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fixed income analysis

Fixed Income Analysis Workbook 2nd Edition Frank J. Fabozzi - Solutions

15. There are two forms of the ‘‘biased’’ expectations theory.Why are these two forms referred to as ‘‘biased’’ expectations?
14. Based on arbitrage arguments give two interpretations for each of the following three forward rates:a. The 1-year forward rate seven years from now is 6.4%.b. The 2-year forward rate one year from now is 6.2%.c. The 8-year forward rate three years from now is 7.1%.
13. Comment on the following statement made by a portfolio manager to a client:Proponents of the unbiased expectations theory argue that the forward rates built into the term structure of interest rates are the market’s consensus of future interest rates. We disagree with the theory because
12. Based on the local expectations form of the pure expectations theory, what would be the difference in the 6-month total return if an investor purchased a 5-year zero-coupon bond or a 2-year zero-coupon bond?
11. Based on the broadest interpretation of the pure expectations theory, what would be the difference in the 4-year total return if an investor purchased a 7-year zero-coupon bond or a 15-year zero-coupon bond?
10.a. What is the pure expectations theory?b. What are the shortcomings of the pure expectations theory?
9.a. What is a swap spread?b. What is the swap spread indicative of?
8. How can a spot rate curve be constructed for a country that has a liquid swap market?
7. What are the advantages of using the swap curve as a benchmark of interest rates relative to a government bond yield curve?
6.a. What are the problems with using the yield on Treasury strips to construct the theoretical spot rate curve?b. Why, even if a practitioner decides to use the yield on Treasury strips to construct the theoretical spot rate curve despite the problems identified in parta, will the practitioner
5.a. What are the limitations of using just the on-the-run Treasury issues to construct the theoretical spot rate curve?b. Why if all Treasury bills and Treasury coupon securities are used to construct the theoretical spot rate curve is it not possible to use the bootstrapping method?
4.a. What are the three factors that have empirically been observed to affect Treasury returns?b. What has been observed to be the most important factor in affecting Treasury returns?c. Given the most important factor identified in partb, justify the use of duration as a measure of interest rate
3. Historically, how has the slope of the long end of the yield curve differed from that of the short end of the yield curve at a given point in time?
2. How is the slope of the yield curve defined and measured?
1. What are the four types of shapes observed for the yield curve?
• explain how yield volatility is forecasted.
• differentiate between historical yield volatility and implied yield volatility.
• compute and interpret the yield volatility given historical yields.
• compute the effects of how to measure the yield curve risk of a security or a portfolio using key rate duration.
• explain the various theories of the term structure of interest rates (i.e., pure expectations theory, liquidity preference theory, preferred habitat theory, and market segmentation) and the implications of each theory for the shape of the yield curve.
• explain the swap rate curve (LIBOR curve) and discuss the reasons that market participants have increasingly used the swap rate curve as a benchmark rather than a government bond yield curve.
• explain the various universes of Treasury securities that are used to construct the theoretical spot rate curve, and discuss their advantages and disadvantages.
• describe and explain the factors that have been observed to drive zero-coupon U.S. Treasury returns and discuss the relative importance of each factor.
• illustrate and explain parallel and nonparallel shifts in the yield curve, a yield curve twist, and a change in the curvature of the yield curve (i.e., butterfly shift).
17. Why is information about a bond’s duration and convexity adjustment insufficient to quantify interest rate risk exposure?
16.a. Given the information below for a 6.2% 18-year bond compute the price value of a basis point:price = 114.1338 yield = 5% price if yield is 5.01% = 114.0051b. If the duration of the 6.2% 18-year bond is 11.28, what is the estimated price change for a 1 basis point change in yield.
