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标题: Fixed Income【Session10- Reading 26】 习题精选 [打印本页]
作者: burning0spear    时间: 2012-4-1 17:13     标题: [2012 L3] Fixed Income【Session10- Reading 26】 习题精选

Hedging a mortgage security with a short Treasury futures contract is most effective if:
A)
it is trading above par.
B)
it is trading at par.
C)
it is trading below par.


If the security is trading below par, then it is most likely to exhibit positive convexity, and this will make a hedge formed with a Treasury futures contract that has positive convexity more effective.
作者: burning0spear    时间: 2012-4-1 17:13

A mortgage security’s convexity is most likely to become negative if the market yield is:
A)
increasing and the price moves below par.
B)
declining and the price moves above par.
C)
declining and the price moves below par.


A declining market yield will cause the price to increase. This condition will make prepayment more likely, and make the convexity negative.
作者: burning0spear    时间: 2012-4-1 17:13

For a mortgage backed security trading at par, a large increase in market rates is most likely to make the security’s convexity:
A)
become infinite.
B)
go from positive to negative.
C)
go from negative to positive.


The best answer is go from negative to positive. As rates increase and the price declines, the prepayment option goes out of the money. We could also say the convexity, if already positive, can become more positive, but that was not one of the answers.
作者: burning0spear    时间: 2012-4-1 17:14

For a mortgage security trading at par and a hedge formed with a short position in a Treasury futures position that is designed to maintain a stable value, the hedge would still be effective if:
A)
there is a 100 basis point decrease in yield.
B)
there is a 100 basis point increase in yield.
C)
there is a 75 basis point decrease in yield.


A hedge that is designed to be effective for changes of +/-50 basis points for a mortgage security trading at par will likely be less effective for decreases greater than 50 basis points. This is because of negative convexity. Since the mortgage security is likely to exhibit positive convexity for prices below par, the hedge is more likely to be effective for the larger increase in yield.
作者: burning0spear    时间: 2012-4-1 17:15

A portfolio manager has used a Treasury bond futures contract to hedge a mortgage security, which is trading at par, against a decrease in value from a 50 basis point increase in yield. If the yield were to decrease 50 basis points, the most likely result is:
A)
the net value of the position with the hedge will decline.
B)
the net value of the position with the hedge will increase.
C)
the net value of the position with the hedge will not change.


The most likely result is that the position with the hedge will decline because of the mortgage security’s negative convexity. As the yield decreases, the prepayment option goes in the money and the value of the security does not go up by as much as the value of the short futures position goes down because the futures position has positive convexity.
作者: burning0spear    时间: 2012-4-1 17:15

A mortgage security is most likely to exhibit positive convexity if:
A)
the price is below par.
B)
the yield curve has a parallel downward shift.
C)
the price is above par.


If the price is below par, the market yield must be higher than the yield on the underlying mortgages, and the prepayment rate will be lower. This means the instrument is more likely to exhibit positive convexity.
作者: burning0spear    时间: 2012-4-1 17:15

A mortgage security with a face value had a price of 99 at the opening of the trading day. During the day, the yield declined by 80 basis points below its opening yield and then increased 80 basis points above its opening yield. The corresponding prices of the instrument were 99.5 and 98 respectively. From this we can say the security:
A)
exhibited excess volatility.
B)
exhibited positive convexity.
C)
exhibited negative convexity.


The fact that the price increase from the yield decline was less than the price decrease from the yield increase is indicative of negative convexity caused by a prepayment option.
作者: burning0spear    时间: 2012-4-1 17:16

The effects of recent technological and institutional innovations on the market for mortgage-backed securities has increased:
A)
volatility risk.
B)
model risk.
C)
spread risk.


The innovations have had a direct effect on the ability of models to predict prepayment rates.
作者: burning0spear    时间: 2012-4-1 17:16

All of the following are risks associated with mortgage securities EXCEPT:
A)
volatility risk.
B)
model risk.
C)
beta risk.


Beta is not generally a concept directly associated with mortgage securities. Model risk is important because the current value depends upon patterns of interest rates and prepayment rates. The changing spread can influence the asset’s value. Because of the embedded option, volatility risk is important too.
作者: burning0spear    时间: 2012-4-1 17:17

If a manager of mortgage backed securities is not hedging spread risk, the most likely reason is because hedging spread risk:
A)
reduces profitable opportunities.
B)
is impossible.
C)
increases volatility risk.


A manager can earn profits by buying mortgage backed securities when the spread widens and selling when the spread narrows.
作者: burning0spear    时间: 2012-4-1 17:18

Negative convexity is more likely to become more severe if:
A)
volatility decreases.
B)
volatility increases.
C)
the spread increases.


Negative convexity can be interpreted as the negative effect on price caused by an increase in the value of the embedded, short call option in the mortgage security. An increase in volatility will increase the value of that option and increase the severity of the negative convexity. An increase in the spread and/or Treasury rate will likely increase the yield of the mortgage security, and this will tend to make the security’s convexity more positive.
作者: burning0spear    时间: 2012-4-1 17:18

An increase in the credit spread of a mortgage backed security:
A)
increases the security’s value relative to Treasuries.
B)
does not change the security’s value relative to Treasuries.
C)
decreases the security’s value relative to Treasuries.


An increase in the spread means the yield of the mortgage backed security has increased relative to Treasuries so the security’s value has decreased relative to Treasuries. This would be an opportunity to buy mortgage backed securities.
作者: burning0spear    时间: 2012-4-1 17:18

In analyzing the risk of mortgage backed securities, we say that:
A)
interest rate risk is a component of spread risk.
B)
interest rate risk and spread risk are distinct measures.
C)
spread risk is a component of interest rate risk.


