FIN487 Homework

Frank Meyers, CFA, is a fixed-income portfolio manager for a large pension fund. A member of the Investment Committee, Fred Spice, is very interested in learning about the management of fixed-income portfolios. Spice has approached Meyers with several questions. Meyers decides to illustrate fixed-income trading strategies to Spice using a fixed-rate bond and note. Both bonds have semiannual coupon periods. Unless otherwise stated, all interest rate changes are parallel. The characteristics of these securities are shown in the following table. He also considers a 9-year floating-rate bond (floater) that pays a floating rate semiannually and is currently yielding 5%. Characteristics of Fixed-Rate Bond and Fixed-Rate Note Fixed-Rate Bond Fixed-Rate Note Price 107.18 100.00 Yield to maturity 5.00% 5.00% Time to maturity (years) 18 8 Modified duration (years) 6.9848 3.5851 Spice asks Meyers to quantify price changes from changes in interest rates. To illustrate, Meyers computes the value change for the fixed-rate note in the table. Specifically, he assumes an increase in the level of interest rate of 100 basis points. Using the information in the table, what is the predicted change in the price of the fixed-rate note?

100*0.1*-3.5851=(3.59) ??? prof said system did it wrong but the formula given for it is =(−$3.5851/1.05) × 0.01× 100=−$3.41 (decrease)

Find the duration of a 6% coupon bond making semiannually coupon payments if it has three years until maturity and has a yield to maturity of 6%. What is the duration if the yield to maturity is 10%? Note: The face value of the bond is $100

2.7899 2.7761 https://www.chegg.com/homework-help/questions-and-answers/find-duration-6-coupon-bond-making-semiannually-coupon-payments-three-years-maturity-yield-q42444546

a. Find the duration of a 6% coupon bond making annual coupon payments if it has three years until maturity and has a yield to maturity of 6%. Note: The face value of the bond is $1,000. 6% YTM= b. What is the duration if the yield to maturity is 10%? Note: The face value of the bond is $1,000. 10% YTM=

2.833 years 2.824 years https://www.studysmarter.us/textbooks/business-studies/essentials-of-investments-9th/debt-securities/q11-8b-find-the-duration-of-a-6-coupon-bond-making-annual-co/#:~:text=Find%20the%20duration%20of%20a%206%25%20coupon%20bond%20making%20annual,2.8334%20years%20and%202.824%20years.

The yield to maturity (YTM) on 1-year zero-coupon bonds is 5% and the YTM on 2-year zeros is 6%. The yield to maturity on 2-year-maturity coupon bonds with coupon rates of 12% (paid annually) is 5.8%. a. What arbitrage opportunity is available for an investment banking firm? b. What is the profit on the activity?

A] The price of the coupon bond, based on its YTM, is: Using Calculator, N = 2, I/Y = 5.8, PMT = -120, FV = -1000 and Compute PV = $1113.99 If the coupons were stripped and sold separately as zero-coupon bonds, then based on the YTM of zero-coupon bonds with maturities of one and two years, the coupon payments could be sold separately for [120/1.05] + [1,120/(1.06)2] = $1,111.08. B] The arbitrage strategy is to: Buy zero-coupon bonds with face values of $120 and $1,120 and respective maturities of 1 and 2 years Simultaneously sell the coupon bond. The profit equals $2.91 on each bond.

A 30-year maturity bond has a 7% coupon rate, paid annually. It sells today for $867.42. A 20-year maturity bond has a 6.5% coupon rate, also paid annually. It sells today for $879.50. A bond market analyst forecasts that in five years, 25-year maturity bonds will sell at yields to maturity of 8% and 15-year maturity bonds will sell at yields of 7.5%. Because the yield curve is upward sloping, the analyst believes that coupons will be invested in short-term securities at a rate of 6%. a. Calculate the (annualized) expected rate of return of the 30-year bond over the 5-year period. (Round your answer to 2 decimal places.) b. What is the (annualized) expected return of the 20-year bond?

