF is sold(shares are just sold from one investor to another).Investors buy from brokers, thus eliminating the cost ofdirect marketing to individual small investors. This implieslower management fees.Disadvantages of an ETF over a mutual fund:Prices can depart from NAV (unlike an open-end fund).There is a broker fee when buying and selling (unlike a no-load fund).7. The offering price includes a 6% front-end load, or salescommission, meaning that every dollar paid results in only $ going toward purchase of shares. Therefore: Offering price =06.0170.10$Load 1NAV -=-= $8. NAV = Offering price (1 –Load) = $ .95 = $9. Stock Value Held by FundA $ 7,000,000B 12,000,000C 8,000,000D 15,000,000Total $42,000,000Net asset value =000,000,4000,30$000,000,42$-= $10. Value of stocks sold and replaced = $15,000,000 Turnover rate =000,000,42$000,000,15$= , or %11. a. 40.39$000,000,5000,000,3$000,000,200$NAV =-=b. Premium (or discount) = NAVNAV ice Pr - = 40.39$40.39$36$-= –, or % The fund sells at an % discount from NAV.12. 100NAV NAV Distributions $12.10$12.50$1.500.088, or 8.8%NAV $12.50-+-+==13. a. Start-of-year price: P 0 = $ × = $End-of-year price: P 1 = $ × = $Although NAV increased by $, the price of the fund decreased by $. Rate of return =100Distributions $11.25$12.24$1.500.042, or 4.2%$12.24P P P -+-+==b. An investor holding the same securities as the fund managerwould have earned a rate of return based on the increase in the NAV of the portfolio:100NAV NAV Distributions $12.10$12.00$1.500.133, or 13.3%NAV $12.00-+-+==14. a. Empirical research indicates that past performance of mutualfunds is not highly predictive of future performance,especially for better-performing funds. While there may be some tendency for the fund to be an above average performer nextyear, it is unlikely to once again be a top 10% performer.b. On the other hand, the evidence is more suggestive of atendency for poor performance to persist. This tendency isprobably related to fund costs and turnover rates. Thus if the fund is among the poorest performers, investors should beconcerned that the poor performance will persist.15. NAV 0 = $200,000,000/10,000,000 = $20Dividends per share = $2,000,000/10,000,000 = $NAV1 is based on the 8% price gain, less the 1% 12b-1 fee: NAV1 = $20 (1 – = $Rate of return =20$20 .0$20$384.21$+-= , or %16. The excess of purchases over sales must be due to new