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fixed income analysis
Fixed Income Analysis Workbook 2nd Edition Frank J. Fabozzi - Solutions
• explain the limitations of the nominal spread.
• compute using the method of bootstrapping the theoretical Treasury spot rate curve given the Treasury yield curve derived from the on-the-run Treasury issues.
• calculate the yield on a discount basis for a Treasury bill and explain its limitations.
• calculate the spread for life and discount margin measure for a floating-rate security and explain the limitations of both.
• explain the factors affecting reinvestment risk.
• calculate the reinvestment income required to generate the yield computed at the time of purchase.
• explain the assumptions underlying traditional yield measures and the limitations of the traditional yield measures.
• compute the traditional yield measures for fixed-rate bonds (current yield, yield tomaturity, yield to first call, yield to first par call date, yield to refunding, yield to put, yield to worst, and cash flow yield).
• explain the sources of return from investing in a bond (coupon interest payments. capital gain/loss, and reinvestment income).
11. Suppose that the prevailing Treasury spot rate curve is the one shown in Exhibit 5.a. What is the value of a 4% 8-year Treasury issue?b. Suppose that the 4% 8-year Treasury issue is priced in the market based on the on-the-run 8-year Treasury yield. Assume further that yield is 5.65%, so that
10. Suppose that the prevailing Treasury spot rate curve is the one shown in Exhibit 5.a. What is the value of a 7.4% 8-year Treasury issue?b. Suppose that the 7.4% 8-year Treasury issue is priced in the market based on the on-the-run 8-year Treasury yield. Assume further that yield is 5.65%, so
9. Suppose that a bond is purchased between coupon periods. The days between the settlement date and the next coupon period is 115. There are 183 days in the coupon period. Suppose that the bond purchased has a coupon rate of 7.4% and there are 10 semiannual coupon payments remaining.a. What is the
8. What is the value of a zero-coupon bond paying semiannually that matures in 20 years, has a maturity of $1 million, and is selling to yield 7.6%.
7. What is the value of a 5-year 7.4% coupon bond selling to yield 5.6% assuming the coupon payments are made semiannually?
6. What is the value of a 5-year 5.8% annual coupon bond if the appropriate discount rate for discounting each cash flow is as follows:Year Discount rate 1 5.90%2 6.40%3 6.60%4 6.90%5 7.30%
5. A 4-year 5.8% coupon bond is selling to yield 7%. The bond pays interest annually. One year later interest rates decrease from 7% to 6.2%.a. What is the price of the 4-year 5.8% coupon bond selling to yield 7%?b. What is the price of this bond one year later assuming the yield is unchanged at
4. A client is reviewing a year-end portfolio report. Since the beginning of the year, market yields have increased slightly. In comparing the beginning-of-the-year price for the bonds selling at a discount from par value to the end-of-year prices, the client observes that all the prices are
3.a. Assuming annual interest payments, what is the value of a 5-year 6.2% coupon bond when the discount rate is (i) 4.5%, (ii) 6.2%, and (iii) 7.3%?b. Show that the results obtained in part a are consistent with the relationship between the coupon rate, discount rate, and price relative to par
2. A 5-year amortizing security with a par value of $100,000 and a coupon rate of 6.4%has an expected cash flow of $23,998.55 per year assuming no prepayments. The annual cash flow includes interest and principal payment. What is the value of this amortizing security assuming no principal
1. Compute the value of a 5-year 7.4% coupon bond that pays interest annually assuming that the appropriate discount rate is 5.6%.
• explain the basic features common to models used to value bonds with embedded options.
• compute the price of the bond given the term structure of default free spot rates and the term structure of credit spreads.
• demonstrate how a dealer can generate an arbitrage profit if a bond is mispriced.
• explain how the process of stripping and reconstitution forces the price of a bond towards its arbitrage-free value.
• explain the arbitrage-free bond valuation approach and the role of Treasury spot rates in the valuation process.
• explain the deficiency of the traditional approach to bond valuation.
• compute the value of a bond that is between coupon payments.
• compute the value of a zero-coupon bond.
• explain how the price of a bond changes as the bond approaches its maturity date.
• explain how the value of a bond changes if the discount rate increases or decreases.
• compute the value of a bond, given the expected cash flows and the appropriate discount rates.
