答案6

第六章(p.141)1. 利用玻尔理论推得的轨道能量公式，计算氢原子的电子从第五能级跃迁到第二能级所释放的能量及谱线的波长。

解：J 10576.4)5121(10179.2E 192218--⨯=-⨯=nm 1.43410576.410998.210626.6E hc 191734=⨯⨯⨯⨯==λ-- 2. 利用德布罗衣关系式计算(1) 质量为9.1⨯10-31 kg ，速度为6.0⨯106 m/s 的电子，其波长为多少？ (2) 质量为1.0⨯10--2kg ，速度为1.0⨯103m/s 的子弹，其波长为多少？ 此两小题的计算结果说明什么问题？解：(1) pm 101.2m 102.1100.6101.910626.6m h 210-63134⨯=⨯=⨯⨯⨯⨯=ν=λ-- (2) pm 106.6m 106.6100.1100.110626.6m h 23-353234⨯=⨯=⨯⨯⨯⨯=ν=λ--- 由于电子的波长与原子的大小相近，讨论原子核外电子运动状态时，必须考虑它的波动性；而子弹的波长极短，以致于用常规手段无法测得其波动性而只表现其粒子性。

3. 原子中电子运动有什么特点？概率和概率密度有何区别？答：原子核外的电子运动符合微观粒子的运动规律，具有波粒二象性，即：不能同时精确地确定电子的位置和动量，只能用统计的方法指出电子在核外某处出现的可能性。

概率是随机事件出现的可能性大小的量度，就核外电子的运动而言，是指电子在空间某点上出现的可能性；概率密度则是指电子在空间某点上单位体积内出现的概率。

4. 定性地画出：3d xy 轨道的原子轨道角度分布图，22y x d 4-轨道的电子云角度分布图，4p 轨答5. 简单说明四个量子数的物理意义及量子化条件。

答：主量子数n 表征了电子出现概率最大的区域距核的远近，n = 1, 2, 3, 4, ⋯等正整数，数3d xy 原子轨道角度分布图22y x d 4-电子云角度分布图xx值越小，电子出现概率最大的区域距核越近；角量子数l 表征了波函数和电子云角度部分的形状，l = 0, 1, 2, ⋯, (n – 1)；磁场量子数m 表征了波函数和电子云角度部分在空间伸展的方向，m = 0, ±1, ±2, ⋯, ±l ；自旋量子数m s 表征了电子自旋运动的状态，m s = ±1/2。

第六章1．银行与客户间的外汇交易构成了（）。

A. 批发市场B. 结汇市场C. 售汇市场D. 零售市场正确答案是：零售市场2．下列属于所有权凭证的金融工具是（）。

A. 公司债券B. 短期国债C. 银行承兑票据D. 股票正确答案是：股票3．中央银行通过货币市场进行（），买卖有价证券以调节货币供应量。

A. 发行国债B. 公开市场业务操作C. 实施准备金政策D. 实施再贴现政策正确答案是：公开市场业务操作4．于1613年开市的（）被认为是以股票交易为中心的证券市场的开端。

A. 泛欧交易所B. 纽约证券交易所C. 伦敦证券交易所D. 阿姆斯特丹证券交易所正确答案是：阿姆斯特丹证券交易所5．同业拆借市场的形成源于中央银行对商业银行（）的要求。

A. 法定存款准备金B. 盈利水平C. 信贷规模D. 资金总量正确答案是：法定存款准备金6．资本市场从广义的角度，包括哪几个部分：（）。

B. 黄金市场C. 中长期债券市场D. 股票市场E. 银行间市场正确答案是：银行中长期信贷市场, 中长期债券市场, 股票市场7．按照金融交易的交割期限可以把金融市场划分为（）。

A. 资本市场B. 衍生品市场C. 期货市场D. 现货市场E. 货币市场正确答案是：现货市场, 期货市场8．下列金融工具中，没有偿还期的是（）。

A. 商业票据B. 大额可转让存单C. 银行定期存款D. 普通股E. 优先股正确答案是：优先股, 普通股10．金融市场的功能包括（）。

A. 风险分散和规避B. 价格发现C. 资源配置D. 资源转化E. 宏观调控传导正确答案是：资源配置, 资源转化, 价格发现, 风险分散和规避, 宏观调控传导10．保险市场除了具备一般金融市场的功能外，还有如下一些特殊的功能（）。

A. 可以形成较为合理的交易价格B. 提供有效的保险供给D. 可以提供最广泛的风险分散机制E. 提高保险交易的效率正确答案是：提供有效的保险供给, 提高保险交易的效率, 可以形成较为合理的交易价格, 可以提供最广泛的风险分散机制11．金融机构是金融市场上的最重要的中介机构。

