Fixed Income Securities: Valuation, Risk, And Risk Management, 1st Edition Test Bank

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Test bankto accompany the textbookFixed Income Securities: Valuation, Risk, and RiskManagement by Pietro VeronesiPreliminary VersionAuthor: Javier Francisco Madrid1

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Chapter 11. Is the following an arbitrage opportunity? A gift that makes me feel goodjust by having it.Ans.This is an arbitrage opportunity because it doesn’t cost anything at initi-ation and it generates a positive profit by a certain date in the future (i.e.’you feel good’).2. Is the following an arbitrage opportunity? A bond that cost nothing butwill payoff zero with certainty in the future.Ans.This is not an arbitrage opportunity, since it doesn’t give a positive payoffin the future.3. Is the following an arbitrage opportunity? A free car that if I repair well, Iwon’t have to spend money on gasoline or maintenance costs (i.e. repairs)ever.Ans.This is not an arbitrage opportunity, since I have to pay money (to repairthe car) in order to be free of future costs.4. Is the following an arbitrage opportunity? Suppose you are in the desertand are given a bag of ice with a penny inside. Assume that the ice willmelt instantly and the cost of disposing of the bag is zero.Ans.This is an arbitrage opportunity because even though I can’t take advan-tage of the ice, I gain the penny for free.5. Is the following an arbitrage opportunity? A security that cost zero andmight pay a dollar in the future, but pays zero otherwise.Ans.This is an arbitrage opportunity because I get for free the chance of gettinga dollar in the future.6. What steps would you follow in order to take advantage of the followingarbitrage opportunity (if there is one)? Security A costs $3 and pays $5in 2 years, while security B costs $3 and pays $4 in 2 years.Ans.You borrow security B and sell it, which means you receive $3, with theseproceeds you buy security A. In 2 years you receive $5 and have to pay$4. You make a $1 profit.7. What steps would you follow in order to take advantage of the followingarbitrage opportunity (if there is one)?Security A costs $100 and pays$120 in 3 years. Security B costs $100 and pays $110 in one year. Yourfriend tells you that he would like you to lend him $110 in a year and thathe would give $130 the following year. Finally you know that in two years,with $130, you can invest in a security that will pay you either $140 or$121 (with equal probability) after a year.2

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Ans.You borrow security A and sell it, with the proceeds you buy security B.After a year you lend the money to your friend. The next year when hepays back, you invest in the risky security. After the third year, this willgive you either $140 or $121, while you have to pay $120. So you eitherhave a profit of $20 or $1.8. What steps would you follow in order to take advantage of the followingarbitrage opportunity (if there is one)?Security A costs $100 and pays$110 in 2 years.Security B costs $100 and pays $109 in one year.Youknow that in a year with $109 you can invest in a security that pays $120or $109 (with equal probability) the following year.Ans.This is not an arbitrage opportunity.9. Intuitively, is the Federal Funds rate generally higher, lower or the sameas LIBOR? Why?Ans.The LIBOR rate should be higher than the Federal Funds rate, since itshould include a higher probability of default by the banks trading LIBOR.10. Intuitively, is LIBOR generally higher, lower or the same as the repo rate?Why?Ans.LIBOR should be higher than the repo rate since it is not collateralizedwith another security, as it occurs with the repo rate.11. What are the steps to take a long position on a given U.S. security via therepo market?Ans.The trader must take the following steps (repo):At timet:i. Buy bond atPtand deliver the bond to the repo dealer.ii. The repo dealer will payPt−haircut to the trader, which is madewhole (minus the haircut) for the cost of the bond.At timeT:iii. The trader gets the bond from the repo dealer and sells it forPT.iv. With the proceedsPTthe trader pays back (Pt−haircut)×(1+Repo)to the repo dealer.12. What are the steps to take a short position on a given U.S. security viathe repo market?Ans.The trader must take the following steps (reverse repo):At timet:3

