Reading 30: Hedging Mortgage Securities to Capture Relativ account, 直播间, level, takes, 连载

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CFA Institute Area 8-11, 13: Asset Valuation
Session 9: Portfolio Management of Global Bonds and Fixed Income Derivatives
Reading 30: Hedging Mortgage Securities to Capture Relative Value
LOS e: Contrast a two-bond hedge that takes account of yield curve level and twist changes with a duration hedge.

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In contrast to hedging a Treasury security with a one-bond hedge, when hedging mortgage securities, a two-bond hedge:

A) is less appropriate and requires fewer assumptions.

B) is more appropriate and requires fewer assumptions.

C) is more appropriate and requires more assumptions.

D) is less appropriate and requires more assumptions.

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Answer and Explanation

Because there is not a bullet payment at maturity, a two-bond hedge is usually more appropriate for mortgage securities. More assumptions are needed for such a hedge such as prepayment rates and whether the average-price method yields usable results.

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In contrast to a one-bond hedge, a two bond hedge relies:

A) less on duration measures and more on simulations of interest rates.

B) more on duration measures and less on simulations of interest rates.

C) less on duration measures and less on simulations of interest rates.

D) more on duration measures and more on simulations of interest rates.

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Answer and Explanation

The usual reason a two-bond hedge is needed is that a duration-based approach is inadequate. Simulations of interest rates play more of a role in cases where a duration-based strategy is inadequate.

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When a one-bond hedge is inadequate for hedging a mortgage security and a two-bond hedge is required, all of the following are necessary assumptions for using a two-bond hedge EXCEPT:

A) the yield curve will shift in a parallel fashion.

B) reliable assumptions in the Monte Carlo simulations of interest rates.

C) a model for predicting prepayments given certain changes in yield.

D) the securitys price change given a small change in yield.

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Answer and Explanation

A usual reason a two-bond hedge is required is that the yield curve is expected to shift in a non-parallel fashion.

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A given mortgage security is trading at par. The expected average price change from a projected change in a given market yield is 1 for the mortgage security and 0.4 and 2.0 for hedging instrument one and two respectively. The expected average price change from a projected twist in the yield curve is 0.4 for the mortgage security and 0.3 and 0.5 for hedging instrument one and two respectively. What positions in hedging instruments one and two should a manager take to hedge the price of the mortgage security from the projected market changes? For every dollar of face value of the mortgage security:

A) buy $2.5 of hedging instrument one and $0.5 of hedging instrument two.

B) sell $0.75 of hedging instrument one and $0.35 of hedging instrument two.

C) sell $2.5 of hedging instrument one and $0.5 of hedging instrument two.

D) sell $2.0 of hedging instrument one and $0.56 of hedging instrument two.

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Answer and Explanation

To answer this, we set up the following two equations and two unknowns.

(N_H1)(0.4) + (N_H2)(2.0) = -1.0
(N_H1)(0.3) + (N_H2)(0.5) = -0.4,

where N_H1 and N_H2 are the positions to take in hedging instruments one and two respectively. Multiplying the second equation by 4 and subtracting it from the first gives (N_H1)(-0.8)=0.6, and thus N_H1=-0.75. Substituting this into either expression and solving N_H2 gives N_H2=-0.35.

(-0.75)(0.4)+(-0.35)(2)=-1
(-0.75)(0.3)+(-0.35)(0.5)=-0.4

To answer this, we set up the following two equations and two unknowns.

(N_H1)(0.4) + (N_H2)(2.0) = -1.0
(N_H1)(0.3) + (N_H2)(0.5) = -0.4,

where N_H1 and N_H2 are the positions to take in hedging instruments one and two respectively. Multiplying the second equation by 4 and subtracting it from the first gives (N_H1)(-0.8)=0.6, and thus N_H1=-0.75. Substituting this into either expression and solving N_H2 gives N_H2=-0.35.

(-0.75)(0.4)+(-0.35)(2)=-1
(-0.75)(0.3)+(-0.35)(0.5)=-0.4

To answer this, we set up the following two equations and two unknowns.

(N_H1)(0.4) + (N_H2)(2.0) = -1.0
(N_H1)(0.3) + (N_H2)(0.5) = -0.4,

where N_H1 and N_H2 are the positions to take in hedging instruments one and two respectively. Multiplying the second equation by 4 and subtracting it from the first gives (N_H1)(-0.8)=0.6, and thus N_H1=-0.75. Substituting this into either expression and solving N_H2 gives N_H2=-0.35.

(-0.75)(0.4)+(-0.35)(2)=-1
(-0.75)(0.3)+(-0.35)(0.5)=-0.4

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