15.a. Using the value for C computed in question 12, compute the convexity adjustment for the two 25-year bonds assuming that the yield changes by 200 basis points(y∗ = 0.02).b. Compute the estimated percentage price change using duration (as computed in question 11a) and convexity adjustment if
14.a. Using the duration computed in question 11a, compute the approximate percentage price change using duration for the two 8% coupon bonds assuming that the yield changes by 200 basis points (y∗ = 0.02).b. How does the estimated percentage price change compare to the actual percentage price
13.a. Using the duration computed in question 11a, compute the approximate percentage price change using duration for the two 8% coupon bonds assuming that the yield changes by 10 basis points (y∗ = 0.0010).b. How does the estimated percentage price change compare to the actual percentage price
12. Assuming all four bonds are selling to yield 5%, compute the value for C in the convexity equation for each bond using a 25 basis point rate shock (y = 0.0025).
11. Assuming all four bonds are selling to yield 5%, compute the following for each bond:a. duration based on a 25 basis point rate shock (y = 0.0025)b. duration based on a 50 basis point rate shock (y = 0.0050)
10. Suppose that a 7% coupon corporate bond is immediately callable. Also suppose that if this issuer issued new bonds the coupon rate would be 12%. Why would the modified duration be a good approximation of the effective duration for this bond?Questions 11–15 are based on the following price
9.a. Why is modified duration an inappropriate measure for a high-coupon callable bond?b. What would be a better measure than modified duration?
8. Suppose that you are given the following information about two callable bonds of the same issuer that can be called immediately:Estimated percentage change in price if interest rates change by:−50 basis points + 50 basis points Bond ABC +2% −5%Bond XYZ +11% −8%You are told that both bonds
7. A client is reviewing information about the portfolio. For one of the issues in the portfolio the client sees the following:Issue Maturity Duration X 10 years 13 The client has questioned you as to whether or not the reported duration of 13 is correct. The client’s concern is that he has heard
6. LewisMarlo, an assistant portfolio manager, was reviewing a potential buy list of corporate bonds. The list provided information on the effective duration and effective convexity adjustment assuming a 200 basis point change in interest rates for each corporate bond on the list. The senior
The minutes of the board meeting indicated the following response by Mr. Renfro to each of these questions:a. Duration is a measure of the approximate weighted average life of a bond or a bond portfolio. For example, a portfolio duration of 5 means that the fund will realize the return of the
5. At its quarterly meeting, the trustees of the National Baggage Handlers Pension Fund reviewed the status of its bond portfolio. The portfolio is managed by William Renfro of Wiser and Wiser Management Company. The portfolio consists of 20% Treasury bonds,10% corporate bonds that are noncallable
4. James Smith and Donald Robertson are assistant portfolio managers for Micro Management Partners. In a review of the interest rate risk of a portfolio, Smith and Robertson discussed the riskiness of two Treasury securities. Following is the information about these two Treasuries:Bond Price
3. Explain why you agree or disagree with the following statement:If two bonds have the same duration, then the percentage change in price of the two bonds will be the same for a given change in interest rates.
2. Explain why you agree or disagree with the following statement:The problem with both the full valuation approach and the duration/convexity approach is that they fail to take into account how the change in the yield curve can affect a portfolio’s value.
1. Explain why you agree or disagree with the following statement:The disadvantage of the full valuation approach to measuring interest rate risk is that it requires a revaluation of each bond in the portfolio for each interest rate scenario. Consequently, you need a valuation model. In contrast,
• explain the importance of yield volatility when measuring the exposure of a bond position to interest rate risk.
• state the relationship between duration and the price value of a basis point.
• compute the price value of a basis point (‘‘dollar value of an 01’’) of a bond.
• explain the difference between a modified convexity adjustment and an effective convexity adjustment.
• compute the estimated percentage price change for a bond for a given change in yield using the bond’s duration and convexity adjustment.
• compute the convexity adjustment to the duration estimate of a bond’s percentage price change for a given change in yield.
• compute the duration of a portfolio given the duration of the bonds comprising the portfolio and the limitations of portfolio duration.
• explain the relationship between modified duration and Macaulay duration and the limitations of using either for measuring the interest rate risk for bonds with embedded options.
• explain why effective duration should be used for bonds with embedded options.