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i. Borrows the bond from the repo dealer and sells it atPt.ii. ReceivesPtwhich he posts as collateral with the repo dealer.At timeT:iii. The trader buys the bond forPTand gives it back to the repo dealer.iv. The repo dealer paysPt×(1+Repo).The dealer makes a profit ifthis is larger thanPT.13. What’s the return on capital for a trader who entered into a one-monthrepo wherePt= 98.5,PT= 99.01, Repo= 5% and haircut= 0.8?Ans.The return on capital is 0.13.14. What’s the profit for a trader who entered into a one-week reverse repowherePt= 99.40,PT= 99.48 and Repo= 6%?Ans.The profit is 0.0347.15. You find a bond that has a repo rate substantially lower than the GCR.Is this, for certain, an arbitrage opportunity?Ans.No, it might be that the bond is short on supply (hard to find), whichmeans that the trader might be thinking that the bond is overpriced andis speculating that the price will fall. By entering in a reverse repo, thetrader might make a substantial profit, even willing to forgo part of therate to be in the transaction.16. You are told that there is an ample supply for the bond mentioned inquestion 13. Does this affect your previous answer?Ans.Yes, since it shows that the lower rate is not due to scarcity of a specifictype of bond.17. What are the gains from trade of entering into a swap for these two firms?Firm AFirm BFixed Rate13%16%Floating RateLIBOR + 3%LIBOR + 6%Ans.Gains from trade are zero.18. What are the gains from trade of entering into a swap for these two firms?Firm AFirm BFixed Rate10%15.5%Floating RateLIBOR + 2%LIBOR + 4%Ans.Gains from trade are 3.5%.4

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19. What are the gains from trade of entering into a swap for these two firms?Firm AFirm BFixed Rate9%5%Floating RateLIBOR + 7%LIBOR + 4%Ans.Gains from trade are 1%.5

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Chapter 21. Do discount factors depend on compounding frequency? Why?Ans.No, discount factors do not depend on compounding frequency, since theyare terms of exchange (prices) between having money at timetversushaving at a later dateT.If they changed with compounding frequency,there would be an arbitrage opportunity.2. What effect does inflation have on discount factors?Ans.Higher inflation makes less appealing money in the future, so discountfactors will go down.3. Can a bond be quoted in more than one interest rate?Ans.Yes. It can be quoted in various compounding frequencies.4. From the following data obtain the discount curve:a. A zero coupon bondPz(0,0.5) = 99.20.b. A coupon bond paying 3% quarterlyP(0,0.25) = 100.5485.c. A coupon bond paying 6% quarterlyP(0,0.75) = 100.1655.d. A coupon bond paying 5% semiannuallyP(0,1) = 103.0325.Ans.The discount factors are the following:tZ(0, t)0.250.99800.500.99200.750.98701.000.98105. Using the previous discount curve price the following: A zero coupon bondexpiring att= 0.75.Ans.The price of the bond is 98.70.6. Using the previous discount curve price the following: A 1-year couponbond paying 4% quarterly.Ans.The price of the bond is 102.0580.7. Using the previous discount curve price the following: A 6-month couponbond paying 7% semiannually.Ans.The price of the bond is 102.6720.8. Using the previous discount curve price the following: A 9-month couponbond paying 5% semiannually.6

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Ans.The price of the bond is 103.6625.9. For the following scenario, check if there is a mispriced security:a. A zero coupon bondPz(0,0.5) = 99.00.b. A coupon bond paying 6% quarterlyP(0,0.25) = 101.1955.c. A coupon bond paying 4% quarterlyP(0,0.50) = 102.0830.d. A coupon bond paying 7% semiannuallyP(0,0.75) = 105.8440.Ans.The mispriced bond is [a.] the zero coupon bond.10. For the following scenario, check if there is a mispriced security:a. A zero coupon bondPz(0,0.25) = 99.40.b. A zero coupon bondPz(0,0.50) = 98.00.c. A coupon bond paying 3% quarterlyP(0,0.50) = 100.4880.Ans.The mispriced security is [b.].11. For the following scenario, check if there is a mispriced security:a. A coupon bond paying 1% quarterlyP(0,0.25) = 100.6498.b. A coupon bond paying 4% semiannuallyP(0,0.25) = 101.8980.c. A coupon bond paying 3% quarterlyP(0,0.50) = 101.2978.d. A coupon bond paying 5% quarterlyP(0,0.75) = 103.4425.e. A coupon bond paying 4% semiannuallyP(0,1.00) = 103.5880.Ans.The mispriced bond is [a.].12. For the following scenario, check if there is a mispriced security:a. A zero coupon bondPz(0,0.5) = 99.50.b. A coupon bond paying 3% quarterlyP(0,0.50) = 100.9948.c. A coupon bond paying 5% quarterlyP(0,0.75) = 102.7288.d. A coupon bond paying 2% semiannuallyP(0,1.25) = 102.8720.e. A zero coupon bondPz(0,1.25) = 98.4.Ans.The mispriced bond is [d.].13. For the following scenario, check if there is a mispriced security:a. A zero coupon bondPz(0,0.25) = 99.30.b. A zero coupon bondPz(0,0.50) = 98.70.c. A coupon bond paying 3% semiannuallyP(0,0.50) = 100.1850.d. A coupon bond paying 2% semiannuallyP(0,0.75) = 101.4880.7