Maturity of the 30-year bond falls to 25 years, so n=25 The yield is forecast i = 8%. PMT = 70 FV = 1000 The price forecast = $893.25 Step 2: Calculation of total proceeds, five year return and annual return The total payment accumulation of five coupon payments after five years at a 6% interest rate= $394.60. So total proceeds: $394.60 + $893.25 = $1,287.85 The five-year return = ($1,287.85/867.42) - 1 = 1.48469 - 1 = 48.469% The annual rate of return = (1.48469)(1/5) -1 = 0.0822 = 8.22% Step 3: Calculation of total proceeds five year return and annual return Maturity of the 20-year bond falls to 15 years, so n=15 The yield is forecast i = 7.5%. PMT = 65 FV = 1000 The price forecast = $911.73 The total payment accumulation of five coupon payments after five years at a 6% interest rate= $366.41. So total proceeds: $366.41 + $911.73 = $1,278.14 The five-year return = ($1,278.14/$879.50) - 1 = 1.45326 - 1 = 45.326% The annual rate of return = 1.45326(1/5) - 1 = 0.0776 = 7.76% So 30-year bond offers the higher expected return i.e. 8.22% against 20-year bond which gives 7.76% return.

Prices of zero-coupon bonds reveal the following pattern of forward rates: Year Forward Rate 1 5 % 2 7 3 8 In addition to the zero-coupon bond, investors also may purchase a 3-year bond making annual payments of $60 with par value $1,000. a. What is the price of the coupon bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. What is the yield to maturity of the coupon bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.) c. Under the expectations hypothesis, what is the expected realized compound yield of the coupon bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.) d. If you forecast that the yield curve in 1 year will be flat at 7%, what is your forecast for the expected rate of return on the coupon bond for the 1-year holding period?

a Price 984.14 =60/(1+5%)+60/((1+5%)*(1+7%))+1060/((1+5%)*(1+7%)*(1+8%)) b Yield to maturity 6.66% =((1+5%)*(1+7%)*(1+8%))^(1/3)-1 c Realized compound yield 6.66% =((60*1.07*1.08+60*1.08+1060)/984.14)^(1/3)-1 d Next year bond price 981.92 =60/(1+7%)+1060/(1+7%)^2 Holding period return (981.92+60-984.14)/984.14= 5.87%

Long-term Treasury bonds currently are selling at yields to maturity of nearly 6%. You expect interest rates to fall. The rest of the market thinks that they will remain unchanged over the coming year. If you are correct, choose the bond that will provide the higher holding-period return over the next year in each of the following: a. i. A Baa-rated bond with coupon rate 6% and time to maturity 20 years. ii. An Aaa-rated bond with coupon rate of 6% and time to maturity 20 years. multiple choice 1 i ii b. i. An A-rated bond with coupon rate 3% and maturity 20 years, callable at 105. ii. An A-rated bond with coupon rate 6% and maturity 20 years, callable at 105. multiple choice 2 i ii c. i. A 4% coupon noncallable T-bond with maturity 20 years and YTM = 6%. ii. A 7% coupon noncallable T-bond with maturity 20 years and YTM = 6%.

a ii b i c i

You will be paying $10,000 a year in tuition expenses at the end of the next two years. Bonds currently yield 8%. a. What is the present value and duration of your obligation? b. What maturity zero-coupon bond would immunize your obligation? c. Suppose you buy a zero-coupon bond with value and duration equal to your obligation. Now suppose that rates immediately increase to 9%. What happens to your net position, that is, to the difference between the value of the bond and that of your tuition obligation? d. What if rates fall immediately to 7%?

