Questions and Answers of Fixed Income Analysis

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-=
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
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
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
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,
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)
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
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 ,
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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 +.
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
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
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
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
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
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
Exercise . Consider a bond market in which the annually compounded zerocoupon yields of maturities from  to  years are yˆ = %, yˆ = %, yˆ = .%, yˆ = .%,
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
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
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
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
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 .
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
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 .
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
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
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
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,
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
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
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
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 .
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
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
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)
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
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
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,
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
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
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
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 .
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
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
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
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
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
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
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
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 .
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
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
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
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
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
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

Showing 1 - 100 of 1397