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Ans.The mispriced bond is [d.], since it requires the discount factorZ(0,0.75)to be larger than the previous ones.14. What is the price on a 4.5-year floating rate bond that pays a semiannualcoupon (no spread)?Ans.The price of the coupon is 100.15. What is the price on a 5.75-year floating rate bond that pays a semiannualcoupon (no spread)? We know the following:a. There is a coupon bond paying 3% quarterlyP(0,0.25) = 100.0448.b. Last quarter the semiannually compounded rate was 3%.Ans.The price of the floating rate bond is 100.7895.16. What is the price of a 0.5-year floating rate bond that pays a quarterlycoupon equal to floating rate plus a 1% spread? We know the following:a. There is a zero coupon bondPz(0,0.25) = 99.80.b. There is a coupon bond paying 2% quarterlyP(0,0.5) = 100.3960.Ans.The price of the floating rate bond is 100.4980.17. What is the price of a 0.75-year floating rate bond that pays a semiannualcoupon equal to floating rate plus 2% spread? We know the following:a. There is a zero coupon bondPz(0,0.25) = 99.70.b. There is a zero coupon bondPz(0,0.50) = 99.20.c. There is a coupon bond paying 3% quarterlyP(0,0.75) = 101.7380.Ans.The price is 102.3145.18. You have two coupon bonds with same maturity, one pays 5% semiannu-ally and the other 5% quarterly. Which one has a higher yield?Ans.The second bond has a higher yield because it compounds more frequentlythan the first one, increasing the expected return.19. A Treasury dealer quotes the following 182-day bill at a 3.956% discount.What is the price of the security?Ans.The price of the Treasury is 98.00.20. A Treasury dealer quotes the following 91-day bill at a 3.956% discount.What is the price of the security?Ans.The price of the Treasury is 99.00.8

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Chapter 3Use the following discount factors when needed.tZ(0, t)0.250.98400.500.96800.750.95201.000.93601.250.91901.500.90401.750.88802.000.87302.250.85872.500.84452.750.83083.000.81753.250.80473.500.79243.750.78064.000.76911. Calculate the duration of the following security: 5-year zero coupon bond.Ans.The duration of the security is 5.00.2. Calculate the duration of the following security: 2-year fixed coupon pay-ing 5% quarterly.Ans.The duration of the security is 1.9138.3. Calculate the duration of the following security: 1.25-year floating couponpaying float + 50 bps semiannually. You know that last quarter the semi-annual rate was 6.4%.Ans.The duration of the security is 0.2534.4. Calculate the duration of the following portfolio:i. 5 units of a 2-year fixed rate bond paying 6% quarterly.ii. 2 units of a 1.75-year floating rate bond paying float + 80 bps semi-annually. You know that the reference rate was 6.5% three monthsago.iii. 6 units of a 1-year zero coupon bond.iv. 5 units of a 1.5-year floating rate bond with no spread paid semian-nually.Ans.The duration of the portfolio is 0.8805.5. Calculate the duration of the following portfolio:9

