James Prescott is a portfolio manager with Atlantic Investment Management Company. Prescott forecasts that interest rates will remain at their current level, however he expects that their volatility will decline. As a result, he is adjusting a fixed-income portfolio. The goal is to increase the return of the portfolio while managing the risk appropriately. The current portfolio consists of $80 million long-term Treasury bonds and $60 million short-term Treasury bonds. Given his interest-rate forecast of stable rates with low volatility, he uses a parallel yield curve shift of 20 basis points to compute the bonds dollar durations. For a 20 basis point change, the dollar duration of the long-term bonds is $1.2 million and the dollar duration of the short-term bonds is $0.5 million. Before adjusting the portfolio, Prescott fully hedges the portfolio for the potential 20 basis point shift with futures contracts that have the same maturity as the short-term and long-term position and in the same relative amounts.
Prescott is considering two possible choices to increase the return of the portfolio. - Choice A would convert half of the short-term bonds to long-term bonds.
- Choice B would convert half of both positions to mortgage backed securities with maturities equal to each of the previous positions.
The mortgage-backed securities are trading at a discount from par and offer a 70 basis point spread over the long-term Treasury securities. Prescott determines that for the forecasted yield curve shift, a duration-based strategy is appropriate.
Prescott decides on choice B. He decides to keep the same position in Treasury futures as a hedge. Shortly thereafter, there is a 40 basis point increase in short-term rates and a 60 basis point increase in long-term rates. The hedge proves to be ineffective.
For a 20 basis point shift, what was the dollar duration of the original bond portfolio without the hedge?
Answer and Explanation
Dollar durations are additive. The sum of the durations of the two bond positions would give the dollar duration of the entire portfolio: $1.2 million plus $0.5 million.
If Prescott had chosen Choice A and had not changed the hedge, the dollar duration of the entire position including the futures would most likely have:
Answer and Explanation
Shifting the actual bond positions to a longer duration while leaving the hedge unchanged would increase the duration of the entire portfolio.
Which of the following would be most appropriate to improve the hedge for Choice B? Purchasing: | A) | calls on Treasury futures to hedge against large interest rate increases. |
| B) | calls on Treasury futures to hedge against large interest rate decreases. |
| | C) | puts on Treasury futures to hedge against large interest rate decreases. |
| | D) | puts on Treasury futures to hedge against large interest rate increases. |
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Answer and Explanation
A duration-based hedge on a portfolio of mortgage securities can actually make the value of the entire portfolio decline if rates decline. This is because the hedge will decline in value while the negative convexity of the mortgage securities will mean the value of the mortgage securities may not increase by as much as the futures decline. A long position in calls on Treasury futures will have an asymmetric payoff that can offset the asymmetric price behavior of mortgage securities. Adding long calls that will increase in value when rates decline compensates for the short call that is implicit in the mortgage security.
All of the following support Prescotts assessment that a duration-based hedge of the mortgage securities would be adequate EXCEPT: | A) | the forecast of a low volatility of rates. |
| | B) | the forecast of the level of rates remaining the same. |
| | C) | the mortgage securities were trading below par. |
| D) | he replaced the Treasury securities with equal amounts of mortgage securities of the same maturity. |
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Answer and Explanation
Because of the different payment scheme (mortgages are annuities, while Treasuries have a bullet payment at maturity), substituting mortgage securities for Treasury securities will lessen the effectiveness of a duration-based strategy even if the maturities are the same. Since the mortgage securities are trading below par, they are likely to exhibit positive convexity, and that means a duration-based strategy could be appropriate. If the volatility of rates remains low, the effect of the call embedded in the mortgage securities will be less important. A duration-based hedge is not effective against changes in volatility when embedded options are present even if the level of rates remains the same. If the level of rates remains the same in a low volatility environment a duration-based hedge is adequate.
Reasons for the hedge proving ineffective include all of the following EXCEPT: | A) | only two key rates were used in the hedge. |
| | B) | there was a non-parallel yield curve shift. |
| C) | the negative convexity of the mortgage securities. |
| | D) | the interest rate changes were more than 20 basis points. |
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Answer and Explanation
The fact that the mortgage securities were trading below par and then interest rates increased means that the mortgage securities were likely in a region where they exhibited positive convexity so negative convexity probably did not play a role. In the face of non-parallel shifts of the yield curve, most hedges on fixed income securities and particularly mortgage securities will be less effective. The fact that only two key rates were used is a problem. There would probably need to be at least three key rates: one for the short-term bonds, one for the long-term bonds which would cover some of the mortgage securities, and a third intermediate rate for the additional risk of the mortgage securities which do not have a bullet payment at maturity. The fact that the hedge was set up for only a 20 basis point change will mean the bonds would be poorly hedged for the indicated shifts.
For this question only, suppose now that the Treasury yield curve had not shifted. Instead, the spread of the mortgage securities increases while the Treasury rates do not change. If the same hedge is in place, then the value of the: | A) | hedged portfolio would remain the same. |
| B) | hedged portfolio would decline. |
| | C) | hedged portfolio would increase. |
| | D) | securities would be unaffected, but the futures contracts would change in an uncertain fashion. |
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Answer and Explanation
Since the Treasury rates remained the same, the futures contracts would not change in value. The value of the mortgage securities would decline because the yield would increase from the spread increase.
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发表于 2008-9-16 09:48
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