CFA Level 3 - Fixed Income Session 10 - Reading 26

CFA Level 3 - Fixed Income Session 10 - Reading 26 (Notes, Practice Questions, Sample Questions) 1. 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. Explanation : If the security is trading below par, then it is most likely to exhibit positive convexity, and this will make a hedge formed with aTreasury futures contract that has positive convexity more effective 2. 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. Explanation: A declining market yield will cause the price to increase. This condition will make prepayment more likely, and make the convexitynegative 3. 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 Explanation: The best answer is go from negative to positive. As rates increase and the price declines, the prepayment option goes out of themoney. We could also say the convexity, if already positive, can becomemore positive, but that was not one of the answer 4. 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 astable 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. Explanation: A hedge that is designed to be effective for changes of +/-50 basis points for a mortgage security trading at par will likely be lesseffective for decreases greater than 50 basis points. This is because ofnegative convexity. Since the mortgage security is likely to exhibit positiveconvexity for prices below par, the hedge is more likely to be effective for thelarger increase in yield 5. A portfolio manager has used a Treasury bond futures contract to hedge a mortgage security, which is trading at par, against a decrease invalue from a 50 basis point increase in yield. If the yield were to decrease50 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

Explanation: The most likely result is that the position with the hedge will decline because of the mortgage security’s negative convexity. As the yielddecreases, the prepayment option goes in the money and the value of thesecurity does not go up by as much as the value of the short futures positiongoes down because the futures position has positive convexity 6. 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 Explanation: If the price is below par, the market yield must be higher than the yield on the underlying mortgages, and the prepayment rate will belower. This means the instrument is more likely to exhibit positiveconvexity 7. 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 pointsbelow its opening yield and then increased 80 basis points above itsopening yield. The corresponding prices of the instrument were 99.5 and98 respectively. From this we can say the security: A)exhibited excess volatility.B)exhibited positive convexity. C)exhibited negative convexity. Explanation: The fact that the price increase from the yield decline was less than the price decrease from the yield increase is indicative of negativeconvexity caused by a prepayment option

8. 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. Explanation: The innovations have had a direct effect on the ability of models to predict prepayment rates. 9. All of the following are risks associated with mortgage securities EXCEPT: A)volatility risk.B)model risk. C)beta risk. Explanation: Beta is not generally a concept directly associated with mortgage securities. Model risk is important because the current valuedepends upon patterns of interest rates and prepayment rates. Thechanging spread can influence the asset’s value. Because of the embeddedoption, volatility risk is important too. 10. 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. Explanation: A manager can earn profits by buying mortgage backed securities when the spread widens and selling when the spread narrows

11. Negative convexity is more likely to become more severe if: A)volatility decreases. B)volatility increases. C)the spread increases Explanation: Negative convexity can be interpreted as the negative effect on price caused by an increase in the value of the embedded, short calloption in the mortgage security. An increase in volatility will increase thevalue of that option and increase the severity of the negative convexity. Anincrease in the spread and/or Treasury rate will likely increase the yield ofthe mortgage security, and this will tend to make the security’s convexitymore positive 12. 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 Explanation: An increase in the spread means the yield of the mortgage backed security has increased relative to Treasuries so the security’s valuehas decreased relative to Treasuries. This would be an opportunity to buymortgage backed securities 13. 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.

Explanation: Interest rate risk is associated with the risk from movements in Treasury securities. Spread risk is a separate component associatedwith the credit properties of the security as well as macroeconomic factors 14. When comparing the number of key rates needed in hedging a mortgage security versus a Treasury security, we generally need toconsider: A)more key rates for the mortgage security because of its bullet paymentat maturity. B)more key rates for the mortgage security because it lacks a bulletpayment at maturity. C)fewer key rates for the mortgage security because it lacks a bulletpayment at maturity Explanation: A Treasury bond’s price is affected most by changes in the yield associated with its maturity, and this is because of the large bulletpayment for that type of bond. Because a mortgage security is essentiallyan annuity, changes of other rates become more important 15. 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 ofthe yield curve.B)less important and increases in importance for non-parallel shifts of theyield curve. C)more important and increases in importance for non-parallel shifts ofthe yield curve Explanation: 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 theyield curve 16. A duration-based framework for hedging a mortgage security may lead to be a greater loss than not hedging if the price of the mortgagesecurity is: A)below par.B)at all values. C)above par Explanation: When the price is above par, negative convexity is more likely to be a problem. If the market yield declines, the hedge will decline invalue while the price of the mortgage security may not increase. This willlead to a greater loss than if the security were not hedged at all 17. 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 yieldcurve Explanation: 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 amortgage security, then the price is more likely to exhibit positiveconvexity, and a duration-based hedge will be more effective 18. 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 Explanation: Duration-based techniques are more important for Treasury securities with positive convexity. The negative convexity of mortgagesecurities makes duration a less meaningful measure in hedging them 19. 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 themortgage security and 0.4 and 2.0 for hedging instrument one and tworespectively. The expected average price change from a projected twist inthe yield curve is 0.4 for the mortgage security and 0.3 and 0.5 forhedging instrument one and two respectively. What positions in hedginginstruments one and two should a manager take to hedge the price of themortgage security from the projected market changes? For every dollar offace value of the mortgage security: A)buy $2.5 of hedging instrument one and $0.5 of hedging instrumenttwo. B)sell $0.75 of hedging instrument one and $0.35 of hedging instrumenttwo. C)sell $2.5 of hedging instrument one and $0.5 of hedging instrumenttwo. Explanation: 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 oneand two respectively. Multiplying the second equation by 4 and subtractingit from the first gives (NH1)(-0.8)=0.6, and thus NH1=-0.75.Substituting this into either expression and solving NH2 givesNH2=-0.35.(-0.75)(0.4)+(-0.35)(2)=-1(-0.75)(0.3)+(-0.35)(0.5)=-0.4

