第八章債券定價(jià)和風(fēng)險(xiǎn)管理(證券投資學(xué)-北大)

1、第八章債券定價(jià)和風(fēng)險(xiǎn)管理(證券投資學(xué)-北大)CAPM, APT: treat securities at a high level of abstraction, assuming implicitly that a prior, detailed analysis of each security already had been performed, and that its risk and return features had been assessed.Specific analyses of particular security markets: valuation princ

2、iples, determinants of risk and return, portfolio strategies commonly used within and across the various markets固定收益證券Promise either a fixed stream of income or a stream of income that is determined according to a specified formula.Have the advantage of being relative easy to understand because the

3、level of payments is fixed in advance.Risk consideration are minimal as long as the issuer of the security is sufficiently creditworthy.Bond analysis Bond attributesBond pricingAppropriate yield to maturityIntrinsic valueThe relationship between the yield and priceBond risk managementWhen the maturi

4、ty and the payment time is not consistentInterest riskReinvestment riskThe approach of risk managementDurationConvexity1. Bond analysis債券是最基本的固定收益證券。債券的定價(jià)債券的特性1.1 Capitalization of Income Method of ValuePromised yield-to-maturity如果 ，則定價(jià)過(guò)低(underpriced)。如果 ，則定價(jià)過(guò)高(overpriced)。 的確定依賴于債券的特征以及現(xiàn)時(shí)的市場(chǎng)條件。例子：一

5、個(gè)債券，現(xiàn)價(jià)為900元，面值為1000元，三年到期，息率為6%。得到如果通過(guò)分析，得到問題：定價(jià)如何？如何確定 ？Intrinsic value例子：兩種程序所得結(jié)果的一致性，即價(jià)格與回報(bào)率之間的關(guān)系。為了利用Capitalization of Income Method of Value，必須決定 ， ， 的值。 和 容易確定 的確定依賴于投資者對(duì)債券的特征的主觀看法，以及現(xiàn)實(shí)的市場(chǎng)條件。從而債券分析中，最關(guān)鍵的部分是確定1.2 Bond attributes在債券定價(jià)過(guò)程中，債券的六個(gè)重要的屬性：length of time until maturitycoupon ratecall pr

6、ovisionstax statusmarketability likelihood of default在任何時(shí)間，這些性質(zhì)不同的債券的市場(chǎng)價(jià)格結(jié)構(gòu)，以到期收益來(lái)描述。整個(gè)結(jié)構(gòu)也稱為收益結(jié)構(gòu)(yield structure)。期限結(jié)構(gòu)(different maturities)：不同到期日風(fēng)險(xiǎn)結(jié)構(gòu)(different default risk)：不同違約風(fēng)險(xiǎn)yield spread：兩種債券之間的收益差。被考慮債券和具有相同的到期日和息率的無(wú)違約風(fēng)險(xiǎn)債券定價(jià)是一個(gè)相對(duì)的概念Coupon rate and length of time until maturity這兩個(gè)性質(zhì)決定了發(fā)行者承諾支付

7、給持有者的現(xiàn)金流的時(shí)間和規(guī)模。由這兩個(gè)屬性可以決定債券的到期收益率，再與基準(zhǔn)的收益率作比較。通常以國(guó)庫(kù)券的到期收益作為基準(zhǔn)。例子：前面例子里的債券與下面的國(guó)庫(kù)券比較：面值1000元，息率5%，價(jià)格910.61元。到期收益為8.5%，yield spread 為152個(gè)基點(diǎn)。Call and put provisionscall pricecall premium當(dāng)收益率劇烈下降后，債券的發(fā)行者回購(gòu)已經(jīng)發(fā)行的債券具有財(cái)務(wù)上的優(yōu)勢(shì)，因?yàn)榘l(fā)行者能夠用收益更低的債券來(lái)代替。例子：考慮10年期債券以面值（1000元）發(fā)行，息率為12%，上市5年以后，可以以回購(gòu)價(jià)格1050元進(jìn)行回購(gòu)。5年后，類似的5年期

8、的債券的收益為8%。為什么會(huì)回購(gòu)10年的到期收益（實(shí)際回報(bào)）為10.96%。Yield to call例子：面值為1000元，息率8%，30年到期的無(wú)回購(gòu)協(xié)議的債券和面值為1000元，息率8%，30年到期，回購(gòu)價(jià)格為1100元的債券price12001000 0 5% 10% 15% 20% interest rateAt high interest rates, the risk of call is negligible, and the values of the straight and callable bonds converge. At lower rates, however,