6《藤野先生》课后习题参考答案一、本文是一篇回忆性散文。

看看文章记录了作者留学过程中的哪几件事，试为每件事拟一个小标题。

.参考答案：①离开东京之缘由；②仙台求学受优待；③初识藤野先生；④添改讲义；⑤纠正解剖图；⑥关心解剖实习；⑦了解女人裹脚；⑧匿名信事件；⑨看电影事件；⑩“我”与藤野先生惜别。

二、阅读课文中作者与藤野先生交往的部分，说说为什么他“在我的眼里和心里是伟大的”。

参考答案：藤野先生治学严谨，教学认真，没有狭隘的民族偏见，能以公正之心对待来自弱国的学生，而且给予了极大的关心、鼓励和真诚的帮助，在当时的历史背景下，能够做到这些尤其难能可贵。

作者评价说：“他的对于我的热心的希望，不倦的教诲，小而言之，是为中国，就是希望中国有新的医学；大而言之，是为学术，就是希望新的医学传到中国去。

”这段精要的议论性文字，直接表明了藤野先生的伟大。

他是一个对来自弱国的学生及其贫弱的祖国抱着同情与尊重，而又矢志于医学事业的正直学者。

所以，虽然他只是一个普通的日本人，但他“在我的眼里和心里是伟大的”。

三、本文题为《藤野先生》，可是作者还用了大量篇幅写和藤野先生无关的见闻和感受，你认为写这些内容有什么作用？参考答案：这可以从两个层面来分析。

第一，从整篇文章的结构看，全文是围绕藤野先生这个中心人物来组织材料的。

写对东京学习环境的厌恶，离开东京到仙台，是写与藤野先生结识的前因，接下来写仙台的学习生活，基本上都与藤野先生有关。

而且，作者着力正面描述了与藤野先生的交往，写“爱国青年”的寻衅和看电影所受到的刺激，这些事或与藤野先生有直接关系，或衬托出藤野先生的公正、真诚在那种环境下的难能可贵。

可以说，作者写自己的生活经历和感受，也都与写藤野先生有关联。

第二，回忆性散文的基本特点，便是时时处处都有“我”的存在，表现“我”的生活经历和感受。

这篇散文的另一条线索，就是“我”的爱国之情，具体表现为“我”弃医从文的心路历程。

从东京到仙台留学的这段经历在鲁迅的一生中产生了重要的影响，他的思想在这一阶段也发生了重要转变，而藤野先生与“我”的交往，是这段经历中最让“我”感怀的片段，也为“我”这段经历增添了一抹亮色。