• differentiate between modified duration and effective (or option-adjusted) duration.
• explain how the interest rate shocks used to compute duration may affect the duration calculation.
• diagram the relationship between price and yield for a putable bond.
• compute the approximate percentage price change for a bond given its effective duration and a specified change in yield.
• compute the effective duration of a bond given information about how the price will increase and decrease for a given shock in interest rates.
• diagram the relationship between price and yield for a callable and prepayable security and show what is meant by negative convexity.
• diagram the relationship between price and yield for an option-free bond and show why duration is effective in estimating price changes for small changes in yield but is not as effective for a large change in yield.
• state the price volatility characteristics of callable bonds and prepayable securities (including the concept of ‘‘negative convexity’’).
• state the price volatility characteristics for option-free bonds when interest rates change(including the concept of ‘‘positive convexity’’).
• explain the advantage of using the full valuation approach compared to the duration/convexity approach.
• compute the interest rate risk exposure of a bond position for a given scenario.
• distinguish between the full valuation and the duration/convexity approaches formeasuring interest rate risk.
28.a. Given the following 6-month forward rates, compute the forward discount factor for each period Period Annual forward rate (BEY)1 4.00%2 4.40 3 5.00 4 5.60 5 6.00 6 6.40b. Compute the value of a 3-year 8% coupon bond using the forward rates.
27. Two sales people of analytical systems are making a presentation to you about the merits of their respective systems. One sales person states that in valuing bonds the system first constructs the theoretical spot rates and then discounts cash flows using these rates. The other sales person
26. For the previous question, demonstrate that the 6-month forward rate six month from now is the rate that will produce at the end of one year the same future dollars as investing either (1) at the current 1-year spot rate of 5.4% or (2) at the 6-month spot rate of 5.0%and reinvesting at the
25. Assume the following Treasury spot rates:Period Years to maturity Spot rate 1 0.5 5.0%2 1.0 5.4 3 1.5 5.8 4 2.0 6.4 5 2.5 7.0 6 3.0 7.2 7 3.5 7.4 8 4.0 7.8 Compute the following forward rates:a. the 6-month forward rate six months from now.b. the 6-month forward rate one year from now.c. the
24. Max Dumas is considering the purchase of a callable corporate bond. He has available to him two analytical systems to value the bond. In one system, System A, the vendor uses the on-the-run Treasury issues to construct the theoretical spot rate that is used to construct a model to compute the
23. John Tinker is a a junior portfolio manager assigned to work for Laura Sykes, the manager of the corporate bond portfolio of a public pension fund. Ms. Sykes asked Mr. Tinker to construct a portfolio profile that she could use in her presentation to the trustees. One of the measures Ms. Sykes
22. The Prestige InvestmentManagement Company sent a report to its pension client. In the report, Prestige indicated that the yield curve is currently flat (i.e., the yield to maturity for each maturity is the same) and then discussed the nominal spread for the corporate bonds held in the
21. Suppose that the Treasury spot rate curve is as follows:Period Years to maturity Spot rate 1 0.5 5.0%2 1.0 5.4 3 1.5 5.8 4 2.0 6.4 5 2.5 7.0 6 3.0 7.2 7 3.5 7.4 8 4.0 7.8 Suppose that the market price of a 4-year 6% coupon non-Treasury issue is $91.4083 Determine whether the zero-volatility
20. What are the two limitations of the nominal spread as a measure of relative value of two bonds?
19. Given the spot rates computed in the previous question and the 6-month and 1-year spot rates, compute the arbitrage-free value of a 3-year Treasury security with a coupon rate of 8%.
18. Suppose that the annual yield to maturity for the 6-month and 1-year Treasury bill is 4.6% and 5.0%, respectively. These yields represent the 6-month and 1-year spot rates.Also assume the following Treasury yield curve (i.e., the price for each issue is $100) has been estimated for 6-month
17. Explain how a Treasury yield curve is constructed even though there are only a limited number of on-the-run Treasury issues available in the market.
