solution manual for 《investment analysis and portfolio management》 ch19

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1、CHAPTER 19THE ANALYSIS AND VALUATION OF BONDSAnswers to Questions1. The present value equation is more useful for the bond investor largely because the bond investor has fewer uncertainties regarding future cash flows than does the common stock investor. By investing in bonds with relatively no defa

2、ult risk (i.e., government securities) the investor can value a bond based primarily on expected cash flows (coupon rate and par value), required return (market yield), and the number of periods in the investment horizon (maturity date). Each of these factors can be incorporated into the present val

3、ue equation.By contrast, common stocks have no stated maturity date and the valuation process is predominantly an estimate of future earnings. Although the present value method can be used for common stock analysis by estimating dividend payments and change in price over a given time frame, the unce

4、rtainties involved are much greater.2.The most crucial assumption the investor makes is that cash flows will be received in full and reinvested at the promised yield. This assumption is crucial because it is implicit in the mathematical equation that solves for promised yield. If the assumption is n

5、ot valid, an alternative method must be used, or the calculations will yield invalid solutions.3(a).RFR is the riskless rate of interest, I is the factor for expected inflation, and RP is the risk premium for the individual firm.3(b).The model considers the firms business conditions. The risk of not

6、 breaking even would be reflected in the model through changes in the variable RP. This uncertainty would change the nature of the frequency distribution for earnings.4.The expectations hypothesis imagines a yield curve that reflects what bond investors expect to earn on successive investments in sh

7、ortterm bonds during the term to maturity of the longterm bond. The liquidity preference hypothesis envisions an upwardsloping yield curve owing to the fact that investors prefer the liquidity of shortterm loans but will lend long if the yields are higher. The segmented market hypothesis contends th

8、at the yield curve mirrors the investment policies of institutional investors who have different maturity preferences.5. CFA Examination I (June 1982)5(a).The term structure of interest rates refers to the relationship between yields and maturities for fixed income securities of the same or similar

9、issuer. Expectations regarding future interest rate levels give rise to differing supply and demand pressures in the various maturity sectors of the bond market. These pressures are reflected in differences in the yield movements of bonds of different maturity.The “term structure of interest rates,”

10、 or “yield curve,” will normally be upward sloping in a period of relatively stable expectations. The theoretical basis for the upward sloping curve is the fact that investors generally demand a premium, the longer the maturity of the issue, to cover the risk through time, and also to compensate for

11、 the greater price volatility of longer maturity bonds.5(b).According to the expectations theory of yield curve determination, if borrowers prefer to sell short maturity issues at the time lenders prefer to invest in longs, which happens when interest rates are expected to fall, longer maturity issu

12、es will tend to yield less than shorter maturity issues. The yield curve will be downward sloping. This generally occurs in periods when restrictive monetary policy by the Federal Reserve System, in an attempt to control inflation and inflation expectations causes very high short-term interest rates

13、. In these circumstances, demand for short-term maturities is severely dampened.5(c).The “real” rate of interest is simply the difference between nominal interest rates and some measure of inflation, such as the current consumer price index or GNP deflator. In other words, it is an inflation-adjuste

14、d interest rate.5(d).The market for U.S. Treasury securities is very large and highly liquid as a result of the huge cumulative debt of the United States Government over time. Features of Treasury securities tend to be fairly standardized and, by definition, all from one issuer. AAA corporate bonds,

15、 on the other hand, are issued by hundreds of different corporations and there are unique features to every different issue even from the same corporation. Thus, the market for these corporate bonds is much more complex in terms of assessing individual securities.Some corporate issues are large and

16、trade in very liquid markets. Others, however, are much smaller and tend to have restricted marketability. With so many issuers as well as issues, there is more room for inefficiencies to exist for short periods of time, given the diversity of the marketplace.Any market that is less than efficient o