9、 the values of bonds begin to diverge, with the difference reflecting the value of the firms option to reclaim the callable bond at the call price. 兩者之差反映了公司以1100元進(jìn)行回購(gòu)這樣一個(gè)權(quán)利的價(jià)值。當(dāng)有回購(gòu)風(fēng)險(xiǎn)時(shí)，更加關(guān)注回購(gòu)收益而不是到期收益回購(gòu)收益的計(jì)算例子：假設(shè)息率為8%，30年到期的債券價(jià)格為1150元，10年后以1100元回購(gòu)回購(gòu)收益為6.64%，到期收益為6.82%The higher the coupon rate of a

10、callable bond, the greater is the likely divergence between actual and promised yields.一般來(lái)說(shuō)，息率超過(guò)5%的債券都會(huì)回購(gòu)回購(gòu)可能性越大，到期收益應(yīng)該越高，即，息率越高，或者回購(gòu)酬金越低，到期收益應(yīng)該越高當(dāng)別的性質(zhì)相同時(shí)，息率越高或者回購(gòu)酬金越低的可回購(gòu)債券，其內(nèi)在價(jià)值(intrinsic value) 應(yīng)該越低。Put provisionsputable bonds當(dāng)利率上漲時(shí)，投資者采用該策略Tax status因?yàn)槎愂盏难舆t性，低息債券比高息債券有更高的內(nèi)在價(jià)值。Marketability度量債券流動(dòng)

11、性的一個(gè)方式是Bid-Ask spread交易活躍的債券比交易不活躍的債券具有更低的bid-ask spread.交易活躍的債券比交易不活躍的債券具有更低的到期收益和更高的內(nèi)在價(jià)值。Likelihood of defaultinvestment gradespeculative grade對(duì)公司債券而言，好的級(jí)別一般與下列條件有關(guān)：低的財(cái)務(wù)杠桿大的和穩(wěn)定的利潤(rùn)大的公司規(guī)模大的現(xiàn)金流從屬債務(wù)少級(jí)別評(píng)估公司以發(fā)行公司的財(cái)務(wù)比的水平和未來(lái)趨勢(shì)為基礎(chǔ)，通過(guò)建立模型對(duì)公司債券級(jí)別進(jìn)行評(píng)估：Coverage ratios-ratio of company earnings to fixed costsLe

12、verage ratio-debt to equity ratioLiquidity ratios-current assets to current liability ratioProfitability ratios-return on assets or equityCash flow-to-debt ratio-total cash flow to outstanding debt債券有違約風(fēng)險(xiǎn)，計(jì)算期望到期收益率(expected yield-to-maturity)只要有違約或者推遲支付的可能，期望收益就會(huì)小于承諾收益(promised yield)一般來(lái)說(shuō)，違約的風(fēng)險(xiǎn)越大，違約

13、時(shí)損失的數(shù)量越大，在收益上的差別越大。Promised yield to maturity and expected yield to maturity.例子：在1993年8月，Wang Laboratories, Inc.即將破產(chǎn)，它的到期日為2009年的債券發(fā)行時(shí)以面值的35%折價(jià)發(fā)行，使得Promised yield to maturity 超過(guò)26%。投資者并不真正期望獲得26%的回報(bào)率，他們預(yù)期不可能得到所有承諾支付，以期望現(xiàn)金流為基礎(chǔ)的收益遠(yuǎn)遠(yuǎn)小于以承諾現(xiàn)金流為基礎(chǔ)的收益。例子：某公司20年前發(fā)行的債券還有10年到期，息率為9%，現(xiàn)在公司有財(cái)務(wù)困難，投資者預(yù)期利息將不受影響，但在到

14、期日，公司將破產(chǎn)，投資者只能得到面值的70%，債券現(xiàn)在的價(jià)格為750元。具體情況見下表承諾到期收益為13.7%.期望到期收益為11.6%Default premium: the difference between the promised yield on a corporate bond and the expected yield.違約的概率越大，違約酬金越高。一個(gè)關(guān)于違約酬金大小的模型：如果每期違約的概率為 ，違約時(shí)支付的數(shù)量為前一年市價(jià)的 ，則當(dāng)債券公平定價(jià)時(shí)承諾的到期收益 為承諾到期收益和期望到期收益 之間的差為債券的違約酬金。例子：One particular manner in