博迪投资学第10版英⽂教材课后答案（6）CAPITAL ALLOCATION TO RISKY ASSETSCHAPTER 6: RISK AVERSION ANDCAPITAL ALLOCATION TO RISKY ASSETS PROBLEM SETS1. (e)2. (b) A higher borrowing rate is a consequence of the risk of the borrowers’ default.In perfect markets with no additional cost of default, this increment would equal the value of the borrower’s option to default, and the Sharpe measure, with appropriate treatment of the default option, would be the same. However, in reality there are costs to default so that this part of the increment lowers the Sharpe ratio. Also,notice that answer (c) is not correct because doubling the expected return with afixed risk-free rate will more than double the risk premium and the Sharpe ratio. 3. Assuming no change in risk tolerance, that is, an unchanged risk aversioncoefficient (A), then higher perceived volatility increases the denominator of theequation for the optimal investment in the risky portfolio (Equation 6.7). Theproportion invested in the risky portfolio will therefore decrease.4. a. The expected cash flow is: (0.5 × $70,000) + (0.5 × 200,000) = $135,000With a risk premium of 8% over the risk-free rate of 6%, the required rate ofreturn is 14%. Therefore, the present value of the portfolio is:$135,000/1.14 = $118,421b. If the portfolio is purchased for $118,421, and provides an expected cashinflow of $135,000, then the expected rate of return [E(r)] is as follows:$118,421 × [1 + E(r)] = $135,000Therefore, E(r) =14%. The portfolio price is set to equate the expected rate ofreturn with the required rate of return.c. If the risk premium over T-bills is now 12%, then the required return is:6% + 12% = 18%The present value of the portfolio is now:$135,000/1.18 = $114,4076-1CAPITAL ALLOCATION TO RISKY ASSETSd. For a given expected cash flow, portfolios that command greater riskpremia must sell at lower prices. The extra discount from expected valueis a penalty for risk.5.When we specify utility by U =E(r) – 0.5A σ2, the utility level for T-bills is: 0.07The utility level for the risky portfolio is:U = 0.12 – 0.5 × A × (0.18)2 = 0.12 – 0.0162 × AIn order for the risky portfolio to be preferred to bills, the following must hold:0.12 – 0.0162A > 0.07 ? A < 0.05/0.0162 = 3.09A must be less than 3.09 for the risky portfolio to be preferred to bills.6. Points on the curve are derived by solving for E(r) in the following equation:U = 0.05 = E(r) – 0.5A σ2 = E(r) – 1.5σ2The values of E(r), given the values of σ2, are therefore:σσ 2E(r)0.00 0.0000 0.050000.05 0.0025 0.053750.10 0.0100 0.065000.15 0.0225 0.083750.20 0.0400 0.110000.25 0.0625 0.14375The bold line in the graph on the next page (labeled Q6, for Question 6) depicts the indifference curve.7. Repeating the analysis in Problem 6, utility is now:U = E(r) – 0.5Aσ2 = E(r) – 2.0σ2 = 0.05The equal-utility combinations of expected return and standard deviation arepresented in the table below. The indifference curve is the upward sloping line in the graph on the next page, labeled Q7 (for Question 7).σσ 2E(r)0.00 0.0000 0.05000.05 0.0025 0.05500.10 0.0100 0.07000.15 0.0225 0.09506-2CAPITAL ALLOCATION TO RISKY ASSETS0.20 0.0400 0.13000.25 0.0625 0.1750The indifference curve in Problem 7 differs from that in Problem 6 in slope.When A increases from 3 to 4, the increased risk aversion results in a greaterslope for the indifference curve since more expected return is needed in order to8. The coefficient of risk aversion for a risk neutral investor is zero. Therefore, thecorresponding utility is equal to the portfolio’s expected return. The corresponding indifference curve in the expected return-standard deviation plane is a horizontal line, labeled Q8 in the graph above (see Problem 6).9. A risk lover, rather than penalizing portfolio utility to account for risk, derivesgreater utility as variance increases. This amounts to a negative coefficient of risk aversion. The corresponding indifference curve is downward sloping in the graph above (see Problem 6), and is labeled Q9.6-3CAPITAL ALLOCATION TO RISKY ASSETS6-410. The portfolio expected return and variance