Exam 1 - solutions

pdf

School

University of Nebraska, Lincoln *

*We aren’t endorsed by this school

Course

802

Subject

Finance

Date

Feb 20, 2024

Type

pdf

Pages

Uploaded by Jreis2

Exam 1 FINA 802 Spring 2022 Dr. S. Nikolova Instructions: 1. For partial credit, show all your work rather than simply the final answers to the numerical problems. 2. All rates are annualized on a semi-annual bond equivalent yield basis. Your answers should be as well. 3. Remember that you have only 3 hours to complete the exam and turn it in. You can only submit one file, so plan accordingly. Question 1. (4 pts.) Briefly answer one of the two questions below: a.) Explain the two main differences between brokers and dealers. b.) Describe the two main types of municipal bonds and compare them in terms of credit risk. Answer: a.) Dealers take ownership of the asset, keep it in inventory and then re-sell it. Their compensation is the difference between the price at which they buy the asset and then re-sell it (bid-ask spread). In contrast, brokers never take ownership of the asset but instead immediately connect a buyer and a seller. They are compensated based on a commission. b.) The two main types of municipal bonds are general obligation and revenue bonds. General obligation (GO) bonds are backed by the taxing ability of the issuer, i.e. the full faith and credit of the state, city or local government that issues them. Revenue bonds are issued to finance a specific project and are backed by the revenues from this project. Because of uncertainty about the success of the project, revenue bonds are usually regarded as having more credit risk. Question 2. (3 pts.) Who are the largest investors in Treasury securities? What are the implications of this for the issuer of Treasury securities? Briefly discuss. Answer: Foreign entities are the largest investors in Treasury securities and of these foreign governments are especially big players in this market. This requires the U.S. government, the issuer of Treasuries, to take into consideration how its actions will affect foreign governments and causes politics and finance to intersect. E.g., a few years back during the Trump administration’s trade war with China, China threatened to pull out of its Treasury investments. If it had done so, then this would have inevitably increased the U.S. government’s borrowing cost. Question 3. (5 pt.) Bond XYZ has 8 years to maturity, pays a coupon based on the 3-month LIBOR plus a quoted margin of X bps (quarterly frequency), and is currently quoted at a price of 95.44. T he bond’s discount margin is 280 bps. The 3-month LIBOR is currently 4% and the 6-month LIBOR is currently 4.2%. What must be the bond’s quoted margin?

Answer: N=8*4=32 Y=(4% + 280 bps)/4=1.7 PV= -95.44 FV=100 PMT=? PMT=1.5141*4=6.0563 The payment is based on the 3-month LIBOR plus the quoted margin. So you need to subtract the 3- month LIBOR rate to obtain the quoted margin: Quoted margin = 6.0563% – 4% = 206 bps Question 4. (4 pts.) A Treasury inflation-protected security has a par value of $1,000,000 and a coupon rate of 4%. Assume that the 6-month annualized inflation rate over the first 6 months after the security is issued is 2%, the 6- month annualized inflation rate over the next 6 months is 3%, and the 6-month annualized inflation rate over the next 6 months is 2.5%. Calculate the coupon payment on the security one and a half years after it is issued. Answer: Inflation adjust the principal over three consecutive 6-month periods to obtain the inflation-adjusted principal at the end of a year and a half. That is, 1,000,000*(1+0.02/2)*(1+0.03/2)*(1+0.025/2) = 1,037,964.375 Calculate the coupon, accounting for the semi-annual payment frequency: 1,037,964.375*(0.04/2)=20,759.2875 Question 5. (10 pt.) You observe the following prices of Treasury securities: • a 6-month T-bill sells for 97.9432 • a 1-year T-bill sells for 95.3674 • a 1.5-year 8% coupon T-note sells for 104.1656 You also observe that the 2-year spot rate is 5.3%. All rates are annualized on a semi-annual bond equivalent yield basis. a.) Calculate the 6-month, 1-year, and 1.5-year spot rates on a bond-equivalent yield basis. b.) Roughly sketch the spot rate curve implied by these Treasury securities’ prices . c.) Calculate the 6-month and 1-year rates investors expect to see in 6 months on a bond-equivalent yield basis. d.) Calculate the expected 6-month holding period return on the T-note. Answer: a.) The YTM on the 6-month T-bill is the 6-month spot rate: 97.9432= 100 / (1+r 0.5 /2) r 0.5 =4.2% Same for the 1-year T-bill:

95.3674= 100 / (1+ r 1 /2) 2 r 1 =4.8% Unfortunately, the yield to maturity on a coupon paying bond is different from the spot rate at that maturity, so for the T-bond we need to use a pricing equation. The price of the bond must equal the present value of all its future cash flow discounted at the appropriate spot rates: 104.1656= 4/(1 + 0.042/2) + 4/(1+0.048/2) 2 + 104/(1+r 1.5 /2) 3 r 1.5 = 5.1% b.) The spot rate curve will look like this: c.) Design two strategy for investing over the same time period and set their returns to be equal: 1-year rate investors expect to see in 6 months: (1+0.042/2)*(1+f 0.5,1.5 /2) 2 = (1+ 0.051/2) 3 f 0.5,1.5 =5.5515% 6-month rate investors expect to see in 6 months: (1+0.042/2)*(1+f 0.5,1 /2) = (1+ 0.048/2) 2 f 0.5,1 =5.4018% d.) You need to calculate the expected price in 6 months as the present value of the future cash flows: P 0.5 =4/(1 + 0.0540/2) + 104/(1+0.0555/2) 2 =102.3530 Then you need to calculate the reinvested value of the cash flows, which is 4 since the first one just happened and you had no time to reinvest it. Ret=(102.3530 + 4 – 104.1656)/104.1656 = 0.0210 Now annualize it: 0.0210*2= 4.2%. The final answer should have been expected since this is the 6-month spot rate. 0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% 0.5 1 1.5 2 Spot rate (%) Maturity (yrs) Spot rate curve

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Question 6. (9 pt.) Bond ABC has maturity of 1.5 years, coupon rate of 4.2% (interest paid semiannually), and YTM of 8.5%. Answer the questions below about this bond. a.) Calculate the bond’s Macaulay or modified duration in years, using either precise calculations/formulas or the approximation approach. If using the approximation approach, use 10 bps as the yield change needed for the approach. b.) Calculate the bond’s convexity in years, using either precise calculations/formulas or the approximation approach. If using the approximation approach, use 10 bps as the yield change needed for the approach. c.) Use the bond’s duration and convexity to estimate its dollar price change if interest rates increase by 40 bps. d.) Bond XYZ has maturity of 1.5 years, coupon rate of 4.2% (interest paid semiannually), and YTM of 7%. Would its duration be higher, lower or the same as that of bond ABC? In one sentence, why? Hint: No calculation is needed to answer these questions. e.) Bond QWE has maturity of 10 years, Macaulay duration of 7.4942 years, modified duration of 7.1886 years, coupon rate of 5.6% (interest paid semiannually), and YTM of 8.5%. You have a 4.5-year intended investment horizon and want to form an immunized portfolio of bonds ABC and QWE. If you have $300,000 to invest, how much would you allocate to bond ABC? Answer: a.) Here are the answers using precise calculations: t CF PV(CF) t*PV(CF) 1 2.1 2.014 2.0144 2 2.1 1.932 3.8645 3 102.1 90.115 270.3453 Total 94.062 276.224 Duration in half-years 2.9366 Duration in years 1.4683 ModD in half years 2.8169 ModD in years 1.4085 Here are the answers using the approximation approach: YTM 8.5% 8.4% 8.6% Price $94.0618 $94.1944 $93.9294 Modified D 1.4085 Macaulay D 1.4683 b.) Here are the calculations for convexity using precise formulas:

t CF CF/[(1+y)^(t+2)] t*(1+t)*CF/[(1+y)^(t+2)] 1 2.1 1.8535 3.7070 2 2.1 1.7779 10.6676 3 102.1 82.9174 995.0082 1009.3828 C in periods 10.7311 =1009.3832/94.062 C in years 2.6828 =10.7311/4 And here are the calculations using the approximation approach: YTM 8.5% 8.4% 8.6% Price $94.0618 $94.1944 $93.9294 Convexity 2.6828 c.) To calculate the dollar price change you start with the percentage price change due to duration: - MD * dy = -1.4085*(0.004) = -0.5634% Then you calculate the percentage price change due to convexity: 0.5*Convexity*dy 2 =0.5*2.6828*0.004 2 = 0.0021% Sum them up and multiple them by the price to obtain the dollar price change: dP = (-0.5634% + 0.0021%) * 94.0618 = -$0.5279 d.) Higher . Bond XYZ is the same as bond ABC except for its yield to maturity. Lower yield to maturity, all else equal, implies higher duration. e.) An immunized portfolio is one, whose Macaulay duration equals the intended investment horizon. Let X be the proportion invested in bond ABC and (1-X) the proportion invested in bond QWE. The Macaulay duration of the portfolio is then set equal to 4.5: X*(1.4683) + (1-X)*(7.4942) =4.5 X=49.69% Then the allocation to ABC is (0.4969)*(300000) = $149,067.