15、 which yield spreads seem to very over time is related to the business cycle. Yield spreads tend to be wider when the economy is in a recession. Apparently, investors perceive a higher probability of bankruptcy when the economy is faltering, even holding bond ratings constant. They require a commens

16、urately higher default premium. Risk premium對(duì)風(fēng)險(xiǎn)債券而言，它的期望到期收益和具有同樣到期日、息率的無(wú)風(fēng)險(xiǎn)債券到期收益之間的差稱為風(fēng)險(xiǎn)酬金。每種具有違約風(fēng)險(xiǎn)的債券都有違約酬金。但風(fēng)險(xiǎn)酬金是另一種酬金。例子：考慮一組公司，都有破產(chǎn)的可能性，但破產(chǎn)的原因各不相同，由這些公司的債券組成的證券組合的實(shí)際回報(bào)率近似等于其期望回報(bào)率，系統(tǒng)風(fēng)險(xiǎn)為0。每種債券的風(fēng)險(xiǎn)酬金為0，但違約酬金顯然大于0。一種債券，它的持有期收益率可能和別的債券以及股票的收益率相關(guān)。最重要的，在某種程度上，它 的持有期收益率可能和風(fēng)險(xiǎn)分散化的市場(chǎng)證券組合的收益率相關(guān)。這部分風(fēng)險(xiǎn)稱為債券的系統(tǒng)

17、風(fēng)險(xiǎn)，使得債券具有風(fēng)險(xiǎn)酬金，以它的期望收益率與無(wú)違約風(fēng)險(xiǎn)利率的差表示。例子： Default premiumyieldspread Risk premiumDefault-free yield-to-Maturity12% promised yield-to-maturity9% expected yield-to-maturity8% yield-to-maturity on a default-freebond of similar and coupon rate0%債券的違約性越大，它對(duì)市場(chǎng)潛在的敏感度越大。實(shí)證結(jié)果表明，債券的級(jí)別越低，平均回報(bào)率越高，標(biāo)準(zhǔn)差越大。實(shí)證結(jié)果表明，與股票市

18、場(chǎng)比較，級(jí)別越低的債券，對(duì)股票市場(chǎng)的波動(dòng)敏感性越大。預(yù)測(cè)違約的財(cái)務(wù)比(financial ratio)對(duì)一個(gè)公司而言，當(dāng)下面情況發(fā)生時(shí)，違約的概率變大：the existing cash balance is smallerthe expected net cash flow is smallerthe net cash flow is more variable單變量方法多變量方法單變量方法the ratio of net cash flow（income before depreciation, depletion, and amortization charges) to total d

19、ebt 多變量方法Z-score =(current assets-current liabilities)/total assets =retained earnings/total assets =earnings before interest and taxes/total assets =market value of equity/book value of total debt =sales/total assetsZ-score小于1.8公司作為違約對(duì)象，并且Z-score越小，違約的可能性越大。1.3. Yield spread 的確定評(píng)估 yield spread 的四種測(cè)

20、度：The extent to which the firms net income had varied over the preceding nine years(measured by the coefficient of variation of earnings-that is, the ratio of standard deviation of earnings to average earnings)The length of time that the firm had operated without forcing any of its creditors to take

21、 a loss.The ratio of the market value of the firms equity to the par value of its debt.The market value of the firms outstanding debt.Yield spread=1.987 +0.307(earnings variability) -0.253(time without default) -0.537(equity/debt ratio) -0.275(market value of debt)This form of the relationship accou

22、nted for roughly 75% of the variation in the bonds yield spread1.4. 債券定價(jià)給定合理的利率，給債券公平定價(jià)何為合理利率？合理的利率（或者折現(xiàn)率）是由市場(chǎng)唯一確定的，包括：實(shí)利率通貨膨脹率yield spread一級(jí)市場(chǎng)：以面值發(fā)行息率近似為市場(chǎng)收益率二級(jí)市場(chǎng)：債券價(jià)格受市場(chǎng)的影響，市場(chǎng)利率波動(dòng)是固定收入證券市場(chǎng)的主要風(fēng)險(xiǎn)根源。The inverse relationship between price and yield is a central feature of fixed-income securities. Inte

