Fixed Income Modelling 1st Edition Claus Munk - Solutions

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2. Why do rating agencies assign two types of ratings to the debt of a sovereign entity?
1. Explain whether you agree or disagree with each of the following statements:a. ‘‘The foreign bond market sector of the Japanese bond market consists of bonds of Japanese entities that are issued outside of Japan.’’b. ‘‘Because bonds issued by central governments are backed by the
• describe the structure of the primary and secondary market for bonds.
• explain a collateralized debt obligation.
• explain the motivation for a corporation to issue an asset-backed security.
• summarize the role of a special purpose vehicle in an asset-backed securities transaction.
• describe an asset-backed security.
• describe the different types of bank obligations.
• describe commercial paper and identify the different types of issuers.
• describe a structured note and explain the motivation for their issuance by corporations.
• describe a medium-term note and explain the differences between a corporate bond and a medium-term note.
• describe secured debt, unsecured debt, and credit enhancements for corporate bonds.
• list the factors considered by rating agencies in assigning a credit rating to corporate debt.
• summarize the bankruptcy process and bondholder rights.
• identify the types of securities issued by municipalities in the United States.
• distinguish between a mortgage passthrough security and a collateralized mortgage obligation and explain the motivation for creating a collateralized mortgage obligation.
• define prepayment and explain prepayment risk.
• describe a mortgage-backed security and identify the cash flows for a mortgage-backed security.
• for the U.S. bond market, explain the difference between federally related institutions and government sponsored enterprises.
• describe a semi-government or government agency bond.
• outline how stripped Treasury securities are created.
• identify the types of securities issued by the U.S. Department of the Treasury.
• list the different methods used by central governments to issue bonds.
• describe a sovereign bond and explain the credit risk associated with investing in a sovereign bond.
• explain how a country’s bond market sectors are classified.
21. Comment on the following statement: ‘‘Sovereign risk is the risk that a foreign government defaults on its obligation.’’
20. Explain how certain types of event risk can result in downgrade risk.
19. A British portfolio manager is considering investing in Japanese government bonds denominated in yen. What are the major risks associated with this investment?
18. In January 1994, General Electric Capital Corporation (GECC) had outstanding $500 million of Reset Notes due March 15, 2018. The reset notes were floating-rate securities.In January 1994, the bonds had an 8% coupon rate for three years that ended March 15, 1997. On January 26, 1994, GECC
17.a. A treasurer of a municipality with a municipal pension fund has required that its in-house portfolio manager invest all funds in the highest investment grade securities that mature in one month or less. The treasurer believes that this is a safe policy.Comment on this investment policy.b. The
16. Sam Stevens is the trustee for the Hole Punchers Labor Union (HPLU). He has approached the investment management firm of IM Associates (IMA) to manage its $200 million bond portfolio. IMA assigned Carol Peters as the portfolio manager for the HPLU account. In their first meeting, Mr. Stevens
15. Identify the difference in the major risks associated with the following investment alternatives:a. For an investor who plans to hold a security for one year, purchasing a Treasury security that matures in one year versus purchasing a Treasury security that matures in 30 years.b. For an
14. A portfolio manager is considering the purchase of a new type of bond. The bond is extremely complex in terms of its embedded options. Currently, there is only one dealer making a market in this type of bond. In addition, the manager plans to finance the purchase of this bond by using the bond
13. Suppose that the bid and ask prices of five dealers for Issue XYX is 96 plus the number of 32nds shown:Dealer 1 2 3 4 5 Bid price 14 14 15 15 13 Ask price 18 17 18 20 19 What is the market bid-ask spread for Issue XYX?
12. Using the hypothetical rating transition matrix shown in Exhibit 4 of the chapter, answer the following questions:a. What is the probability that a bond rated BBB will be downgraded?b. What is the probability that a bond rated BBB will go into default?c. What is the probability that a bond
11. Investors are exposed to credit risk when they purchase a bond. However, even if an issuer does not default on its obligation prior to its maturity date, there is still a concern about how credit risk can adversely impact the performance of a bond. Why?
10. For the investor in a callable bond, what are the two forms of reinvestment risk?
9. What measure can a portfolio manager use to assess the interest rate risk of a portfolio to a change in the 5-year yield?
8. Duration is commonly used as a measure of interest rate risk. However, duration does not consider yield curve risk. Why?
