SECTION A: MULTIPLE CHOICE QUESTIONS. 1. All else equal, which of the following would most likely increase the yield to maturity on a debt security?

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1 SECTION A: MULTIPLE CHOICE QUESTIONS 2 (40 MARKS) 1. All else equal, which of the following would most likely increase the yield to maturity on a debt security? 1. Put option. 2. Conversion option. 3. Negative covenants. 4. Cap on a floating-rate security. A cap on a floating-rate secutity is an embedded option that favours the issuer, not the buyer, so buyers will would demand a higher YTM for a bond with such a feature. The other alternatives favour the buyer and decrease the YTM that buyers require. 2. One year ago, an investor purchased a 10-year, R1,000 par value, 8% semiannual coupon bond with an 8% yield to maturity. Today interest rates remain unchanged at 8%. If the investor sells the bond today (immediately after receiving the second coupon payment, and with no transaction costs), he will have: 1. a capital loss of R a capital gain of R no capital gain or loss. 4. a capital gain of R1,080. One year ago (when he bought the bond) the coupon rate was equal to the YTM, so the bond would have traded at par. Now (one year later), with interest rates unchanged, the bond will still sell at par. There would therefore be no capital gain or loss from the sale. 3. A 15-year, 8% semiannual-pay bond has a par value of R10,000. If it were priced to yield 7.4%, this bond would be trading for: 1. R10, R10,528.

2 3 3. R10, R10, N 3.7 I/YR FV 400 PMT PV = 10, The price of a 5-year zero coupon bond with a current yield to maturity (YTM) of 8.4% is If the YTM increases to 8.9%, the price will decrease to If the YTM decreases to 7.9%, the price will increase to The effective duration is closest to: Effective duration = ( ) (66.27 x 2 x 0.005) = 4.80 (Price changes are based on 50 basis point change in yield) 5. Which of the following statements about the risks associated with investing in bonds is least accurate? 1. If the issuer/borrower prepays, the holder of the bond has reinvestment risk. 2. Credit risk is the risk that an investor will be unable to sell the security quickly and at a fair price. 3. Volatility risk is the risk that the price of a bond with an embedded option will decline when expected yield volatility changes. 4. Interest rate risk is the risk that a bondholder faces if the price of a bond held in a portfolio will decline due to rising market interest rates.

3 4 Liquidity risk is the risk that an investor will be unable to sell the security quickly without offering it at a significantly lower price. Credit risk is the possibility that the issuer will fail to meet its obligations, such as timely payment of interest and principal. 6. A company has two R1,000 face value bonds outstanding, both currently selling for R The first issue has an annual coupon of 8% and 20 years to maturity. The second bond has the same yield to maturity as the first bond but has only 5 years remaining until maturity. Both bonds pay coupons once per year. What is the annual interest payment on the second issue? 1. R R R R Find the YTM of the first bond and use it in the second bond calculation: PV 1000 FV 80 PMT 20 N I/Y = N PMT = A semiannual-pay bond is callable in five years at R1,080. The bond has an 8% coupon and 15 years to maturity. If an investor pays R895 for the bond today, the yield to call is closest to: % % % %.

4 5 10 N -895 PV 40 PMT 1080 FV I/Y=6.035 x 2 = 12.07% 8. The following information applies to a portfolio of U.S. Treasuries. Maturity Key rate duration 3-month year year year year year year year year 0.03 This is most likely an example of a: 1. bullet portfolio. 2. ladder portfolio. 3. barbell portfolio. 4. humped portfolio. Key rates are affected by the weight of a portfolio that is attributed to the corresponding maturity sector. A ladder portfolio is one with approximately equal dollar amounts (market values) in each maturity sector. A barbell portfolio has considerably greater weights given to the shorter and longer maturity bonds than to the intermediate maturity bonds. A bullet portfolio has greater weights concentrated in the intermediate maturity relative to the shorter and longer maturities. 9. If the yield curve shifts up by 50 basis points for all maturities, which of the following bonds would be the best one to own?