23、rest rate fluctuations represent the main source of risk in the fixed-income market, and one key factor that determines that sensitivity is the maturity of the bond. A general rule in evaluating bond price risk is that, keeping all other factors the same, the longer the maturity of the bond, the gre

24、ater the sensitivity of price to fluctuations in the interest rate. This is why short-term Treasury securities such as T-bills are considered to be the safest. They are free not only of default risk, but also largely free of price risk attributable to interest rate volatility.當(dāng)息率等于市場(chǎng)利率時(shí)，價(jià)格等于面值In the

25、se circumstances, the investor receives fair compensation for the time value of money in the form of the recurring interest payments. No further capital gain is necessary to provide fair compensation.當(dāng)息率小于市場(chǎng)利率時(shí)，價(jià)格小于面值The coupon payments alone will not provide investors as high a return as they could

26、 earn elsewhere in the market. To receive a fair return on such an investment, investors also need to earn price appreciation on their bonds. The bond would have to sell below par value to provide a “built-in” capital gain on the investment.例子：面值1000元，息率7%，公平利率8%，三年到期現(xiàn)在公平價(jià)格=70講義+1000講義=974.23一年后公平價(jià)格

27、為=70講義+1000講義=982.17過(guò)去的一年的回報(bào)率為70+7.94/973.23=8%When bond prices are set according to the present value formula, any discount from par value provides an anticipated capital gain that will augment a below-market coupon rate just sufficiently to provide a fair total rate of return. If the coupon rate e

28、xceeds the market interest rate, the interest income by itself is greater than available elsewhere in the market. The price is greater than the par value, the resulting capital losses offset the large coupon payments so that the investor receive only a fair rate of return.Each bond offers investors

29、the fair total rate of return. Although the capital gain versus income components differ, the price of each bond is set to provide competitive rates, as we should expect in well-functioning capital markets. Security returns all should be comparable on an after-tax risk-adjusted basis. If they are no

30、t, investors will try to sell low-return securities, thereby deriving down the prices until the total return at the now lower price is competitive with other securities. Prices should continue to adjust until all securities are fairly priced in that expected returns are appropriate(given necessary r

31、isk and tax adjustments)2. Fixed-income portfolio management這里所謂的風(fēng)險(xiǎn)管理，是針對(duì)債券的利率風(fēng)險(xiǎn)控制，而債券本身的風(fēng)險(xiǎn)（例如，違約風(fēng)險(xiǎn)）不在討論范圍之內(nèi)。2.1 利率風(fēng)險(xiǎn)As interest rates rise and fall, bondholders experience capital losses and gains. These gains or losses make fixed-income investments risky, even if the coupon and principal payments

32、are guaranteed, as in the case of Treasury obligations.Why do bond prices respond to interest rate fluctuations?In a competitive market all securities must offer investors fair expected rates of return. The sensitivity of bond prices to changes in market interest rates is obviously of great concern

33、to investors.債券定價(jià)定理：說(shuō)明市場(chǎng)收益變化和價(jià)格變動(dòng)之間的關(guān)系（定性描述）。假設(shè)每年支付一次利息，以到期收益為研究對(duì)象：1. 如果債券的市場(chǎng)價(jià)格上升，則收益下降；反過(guò)來(lái)，如果債券價(jià)格下降，則收益上升。2. 如果債券的收益在到期日之前不變，則它的折價(jià)或者酬金的規(guī)模將隨著到期日的接近而下降。TodayMaturity DatePar ValuePrice of a premium bondPrice of a discount bondpremiumdiscount3. 如果債券的收益在到期日之前不變，則它的折價(jià)或者酬金的規(guī)模變化速度隨著到期日的靠近加快。4. 當(dāng)債券的收益上升和下降

34、相同的數(shù)量時(shí)，收益上升導(dǎo)致價(jià)格下降的規(guī)模，小于收益下降導(dǎo)致價(jià)格上升的規(guī)模。5. 債券的息率越高，由收益變化導(dǎo)致的價(jià)格變化的百分比越小。例子Bond C: coupon rate=7%, yield=7%, P=1000Bond D: coupon rate=9%, yield=7%, P=1082when yield change to be 8% bond C: price 1000 960.03, 3.993%bond D: price 1082 1039.93 3.889%6. 長(zhǎng)期債券的價(jià)格對(duì)利率變化的敏感度大于短期債券的敏感度。即，長(zhǎng)期債券有更大的利率風(fēng)險(xiǎn)。7. 債券發(fā)行時(shí)的初始到期