are computed as follows:(1) W Bills (2) r Bills (3) W Index (4) r Index r Portfolio (1)×(2)+(3)×(4) σPortfolio(3) × 20% σ 2 Portfolio0.0 5% 1.0 13.0% 13.0% = 0.130 20% = 0.20 0.0400 0.2 5% 0.8 13.0% 11.4% = 0.114 16% = 0.16 0.0256 0.4 5% 0.6 13.0% 9.8% = 0.098 12% = 0.12 0.0144 0.6 5% 0.4 13.0% 8.2% = 0.082 8% = 0.08 0.0064 0.8 5% 0.2 13.0% 6.6% = 0.066 4% = 0.04 0.0016 1.05%0.013.0%5.0% = 0.0500% = 0.00 0.000011. Computing utility from U = E(r) – 0.5 × A σ2 = E(r) – σ2, we arrive at the valuesin the column labeled U(A = 2) in the following table:W Bills W Index r Portfolio σPortfolio σ2Portfolio U(A = 2)U(A = 3) 0.0 1.0 0.130 0.20 0.0400 0.0900 .0700 0.2 0.8 0.114 0.16 0.0256 0.0884 .0756 0.4 0.6 0.098 0.12 0.0144 0.0836 .0764 0.6 0.4 0.082 0.08 0.0064 0.0756 .0724 0.8 0.2 0.066 0.04 0.0016 0.0644 .0636 1.00.00.0500.00 0.00000.0500 .0500The column labeled U(A = 2) implies that investors with A = 2 prefer a portfolio that is invested 100% in the market index to any of the other portfolios in the table.12. The column labeled U(A = 3) in the table above is computed from:U = E(r) – 0.5A σ2 = E(r) – 1.5σ2The more risk averse investors prefer the portfolio that is invested 40% in the market, rather than the 100% market weight preferred by investors with A = 2.13. Expected return = (0.7 × 18%) + (0.3 × 8%) = 15%Standard deviation = 0.7 × 28% = 19.6%14. Investment proportions: 30.0% in T-bills 0.7 × 25% = 17.5% in Stock A 0.7 × 32% = 22.4% in Stock B 0.7 × 43% = 30.1% in Stock CCAPITAL ALLOCATION TO RISKY ASSETS6-515. Your reward-to-volatility ratio: .18.080.3571.28S -== Client's reward-to-volatility ratio: .15.080.3571.196S -== 16.17. a.E(r C ) = r f + y × [E(r P ) – r f ] = 8 + y × (18 - 8) If the expected return for the portfolio is 16%, then:16% = 8% + 10% × y ?.16.080.8.10y -== Therefore, in order to have a portfolio with expected rate of return equal to 16%, the client must invest 80% of total funds in the risky portfolio and 20% in T-bills.CAPITAL ALLOCATION TO RISKY ASSETS6-6b.Client’s investment proportions: 20.0% in T-bills0.8 × 25% = 20.0% in Stock A 0.8 × 32% = 25.6% in Stock B 0.8 × 43% = 34.4% in Stock Cc.σC = 0.8 × σP = 0.8 × 28% = 22.4%18. a.σC = y × 28%If your client prefers a standard deviation of at most 18%, then:y = 18/28 = 0.6429 = 64.29% invested in the risky portfoliob. ().08.1.08(0.6429.1)14.429%C E r y =+?=+?=19. a.y*0.36440.27440.100.283.50.080.18A σr )E(r 22Pf P ==?-=-=Therefor e, the client’s optimal proportions are: 36.44% invested in the risky portfolio and 63.56% invested in T-bills.b. E(r C ) = 8 + 10 × y* = 8 + (0.3644 × 10) = 11.644% σC = 0.3644 × 28 = 10.203%20. a.If the period 1926 - 2009 is assumed to be representative of future expected performance, then we use the following data to compute the fraction allocated to equity: A = 4, E(r M ) ? r f = 7.93%, σM = 20.81% (we use the standard deviation of the risk premium from Table 6.7). Then y * is given by:M f 22ME(r )r 0.0793y*0.4578A σ40.2081-===? That is, 45.78% of the portfolio should be allocated to equity and 54.22%should be allocated to T-bills.b.If the period 1968 - 1988 is assumed to be representative of future expected performance, then we use the following data tocompute the fraction allocated to equity: A = 4, E(r M ) ? r f = 3.44%, σM = 16.71% and y* is given by:CAPITAL ALLOCATION TO RISKY ASSETS6-7M f 22M E(r )r 0.0344y*0.3080A σ40.1671-===? Therefore, 30.80% of the complete portfolio should be allocated to equity and69.20% should be allocated to T-bills.c.In part (b), the market risk premium is expected to be lower than in part (a) and market risk is higher. Therefore, the reward-to-volatility ratio is expected to be lower in part (b), which explains the greater proportion invested in T-bills.21. a. E(r C ) = 8% = 5% + y × (11% – 5%) ? .08.050.5.11.05y -==-b. σC = y × σP = 0.50 × 15% = 7.5%c.The first client is more risk averse, allowing a smaller standard deviation.22. Johnson requests the portfolio standard deviation to equal one half the marketportfolio standard deviation. The market portfolio 20%M σ=which implies 10%P σ=. The intercept of the CML equals 0.05f r =and the slope of the CML equals the Sharpe ratio for the market portfolio (35%). Therefore using the CML:()()0.050.350.100.0858.5%M fP f P ME r r E r r σσ-=+=+?