17、ffers arbitrage opportunities. Because of these inefficiencies, issues of comparable quality, maturity, and other features can be priced differently, offering swap opportunities for bond traders or portfolio managers. Also, bonds that may appear identical for various reasons, could have better tradi

18、ng characteristics and may warrant a certain premium because of the superior liquidity.5(e).Over the past several years, fairly wide spreads have existed between AAA-corporates and Treasuries. Investor preference for Treasuries stems from several factors. Treasury securities typically are extremely

19、liquid and provide investors with more flexibility. Secondly, Treasury securities typically do not have restrictive call features generally encountered with high-grade corporates. Thus, in a period of high interest rates, investors purchasing long-term securities anticipate an eventual decline in in

20、flation and interest rates and thus prefer to lock in higher long-term yields.6.CFA Examination III (June 1982)The mini-coupon bonds would be preferable to the current coupon bond for three reasons:1.A mini-coupon bond will have a longer duration than the current bond because of the smaller coupon.

21、Its price will be more volatile for a given change in market interest rates and this is a plus under the assumption of a decline in interest rates over the next three years.2.The mini-coupon bonds have less reinvestment risk because more of the return comes from the price change over time, which is

22、assumed to increase at the YTM rate. In contrast, the total coupon for the 14 percent bond must be reinvested at the 13.75 percent rate; this could be difficult if rates are declining during this period.3.The mini-coupon bonds have greater call protection, as they are callable at 103, or more than d

23、ouble the current market. In contrast, if rates decline about 2 percent, the current coupon bond could be called at 114 (against the current market of about 102). Between the two mini-coupon bonds, the large pension fund would buy the original issue discount bond with its lower price and higher yiel

24、d to maturity. This price discrepancy between the two bonds that are otherwise similar reflects the fact that an investor subject to income taxes has to pay a capital gain each year of the OID. It is possible to also make an argument for the other mini-coupon bond on the basis of its longer duration

25、 because it has a lower yield to maturity, all else the same. The point is, because you expect lower rates, you want the longest duration security.7(a).Given that you expect interest rates to decline during the next six months, you should choose bonds that will have the largest price increase, that

26、is, bonds with long durations.7(b).Case 1: Given a choice between bonds A and B, you should select bond B, since duration is inversely related to both coupon and yield to maturity.Case 2: Given a choice between bonds C and D, you should select bond C, since duration is positively related to maturity

27、 and inversely related to coupon.Case 3: Given a choice between bonds E and F, you should select bond F, since duration is positively related to maturity and inversely related to yield to maturity.8.You should select portfolio A because it has a longer duration (5.7 versus 4.9 years) and greater con

28、vexity (125.18 versus 40.30), thereby offering greater price appreciation. Portfolio A is also noncallable, therefore there is no danger of the bonds being called in by the issuer when interest rates decline (as you expect they will). 9(a).Calladjusted duration takes into account the probability of

29、a call and its impact on the actual duration of a bond. If a bond is noncallable, duration is based on all cash flows up to and including maturity. If interest rates drop and a call becomes likely, then duration should be calculated based on the time to call, which can be substantially sooner than m

30、aturity.The range for duration now is 8.2 to 2.1 years. Because the bond is trading at par, its duration should be near 8.2 years.9(b).If rates increase, then duration will drop (recall that duration is inversely related to yield to maturity.) However, call is now very unlikely, so call-adjusted dur

31、ation will stay near the high end of the range.9(c).If rates fall to 4%, call becomes highly probable, so calladjusted duration will drop to the low end. (Remember here that duration to call is now greater than 2.1 years because of the inverse relationship between duration and yield to maturity).9(d

32、). Negative convexity refers to slow price increases of callable bonds as interest rates fall. Indeed, at some point the price change will be zero. This is due to the call price placing a ceiling on the price of a callable bond.10. CFA Examination I (1990)The two methods are modified and Macaulay du

33、ration.Macaulay duration measures the average life of a bond, ignoring any options embedded in the security. Modified duration measures the price sensitivity of a bond to the change in yield to maturity.Modified duration is the more widely used method particularly for corporate and mortgage backed i