• describe the difficulties of estimating the expected cash flows for some types of bonds.
• define a bond’s cash flows.
• explain the steps in the valuation process (i.e., estimate expected cash flows, determine an appropriate discount rate or rates, and compute the present value of the cash flows).
• describe the fundamental principles of bond valuation.
17. An investor has purchased a floating-rate security with a 5-year maturity. The coupon formula for the floater is 6-month LIBOR plus 200 basis points and the interest payments are made semiannually. The floater is not callable. At the time of purchase, 6-month LIBOR is 7.5%. The investor
16. Suppose that an institutional investor has entered into an interest rate swap, as the fixed-rate payer, with the following terms:Term of swap: 2 years Frequency of payments: quarterly Notional amount: $10 million Reference rate: 3-month LIBOR Swap spread: 100 basis points At the time of the
15. Why is the swap spread an important spread measure?
14. If the swap spread for a 5-year interest rate swap is 120 basis points and the yield on the 5-year Treasury is 4.4%, what is the swap rate?
13. Why are funded investors who borrow short term interested in a LIBOR yield curve rather than the Treasury yield curve?
12.a. What is the after-tax yield for an investor in the 40% tax bracket if the taxable yield is 5%?b. What is the taxable-equivalent yield for an investor in the 39% tax bracket if the tax-exempt yield on an investment is 3.1%?
11.a. Why isn’t the Treasury yield curve used as a benchmark in measuring yield spreads between different sectors of the municipal bond market?b. What benchmark is used?
10. If proposals are being considered by Congress to reduce tax rates and the market views that passage of such legislation is likely, what would you expect to happen to municipal bond yields?
9. Following is a quote that appeared in theMay 19, 1999 Global Relative Value by Lehman Brothers (COR-1):As we have written in the past, percent yield spreads (spread as a percent of Treasury yields) are still cheap on an historical basis. As an illustration, the average single A 10-year
8. Suppose that the yield on a 10-year noncallable corporate bond is 7.25% and the yield for the on-the-run 10-year Treasury is 6.02%. Compute the following:a. the absolute yield spreadb. the relative yield spreadc. the yield ratio
7.a. Why is the yield spread between a bond with an embedded option and an otherwise comparable Treasury security referred to as a ‘‘nominal spread’’?b. What is an option-adjusted spread and why is it superior to a nominal spread as a yield spread measure for a bond with an embedded option?
6. Comment on the following statement by a representative of an investment management firm who is working with a client in selecting sectors in which the manager for the account will be permitted to invest:Mortgage-backed securities give our managers the opportunity to increase yield because these
5. Assume the following information pertaining to federal agency spreads was reported:Agency Spreads versus Benchmark Treasury (basis points)Last 12 months Yield spread High Low Average Noncallable 3-year 70 70 28 44.1 5-year 80 80 32 55.4 10-year 95 95 45 71.2 Callable 3-year (NC1) 107 107 50 80.2
4. According to the pure expectations theory, what does a humped yield curve suggest about the expectations of future interest rates?
3. How does the liquidity preference theory differ from the pure expectations theory?
2. Ms. Peters is a financial advisor. One of her clients called and asked about a recent change in the shape of the yield curve from upward sloping to downward sloping. The client told Ms. Peters that she thought that the market was signaling that interest rates were expected to decline in the
1. The following statement appears on page 2 of the August 2, 1999 issue of Prudential Securities’ Spread Talk.The market appears to be focusing all of its energy on predicting whether or not the Fed will raise rates again at the August and/or October FOMC [Federal Open Market Committee]
• discuss the observed relationship between swap spreads and credit spreads.
• describe the factors that determine the swap spread.
• explain how an interest rate swap can be used to create synthetic fixed-rate assets or floating-rate assets.
• describe an interest rate swap, the swap rate, the swap spread, and the swap spread curve.
• define LIBOR and why it is an important measure to funded investors who borrow short term.
• calculate the after-tax yield of a taxable security and the tax-equivalent yield of a tax-exempt security.
• explain the relationship between the yield on Treasury securities and the yield on tax-exempt municipal securities.
• explain how the liquidity of an issue affects its yield spread.
• explain an option-adjusted spread.
• define a nominal spread.