35、收益越低，則它對(duì)收益變化的敏感度越大。債券價(jià)格對(duì)市場(chǎng)利率變化的敏感度受三個(gè)關(guān)鍵因素的影響：到期日，息率，到期收益2.2 DurationThe propositions confirm that maturity is a major determinant of interest rate risk. However, the also show that maturity alone is not sufficient to measure interest rate sensitivity.例子：息率8%的債券Because we know that long term bonds ar

36、e more sensitive to interest rate movements than are short term bonds, in some sense a zero coupon bond represents a longer-term bond than an equal-time-maturity coupon bond. This is the insight about effective maturity.比較20年到期的零息債券和帶息債券(8% coupon rate)。The 20-year 8% bond makes many coupon payments

37、, most of which come years before the bonds maturity date. Each of these payments may be considered to have its own “maturity date”, and the effective maturity of the bond is therefore some sort of average of the maturities of all the cash flows paid out by the bond.The zero-coupon bond, by contrast

38、, makes only one payment at maturity. Its time to maturity is a well defined concept. To deal with the ambiguity of the maturity of a bond making many payments, we need a measure of the average maturity of the bonds promised cash flows to serve as a useful summary statistic of the effective maturity

39、 of the bond. We would like also to use the measure as a guide to the sensitivity of a bond to interest rate changes.Duration這里 表示在時(shí)間 接受的現(xiàn)金流的現(xiàn)值，利用債券的到期收益作為折現(xiàn)率得到。 表示債券現(xiàn)在的市場(chǎng)價(jià)格。 表示債券剩下的距到期日的時(shí)間。8%BondTimeyearsPaymentPV of CF(10%)WeightC1 XC4.54038.095.0395.019714036.281.0376.03761.52.0401040sum34.553855

40、.611964.540.0358.88711.000.05371.77421.8852Duration Calculation: Exle using Table 16.3Duration當(dāng)?shù)狡谑找姹３植蛔儠r(shí)，證券組合duration 是單個(gè)債券duration的加權(quán)和Duration 在固定收益投資組合管理中的作用測(cè)量證券組合有效平均到期日的統(tǒng)計(jì)量度量證券組合對(duì)利率的敏感度（定量刻畫） an essential tool in immunizing portfolios from interest rate riskDuration 和股票價(jià)格變化之間的關(guān)系這里 表示債券價(jià)格的變化 是債券的

41、初始價(jià)格 是到期收益的變化 是初始的到期收益例子Bond : coupon rate 8%, yield to maturity 8%, par value 1000, price 1000, duration 10 when yield to maturity 8% 9% What determines duration?Duration MaturityZero coupon bond15% coupon YTM=6%3% coupon YTM=15%15% coupon YTM=15%Rule for duration零息債券的duration等于其到期日到期日保持不變，息率越低， du

42、ration越高息率不變，到期日越大， duration一般越大。對(duì)等價(jià)或者溢價(jià)發(fā)行的債券，上述關(guān)系總是成立別的因素不變，到期收益越低，帶息債券的duration越高。永久性現(xiàn)金流的duration為到期日與duration的差別當(dāng)?shù)狡谌赵絹?lái)越大時(shí)， duration接近于相應(yīng)永久性現(xiàn)金流的duration注意支付時(shí)間單位與利率之間的一致性2.3 ConvexityAs a measure of interest rate sensitivity, duration clearly is a key tool in fixed income portfolio management.The d

43、uration rule for the impact of interest rates on bond prices is only an approximation.YieldPriceDurationPricing Error from convexityDuration and ConvexityThe duration rule is a good approximation for small changes in bond yield, but it is less accurate for larger changes.The duration approximation a

44、lways understates the value of the bond, it underestimates the increase in bond price when the yield falls, and it over estimates the decline in price when the yield rises.The curvature of the price yield curve is called the convexity of the bond.As a practical rule, we can view bonds with higher co

45、nvexity as exhibiting higher curvature in the price yield relationship.Convexity allows us to improve the duration approximation for bond price changes.Correction for ConvexityCorrection for Convexity:Ex. A 30-year maturity, an 8% coupon, and sells at an initial yield to maturity of 8%. The bond sel