inflows intothe fund. Therefore, $400 million of stock previously held by the fund was replaced by new holdings. So turnover is: $400/$2,200 = , or %.17. Fees paid to investment managers were: $ billion = $ millionSince the total expense ratio was % and the management fee was %, we conclude that % must be for other expenses. Therefore, other administrative expenses were: $ billion = $ million.18. As an initial approximation, your return equals the return on the shares minus the total of the expense ratio and purchase costs: 12% % 4% = %.But the precise return is less than this because the 4% load is paid up front, not at the end of the year. To purchase the shares, you would have had to invest: $20,000/(1 = $20,833. The shares increase in value from $20,000 to: $20,000 = $22,160. The rate of return is: ($22,160 $20,833)/$20,833 = %.19. Assume $1,000 investmentLoaded-Up Fund Economy Fund Yearly growth (r is 6%) (1.01.0075)r +-- (.98)(1.0025)r ⨯+- t = 1 year$1, $1, t = 3 years$1, $1, t = 10 years$1, $1,20. a. $450,000,000$10,000000$1044,000,000-= b. The redemption of 1 million shares will most likely triggercapital gains taxes which will lower the remaining portfolio by an amount greater than $10,000,000 (implying a remaining total value less than $440,000,000). The outstanding shares fall to 43 million and the NAV drops to below $10.21. Suppose you have $1,000 to invest. The initial investment in ClassA shares is $940 net of the front-end load. After four years, yourportfolio will be worth:$940 4 = $1,Class B shares allow you to invest the full $1,000, but yourinvestment performance net of 12b-1 fees will be only %, and you will pay a 1% back-end load fee if you sell after four years. Your portfolio value after four years will be:$1,000 4 = $1,After paying the back-end load fee, your portfolio value will be:$1, .99 = $1,Class B shares are the better choice if your horizon is four years.With a 15-year horizon, the Class A shares will be worth:$940 15 = $3,For the Class B shares, there is no back-end load in this casesince the horizon is greater than five years. Therefore, the value of the Class B shares will be:$1,000 15 = $3,At this longer horizon, Class B shares are no longer the betterchoice. The effect of Class B's % 12b-1 fees accumulates over time and finally overwhelms the 6% load charged to Class A investors.22. a. After two years, each dollar invested