Fixed Income Analysis 3rd Edition Barbara S. Petitt, Jerald E. Pinto, Wendy L. Pirie, Bob Kopprasch - Solutions

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Exercise . (The Ritchken–Sankarasubramanian model) Show the Equations (.), (.), and (.).
Exercise . (A Gaussian HJM) Assume that the risk-neutral forward rate dynamics is given by df T t = ˆα (T − t) dt + β(T − t) dzQ t ,  ≤ t ≤ T, where zQ is a standard Brownian motion under Q, andβ(τ ) = ( + γ τ )σe− ν τfor non-negative constants σ, γ , and ν
Exercise . (The Hull–White model calibrated to the Vasicek yield curve) Suppose the observable bond prices are fitted to a discount function of the form(∗)B¯(t) = e−a(t)−b(t)r , where b(t) = κ − e−κt, a(t) = y∞[t − b(t)] + βκb(t), where y∞, κ, and β
Exercise . (Calibration of the CIR model) Compute b(τ ) in the CIR model by differentiation of (.). Find out which types of initial forward rate curves the CIR model can be calibrated to, by computing (using a spreadsheet for example)the right-hand side of (.) for
Exercise . (Negative short rate in two-factor Vasicek) In the two-factor Vasicek model, derive an expression for the (risk-neutral) probability that the short rate is negative at time T given that rt = r and εt = ε at time t < T. Illustrate graphically how this probability depends on T
Exercise . (Yield curves in two-factor Vasicek) In the two-factor Vasicek model, the zero-coupon yields are given by (.). Develop a spreadsheet in which you can compute yields for a large number of maturities and illustrate the yield curve graphically. What shapes can the yield curve
Exercise . (P and Q dynamics in the general affine model) Verify (.).Exercise . (Bond prices in the general affine model) Show Theorem ..Exercise . (Solution of ODE in two-factor Vasicek) Show that (.) is a solution to (.).
Exercise . (Expectation hypothesis in Vasicek) Verify that the local weak and the weak yield-to-maturity versions of the expectation hypothesis hold in the Vasicek model.
Exercise . (Comparison of prices in the models of Vasicek and CIR) Compare the prices according to Vasicek’s model (.) and the CIR-model (.) of the following securities:(a) -year and -year zero-coupon bonds;(b) -month European call options on a -year
Exercise . (Futures on bonds) Show the last claim in Theorem ..Exercise . (CIR zero-coupon bond price) Show that the functions b and a given by (.) and (.) solve the ordinary differential equations (.) and (.).
Exercise . (Call on zero-coupon bonds in Vasicek’s model) Figure . shows an example of the relation between the price of a European call on a zero-coupon bond and the current short rate r in the Vasicek model, compare (.). The purpose of this exercise is to derive an explicit
Exercise . (Parallel shifts of the yield curve) The purpose of this exercise is to find out under which assumptions the only possible shifts of the yield curve are parallel, that is such that dy¯τt is independent of τ where y¯τt = yt+τ t .(a) Argue that if the yield curve only changes
Exercise . (Slope of the yield curve at zero maturity) Consider a time-homogeneous affine model in which the yield curve at time t is given by y¯τt = a(τ )τ+b(τ )τr, compare (.).The slope of the yield curve at zero maturity is the limit limτ→∂ y¯τt∂τ .(a) Show by
Exercise . Consider a swap with starting date T and a fixed rate K. For t ≤ T, show that Vfl t /Vfix t = L˜ δ,Tt /K, where L˜ δ,Tt is the forward swap rate.
Exercise . Show the parity (.). Show that a payer swaption and a receiver swaption (with identical terms) will have identical prices, if the exercise rate of the contracts is equal to the forward swap rate L˜ δ,Tt .
Exercise . Let ˜lδT (k) be the equilibrium swap rate for a swap with payment dates T, T, ... , Tk, where Ti = T + iδ as usual. Suppose that ˜lδT (), ... , ˜lδT (n)
Exercise . Show that the no-arbitrage price of a European call on a zero-coupon bond will satisfy max , BS t − KB T t≤ CK,T,S t ≤ BS t ( − K)provided that all interest rates are non-negative. Here, T is the maturity date of the option, K is the exercise price, and S is the
Exercise . Constantinides () develops a theory of the nominal term structure of interest rates by specifying exogenously the nominal state-price deflator ζ˜.In a slightly simplified version, his assumption is that
Exercise . Go through the derivations in Section ...