a) PV of tuition fees=10000/(1+8%)+10000/(1+8%)^2=$17832.65 !!! To find the duration of obligation, First we find the PV of two annual tuition fees PV of tuition fee to be paid at the end of year 1=10000/(1+8%)^1=$9259.26 PV of tuition fee to be paid at the end of year 2=10000/(1+8%)^2=$8573.39 Weight of payment 1 =w1=9259.26/(9259.26+8573.39)=0.519231 Weight of payment 2 =w2=8573.39/(9259.26+8573.39)=0.480769 Duration of obligation is given by Duration =\nW*t=0.519231 *1 + 0.480769 * 2 = 1.480769\n !!!! b) Zero coupon bond with maturity 1.480769 years!!! is needed to immunize the obligation. Present value of zero coupon bond=PV of tuition payments=$17832.65 Maturity amount of zero coupon bond=17832.65*(1+8%)^1.480769=$19985.21 !!! c) If the interest rate increases to 9% PV of tuition fees=10000/(1+9%)+10000/(1+9%)^2=$17591.11 PV of bond=19985.21/(1+9%)^1.480769=$17590.92 Change in net position=17591.11-17590.92=$0.19 (decreased)!!! d.) If the interest rate decreases to 7% PV of tuition fees=10000/(1+7%)+10000/(1+7%)^2=$18080.18 PV of bond=19985.21/(1+7%)^1.480769=$18079.99 Change in net position=18080.18-18079.99=$0.19 (decreased)!!!

You observe the following term structure: Effective Annual YTM1-year zero-coupon bond6.1%2-year zero-coupon bond6.2 3-year zero-coupon bond6.3 4-year zero-coupon bond6.4 a. If you believe that the term structure next year will be the same as today's, calculate the return on (i) the 1-year zero and (ii) the 4-year zero b. Which bond provides a greater expected 1-year return?

a. 1 year = 6.1% 4 year= 6.7% b. 4 year zero coupon bond

Currently, the term structure is as follows: 1-year zero-coupon bonds yield 7%; 2-year zero-coupon bonds yield 8%; 3-year and longer-maturity zero-coupon bonds all yield 9%. You are choosing between 1-, 2-, and 3-year maturity bonds all paying annual coupons of 8%. a. What is the price of each bond today? (Do not round intermediate calculations. Round your answers to 2 decimal places.) b. What will be the price of each bond in one year if the yield curve is flat at 9% at that time? (Do not round intermediate calculations. Round your answers to 2 decimal places.) c. What will be the rate of return on each bond?

a. 1- $1000 2- 990.83 3- 982.41 b. 1- 1009.35 2- 1000 3- 974.69 c. 1- 7% 2- 7.08 3- 9 https://www.chegg.com/homework-help/questions-and-answers/currently-term-structure-follows-1-year-zero-coupon-bonds-yield-7-2-year-bonds-yield-8-3-y-q19976191

The current yield curve for default-free zero-coupon bonds is as follows: Maturity (Years) YTM (%) 1 10 % 2 11 3 12 a. What are the implied 1-year forward rates? b. Assume that the pure expectations hypothesis of the term structure is correct. If market expectations are accurate, what will be the yield to maturity on 1-year zero-coupon bonds next year? c. Assume that the pure expectations hypothesis of the term structure is correct. If market expectations are accurate, what will be the yield to maturity on 2-year zero-coupon bonds next year? d. If you purchase a 2-year zero-coupon bond now, what is the expected total rate of return over the next year? (Hint: Compute the current and expected future prices.) Ignore taxes. e. What is the expected total rate of return over the next year on a 3-year zero-coupon bond? f. What should be the current price of a 3-year maturity bond with a 12% coupon rate paid annually? g. If you purchased the coupon bond at the price you computed in part (f), what would your total expected rate of return be over the next year (coupon plus price change)? Ignore taxes

a. 2 years = 12.01% 3 years= 14.03% b. shift upward c. shift upward d. 10% e. 10% f. $1003.68 g. 10%