==23. Data: r f = 5%, E(r M ) = 13%, σM = 25%, and B f r = 9%The CML and indifference curves are as follows:CAPITAL ALLOCATION TO RISKY ASSETS6-824. For y to be less than 1.0 (that the investor is a lender), risk aversion (A) must be large enough such that:1A σr )E(r y 2M f M <-=1.280.250.050.13A 2=-> For y to be greater than 1 (the investor is a borrower), A must be small enough: 1A σr )E(r y 2M f M >-=0.640.250.090.13A 2=-< For values of risk aversion within this range, the client will neither borrow nor lend, but will hold a portfolio comprised only of the optimal risky portfolio:y = 1 for 0.64 ≤ A ≤ 1.2825. a.The graph for Problem 23 has to be redrawn here, with: E(r P ) = 11% and σP = 15% CAPITAL ALLOCATION TO RISKY ASSETS6-9E(r)σ913251115b.For a lending position: 2.670.150.050.11A 2=->For a borrowing position: 0.890.150.090.11A 2=-<Therefore, y = 1 for 0.89 ≤ A ≤ 2.6726. The maximum feasible fee, denoted f, depends on the reward-to-variability ratio.For y < 1, the lending rate, 5%, is viewed as the relevant risk-free rate, and we solve for f as follows: .11.05.13.05.15.25f ---= ? .15.08.06.012 1.2%.25f ?=-== For y > 1, the borrowing rate, 9%, is the relevant risk-free rate. Then we notice that,even without a fee, the active fund is inferior to the passive fund because:`More risk tolerant investors (who are more inclined to borrow) will not be clients ofCAPITAL ALLOCATION TO RISKY ASSETS6-10the fund. We find that f is negative: that is, you would need to pay investors to choose your active fund. These investors desire higher risk-higher return complete portfolios and thus are in the borrowing range of the relevant CAL. In this range, the reward-to-variability ratio of the index (the passive fund) is better than that of the managed fund..13.08-28. a.With 70% of his money invested in my fund’s portfolio, the client’s expected return is 15% per year and standard deviation is 19.6% per year. If he shifts that money to the passive portfolio (which has an expected return of 13% and standard deviation of 25%), his overall expected return becomes: E(r C ) = r f + 0.7 × [E(r M ) ? r f ] = .08 + [0.7 × (.13 – .08)] = .115 = 11.5% The standard deviation of the complete portfolio using the passive portfolio would be:σC = 0.7 × σM = 0.7 × 25% = 17.5%Therefore, the shift entails a decrease in mean from 15% to 11.5% and adecrease in standard deviation from 19.6% to 17.5%. Since both mean return and standard deviation decrease, it is not yet clear whether the move isCAPITAL ALLOCATION TO RISKY ASSETS6-11beneficial. The disadvantage of the shift is that, if the client is willing to accept a mean return on his total portfolio of 11.5%, he can achieve it with a lower standard deviation using my fund rather than the passive portfolio. To achieve a target mean of 11.5%, we first write the mean of the complete portfolio as a function of the proportion invested in my fund (y ):E(r C ) = .08 + y × (.18 ? .08) = .08 + .10 × yOur target is: E(r C ) = 11.5%. Therefore, the proportion that must be invested in my fund is determined as follows:.115 = .08 + .10 × y ? .115.080.35.10y -== The standard deviation of this portfolio would be:σC = y × 28% = 0.35 × 28% = 9.8%Thus, by using my portfolio, the same 11.5% expected return can be achieved with a standard deviation of only 9.8% as opposed to the standard deviation of 17.5% using the passive portfolio.b.The fee would reduce the reward-to-volatility ratio, i.e., the slope of the CAL. The client will be indifferent between my fund and the passive portfolio if the slope of the after-fee CAL and the CML are equal. Let f denote the fee:Slope of CAL with fee .18.08.10.28.28f f---==Slope of CML (which requires no fee).13.080.20.25-== Setting these slopes equal we have:.100.200.044 4.4%.28ff -=?