Exercise . The purpose of this exercise is to show that the claim of the gross return pure expectation hypothesis is inconsistent with interest rate uncertainty.In the following we consider time points t < t < t.(a) Show that if the hypothesis holds, thenB tt= B
Exercise . Verify (.) by applying Itô’s Lemma on the relation ζ˜t = ζt/It.
Exercise . Verify (.).
Exercise . The term premium at time t for the future period [t, T] is the current forward rate for that period minus the expected spot rate, that is f t,T t − Et[yT t].This exercise will give a link between the term premium and a state-price deflatorζ = (ζt).(a) Show that B T t = B t t
Exercise . Suppose the market is complete and ζ = (ζt) is the unique stateprice deflator. Then the present value (the costs) of any consumption process c = (ct)t∈[,T] is E[T ζtct dt]. For an agent with time-additive preferences, an initial wealth of W and no future income except
Exercise . Consider an asset paying a dividend of DT at time T and no other dividends. You want to price the asset at time t < T. Assume that DT = Et[DT]eX for a normally distributed random variable X ∼ N(−  σ X, σ X), so that E[eX] = .Also assume that the state-price
Exercise . Show Equation (.).
Exercise . Show that if there is no arbitrage and the short rate can never go negative, then the discount function is non-increasing and all forward rates are non-negative.
Exercise . Find the dynamics of the process ξλ defined in (.).
Exercise . Consider the two general stochastic processes x = (xt) and x =(xt) defined by the dynamics dxt = μt dt + σt dzt, dxt = μt dt + ρtσt dzt +. − ρt σt dzt,where z and z are independent one-dimensional standard Brownian
Exercise . (Adapted from Björk ().) Define the process y = (yt) by yt =eazt , where a is a constant and z = (zt) is a standard Brownian motion. Find the dynamics of y. Show that yt =  +atys ds + a tys dzs.Define m(t) = E[yt]. Show that m satisfies the ordinary
Exercise . (Adapted from Björk ().) Define the process y = (yt) by yt =zt , where z = (zt) is a standard Brownian motion. Find the dynamics of y. Show that yt = tzs ds + tzs dzs.Show that E[yt] ≡ E[zt ] = t, where E[ ] denotes the expectation given
Exercise . Suppose x = (xt) is a geometric Brownian motion, dxt = μxt dt +σxt dzt. What is the dynamics of the process y = (yt) defined by yt =(xt)n? What can you say about the distribution of future values of the y process?Exercise . Let y be a random variable and define a stochastic
Exercise . Find a list of current price quotes on government bonds at an exchange in your country. Derive as many discount factors and zero-coupon yields as possible using only the no-arbitrage pricing principle, that is the bootstrapping approach.Exercise . Consider a bond market in
Exercise . What bonds are currently traded in your domestic market? Try to find information about historical interest rates in your country, either yields on government bonds or official interest rates fixed by the central bank or both.
Exercise . Consider a coupon bond with payments Yi at time Ti = i, i =, ... , n, such that is there is a payment of Y in  year, a payment of Y in  years, and so on. Suppose you discount all future payments with a constant, annually compounded interest rate of r. Let B denote
Exercise . Consider a bond market in which the annually compounded zerocoupon yields of maturities from  to  years are yˆ = %, yˆ = %, yˆ = .%, yˆ = .%, yˆ = .%.What are the corresponding discount factors BT, T = , , ... , ? What are
Exercise . Consider two bullet bonds, both with annual payments and exactly years to maturity. The first bond has a coupon rate of % and is traded at a price of .. The other bond has a coupon rate of % and is traded at a price of ..What is the -year
Exercise . Show that if the discount function does not satisfy the condition B T t ≥ B S t , t ≤ T < S, then negative forward rates will exist. Are non-negative forward rates likely to exist? Explain!
Which of the following statements most accurately evaluates the use of the option-adjusted spread (OAS) to analyze the bonds held in Hanover-Green’s portfolio?A . OAS excludes default risk from its calculation; therefore OAS has limited applicability to the analysis of speculative grade bonds.B .
Consider Warren’s expectations regarding the supply of new issues in the primary market.Given recent research into primary markets, is Warren most likely correct or incorrect regarding the eff ect on spreads and the probability of the bonds being callable?Eff ect on Spreads Bonds Being Callable
Based solely on the information in Exhibit 1 , which index is the most appropriate benchmark for Hanover-Green’s portfolio?A . Global Government Bond Index.B . Long-Term US Corporate Bond Index.C . Equal-Weighted Corporate Bond Index.