5 year, 6% coupon, 7.5% yield to maturity year, 7% coupon, 7.5% yield to maturity year, 7% coupon, 7.5% yield to maturity year, 6.5% coupon, 7% yield to maturity. The bond with the lowest duration will suffer the least (smallest price decrease) from an increase in rates. The higher the coupon, higher YTM, and shorter time to maturity, the lower the duration will be. 10. Consider a bond with a put option and a bond with a prepayment option. An increase in interest rate volatility will most likely have the following effect on the market yield of each bond. Bond with the prepayment option Bond with the put option 1. Increase Increase 2. Decrease Increase 3. Increase Decrease 4. Decrease Decrease An increase in yield volatility will increase the value of embedded options. The bondholder is short the prepayment option, so the increase in value of the prepayment option decreases the value of the bond, and the required yield will increase. The bondholder is long the put option, so the value of the putable bond will increase with an increase in yield volatility, and the required yield will decrease. 11. Which of the following is a major criticism of the pure expectations theory of the term structure of interest rates? It ignores: 1. the credit risk of an investment. 2. the convexity of an investment. 3. the price risk and reinvestment risk of an investment. 4. the preference of investors for a particular maturity sector.

6 7 The major criticism of the pure expectations theory is that it fails to recognize interest rate risk; specifically, price risk and reinvestment risk. Price risk is the uncertainty associated with future bond prices as a result of interest rate changes, and reinvestment risk reflects the uncertainty associated with the rate at which the bond s cash flows can be reinvested. 12. For an option-free bond, estimating the price change for a 1% decline in its yield to maturity using only its modified duration will most likely produce an answer that: 1. is equal to the actual price change. 2. is larger than the actual price change. 3. is smaller than the actual price change. 4. may be smaller or larger than the actual price change. Duration is a linear measure, but the relationship between bond price and yield for an option-free bond is convex. For a given decrease in yield, the estimated price increase using duration alone will be smaller than actual price increase. 13. A bond with an embedded put option has a modified duration of 8, an effective duration of 7 and a convexity of If interest rates rise by 25 basis points, the bond s price will change by approximately: % % % %. Effective duration must be used for bonds with embedded options. P= -(ED)( y) + (C)( y) 2 P= -(7)(0.0025) + (64.5)(0.0025) 2 = = -1.71%.

7 8 14. Consider a 15-year bond with a 10% coupon, paid semiannually. Calculate the price value of a basis point if the yield changes from 9.00% to 9.01%. 1. R R R R Input 9.00% 9.01% FV PMT 5 5 I/YR N PV = The arbitrage-free approach to bond valuation: 1. requires each cash flow to be discounted at the current yield. 2. requires each cash flow to be discounted at the yield to maturity. 3. requires each cash flow to be discounted at a rate specific to its time period. 4. requires each cash flow to be discounted at its corresponding 6-month forward rate. Textbook: page 110, IV The arbitrage-free valuation approach

8 9 16. Bond A has an embedded option, a nominal yield spread to Treasuries of 1.6%, a zerovolatility spread of 1.4%, and an option-adjusted spread of 1.2%. Bond B is identical to Bond A except that it does not have the embedded option, has a nominal yield spread to Treasuries of 1.4%, a zero-volatility spread of 1.3%, and an option-adjusted spread of 1.3%. The option most likely embedded in Bond A, and the bond that is the best value, are: Embedded option Better value 1. Put Bond A 2. Put Bond B 3. Call Bond A 4. Call Bond B Since the OAS is less than the Z-spread for Bond A, the effect of the embedded option is to decrease the required yield, so it must be a call option and not a put option. The OAS is the spread after taking out the effect of the embedded option. Since OAS is higher for Bond B, it represents the better value after adjusting for the value of the call in Bond A. 17. Spreads on swap rates (based on the LIBOR curve) over comparable U.S. Treasury yields most likely reflect: 1. credit risk. 2. sovereign risk. 3. both credit and sovereign risk. 4. neither credit risk nor sovereign risk. Swap curves are not default-free curves because the LIBOR-based swap spreads over US Treasuries reflect counterparty credit risk. Swap spreads over US Treasuries do not reflect sovereign risk. The swap market is not regulated by any government, which makes swap spreads more comparable across borders than government bond yields, which do reflect sovereign risk.