in a fund with a 4% loadand a portfolio return equal to r will grow to: $ (1 + r–2.Each dollar invested in the bank CD will grow to: $1 .If the mutual fund is to be the better investment, then theportfolio return (r) must satisfy:(1 + r–2 >(1 + r–2 >(1 + r–2 >1 + r– >1 + r >Therefore: r > = %b. If you invest for six years, then the portfolio return mustsatisfy:(1 + r–6 > =(1 + r–6 >1 + r– >r > %The cutoff rate of return is lower for the six-year investment because the “fixed cost” (the one-time front-end load) is spread over a greater number of years.c. With a 12b-1 fee instead of a front-end load, the portfoliomust earn a rate of return (r ) that satisfies:1 + r – – >In this case, r must exceed % regardless of the investmenthorizon.23. The turnover rate is 50%. This means that, on average, 50% of theportfolio is sold and replaced with other securities each year. Trading costs on the sell orders are % and the buy orders toreplace those securities entail another % in trading costs. Total trading costs will reduce portfolio returns by: 2 % = %24. For the bond fund, the fraction of portfolio income given up tofees is: %0.4%6.0= , or % For the equity fund, the fraction of investment earnings given up to fees is:%0.12%6.0= , or % Fees are a much higher fraction of expected earnings for the bond fund and therefore may be a more important factor in selecting the bond fund.This may help to explain why unmanaged unit investment trusts are concentrated in the fixed income market. The advantages of unit investment trusts are low turnover, low trading costs, and low management fees. This is a more important concern to bond-market investors.25. Suppose that finishing in the top half of all portfolio managers ispurely luck, and that the probability of doing so in any year is exactly ½. Then the probability that any particular manager would finish in the top half of the sample five years in a row is (½)5 = 1/32. We would then expect to find that [350 (1/32)] = 11managers finish in the top half for each of the five consecutiveyears. This is precisely what we found. Thus, we should not conclude that the consistent performance after five years is proof of skill. We would expect to find 11 managers exhibiting precisely this level of "consistency" even if performance is due solely to luck.。
博迪《投资学》(第10版)笔记和课后习题详解 第11章~第13章【圣才出品】
第11章有效市场假说11.1复习笔记1．随机漫步与有效市场假说随机漫步理论认为股价变动是随机且不可预测的。