Are Warren’s statements regarding contingent immunization most likely correct or incorrect?Statement 1 Statement 2 A. Correct Correct B. Correct Incorrect C. Incorrect Correct
Th e contingent immunization technique that Hanover-Green currently uses in managing their fi xed-income portfolio is best described as:A . a passive management strategy similar to that of the Index Match Fund.B . an active management strategy similar to that of the Select High-Performance Fund.C .
Th e strategy used by the Yield Curve Plus Fund most likely attempts to enhance portfolio returns by taking advantage of:A . changes in credit spreads.B . changes in the level of interest rates.C . nonparallel changes in the yield curve.
Ms. Smith is the portfolio manager of the Good Corporate Bond Fund, which invests primarily in investment-grade corporate bonds. Th e fund currently has an overweight within the retail industrial sector bonds of retailers. Ms. Smith is concerned that increased competition from internet retailers
Ms. Xu is the senior portfolio manager for the Solid Income Mutual Fund. Th e fund invests primarily in investment-grade credit and agency mortgage-backed securities. For each quarterly meeting of the board of directors of the mutual fund, Ms. Xu provides information on the characteristics of the
A . Suppose that a manager believes that credit spreads are mean reverting. Below are three issues along with the current spread, the mean (average) spread over the past six months, and the standard deviation of the spread. Assuming that the spreads are normally distributed, which issue is the most
Th e following appeared in the “Strategies” section of the September 27, 1999 issue of BondWeek (“Firm Sticks to Corps, Agencies,” p. 6):Th e fi rm, which is already overweight in corporates, expects to invest cash in single A corporate paper in non-cyclical consumer non-durable sectors,
Th e following was reported in the “Strategies” section of the January 3, 2000 issue of BondWeek (“. . . Even as Wright Moves Down.” p. 10):Wright Investors Services plans to buy triple B-rated corporate paper in the industrial sector and sell higher rated corporate paper on the view that
Th e following was reported in the “Strategies” section of the January 3, 2000 issue of BondWeek (“Chicago Trust to Move Up in Credit Quality,” p. 10):Th e Chicago Trust Co. plans to buy single-A corporate bonds with intermediate maturities starting this quarter, as the fi rm swaps out of
An ABC Corporate issue trades at a bid price of 120 bps over the 5-year US Treasury yield of 6.00% at a time when Libor is 5.70%. At the same time, 5-year Libor-based swap spreads equal 100 bps (to the 5-year US Treasury).A . If a manager purchased the ABC Corporate issue and entered into a swap to
A . Why has the swap spread framework become a popular valuation yardstick in Europe for credit securities?B . Why might US managers embrace the swap spread framework for the credit asset class?C . Compare the advantages/disadvantage of the nominal spread framework to the swap spread framework.
What is the motivation for portfolio managers to trade into more current and larger sized“on-the-run” issues?
When would a portfolio manager consider implementing a credit-defense trade?
A . What is meant by the “crossover sector of the bond market”?B . How do portfolio managers take advantage of potential credit upgrades in the crossover sector?
Increases in investment-grade credit securities new issuance have been observed with contracting yield spreads and strong relative bond returns. In contrast, spread expansion and a major decline in both relative and absolute returns usually accompanies a sharp decline in the supply of new credit
What is the limitation of a yield-pickup trade?
Th e following passages are from Leland Crabbe “Corporate Spread Curve Strategies,”Chapter 28 in Frank J. Fabozzi (ed.), Th e Handbook of CorporateDebt Instruments (New Hope, PA: Frank J. Fabozzi Associates, 1998).In the corporate bond market, spread curves often diff er considerably across
Chris Dialynas in “Th e Active Decisions in the Selection of Passive Management and Performance Bogeys” (in Frank J. Fabozzi (ed.), Perspectives on Fixed Income Portfolio Management , Volume 2) wrote:Active bond managers each employ their own methods for relative value analysis. Common elements
In describing the approaches to investing in emerging markets credits, Christopher Taylor wrote the following in “Challenges in the Credit Analysis of Emerging Market Corporate Bonds,” Chapter 16 in Frank J. Fabozzi (ed.), Th e Handbook of Corporate Debt Instruments(New Hope, PA: Frank J.