20. 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. Explanation: The usual reason a two-bond hedge is needed is that a duration-based approach is inadequate. Simulations of interest rates playmore of a role in cases where a duration-based strategy is inadequate 21. 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. Explanation: Because there is not a bullet payment at maturity, a two-bond hedge is usually more appropriate for mortgage securities. Moreassumptions are needed for such a hedge such as prepayment rates andwhether the average-price method yields usable results 22.1 James Prescott is a portfolio manager with Atlantic Investment Management Company. Prescott forecasts that interest rates will remainat 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 increasethe return of the portfolio while managing the risk appropriately. Thecurrent portfolio consists of $80 million long-term Treasury bonds and$60 million short-term Treasury bonds. Given his interest-rate forecast ofstable rates with low volatility, he uses a parallel yield curve shift of 20basis points to compute the bonds’ dollar durations. For a 20 basis pointchange, the dollar duration of the long-term bonds is $1.2 million and thedollar duration of the short-term bonds is $0.5 million. Before adjusting

the portfolio, Prescott fully hedges the portfolio for the potential 20 basispoint shift with futures contracts that have the same maturity as theshort-term and long-term position and in the same relative amounts. Prescott is considering two possible choices to increase the return of theportfolio.Choice A would convert half of the short-term bonds to long-term bonds.Choice B would convert half of both positions to mortgage backedsecurities with maturities equal to each of the previous positions. The mortgage-backed securities are trading at a discount from par andoffer a 70 basis point spread over the long-term Treasury securities.Prescott determines that for the forecasted yield curve shift, aduration-based strategy is appropriate. Prescott decides on choice B. He decides to keep the same position inTreasury futures as a hedge. Shortly thereafter, there is a 40 basis pointincrease in short-term rates and a 60 basis point increase in long-termrates. The hedge proves to be ineffective.For a 20 basis point shift, what was the dollar duration of the originalbond portfolio without the hedge? A)$2.40 million.B)$1.50 million. C)$1.70 million. 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 22.2 If Prescott had chosen Choice A and had not changed the hedge, the dollar duration of the entire position including the futures would mostlikely have:

A)increased. B)decreased.C)been unaffected Explanation: Shifting the actual bond positions to a longer duration while leaving the hedge unchanged would increase the duration of the entireportfolio 22.3 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 ratedecreases. 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 convexityof the mortgage securities will mean the value of the mortgage securitiesmay not increase by as much as the futures decline. A long position incalls on Treasury futures will have an asymmetric payoff that can offsetthe asymmetric price behavior of mortgage securities. Adding long callsthat will increase in value when rates decline compensates for the short callthat is implicit in the mortgage security 22.4 All of the following support Prescott’s assessment that a duration-based hedge of the mortgage securities would be adequateEXCEPT: A)the forecast of a low volatility of rates. B)he replaced the Treasury securities with equal amounts of mortgagesecurities of the same maturity.

C)the mortgage securities were trading below par. 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 theeffectiveness of a duration-based strategy even if the maturities are thesame. Since the mortgage securities are trading below par, they are likelyto exhibit positive convexity, and that means a duration-based strategycould be appropriate. If the volatility of rates remains low, the effect of thecall embedded in the mortgage securities will be less important. 22.5 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. Explanation: The fact that the mortgage securities were trading below par and then interest rates increased means that the mortgage securities werelikely in a region where they exhibited positive convexity so negativeconvexity probably did not play a role. The fact that only two key rateswere used is a problem. There would probably need to be at least three keyrates: one for the short-term bonds, one for the long-term bonds whichwould cover some of the mortgage securities, and a third intermediate ratefor the additional risk of the mortgage securities which do not have a bulletpayment at maturity. The fact that the hedge was set up for only a 20 basispoint change will mean the bonds would be poorly hedged for the indicatedshifts. 22.6 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, thenthe value of the: A)hedged portfolio would decline. B)hedged portfolio would increase.C)hedged portfolio would remain the same Explanation: Since the Treasury rates remained the same, the futures contracts would not change in value. The value of the mortgage securitieswould decline because the yield would increase from the spread increase.