7. A portfolio manager of a bond fund is considering the acquisition of an extremely complex bond issue. It is complex because it has multiple embedded options. The manager wants to estimate the interest rate risk of the bond issue so that he can determine the impact of including it in his current
6. A portfolio manager purchased $8 million in market value of a bond with a duration of 5. For this bond, determine the estimated change in its market value for the change in interest rates shown below:a. 100 basis pointsb. 50 basis pointsc. 25 basis pointsd. 10 basis points
5. A portfolio manager wants to estimate the interest rate risk of a bond using duration. The current price of the bond is 82. A valuation model found that if interest rates decline by 30 basis points, the price will increase to 83.50 and if interest rates increase by 30 basis points, the price
4. John Smith and Jane Brody are assistant portfolio managers. The senior portfolio manager has asked them to consider the acquisition of one of two option-free bond issues with the following characteristics:Issue 1 has a lower coupon rate than Issue 2 Issue 1 has a shorter maturity than Issue 2
3.a. Short-term investors such as money market mutual funds invest in floating-rate securities having maturities greater than 1 year. Suppose that the coupon rate is reset everyday. Why is the interest rate risk small for such issues?b. Why would it be improper to say that a floating-rate security
2. Explain why a callable bond’s price would be expected to decline less than an otherwise comparable option-free bond when interest rates rise?
1. For each of the following issues, indicate whether the price of the issue should be par value, above par value, or below par value:Issue Coupon rate Yield required by marketa. A 51/4% 7.25%b. B 65/8% 7.15%c. C 0% 6.20%d. D 57/8% 5.00%e. E 41/2% 4.50%
• explain what a rating agency does and what is meant by a rating upgrade and a rating downgrade.
• distinguish between investment grade bonds and noninvestment grade bonds.
• explain a rating transition matrix.
• describe the types of credit risk: default risk, credit spread risk, and downgrade risk.
• explain why prepayable amortizing securities expose investors to greater reinvestment risk than nonamortizing securities.
• explain the disadvantages of a callable and prepayable security to an investor.
• identify the factors that affect the reinvestment risk of a security.
• explain key rate duration.
• explain yield curve risk and explain why duration does not account for yield curve risk for a portfolio of bonds.
• use duration to approximate the percentage price change of a bond and calculate the new price if interest rates change.
• interpret the meaning of the duration of a bond.
• compute the duration of a bond given its price changes when interest rates change.
• explain the interest rate risk of a floating-rate security and why its price may differ from par value.
• explain how the yield level impacts the interest rate risk of a bond.
• identify the relationship among the price of a callable bond, the price of an option-free bond, and the price of the embedded call option.
• explain how features of a bond (maturity, coupon, and embedded options) affect its interest rate risk.
• identify the relationships among a bond’s coupon rate, yield required by the market, and price relative to par value (i.e., discount, premium, or par value).
• explain why there is an inverse relationship between changes in interest rates and bond prices.
• explain the various risks associated with investing in bonds (e.g, interest rate risk, call and prepayment risk, yield curve risk, reinvestment risk, credit risk, liquidity risk, exchange-rate risk, inflation risk, volatility risk, and event risk).
11.a. What is the typical arrangement used by institutional investors in the bond market:bank financing, margin buying, or repurchase agreement?b. What is the difference between a term repo and an overnight repo?
10. What is meant by an embedded option?
9. The importance of knowing the terms of bond issues, especially those relating to redemption, cannot be emphasized. Yet there have appeared numerous instances of investors, professional and others, who acknowledge that they don’t read the documentation. For example, in an Augusts 14, 1983
8.a. What is an accelerated sinking fund provision?b. Why can an accelerated sinking fund provision be viewed as an embedded call option granted to the issuer?