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i. 3 units of a 0.75-year fixed rate bond paying 6% quarterly.ii. 4 units of a 2-year fixed rate bond paying 3% semiannually.iii. 7 units of a 1.75-year zero coupon bond.iv. 1 unit of a 2-year floating rate bond with no spread paid semiannually.Ans.The duration of the portfolio is 1.4617.6. You have two bond coupon with the same maturity, one has a 9% couponpaid semiannually and the other a 8% coupon paid semiannually. Whichone has a higher duration?Ans.The one with the lower coupon has a higher duration.Higher couponsmean that a higher proportion of the total cash flows from the bond willbe paid more quickly. These cash flows will also be less sensitive to interestrates as cash flows paid later are more exposed to interest rate variation.7. Calculate the MacCaulay Duration for the following security: 1-year fixedrate coupon bond paying 6% semiannually.You know that the yield ofthe bond is 6.72%.Ans.The MacCaulay Duration for the bond is 0.9854.8. Calculate the Modified Duration for the same security.Ans.The Modified Duration for the bond is 0.9533.9. What is the duration of the following portfolio?i. Long a 1.5-year zero coupon bond.ii. Short a 2-year fixed coupon bond paying 1% quarterly.Ans.Trying to compute duration from this long-short portfolio brings manyproblems since we can’t adequately weigh the securities within the port-folio.10. What is the dollar duration of the following portfolio?i. Long a 1.5-year zero coupon bond.ii. Short a 2-year fixed coupon bond paying 1% quarterly.Ans.Dollar duration for the portfolio is -41.0462.11. What is the dollar duration of the following portfolio:i. Long a 1-year fixed coupon bond paying 4% quarterly.ii. Long a 1.75-year floating rate bond paying float plus 80 bps semian-nually. You know that the reference rate was set at 6% six monthsago.iii. Short a 2-year zero coupon bond.10

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Ans.The dollar duration of the portfolio is -51.8169.12. What is the dollar duration of the following portfolio:i. Long a 2-year fixed coupon bond paying 7% quarterly.ii. Short three 1.25-year floating rate bonds paying float plus 80 bpssemiannually.You know that the reference rate was set at 7% sixmonths ago.iii. Short two 0.5-year zero coupon bonds.Ans.The dollar duration is 13.2098.13. What is the PV01 of the following portfolio?i. Long a 1-year fixed coupon bond paying 4% quarterly.ii. Long a 1.75-year floating rate bond paying float plus 80 bps semian-nually. You know that the reference rate was set at 6% six monthsago.iii. Short a 2-year zero coupon bond.Ans.The PV01 is -0.0052.14. What is the PV01 of the following portfolio?i. Long a 2-year fixed coupon bond paying 7% quarterly.ii. Short three 1.25-year floating rate bonds paying float plus 80 bpssemiannually.You know that the reference rate was set at 7% sixmonths ago.iii. Short two 0.5-year zero coupon bonds.Ans.The PV01 is 0.0013.15. Compute the 95% VaR for the following portfolio:i. A 1.5-year fixed rate bond paying 2% quarterly.ii. A 0.75-year floating rate bond paying float plus 80 basis points semi-annually. You know that the reference rate was set to 6% six monthsago.iii. A 0.25 zero coupon bond.Additionally you know thatμdr= 0 andσdr= 0.4233.Ans.The 95%V aR= 1.3116.16. Suppose that you calculate VaR from Duration. In your many results youfind that:i. using historical data (of whatever length) or a normal distributiondoes not affect the result;11

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ii. you find that kurtosis between historical data and the normal distri-bution is almost identical;iii. You find the expected change in the portfolioμP= 0, with very smallstandard errors.Given the above, can you say that this Duration based VaR is an appro-priate approach to measure risk?Ans.No, it is not.It is still internally inconsistent: Duration measures smallchanges, but VaR uses extreme values (large changes).17. Mr. Brown wants to invest $100,000 for the next five years. He purchasesan annuity from a financial institution.Currently the term structure isflat at 10% (yearly compounded).i. If the payments are made yearly, what is the amount that the finan-cial institution will agree to pay Mr. Brown?ii. Assume that there is a 5-year fixed coupon bond that pays 12%coupon every year. What is the price and duration of the bond?iii. How much must the financial institution invest in the long-term bondin order to hedge the position? What should it do with the remainderof the money?Ans.The results for the immunization exercise are:i. The financial institution would pay a yearly amount of $26,379.75.ii. The price of the security is $107.58 with 4.074 duration.iii. The financial institution should invest 93.05% of the proceeds fromthe investment in the long-term bond and the rest in the moneymarket account.12