Interest rate risk is associated with the risk from movements in Treasury securities. Spread risk is a separate component associated with the credit properties of the security as well as macroeconomic factors.
作者: burning0spear    时间: 2012-4-1 17:19

When comparing the number of key rates needed in hedging a mortgage security versus a Treasury security, we generally need to consider:
A)
more key rates for the mortgage security because of its bullet payment at maturity.
B)
more key rates for the mortgage security because it lacks a bullet payment at maturity.
C)
fewer key rates for the mortgage security because it lacks a bullet payment at maturity.


A Treasury bond’s price is affected most by changes in the yield associated with its maturity, and this is because of the large bullet payment for that type of bond. Because a mortgage security is essentially an annuity, changes of other rates become more important.
作者: burning0spear    时间: 2012-4-1 17:21

When compared to a Treasury security, the yield curve risk of a mortgage security is generally:
A)
more important and decreases in importance for non-parallel shifts of the yield curve.
B)
less important and increases in importance for non-parallel shifts of the yield curve.
C)
more important and increases in importance for non-parallel shifts of the yield curve.


Because of the prepayment option and the fact that there is not a bullet payment option at maturity, mortgage securities have more yield curve risk, which is by definition caused by non-parallel shifts of the yield curve.
作者: burning0spear    时间: 2012-4-1 17:21

A duration-based framework for hedging a mortgage security may lead to be a greater loss than not hedging if the price of the mortgage security is:
A)
below par.
B)
at all values.
C)
above par.


When the price is above par, negative convexity is more likely to be a problem. If the market yield declines, the hedge will decline in value while the price of the mortgage security may not increase. This will lead to a greater loss than if the security were not hedged at all.
作者: burning0spear    时间: 2012-4-1 17:22

Using only a duration-based framework for hedging a mortgage security is most appropriate if the price is:
A)
above par and the expectation is a parallel shift of the yield curve.
B)
below par and the expectation is for a parallel shift of the yield curve.
C)
above par and the expectation is for a non-parallel shift of the yield curve.


For all types of securities, duration-based strategies are most effective for parallel shifts of the yield curve. If the price is below par for a mortgage security, then the price is more likely to exhibit positive convexity, and a duration-based hedge will be more effective.
作者: burning0spear    时间: 2012-4-1 17:23

Using only a duration-based framework for hedging is:
A)
more appropriate for a mortgage security than it is a Treasury security.
B)
more appropriate for a Treasury security than a mortgage security.
C)
equally important for both mortgage and Treasury securities.


Duration-based techniques are more important for Treasury securities with positive convexity. The negative convexity of mortgage securities makes duration a less meaningful measure in hedging them.
作者: burning0spear    时间: 2012-4-1 17:23

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.


To answer this, we set up the following two equations and two unknowns.(NH1)(0.4) + (NH2)(2.0) = -1.0
(NH1)(0.3) + (NH2)(0.5) = -0.4,
where NH1 and NH2 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 (NH1)(-0.8)=0.6, and thus NH1=-0.75. Substituting this into either expression and solving NH2 gives NH2=-0.35.(-0.75)(0.4)+(-0.35)(2)=-1
(-0.75)(0.3)+(-0.35)(0.5)=-0.4
作者: burning0spear    时间: 2012-4-1 17:23

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)
reliable assumptions in the Monte Carlo simulations of interest rates.
B)
the yield curve will shift in a parallel fashion.
C)
the security’s price change given a small change in yield.


A usual reason a two-bond hedge is required is that the yield curve is expected to shift in a non-parallel fashion.
作者: burning0spear    时间: 2012-4-1 17:24

In contrast to a one-bond hedge, a two bond hedge relies:
A)
more on duration measures and less on simulations of interest rates.
B)
less on duration measures and more on simulations of interest rates.
C)
more on duration measures and more on simulations of interest rates.


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.
作者: burning0spear    时间: 2012-4-1 17:24

In contrast to hedging a Treasury security with a one-bond hedge, when hedging mortgage securities, a two-bond hedge:
A)
is more appropriate and requires more assumptions.
B)
is less appropriate and requires fewer assumptions.
C)
is more appropriate and requires fewer assumptions.


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.
作者: burning0spear    时间: 2012-4-1 17:25

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.
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?
A)
$2.40 million.
B)
$1.50 million.
C)
$1.70 million.


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. (Study Session 10, LOS 25.d)
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:
A)
increased.
B)
decreased.
C)
been unaffected.


Shifting the actual bond positions to a longer duration while leaving the hedge unchanged would increase the duration of the entire portfolio. (Study Session 10, LOS 25.d)
Which of the following would be most appropriate to improve the hedge for Choice B? Purchasing:
A)
puts on Treasury futures to hedge against large interest rate increases.
B)
puts on Treasury futures to hedge against large interest rate decreases.
C)
calls on Treasury futures to hedge against large interest rate decreases.


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. (Study Session 10, LOS 25.d)
All of the following support Prescott’s assessment that a duration-based hedge of the mortgage securities would be adequate EXCEPT:
A)
the forecast of a low volatility of rates.
B)
he replaced the Treasury securities with equal amounts of mortgage securities of the same maturity.
C)
the mortgage securities were trading below par.


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. (Study Session 10, LOS 26.d)
Reasons for the hedge proving ineffective include all of the following EXCEPT:
A)
the interest rate changes were more than 20 basis points.
B)
only two key rates were used in the hedge.
C)
the negative convexity of the mortgage securities.


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. 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. (Study Session 10, LOS 26.a)
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 decline.
B)
hedged portfolio would increase.
C)
hedged portfolio would remain the same.


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. (Study Session 10, LOS 26.b)



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