==per year29. a.The formula for the optimal proportion to invest in the passive portfolio is:2MfM A σr )E(r y*-=Substitute the following: E(r M ) = 13%; r f = 8%; σM = 25%; A = 3.5:20.130.08y*0.2286=22.86% in the passive portfolio 3.50.25-==?CAPITAL ALLOCATION TO RISKY ASSETS6-12b.The answer here is the same as the answer to Problem 28(b). The fee that you can charge a client is the same regardless of the asset allocation mix of the client’s portfolio. You can charge a fee that will equate the reward-to-volatility ratio of your portfolio to that of your competition.CFA PROBLEMS1. Utility for each investment = E(r) – 0.5 × 4 × σ2We choose the investment with the highest utility value, Investment 3. Investment ExpectedreturnE(r)Standarddeviationσ Utility U 1 0.12 0.30 -0.0600 2 0.15 0.50 -0.3500 3 0.21 0.16 0.1588 4 0.240.210.15182. When investors are risk neutral, then A = 0; the investment with the highest utility is Investment 4 because it has the highest expected return.3. (b)4. Indifference curve 25. Point E6. (0.6 × $50,000) + [0.4 × (-$30,000)] - $5,000 = $13,0007. (b)CAPITAL ALLOCATION TO RISKY ASSETS6-138. Expected return for equity fund = T-bill rate + risk premium = 6% + 10% = 16% Expected rate of return of the clien t’s portfolio = (0.6 × 16%) + (0.4 × 6%) = 12% Expected return of the client’s portfolio = 0.12 × $100,000 = $12,000 (which implies expected total wealth at the end of the period = $112,000) Standard deviation of client’s overall portfolio = 0.6 × 14% = 8.4% 9.Reward-to-volatility ratio =.100.71.14=CHAPTER 6: APPENDIX1. By year end, the $50,000 investment will grow to: $50,000 × 1.06 = $53,000Without insurance , the probability distribution of end-of-year wealth is:Probability Wealth No fire 0.999 $253,000 Fire0.001$ 53,000For this distribution, expected utility is computed as follows:E[U(W)] = [0.999 × ln(253,000)] + [0.001 × ln(53,000)] = 12.439582 The certainty equivalent is:W CE = e 12.439582 = $252,604.85With fire insurance , at a cost of $P, the investment in the risk-free asset is:$(50,000 – P)Year-end wealth will be certain (since you are fully insured) and equal to:[$(50,000 – P) × 1.06] + $200,000 Solve for P in the following equation:[$(50,000 – P) × 1.06] + $200,000 = $252,604.85 ? P = $372.78This is the most you are willing to pay for insurance. Note that the expected loss is “only” $200, so you are willing to pay a substantial risk premium over the expected value of losses. The primary reason is that the value of the house is a large proportion of your wealth.CAPITAL ALLOCATION TO RISKY ASSETS2. a. With insurance coverage for one-half the value of the house, the premiumis $100, and the investment in the safe asset is $49,900. By year end, theinvestment of $49,900 will grow to: $49,900 × 1.06 = $52,894If there is a fire, your insurance proceeds will be $100,000, and theprobability distribution of end-of-year wealth is:Probability WealthNo fire 0.999 $252,894Fire 0.001 $152,894For this distribution, expected utility is computed as follows:E[U(W)] = [0.999 × ln(252,894)] + [0.001 × ln(152,894)] = 12.4402225 The certainty equivalent is: W CE = e 12.4402225 = $252,766.77b.With insurance coverage for the full value of the house, costing $200, end-of-year wealth is certain, and equal to:[($50,000 – $200) × 1.06] + $200,000 = $252,788Since wealth is certain, this is also the certainty equivalent wealth of the fullyinsured position.c.With insurance coverage for 1? times the value of the house, the premiumis $300, and the insurance pays off $300,000 in the event of a fire. Theinvestment in the safe asset is $49,700. By year end, the investment of$49,700 will grow to: $49,700 × 1.06 = $52,682The probability distribution of end-of-year wealth is:Probability WealthNo fire 0.999 $252,682Fire 0.001 $352,682For this distribution, expected utility is computed as follows:E[U(W)] = [0.999 × ln(252,682)] + [0.001 × ln(352,682)] = 12.4402205 The certainty equivalent is: W CE = e 12.440222 = $252,766.27Therefore, full insurance dominates both over- and under-insurance. Over-insuring creates a gamble (you actually gain when the house burns down).Risk is minimized when you insure exactly the value of the house.6-14。