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Chapter 4Use the following discount factors when needed.TZ(0, T)0.250.98400.500.96800.750.95201.000.93601.250.91901.500.90401.750.88802.000.87302.250.85872.500.84452.750.83083.000.81753.250.80473.500.79243.750.78064.000.76911. Calculate the convexity of the following security:a 5-year zero couponbond.Ans.The convexity of the security is 25.2. Calculate the convexity of the following security: a 3-year fixed rate bondpaying 4% coupon on a semiannual basis.Ans.The convexity of the security is 8.3780.3. Calculate the convexity of the following security:a 3-year floating ratebond with no spread paid quarterly.Ans.The convexity of the security is 0.4. Calculate the convexity of the following portfolio:i. 1 unit of a 2-year fixed coupon bond paying 10% coupon quarterly.ii. 1 unit of a 2-year fixed coupon bond paying 1% coupon semiannually.iii. 1 unit of a 2-year zero coupon bond.Ans.The convexity of the portfolio is 3.8230.5. Calculate the convexity of the following portfolio:i. 2 units of a 1.5-year fixed rate bond paying 6% quarterly.ii. 4 units of a 1.75-year floating rate bond paying float + 80 bps semi-annually.You know that the reference rate was 7% three monthsago.13

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iii. 6 units of a 2-year zero coupon bond.iv. 1 units of a 1.5-year floating rate bond with no spread paid semian-nually.Ans.The convexity of the portfolio is 2.0655.6. Calculate the convexity of the following portfolio:i. 4 units of a 1.5-year fixed rate bond paying 4% quarterly.ii. 5 units of a 1.5-year fixed rate bond paying 5% semiannually.iii. 10 units of a 1.5-year zero coupon bond.iv. 3 units of a 1.5-year floating rate bond with no spread paid semian-nually.Ans.The convexity of the portfolio is 1.8916.7. Calculate annualized expected returns (including convexity) for a 5-yearzero coupon bond, whenE[dr] = 0 andE[dr2] = 6×10−07 (on a dailybasis).Ans.Annualized expected return on the bond is: 0.189%.8. Calculate annualized expected returns (including convexity) for a 30-yearzero coupon bond, whenE[dr] = 0 andE[dr2] = 7×10−07 (on a dailybasis).Ans.Annualized expected return on the bond is: 7.938%.9. Calculate annualized expected returns (including convexity) for a 3-yearfixed rate bond paying 2% coupon semiannually, whenE[dr] = 0 andE[dr2] = 7.5×10−07 (on a daily basis).Ans.Annualized expected return on the bond is 0.0815%.10. Suppose you hold a bond and interest rates suddenly fall. Duration saysthat bond prices will raise a given amount.If Convexity is included inthis estimate, will bond prices go above or below what Duration predicts?Ans.Prices will go up even more than what Duration predicts.11. Suppose you hold a bond and interest rates suddenly rise. Duration saysthat bond prices will fall a given amount. If Convexity is included in thisestimate, will bond prices go above or below what Duration predicts?Ans.Prices will go up, partially countering the decrease predicted by Duration.12. Compute the Term Spread and the Butterfly Spread for the following data.What shape does the yield curve have?1-month yield5-year yield10-year yield5.0%8.0%10.0%14

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Ans.The term spread is 5% and the Butterfly Spread is 1%. The shape of theyield cure is increasing.13. Compute the Term Spread and the Butterfly Spread for the following data.What shape does the yield curve have?1-month yield5-year yield10-year yield6.0%4.5%4.0%Ans.The term spread is -2% and the Butterfly Spread is -1%.The shape ofthe yield cure is decreasing.14. Compute the Term Spread and the Butterfly Spread for the following data.What shape does the yield curve have?1-month yield5-year yield10-year yield3.0%4.0%3.0%Ans.The term spread is 0% and the Butterfly Spread is 2%. The shape of theyield cure is a hump.15. Compute the Term Spread and the Butterfly Spread for the following data.What shape does the yield curve have?1-month yield5-year yield10-year yield4.0%3.0%5.0%Ans.The term spread is 1% and the Butterfly Spread is -3%. The shape of theyield cure is an inverted hump.16. You currently hold a 7-year fixed rate bond paying 5% annually.Youwould like to hedge against changes in the level and the slope of the yieldcurve and you plan to use a 1-year zero coupon bond and a 7-year zerocoupon bond. Use the following table to compute the adequate positionsin the hedging instruments.maturityβ1β2Z(t, T)1.001.1150-0.25400.98002.000.9940-0.30100.96003.000.9640-0.14700.93004.000.93300.00800.89005.000.93000.16200.85006.000.92600.31600.81007.000.92700.42300.77008.000.92700.53000.7300Ans.The position in the short term bond should be -0.4651, while the positionin the long term bond should be -1.1231.15

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