Th e following two passages are from Peter J. Carril, “Relative Value Concepts within the Eurobond Market,” Chapter 29 in Frank J. Fabozzi (ed.), Th e Handbook of Corporate Debt Instruments (New Hope, PA: Frank J. Fabozzi Associates, 1998), p. 552.A . In discussing Eurobond issuers, Carril
Th e following quote is from Lev Dynkin, Peter Ferket, Jay Hyman, Erik van Leeuwen, and Wei Wu, “Value of Security Selection versus Asset Allocation in Credit Markets,”Fixed Income Research, Lehman Brothers, March 1999, p. 3:Most fi xed income investors in the United States have historically
A . What is the dominant type of structure in the investment-grade credit market?B . What are the strategic portfolio implications of the dominant structure answer in Part (A)?C . What is the dominant structure in the high-yield corporate bond market and why is it not the same structure as
What is meant by relative value in the credit market?
Which of the following would best immunize the hospital liability?A . A fi ve-year euro coupon bond.B . A fi ve-year euro zero-coupon bond.C . Equal investment in three- and seven-year euro zero-coupon bonds.
Are Choo’s concerns regarding various risks of funding the hospital liability correct?A . Yes.B . No, because interest rate risk is not a factor.C . No, because contingent claim risk is not a factor.
Based on the data Ferragamo collected on the bund and Exhibit 1, Choo can adjust the EPF portfolio duration to match the benchmark duration by selling:A . 2,240 contracts.B . 2,406 contracts.C . 2,465 contracts.
Is Ferragamo’s comment correct?A . Yes.B . No, because shortfall risk would provide this information.C . No, because value at risk does not indicate the magnitude of the very worst possible outcomes.
Choo’s understanding of contingent immunization (CI) is:A . correct.B . incorrect, because CI does not use a terminal value.C . incorrect, because CI does not allow for active management.
Given the term structure of interest rates and the duration mismatch between EPF’s benchmark and its pension liability, the plan should be most concerned about a:A . fl attening of the yield curve.B . steepening of the yield curve.C . large parallel shift up in the yield curve.
Based on Exhibit 1 , for investors that purchased 10-year US notes, the spread widening in basis points that will wipe out the additional yield gained for a quarter is closest to:A . 6.03 in Singapore.B . 8.09 in Japan.C . 13.48 in the United Kingdom.Th e following information relates to Questions
Based on Exhibit 1 and assuming interest rates remain unchanged, which bond will have the highest expected unhedged return?A . UK 10-year.B . Germany 10-year.C . Singapore 10-year.
Based on Exhibit 1 and assuming interest rates remain unchanged, which bond will have the highest hedged return?A . UK 10-year.B . Japan 10-year.C . Germany 10-year.
Is Santillana correct in her explanation of factors aff ecting the repo rate?A . Yes.B . No, only the quality of collateral is correct.C . No, only the short sellers’ position is correct.
Th e 30-day rate of return on the hypothetical leveraged portfolio of corporate bonds is closest to:A . –0.05 percent.B . 0.05 percent.C . 0.18 percent.
Is Santillana correct in her statements about total return analysis and scenario analysis?A . Yes.B . No, because scenario analysis cannot evaluate how individual assumptions aff ect the total return computation.C . No, because scenario analysis cannot lead to a rejection of a strategy with an
In response to Palme’s two fi nal questions, the levered portfolio’s range of returns and sixmonth return when compared to the unlevered portfolio most likely would be:Levered Portfolio Range of Returns Levered Portfolio Six-month Return A. narrower lower B. narrower higher C. wider lower Th e
In response to Palme’s two fi nal questions, the levered portfolio’s range of returns and sixmonth return when compared to the unlevered portfolio most likely would be:Levered Portfolio Range of Returns Levered Portfolio Six-month Return A. narrower lower B. narrower higher C. wider lower Th e
Is Ibahn’s second response to Palme regarding the cost and margin requirements for the repo most likely correct?High Repo Cost Low Margin Requirement A. No No B. Yes Yes C. Yes No
In Ibahn’s second response to Palme, the duration of the sample leveraged portfolio is closest to:A . 4.10.B . 5.13.C . 6.83.
Referring to Ibahn’s second response to Palme, the levered portfolio would have:A . the same duration if either the overnight repo or the 2-year term repo is used.B . a longer duration if the overnight repo is used instead of the 2-year term repo.C . a shorter duration if the overnight repo is
Referring to Ibahn’s fi rst response to Palme, which of the following best describes TBW’s most likely course of action?A . Sell interest rate futures contracts to increase portfolio duration.B . Buy interest rate futures contracts to increase portfolio duration.C . Buy interest rate futures
Given Ibahn’s recommendation, which of the following interest rate forecasts is TBW Incorporated most likely using?A . A fl attening of the yield curve.B . An upward parallel shift in the yield curve.C . A downward parallel shift in the yield curve.