正是市场上的充分的竞争消化了各种可得的市场信息，使得股价呈现随机游走的状态。
有效市场假定（EMH）认为任何可用于预测股票表现的信息一定已经在股价中被反映出来。
一旦有信息指出某种股票的价位被低估，存在一个套利机会，投资者的蜂拥购买会使股价立刻上升到正常的水平，从而只能得到与股票风险相称的收益率。
所以股价只对新信息做出上涨或下跌的反应。
由于新信息是不可预测的，股价的变动也是不可预测的，呈现随机游走的状态。
股价的这种变化规律正是反映了市场的有效性。
（1）有效性来源于竞争一般来说，只要进行分析，就能比别人得到更多的信息。
但是人们只有在收益高于分析花费的成本时，才愿意进行分析。
由于市场存在着激烈的竞争，证券分析师们具有强大财力支持、领取高薪、有野心，能够进行充分的信息挖掘，使得股价能够以适当的水平保证已有的信息，使市场能够较为接近有效水平。
（2）有效市场假说的形式有效市场假说一般有三种不同的形式：弱有效形式、半强有效形式和强有效形式。
这些形式通过对“全部可获得信息”的定义不同来区分。
①弱有效形式。
弱式有效市场假说认为，股价已经反映了全部能从市场交易数据中得到的信息。
股票的历史价格信息已经被市场充分消化，不可能通过市场的价格趋势分析获利。
②半强有效形式。
半强式有效市场假说认为，与公司前景有关的全部公开的已知信息一定已经在股价中反映出来了。
如果任一投资者能从公开已知资源获取这些信息，都可认为它会被反映在股价中。
③强有效形式。
强式有效市场假说认为股价反映了全部与公司有关的信息，甚至包括仅为内幕人员所知的信息。
所有有效市场假说的一个共同点：都提出价格应该反映可获得的信息。
2．有效市场假说的含义（1）技术分析技术分析中有两个常用的概念：阻力水平和支撑水平。
这些数值是指股价很难超越或不太可能再低于的水平，一般认为它们是由市场心理决定的。
博迪《投资学》笔记和课后习题详解(期权市场介绍)【圣才出品】
第20章期权市场介绍20.1 复习笔记衍生证券，又称衍生工具，其价格取决于或者衍生于其他证券的价格，又称为或有权利(contingent claim)。
衍生工具最基本的分类包括：期权、期货、远期和互换。
1. 期权合约看涨期权是期权出售者给予期权持有者在将来确定的到期日或之前以确定的价格(称为履约或执行价格)购买资产的权利。
看涨期权的净利润是期权价值与初始时购买期权的支付价格两者之差。
看跌期权是期权出售者赋予期权所有者在到期日或之前以确定的执行价格出售某种资产的权利。
当期权持有者执行期权能产生利润时，称此期权为实值期权，当执行期权无利可图时，称为虚值期权。
对看跌期权则情况正相反，当执行价格高于资产价值时其为实值期权，当执行价格等于资产价格时，称期权为两平期权。
（1）期权交易期权的交易可以分为场外交易和场内交易。
场外市场的优势在于期权合约的条款(执行价格、到期时间、标的股数量等)可根据交易的需要而定。
场内交易的期权合约的到期日、执行价格都是标准化的。
每份股票期权合约代表买入或卖出100股的权利(如果在合约有效期内发生股票分割，合约会对此作调整)。
标准化的期权合约条款增加了特定期权的交易深度，从而降低了交易成本，导致激烈的市场竞争。
（2）美式期权与欧式期权美式期权允许其持有者在期权到期日或之前任何一天行使买入或卖出标的物的权利，欧式期权只允许在到期日当天执行。
美式期权比欧式期权的余地多，所以一般说来价值更高。
（3）期权合约条款的调整为解决股票分割问题，期权合约要按分割比降低执行价格，每份合约的数量也按同比增加。
对超过10％的股票红利也要做同样的调整，期权标的股票数量应随股票红利同比增长，而执行价格则应同比减少。
但是现金红利则不影响期权合约的条款。
现金红利降低股票价格而不会在期权合约中增加调整内容，所以期权价格受红利政策的影响。
在其他情况都一致时，高红利股票的看涨期权价格较低，因为高红利减缓了股票增值速度，相反，高红利股票的看跌期权价格较高。
博迪《投资学》(第10版)笔记和课后习题详解 第24章~第25章【圣才出品】
第七部分应用投资组合管理第24章投资组合业绩评价24.1复习笔记1．测算投资收益（1）时间加权收益率与货币加权收益率①时间加权收益率时间加权收益率只考虑每一期的收益，而忽略了每一期股票投资额之间的不同。
一般来说，货币加权和时间加权的收益率是不同的，大小取决于收益的时间结构和资产组合的成分。
对于单个投资者来说，货币加权收益率应该更准确些；但对于资金管理行业来说，由于投资额度的不确定性通常采用时间加权收益率来评估其业绩。
②货币加权收益率利用现金流贴现法（DCF），令现金流入的现值与现金流出的现值相等，便可得到投资期间的平均收益率，该值称为内部收益率，又称为货币加权收益率。
（2）算术平均收益率与几何平均收益率①几何平均收益率一般情况下，对于一个n期投资来说，其几何平均收益率如下：1＋r G＝[（1＋r1）（1＋r2）…（1＋r n）]1/n其中，r t（t＝1，2，…，n）为t期的收益率。
在几何平均中，每一期的收益率权重相同。
因此，几何平均收益率又被称为时间加权收益率。
②算术平均收益率几何平均收益率绝不会超过算术平均收益率，而且在几何平均收益率的算法中，较低的收益率具有更大的影响，得出几何平均收益率要比算术平均收益率低一些。
算术平均收益率是预期未来业绩的正确方法。
（3）风险调整收益在根据投资组合的风险来调整收益的各种方法中，最简单、最普遍的方法是与其他有类似风险的投资基金进行收益率的相互比较。
经风险调整的业绩评价指标主要包括：①夏普比率：（＿r P－＿r f）/σP夏普比率是用资产组合的平均超额收益除以这个时期收益的标准差。