34、ssues.11. CFA Examination II (1995)Optionadjusted duration: Optionadjusted duration (OAD) is the duration of a callable bond after adjusting for the call option. The formula for OAD is:OAD = ( PriceNCB/PriceCB) x DurNCB x (1 Delta)where PriceNCB = price of noncallable bond PriceCB = price of callabl

35、e bond DurNCB = modified duration of the noncallable bond Delta = delta of the call optionAs the equation shows, OAD depends on three elements:1.The ratio of the price of the noncallable bond to the price of the callable bond. The difference between the price of a noncallable bond and a callable bon

36、d is equal to the price of the call option. The higher (lower) the price of the call option, the greater (smaller) the ratio. The OAD will depend on the price of the call option. 2.The modified duration of the corresponding noncallable (optionfree) bond.3.The delta of the call option. The delta, whi

37、ch varies between 0 and 1, measures the change in the price of the call option when the price of the underlying bond changes.OAD permits the analyst to evaluate different fixedincome securities with embedded options (such as a callable bond) by analyzing each of these above components. For a callabl

38、e bond, for example, using modified duration is inappropriate because the expected cash flow changes as the yield changes. OAD covers the call option component, which is important in assessing callable bonds. Unlike modified duration, which calculates duration risk for optionfree bonds, OAD also con

39、siders the value and price sensitivity of the option. The OAD of a callable bond win be less than the modified duration of a noncallable bond anywhere between a deepdiscount bond and a premium bond with a high coupon rate relative to the prevailing market yield.Effective duration. Modified duration

40、is a measure of the sensitivity of a bonds price to interest rate changes, if the expected cash flow does not change with interest rates. Effective duration allows for changes in the cash flow if interest rates chance. The formula for effective duration is:Effective duration = (P - P+)/(P0)(y+ - y-)

41、where P0 = initial price (per $100 of par value) P- = price if yield is decreased by x basis points P+ = price if yield is increased by x basis points y- = initial yield minus x basis points y+ = initial yield plus x basis pointsEffective duration can be used to analyze mortgagedbacked securities fo

42、r changing prepayment rates of cash flows as interest rates change. Effective duration also allows investors to compare the risk (duration) and return (cash flow) between a bond with embedded options and one without any options. Other applications of effective duration include the analysis of asset-

43、backed securities and bonds having call/put options and sinkingfund provisions.12. CFA Examination II (1995)12(a). Description of Adjustment1. Historical real interest rate. The historical real interest rate should be adjusted to remove distortion caused by the U.S. governments “pegging” of interest

44、 rates at artificially low levels in the 1940s and early 1950s, when Treasurybill rates averaged a 0.53 percent return (194150). If the government had not pegged interest rates during this period, the rate probably would have been higher than observed, and the “true” longterm average rates would be

45、higher. This situation suggests an upward adjustment to historical real interest rates.2. Bond maturity premium. The observed bond maturity premium should be adjusted to remove bias caused by the pronounced upward trend in inflation and nominal interest rates during the period 192687, when investors

46、 systematically experienced capital losses on longterm bond holdings. ArnottSorenson estimated the loss on longterm bonds at 0.8 percent a year. Therefore, an upward adjustment to the longterm bond maturity premium is also indicated to remove the trend.Justification: The justification for each of th

47、ese adjustments is that the data contain systematic, longlasting artificial biases. Such biases must be removed if these data items are to be useful for forming valid expectations.12(b). Adjustments are justified when existing or prospective circumstances relating to the economic or market factors t

48、o be considered differ from those reflected in the historical data. Key circumstances to consider when forming expectations about future returns are:1.Current yield curve and rate of inflation. In deriving expected returns, an investor might adjust the historical returns of different asset classes t

49、o consider the current yield curve and inflation rate. Over time, prospective returns may converge on historical experience, but the expectations embedded in current data must also be considered in deriving best expectations of the future.2.“Halo” or markdown effect. A halo effect may develop around