A British fi xed-income fund has substantial holdings in US dollar-denominated bonds.Th e fund’s portfolio manager is considering whether to leave the fund’s exposure to the US dollar unhedged or to hedge it using a UK pound–US dollar forward contract. Assume that the short-term interest
A portfolio manager of a Canadian fund that invests in the yen-denominated Japanese bonds is considering whether or not to hedge the portfolio’s exposure to the Japanese yen using a forward contract. Assume that the short-term interest rates are 1.6 percent in Japan and 2.7 percent in Canada.A .
Assume that the spread between US and German bonds is 300 bps, providing German investors who purchase a US bond with an additional yield income of 75 bps per quarter.Th e duration of the German bond is 8.3. If German interest rates should decline, how much of a decline is required to completely
Assume that a US bond investor has invested in Canadian government bonds. Th e duration of a 12-year Canadian government bond is 8.40, and the Canadian country beta is 0.63. Interest rates in the United States are expected to change by approximately 80 bps. How much can the US investor expect the
Assume that the rates shown in the table below accurately refl ect current conditions in the fi nancial markets.Dollar/Euro Spot Rate 1.21 Dollar/Euro 1-Year Forward Rate 1.18 1-Year Deposit Rate:Euro 3%US 2%In the table, the one-year forward dollar/euro exchange rate is mispriced, because it
Consider a collateralized debt obligation (CDO) that has a $250 million structure. Th e collateral consists of bonds that mature in seven years, and the coupon rate for these bonds is the seven-year Treasury rate plus 500 bps. Th e senior tranche comprises 70 percent of the structure and has a fl
Th e current credit spread on bonds issued by Great Foods Inc. is 300 bps. Th e manager of More Money Funds believes that Great Foods’ credit situation will improve over the next few months, resulting in a smaller credit spread on its bonds. She decides to enter into a six-month credit spread
Th e trustees of a pension fund would like to examine the issue of protecting the bonds in the fund’s portfolio against an increase in interest rates using options and futures. Before discussing this with their external bond fund manager, they decide to ask four consultants about their
Th e futures contract it would use is priced at €130,000 and has a duration of 9.35. Assume that the conversion factor for the futures contract is 1.06.A . Would the fund need to buy futures contracts or sell?B . Approximately, how many futures contracts would be needed to change the duration of
Th e market value of the bond portfolio of a French investment fund is €75 million. Th e duration of the portfolio is 8.17. Based on the analysis provided by the in-house economists, the portfolio manager believes that the interest rates are likely to have an unexpected decrease over the next
Your client has asked you to construct a £2 million bond portfolio. Some of the bonds that you are considering for this portfolio have embedded options. Your client has specifi ed that he may withdraw £25,000 from the portfolio in six months to fund some expected expenses. He would like to be
Th e most appropriate description of the strategy that Haley suggests in his Statement #3 is to create a portfolio that:A . has cash fl ows concentrated around the horizon date.B . is duration matched but uses cash fl ow matching in the later years of the liability schedule.C . is duration matched
Th e condition that Haley cannot remember in his Statement #2 is that the:A . cash fl ows in the portfolio must be dispersed around the horizon date.B . cash fl ows in the portfolio must be concentrated around the horizon date.C . distribution of durations of individual assets in the portfolio must
Is Haley’s Statement #1 correct?A . Yes.B . No, because multiple liability immunization is generally less risky than cash fl ow matching.C . No, because cash fl ow matching is generally less costly than multiple liability immunization.
Which of the following is closest to the required terminal value for the contingent immunization strategy?A . $100 million.B . $156 million.C . $168 million.
Is Chow’s Statement #2 correct?A . No, Portfolio B is exposed to less reinvestment risk than Portfolio A.B . No, Portfolio B is exposed to more reinvestment risk than Portfolio C.C . No, Portfolio C is exposed to more reinvestment risk than Portfolio B.
Is Chow’s Statement #1 correct?A . Yes.B . No, because credit risk must also be considered.C . No, because the risk of parallel shifts in the yield curve must also be considered.

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Fixed Income Analysis 3rd Edition Barbara S. Petitt, Jerald E. Pinto, Wendy L. Pirie, Bob Kopprasch - Solutions

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