46、ls at par value, $1000. The modified duration is 11.26years. If the bonds yield increase from 8% to 10%, the bond price will fall to $811.46, a decline of 18.85%.The duration rule would predictThe duration-with-convexity ruleyWhy do investors like convexity? Bond ABond BBond A has greater price incr

47、eases and smaller price decreases when interest rates fluctuate by larger amounts.2.4 Passive bond managementPassive methods假設(shè)債券市場(chǎng)時(shí)半強(qiáng)有效的。證券選擇(security selection)和決定交易時(shí)間(market timing)都是無(wú)用的，不會(huì)帶來(lái)超平均的收益。Active methods假設(shè)債券市場(chǎng)不是非常有效的。通過(guò)準(zhǔn)確預(yù)測(cè)利率來(lái)辨別誤定價(jià)的債券或者制定交易時(shí)間，從而能夠獲得超額收益。Passive methods消極債券管理認(rèn)為債券的價(jià)格是公平的，只能

48、控制固定收入證券組合的風(fēng)險(xiǎn)主要策略：指標(biāo)化策略:復(fù)制給定債券指標(biāo)的行為Immunization 策略：shield the overall financial status of the institution from exposure to interest rate fluctuations.兩者認(rèn)為市場(chǎng)價(jià)是公平的兩者的區(qū)別債券-指標(biāo)證券組合和債券市場(chǎng)指標(biāo)具有相同的風(fēng)險(xiǎn)-收益回報(bào)Immunization建立了零風(fēng)險(xiǎn)的證券組合，利率的波動(dòng)對(duì)公司的價(jià)值沒有影響。Bond-index fundsCreate a portfolio that mirrors the composition of

49、 an index that measures the broad market.債券市場(chǎng)指標(biāo)Lehman Brothers, Merrill Lynch, Salomon BrothersNumber of issuesmaturity of included bondsexcluded issuesweightingreinvestmentDaily availability 構(gòu)造反映債券市場(chǎng)指標(biāo)的證券組合問題：債券種類過(guò)多，難以一一購(gòu)買交易少，很難以公平市價(jià)買到指標(biāo)中包含的所有債券指標(biāo)不斷更換到期日少于1年的債券不斷調(diào)整，利息收入重投資方法：精確復(fù)制債券指標(biāo)不可行，采用cellular方

50、法把債券市場(chǎng)分成幾類指標(biāo)中債券在各類中占的比例按這一比例構(gòu)造債券組合In these way, the characteristics of the portfolio in terms of maturity, coupon rate, credit risk, industrial representation, and so on, will match the characteristics of the index, and the performance of the portfolio likewise should match the index. SectorT-t-MTre

51、asuryAgencyMortgage-BackedIndustrialFinanceUtilityYankee1 year12.1%1-3 years5.4%3-5 years4.1%5-7 years7-10 years0.1%10-15 years 15-30 years9.2%3.4%30+ yearsImmunization兩種不同的看待利率風(fēng)險(xiǎn)的方式銀行，使得資產(chǎn)凈現(xiàn)值不受利率波動(dòng)的影響?zhàn)B老金，使得資產(chǎn)將來(lái)的值不受風(fēng)險(xiǎn)的影響What is common to the bank and the pension fund is interest rate risk. The net w

52、orth of the firm or the ability to meet future obligations fluctuates with interest rates.通過(guò)適當(dāng)調(diào)整證券組合的到期日結(jié)構(gòu)，規(guī)避利率風(fēng)險(xiǎn)Immunization techniques refer to strategies used by such investors to shed their overall financial status from exposure to interest rate fluctuations.Net worth immunization例子：承諾在兩年后支付1000

53、000元，有兩種債券可供選擇：債券 1年 2年 3年 yield 1 80 80 1080 10% 2 1070 10% 例子：保險(xiǎn)公司以價(jià)格10000元發(fā)行一種guaranteed investment contract(GIC)，5年到期，保證利率為8%。假設(shè)公司選擇息率8%，6年到期、價(jià)格為10000元的帶息債券為債務(wù)提供基金。 價(jià)格風(fēng)險(xiǎn)重投資風(fēng)險(xiǎn)Terminal value of a bond portfolio after 5 years (all proceeds reinvested)A. rates remain at 8%Terminal value of a bond portfolio after 5 years (all proc