50、 an asset class that has done unusually well over a prolonged period, resulting in a historical record needing adjustment. Market participants do not easily forget bad investment experience with a particular asset class. Therefore, investors might want to adjust historical returns on an asset class

51、that has done badly over a prolonged period to eliminate any embedded bias. 3.Distinct period. The historical return data since 1926 include many distinct eras with different capital market and inflation experiences. An investor might want to reflect the possibility that the forecast period might di

52、ffer substantially from the historical norm or might closely resemble a subperiod.4.New dimensions in environment. The environment of todays capital markets has dimensions to it such that history may be of little use. These dimensions include the savings/investment and import export disequilibria in

53、 the U.S. economy, the globalization and integration of capital markets, and rapid innovation in financial instruments. An investor may want to consider these dimensions in forecasting future returns.5.Different growth prospects. If the economic growth prospects today differ from history, an investo

54、r should consider this circumstance when forming expectations about future returns.6.Unavailability of complete or comparable data. The lack of availability of complete or comparable data on a given asset class (e.g., real estate, venture capital, and nonU.S. investments) does not justify ignoring t

55、hem. An investor might use available results plus knowledge of the risk/return characteristics of that asset class to derive useful expected return data and, thus, include that class in the universe of available asset classes.7. Link between risk tolerance and value of capital assets. Sharpe points

56、out that a direct link exists between the collective risk tolerance of investors and the per capita value of capital assets. An increase in this measure should cause risk premia (maturity, default, equity) to decline, and vice versa. An investor who believes market participants have not considered t

57、his may want to adjust historical risk premia appropriately.13. CFA Examination I (1992)Two alternative interpretations of this question are possible.Alternative 1In this alternative, the yields shown in the table in the question are assumed to be current yields to maturity and except for the 30 yea

58、r bonds, all of the Treasury Zeros have higher yields to maturity than equivalent maturity Treasury Coupons. One explanation of the higher yield to maturity on the Zeros is that they have significantly higher durations, and hence higher risk, than equivalent maturity Coupon bonds. Secondly, investor

59、s who are subject to income taxes must pay annual income taxes on the imputed income on the Zeros even though they receive no current income. Thus Zeros have higher “promised yields” because they have higher risk and tax disadvantages.Alternative 2In this alternative, the yields shown in the table i

60、n the question are assumed to be the returns actually realized by the investor at maturity. One explanation of the higher realized return on the Zero is that interest rates declined in the holding period, and there was no reinvestment rate risk on the Zeros (i.e., no coupons to reinvest), while the

61、coupon payments on the other Treasuries were reinvested at the lower interest rates. A second explanation of higher realized yields on the Zeros is that even though transactions costs are usually higher on the initial purchase on Zeros as compared to Coupon Treasuries, the periodic brokerage commiss

62、ions on the reinvested semiannual coupons may have reduced the realized yield.14. CFA Examination II (1993)14(a). The call provision generally causes the offering yield of a bond to be higher, all other things being equal. The call is an option, exercisable by the issuer. From the issuers viewpoint,

63、 the call feature is valuable when prevailing market rates drop below the coupon rate on the existing bonds. Refinancing at a lower rate would lower interest costs to the company. Between the first call date and maturity the company has this right and, therefore, the call is valuable to the company.

64、 Investors are willing to grant this valuable option to the issuer, but only for a price that reflects the likelihood the bond will be called. Therefore, callable bonds sell for a higher offering yield and lower price by the value of the option.l4(b). DurationAdding a call feature to a proposed bond

65、 issue will shorten the duration of the bond.Duration may be lowered because the call feature can potentially accelerate the payments, dependent on what happens to interest rates. When interest rates are high and the option is deep outofthemoney, a call is unlikely, and the calladjusted duration of the callable bond will be slightly lower than the duration of the noncallable bond. With decreasing rates, the likelihood o