它测度了对总波动性权衡的回报，适用于该资产组合为投资者所有投资的情况。
②特雷纳测度：（＿r P－＿r f）/βP与夏普比率指标相类似，特雷纳测度给出了单位风险的超额收益，但它用的是系统风险而不是全部风险。
其适用于该资产组合只是众多子资产组合中某个资产组合的情况。
③詹森α（投资组合α）：αP＝＿r P－[＿r f＋βP（＿r M－＿r f）]詹森α是建立在CAPM测算基础上的资产组合的平均收益，它用到了资产组合的贝塔值和平均市场收益，其结果即为资产组合的阿尔法值。
博迪《投资学》笔记和课后习题详解(证券是如何交易的)【圣才出品】
圣才电子书 十万种考研考证电子书、题库视频学习平台
场外交易市场（OTC）是指在证券交易所之外的证券交易市场，是由证券经营机构单独 或共同设立的非集中地进行证券交易的场所，如证券交易中心、报价中心、柜台交易或转让 的场所。其交易价格采取“一对一”的议价方式。该市场可进行股票整数交易，也可进行股 票零数交易。在该市场上交易的股票通常以非上市股票为主。
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圣才电子书 十万种考研考证电子书、题库视频学习平台
向。统计潜在投资者的过程称为预约准备。预约可以为发行公司提供有价值的信息，因为大 机构投资者时常对证券市场的需求、发行公司的前景、竞争者情况具有敏锐的洞察力。
②首次公开发行的折价 首次公开发行的折价是指首次公开发行的价格通常是偏低的，股票在公开证券市场交易 的当天经常发生价格暴涨。 ③首次公开发行的成本 首次公开发行的直接成本通常约为筹资总额的 7%，而首次公开发行的偏低定价可以看 作是另一种成本。
全国证券交易商协会自动报价系统 NASDAQ（纳斯达克）是美国最著名的场外交易市 场。
③三级市场与四级市场 三级市场是指证券在交易所上市却在场外市场进行交易的市场，即上市股票的场外交易 市场。 四级市场是指投资者之间直接交易在证券交易所上市或在场外市场交易的证券，无经纪 人介入的证券交易市场。该市场适应机构投资者（如大公司）买卖上市股票的特殊需要，一 般利用电子计算机网络系统直接进行交易，可节省可观的交易费用。由于电子通信网络（ECN） 的出现，四级市场特有的投资者之间的直接交易近年来急剧增加。 ④全国交易系统 网络市场交易系统(ITS)通过电脑使不同交易所联系在一起，并允许经纪人和做市商可 以跨市场交易，构成了一个全国交易系统。 （2）交易所交易 ①参与者 由于经纪人公司在交易所拥有席位，佣金经纪商(commission broker)有权在交易所大 厅完成委托交易。 大厅经纪人(floor brokers)是交易所的独立会员，他们拥有属于自己的席位，当佣金经 纪商的订单过多而无力处理时，大厅经纪人可代为处理。
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第四部分固定收益证券
第14章债券的价格与收益
14.1复习笔记
1．债券的特征
（1）中长期国债
中期国债的期限最长为10年，而长期国债的期限为10～30年。
两种国债除了期限的差别以外，主要区别在于，以前发行的部分长期国债可在一个拟定的日期内赎回，通常在其有效期的最后5年内可赎回。
赎回条款使财政部有权在赎回期内以面值购回债券。
在金融行情表上提供的债券价格并非投资者为购买债券实际支付的价格。
这是因为牌价里没有包括计息期间产生的利息。
计算利息支付日期之间的应计利息公式为：
隔天数
两次利息支付时间的间距上次利息支付的天数年度利息应计利息＝
2（2）公司债券
①公司债券的赎回条款大部分公司债券都有可赎回条款。
赎回条款容许发行者在到期日之前以特定赎回价格赎回债券。
可赎回债券通常带有赎回保护期，即初始时期内不可赎回。
②可转换债券
可转换债券为其持有者提供了一种期权，债权人有权将债券转换成一定份额的公司普通股。
转换比例为每张债券可转换的股票数量。
转换价值为债券转换后的当前股票价值。
转换
溢价是指债券价值超出其转换价值的部分。
③可回卖债券
可回卖债券，又称为可延长债券，是指赋予债券持有人以期权的债券。
若债券的票面利率高于现时市场利率，债权人将选择继续持有债券；若债券的票面利率过低，则最好不要继续持有，债权人将会收回本金，以当期收益率进行再投资。
④浮动利率债券
浮动利率债券是指利息率与当前市场利率相联系的债券。
主要风险是公司财务实力的变化，息差在债券存续的很多年内都是固定的。
尽管浮动利率债券的票面利率随市场利率的变化而调整，但不能随公司财务状况变化而调整。
（3）优先股
优先股虽然是股票，但通常与债券一样被分在固定收益工具中。
主要因为优先股承诺支付定量的股息。
而与债券不同的是，在不能支付承诺的股息时，它不会导致公司的破产。
仅仅是应付的优先股股利继续累积，在付清优先股持有人的股息之前，普通股的持有人是不能得到股息的。
破产时优先股对公司财产的索赔权在债券之后，但优先于普通股。
与债券的利率支付不同，对公司来说，优先股股息的支付不享受税赋的扣除，这减少了发行公司以它作为筹资手段的吸引力。
但是，另一方面，优先股又有冲抵税收的优势。
优先股股东很少拥有公司的完全投票权。
然而，如果优先股股利丧失，优先股股东就可获得某些投票权。
（4）其他国内发行方
除了上述的财政部与公司外，还有其他一些债券发行者。
一般来说地方政府发行市政债券，这些债券的显著特征是其利息免税。
联邦住房贷款银行委员会、农业信贷机构以及抵押
贷款二级机构这一类的政府机构也会发行数量可观的债券。
（5）国际债券
国际债券分为两类，外国债券与欧洲债券。