16.a. A Treasury bill with 105 days from settlement to maturity is selling for $0.989 per $1 of maturity value. What is the yield on a discount basis?b. A Treasury bill with 275 days from settlement to maturity is quoted as having a yield on a discount basis of 3.68%. What is the price of this
15. How does the discount margin handle any cap on a floater and the fact that the reference rate may change over time?
14. An investor is considering the purchase of a 5-year floating-rate note that pays interest semiannually. The coupon formula is equal to 6-month LIBOR plus 30 basis points. The current value for 6-month LIBOR is 5% (annual rate). The price of this note is 99.1360.Is the discount margin 40 basis
13. Two portfolio managers are discussing the investment characteristics of amortizing securities.Manager A believes that the advantage of these securities relative to nonamortizing securities is that since the periodic cash flows include principal payments as well as coupon payments, the manager
12. Suppose that an amortizing security pays interest monthly. Based on the projected principal payments and interest, suppose that the monthly interest rate that makes the present value of the cash flows equal to the price of the security is 0.41%. What is the cash flow yield on a bond-equivalent
11. Suppose a 5% coupon 6-year bond is selling for $105.2877 and is putable in four years at par value. The yield to maturity for this bond is 4%. Determine whether the yield to put is 3.38%, 3.44% or 3.57%.
10. Suppose that a 10% 15-year bond has the following call structure:not callable for the next 5 years first callable in 5 years at $105 first par call date is in 10 years The price of the bond is $127.5880.a. Is the yield to maturity for this bond 7.0%, 7.4%, or 7.8%?b. Is the yield to first call
9.a. If the yield to maturity on an annual-pay bond is 5.6%, what is the bond-equivalent yield?b. If the yield of a U.S. bond issue quoted on a bond-equivalent basis is 5.6%, what is the yield to maturity on an annual-pay basis?
8. What is the reinvestment risk and interest rate risk associated with a yield to maturity measure?
7.a. Which of the following three bonds has the greatest dependence on reinvestment income to generate the computed yield? Assume that each bond is offering the same yield to maturity. (No calculations are needed to answer this question.)Bond Maturity Coupon rate X 25 years 0%Y 20 years 7%Z 20
6.a. Suppose that an investor invests $108.32 in a 5-year certificate of deposit that pays 7%annually (on a bond-equivalent basis) or 3.5% semiannually and the interest payments are semiannual. What are the total future dollars of this investment at the end of 5 years (i.e., ten 6-month periods)?b.
5. Comment on the following statement: ‘‘The yield tomaturitymeasure is a useless measure because it doubles a semiannual yield (calling the annual yield a bond-equivalent yield)rather than computing an effective annual yield. This is the major shortcoming of the yield-to-maturity measure.’’
4. The following yields and prices were reported in the financial press. Are any of them incorrect assuming that the reported price and coupon rate are correct? If so, explain why?(No calculations are needed to answer this question.)Bond Price Coupon rate Current yield Yield to maturity A 100 6.0%
3. Determine whether the yield to maturity of a 6.5% 20-year bond that pays interest semiannually and is selling for $90.68 is 7.2%. 7.4%, or 7.8%.
2.a. Suppose a 10-year 9% coupon bond is selling for $112 with a par value of $100. What is the current yield for the bond?b. What is the limitation of the current yield measure?
1. What are the sources of return any yield measure should incorporate?
• calculate the value of a bond given forward rates.
• calculate the forward discount factor from forward rates.
• explain why valuing a bond using spot rates and forward rates produces the same value.
• demonstrate the relationship between short-term forward rates and spot rates.
• define a forward rate and compute forward rates from spot rates.
• explain why the nominal spread hides the option risk for bonds with embedded options.
• explain an option-adjusted spread for a bond with an embedded option and explain what is meant by the option cost.
• explain why the zero-volatility spread will diverge from, and is superior to, the nominal spread.
• describe and compute a zero-volatility spread given a spot rate curve.

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