• identify the relationship between embedded options and yield spreads.
• describe a credit spread and the suggested relationship between credit spreads and the well being of the economy.
• describe an issuer’s on-the-run yield curve.
• distinguish between intermarket and intramarket sector spreads.
• explain the different types of yield spread measures (absolute yield spread, relative yield spread, and yield ratio) and how to calculate yield spread measures given the yields for two securities.
• define a spread product and a spread sector.
• define a Treasury spot rate.
• for each theory of the term structure of interest rates, explain the implication that the shape of the yield curve suggests regarding the market’s expectation about future interest rates.
• describe the three theories of the term structure of interest rates: pure expectations theory, liquidity preference theory, and market segmentation theory.
• describe the term structure of interest rates.
• explain the Treasury yield curve and describe the various shapes of the yield curve.
• identify the interest rate policy tools used by the U.S. Federal Reserve Board.
28. Explain the two major types of electronic bond trading systems.
27. How are private placements classified?
26. What is a bought deal?
25.a. What is a collateralized debt obligation?b. Explainwhether you agree or disagree with the following statement: ‘‘The assetmanager in a collateralized debt obligation is free to manage the portfolio as aggressively or passively as he or she deems appropriate.’’c. What distinguishes an
24.a. What are the various forms of external credit enhancement for an asset-backed security?b. What is the disadvantage of using an external credit enhancement in an asset-backed security structure?
23. What is the role played by a special purpose vehicle in an asset-backed security structure?
22. A financial corporation with a BBB rating has a consumer loan portfolio. An investment banker has suggested that this corporation consider issuing an asset-backed security where the collateral for the security is the consumer loan portfolio. What would be the advantage of issuing an
21. What are the risks associated with investing in a bankers acceptance?
20.a. What is the risk associated with investing in a negotiable certificate of deposit issued by a U.S. bank?b. What is meant by ‘‘1-month LIBOR’’?
19.a. What is the difference between a medium-term note and a corporate bond?b. What is a structured note?c. What factor determines the principal payment for an index amortizing note and what is the risk of investing in this type of structured note?
18.a. Why is the default rate alone not an adequate measure of the potential performance of corporate bonds?b. One study of default rates for speculative grade corporate bonds has found that one-third of all such issues default. Other studies have found that the default rate is between 2.15% and
17.a. What is a subordinated debenture corporate bond?b. What is negative pledge clause?
16.a. What is the difference between a liquidation and a reorganization?b. What is the principle of absolute priority?c. Comment on the following statement: ‘‘An investor who purchases a mortgage bond issued by a corporation knows that should the corporation become bankrupt, mortgage
15.a. What is a prerefunded bond?b. Why does a properly structured prerefunded municipal bond have no credit risk?
14. What is an insured municipal bond?
13. What is a moral obligation bond?
12. What is the difference between a limited and unlimited general obligation bond?
11. Name two U.S. government-sponsored enterprises that issue mortgage-backed securities.
10.a. What is the difference between a mortgage passthrough security and a collateralized mortgage obligation?b. Why is a collateralized mortgage obligation created?
9. What is prepayment risk?
8.a. What is a prepayment?b. What do the monthly cash flows of a mortgage-backed security consist of?c. What is a curtailment?
7. Suppose that a 15-year mortgage loan for $200,000 is obtained. The mortgage is a level-payment, fixed-rate, fully amortized mortgage. The mortgage rate is 7.0% and the monthly mortgage payment is $1,797.66.a. Compute an amortization schedule for the first six months.b. What will the mortgage
6. What is a U.S. federal agency debenture?
5.a. What is the measure of the rate of inflation selected by the U.S. Treasury to determine the inflation adjustment for Treasury inflation protection securities?b. Suppose that there is deflation over the life of a Treasury inflation protection security resulting in an inflation-adjusted
4. Suppose a portfolio manager purchases $1 million of par value of a Treasury inflation protection security. The real rate (determined at the auction) is 3.2%.a. Assume that at the end of the first six months the CPI-U is 3.6% (annual rate).Compute the (i) inflation adjustment to principal at the
3. When issuing bonds, a central government can select from several distribution methods.a. What is the difference between a single-price auction and a multiple-price auction?b. What is a tap system?
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