①外国债券的借款人在本国之外的其他国家发行债券，并以发行市场所在国的货币为面值单位。
②欧洲债券是以发行人所在国的货币为面值单位，但在另一国市场出售的债券。
（6）债券市场的创新
发行者不断创造出具有新特征的债券，主要包括：
①逆向浮动利率债券，其息票与一般利率平均水平的变动方向相反。
②资产支持债券，其息票率与一组资产的收益相关。
③巨灾债券，其最后支付取决于一段时间内某特定地区是否发生特定的灾难。
④指数债券，其偿付与一般物价指数或某种特定的商品物价指数相联系。
2．债券定价
若令到期日为T，利率为r，债券的定价公式为：()()111T t T
t r r ==+++∑利息面值
债券价值价格和收益率的反向关系是固定收益债券的最主要特征。
利率的波动是固定收益市场风险的主要根源，债券的期限是决定其敏感性的关键因素。
评估债券价格风险的一般规律是：保持其他因素不变，债券期限越长，价格相对于利率波动的敏感性就越大。
债券的报价通常不包含应计利息，被称为净价。
购买者实际支付的是全价，它包括了应计利息，即全价＝债券净价＋应计利息。
债券付息时，由于应计利息为零，净价等于全价。
3．债券的收益率
（1）到期收益率
到期收益率是指使债券的支付现值与债券价格相等的贴现率。
通常作为债券自购买日持有至到期日为止所获得的平均收益率的测度。
其不同于债券的当期收益率，当期收益率指债券每年的利息收入除以当时的市场价格。
对于溢价债券，票面利率＞当期收益率＞到期收益率；折价债券的情况则正好相反。
（2）赎回收益率
当债券极有可能赎回时，赎回收益率的效用大于到期收益率。
赎回收益率的计算与到期收益率的计算基本相同，只需以赎回日代替到期日，以赎回价格代替面值。
这种计算有时被称为“首次赎回收益率”，因为它假设赎回发生在债券第一次可赎回的时间。
相对于到期收益率而言，溢价债券的投资者通常对债券的赎回收益率更感兴趣，因为债券在赎回日可能会被赎回。
（3）已实现的复合收益率与到期收益率
已实现的复合收益率是在假定所有息票收益都以与到期收益率相等的利率进行再投资的情况下，使最终收益等于购买债券支付的贴现率。
协定的到期收益率并不总是等于实际的已实现复合收益率。
已实现的复合收益率可在投资期结束后推算出，但由于不能得到未来再投资利率的预期，其值并不能事先推算出来。
预测不同持有期或投资水平下已实现的复合收益率被称为水平分析。
总收益预测取决于两个因素：一个是对到期出售债券的价格的预测；另一个是息票利息的再投资利率。
4．债券价格的时变性
（1）到期收益率和持有期收益率
到期收益率和持有期收益率的区别是：到期收益率只依赖于债券的息票利率、现在的价格和到期的本金。
如果债券投资持有至到期的话，到期收益率可以视为是对平均收益率的衡量。
而持有期收益率是一个特定的投资期间的收益率，而且它依赖于在持有期末债券的市场价格，此价格为未知量。
由于持有期间里债券价格受市场利率波动的影响，因此持有期收益率最多也只能预测。
持有期的债券价格无法依据利率的变化而预测，因此持有期收益率极少能被准确预测。
（2）零息票债券
零息票债券没有票面利率，以价差的方式来提供全部收益，并且仅在到期日为债券持有人提供一次性现金流。
随着时间的推移，零息票债券价格发生的变化：在到期日，它们将以面值销售。
而在到期之前，由于货币的时间价值，债券销售时会按面值打折。
价格随时间推移越来越接近面值。
一般来说，如果利率固定不变，零息票债券价格将完全按利率同比上升。
（3）税后收益
由于原始发行折扣债券（OID），如零息票债券的“内在”价格升值对债券持有人来说代表一种利息支付，因此美国国税局（IRS）专门设计出一个价格增值表，用于估算一个纳税年度中，应税的利息收入所导致的内在升值。
未出售和未到期的资产同样可以用此表计算。
如果原始发行折扣债券在一个税收年度中出售，任何因市场利率变化而导致的收益或损失，都被视为资本损益。
5．违约风险与债券定价
债券违约风险通常称信用风险，由穆迪、标准普尔及惠普进行测定，以上这些机构都提
供商业公司的财务信息并对大型企业债券和市政债券按质量进行信用评级。
它们用字母等级表示所发行债券的安全性。
最好的信用等级是AAA或Aaa。
评级为BBB及更高（标准普尔、惠普）或Baa及更高（穆迪公司）的债券被认为是投资级债券，反之，等级较低则被称为投机级债券或垃圾债券。
（1）垃圾债券
垃圾债券，也被称为高收益债券，它与投机级（低信用等级或没有信用等级）债券基本无异。
市场上垃圾债券的违约率并不能证明其没有可能获得高的收益。
发行垃圾债券比从银行贷款的融资成本更低。
（2）债券安全性的决定因素
债券评级机构主要根据发行公司财务状况的变动趋势与水平对其所发行债券的信用状况进行等级划分。
评价安全性时所用的几个重要参数有：
①偿债能力比率（Coverage ratio）
偿债能力比率是指公司收入与固定成本之间的比率。
例如，获利额对利息的倍数比率（times-interest-earned ratio）是息税前收入与应付利息的比率；固定费用偿付比率（fixed charge coverage ratio）是收益对所有固定现金债务的比率。
②杠杆比率（Leverage ratio）
杠杆比率是指债务与资本总额的比率。
过高的杠杆比率表明负债过多，标志着公司无力获取足够的收益以保证债券的安全性。
③流动性比率（Liquidity ratio）
最常见的两种流动性比率是：流动比率（current ratio），即流动资产与流动负债的比值；速动比率（quick ratio），即不包含存货在内的流动资产与流动负债的比值。
这些比率反映了公司用流动性最大的资产进行偿债的能力。