9 Which of the following most accurately describes an inverse floating-rate bond? 1. Under certain circumstances, it may require the bondholder to make payments to the issuer. 2. Its coupon rate increases when market rates increase and decreases when market rates decrease. 3. It has an implicit cap on the maximum coupon rate and typically includes a floor on the minimum coupon rate. 4. It increases in principal value as market rates decrease and decreases in principal value as market rates increase. The coupon rate, not the principal, in adjusted inversely with market interest rates. Because the coupon rate on an inverse floater increases when market rates decrease, there is an implicit cap on the coupon rate (market rates cannot decline further than zero). The bondholder always receives coupon payments from the issuer; the opposite would imply a negative interest rate. 19. Security Q matures in eight years and has a par value of R1,000. During the first five years, Q has a 5% coupon with semiannual payments. During the remaining three years, Q has an 8% coupon with semiannual payments. The par value is paid at maturity. A second 8-year security, Security W, has a 6% semiannual coupon for its entire life, and is selling at par. Assuming that Q has the same (bond equivalent) yield as W, the price of Security Q is closest to: 1. R R1, R1, R1,372. Since W is selling at par, yield = coupon rate = 6%. Yield on Q is therefore 6% (BEY). Q makes 10 payments of R25, 5 payments of R40, and one payments or R CFj

10 11 25 CFj 10 Nj 40 CFj 5 Nj 1040 CFj 3 I/YR NPV = Suppose you observe a 6-month (zero-coupon) Treasury with a market price of You also observe a 1-year (zero-coupon) Treasury trading at Lastly, you observe a 1.5-year Treasury with a 6% coupon trading at The 1.5-year spot rate, expressed as a bond equivalent yield, is closest to: % % % %. 0.5-year security 1.0-year security HP10bII Function FV 0 0 PMT PV 1 2 N I/YR (semiannual rate) ¹ ¹ 5.7%/2

11 12 SECTION B: LONG QUESTIONS (20 MARKS) Question 1 [10 marks] a) Bootstrapping is a methodology for calculating the theoretical Treasury spot rate curve, given the Treasury yield curve derived from on-the-run Treasury issues. Explain the basic principle underlying the methodology of bootstrapping. (2) Default-free spot rates can be derived from the Treasury yield curve by a method called bootstrapping. The basic principle underlying the bootstrapping method is that the value of a Treasury coupon security is equal to the value of the package of zero-coupon Treasury securities that duplicates the coupon bond s cash flows. *Workbook: page 35.

12 13 b) Why does using both duration and convexity give a better measure of the effect of interest rate risk than using duration alone? (3) Duration is a first (linear) approximation for a small change in yield. It applies only to parallel shifts in the yield curve. It will underestimate the increase and overestimate the decrease in the value of a bond. The approximation can be improved by using a second approximation. This approximation is referred to as the convexity adjustment. It is used to approximate the change in price that is not explained by duration (parallel shifts of the yield curve). *Workbook, page 43. Duration is a first approximation of a bond s price or a portfolio s value to interest rate changes. To improve the estimate provided by duration, a convexity adjustment can be used. Using duration combined with a convexity adjustment to estimate the percentage price change of a bond to changes in interest rates is called the duration/convexity approach to interest rate risk measurement. Duration does a good job of estimating the percentage price change for a small change in interest rates but the estimation becomes poorer the larger the change in interest rates. The duration measure indicates that regardless of whether interest rates increase or decrease, the approximate percentage price change is the same; however, this is not a property of a bond s price volatility for large changes in yield. A convexity adjustment can be used to improve the estimate of the percentage price change obtained using duration, particularly for a large change in yield. The convexity adjustment is the amount that should be added to the duration estimate for the percentage price change in order to obtain a better estimate for the percentage price