7. There are some securities that are backed by a pool of loans. These loans have a schedule of interest and principal payments every month and give each borrower whose loan is in the pool the right to payoff their respective loan at any time at par. Suppose that a portfolio manager purchased one
6. An assistant portfolio manager reviewed the prospectus of a bond that will be issued next week on January 1 of 2000. The call schedule for this $200 million, 7.75% coupon 20-year issue specifies the following:The Bonds will be redeemable at the option of the Company at any time in whole or in
5. An excerpt from Cincinnati Gas & Electric Company’s prospectus for the 101/8% First Mortgage Bonds due in 2020 states, The Offered Bonds are redeemable (though CG&E does not contemplate doing so) prior to May 1, 1995 through the use of earnings, proceeds from the sale of equity securities and
4. An excerpt from the prospectus of a $200 million issue by Becton, Dickinson and Company 7.15% Notes due October 1, 2009:OPTIONAL REDEMPTION We may, at our option, redeem all or any part of the notes. If we choose to do so, we will mail a notice of redemption to you not less than 30 days and not
3. A floating-rate issue has the following coupon formula:1-year Treasury rate + 30 basis points with a cap of 7% and a floor of 4.5%The coupon rate is reset every year. Suppose that at the reset date the 1-year Treasury rate is as shown below. Compute the coupon rate for the next year:1-year
2. Given the information in the first and third columns, complete the table in the second and fourth columns:Price per $1 of Quoted price par value Par value Dollar price 961/4 $1,000 1027/8 $5,000 1099/16 $10,000 6811/32 $100,000
1. Consider the following two bond issues.Bond A: 5% 15-year bond Bond B: 5% 30-year bond Neither bond has an embedded option. Both bonds are trading in the market at the same yield.Which bond will fluctuate more in price when interest rates change? Why?
• identify the typical method used by institutional investors to finance the purchase of a security (i.e., margin or repurchase agreement).
• explain the importance of options embedded in a bond issue.
• identify embedded options (call option, prepayment option, accelerated sinking fund option, put option, and conversion option) and indicate whether each benefits the issuer or the bondholder.
• explain the difference between a regular redemption price and a special redemption price.
• differentiate between nonrefundable and noncallable bonds.
• explain the provisions for the early retirement of debt, including call and refunding provisions, prepayment options, and sinking fund provisions.
• describe the provisions for redeeming bonds, including the distinction between a nonamortizing bond and an amortizing bond.
• define accrued interest, full price, and clean price.
• describe the structure of floating-rate securities (i.e., the coupon formula, interest rate caps and floors).
• identify the various coupon rate structures, such as fixed rate coupon bonds, zero-coupon bonds, step-up notes, deferred coupon bonds, floating-rate securities.
• describe affirmative and negative covenants.
• describe the basic features of a bond (e.g.,maturity, par value, coupon rate, bond redeeming provisions, currency denomination, issuer or investor granted options).
Exercise . Suppose x = (xt) is an affine diffusion with dynamics dxt = (ϕ − κxt) dt + !δ + δxt dzt.Then Section . has shown that Et, e−T t xu du-= e−a(T−t)−b(T−t)xt for functions a and b that solve a system of ordinary differential equations. Show that Et, e−T
Exercise . Consider a basket of corporate bonds. Credit default swaps are traded on all individual bonds in the basket and a first-to-default basket CDS is also traded. Explain why the fair premium on the first-to-default basket CDS has to be smaller than the sum of the fair premia on the
Exercise . Which contract is cheaper: a first-to-default basket CDS or a second-to-default basket CDS (on the same portfolio, with same maturity, etc.)?How does the price difference depend on the default correlations in the portfolio?
Exercise . Use Itô’s Lemma to show (.) and discuss the properties of the process LEV.
Exercise . Consider the basic Merton model of Section ... Define Lt =Fe−r[T−t]/Vt, which is some normalized measure of the firm’s leverage?
Exercise . Show (.).
Exercise . Use Itô’s Lemma to show (.).
Exercise . (Time-denominated duration for non-bonds) Assume that interest rates follow the Vasicek model. Can you define the time-denominated duration for any bond futures or European bond option? If so, derive the time-denominated duration for these assets.Exercise .
Exercise . (Duration-convexity link) Show Equation (.).
Exercise . (Caplets and options on zero-coupon bonds) Assume that the lognormal LIBOR market model holds. Use the caplet formula (.) and the relations between caplets, floorlets, and European bond options known from Chapter  to show that the following pricing formulas for
Exercise . (Spot LIBOR measure) Explain why the process z∗ defined by (.)is a standard Brownian motion under the probability measure Q∗.
Exercise . (HJM with USV) Let the risk-neutral forward rate dynamics be given by df T t = ˆα (t, T, vt) dt + √vte−κ[T−t] dzQt ,  ≤ t ≤ T, where dvt = μv(vt) dt + σv(vt) dzQt, and z Q and z Q are independent standard Brownian motions under Q.(a) Show that

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Fixed Income Modelling 1st Edition Claus Munk - Solutions

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