13 14 change. c) There are two forms of the biased expectations theory. Explain why these two forms are referred to as biased expectations. (3) All expectations theories the pure expectations theory, the liquidity preference theory, and the preferred habitat theory share a hypothesis about the behaviour of short-term forward rates and also assume that the forward rates in current long-term bonds are closely related to the market s expectations about future short-term rates. While the pure expectations theory postulates that no systematic factors other than expected future short-term rates affect forward rates, the liquidity preference theory and the preferred habitat theory postulate that there are other factors and therefore are referred to as biased expectations theories. The liquidity preference theory asserts that investors demand a liquidity premium for extending maturity so that the forward rates are biased by this premium. The preferred habitat theory asserts that investors must be induced by a yield premium in order to accept the risks associated with shifting funds out of their preferred sector and forward rates embody the premium for this inducement. *Workbook: page 227

14 15 d) Give one advantage and one disadvantage to using yields on Treasury strips to construct the theoretical spot rate curve instead of bootstrapping. (2)

15 16 An important disadvantage of using strip yields is that strip markets are less liquid, so strip yields contain a liquidity premium not embedded in on-the-run issues. The primary advantage of using strip yields is that it reduces or eliminates the maturity gaps found in on-the-run Treasury yields.

16 17

17 18 Question 2 [10 marks] a) Explain what forward rates are and how they relate to spot rates. (2) Forward rates are the market s consensus of future interest rates. The spot rate for a given period is the geometric average of the current 6-month spot and subsequent 6-month forward rates. Discounting at the forwards rates (and 6- month spot rate) will give the same present value as discounting by the spot rate for the period. Textbook, pp

18 19 b) Assume that the current 6-month spot rate is 3.5% and the following table provides various 6-month forward rates (all rates are expressed as bond equivalent yields). Time from now (when forward rate begins) Forward Rate 6 months 4.0% 1 year 4.2% 1.5 years 4.5% 2 years 4.7% 2.5 years 4.8% 3 years 4.9% (i) Determine the 1-year and 1.5-year spot rates. (4) (ii) Calculate the value of a 1.5-year, 4.5% Treasury note. (2) (iii) Calculate the 1-year forward rate 1 year from now. (2) (i) 1-year spot rate: (1 + S 1.0 /2) 2 = (1 + S 0.5 /2)( f 0.5 /2) = ( /2)( /2) = S 1.0 /2 = /2 1 = S 1.0 = x 2 = 3.75% 1.5 year spot rate (1 + S 1.5 /2) 3 = ( /2)( /2)( /2) = S 1.5 /2 = /3 1 = S 1.5 = 3.90% (ii) One mark for work shown, and one mark for the answer Using spot rates calculated in (i) above:

19 20 4.5/ / OR Using forward rates: 4.5/ / , (iii) (1 + 1 f 1 /2) 2 = ( f 1 /2) ( f 1.5 /2) = ( /2) ( ) = f 1 /2 = /2 1 = f 1 = x 2 = 4.35%

INV3702 INVESTMENTS: FIXED INCOME ANALYSIS EXAM MEMO MAY/JUNE 2012

INV3702 INVESTMENTS: FIXED INCOME ANALYSIS EXAM MEMO MAY/JUNE 2012 SECTION A: MULTIPLE CHOICE QUESTIONS (30 MARKS) *THERE MAY BE MINOR EDITORIAL DIFFERENCES BETWEEN THE QUESTIONS IN THIS MEMO AND THOSE