The prices of zero-coupon bonds with various maturities are given in the following table. Suppose that you want to construct a 2-year maturity forward loan commencing in 3 years. The face value of each bond is $1,000. Maturity (Years) Price 1 $ 925.93 2 853.39 3 782.92 4 715.00 5 650.00 a. Suppose that you buy today one 3-year maturity zero-coupon bond with face value $1,000. How many 5-year maturity zeros would you have to sell to make your initial cash flow equal to zero (specifically, what must be the total face value of those 5-year zeros)? b. What are the cash flows on this strategy in each year? c. What is the effective 2-year interest rate on the effective 3-year-ahead forward loan? d. Confirm that the effective 2-year forward interest rate equals (1 + f4) ×(1 + f5)− 1. You therefore can interpret the 2-year loan rate as a 2-year forward rate for the last two years. Alternatively, show that the effective 2-year forward rate equals (1 + y5)^5/(1 + y3)^3-1

a. 782.92/650= 1.2045 b. 0=0 3= $1000 5= $-1204.49 c. 1204.49/1000-1= 20.45% d. 20.45%

in each of the following pairs of bonds, select the bond that has the highest duration or effective duration: a. Bond A is a 6% coupon bond, with a 20-year time to maturity selling at par value. Bond B is a 6% coupon bond, with a 20-year time to maturity selling below par value. multiple choice 1 b. Bond A is a 20-year noncallable coupon bond with a coupon rate of 6%, selling at par. Bond B is a 20-year callable bond with a coupon rate of 7%, also selling at par.

a. Duration of bond B is smaller than the duration of Bond A. Both the price of Bond B and Bond A are similar, this implies that Bond A has a higher YTM than that of bond B. Hence duration of bond B is smaller than Bond A!. b. Bond A! has higher duration than Bond B because Bond A has a lower YTM and lower coupon rate.

Suppose that a 1-year zero-coupon bond with face value $100 currently sells at $94.34, while a 2-year zero sells at $84.99. You are considering the purchase of a 2-year-maturity bond making annual coupon payments. The face value of the bond is $100, and the coupon rate is 12% per year. a. What is the yield to maturity of the 2-year zero? b. What is the yield to maturity of the 2-year coupon bond? c. What is the forward rate for the second year? d. If the expectations hypothesis is accepted, what are (1) the expected price of the coupon bond at the end of the first year and (2) the expected holding-period return on the coupon bond over the first year? e. Will the expected rate of return be higher or lower if you accept the liquidity preference hypothesis?

a. year 1: (100/94.34)-1=5.999576% year2: (100/84.99)^(1/2)-1= 8.471610% b. (12/(1+0.05999576))= 11.32 (112/(1+0.08471610^2)=95.19 11.32+95.19= $106.51 c. ((1+0.08471610)^2/(1+0.0599576)^1)-1= 11.00% d. (12+100)/(1+0.11)= 100.90 (100.90+12-106.51)/106.51= 6% e. HIGHER because 11>6

Assuming the pure expectations theory is correct, an upward-sloping yield curve implies

interest rates are expected to increase in the future.

Frank Meyers, CFA, is a fixed-income portfolio manager for a large pension fund. A member of the Investment Committee, Fred Spice, is very interested in learning about the management of fixed-income portfolios. Spice has approached Meyers with several questions. Meyers decides to illustrate fixed-income trading strategies to Spice using a fixed-rate bond and note. Both bonds have semiannual coupon periods. Unless otherwise stated, all interest rate changes are parallel. The characteristics of these securities are shown in the following table. He also considers a 9-year floating-rate bond (floater) that pays a floating rate semiannually and is currently yielding 5%. Characteristics of Fixed-Rate Bond and Fixed-Rate Note Fixed-Rate Bond Fixed-Rate Note Price 107.18 100.00 Yield to maturity 5.00% 5.00% Time to maturity (years) 18 8 Modified duration (years) 6.9848 3.5851 Spice asks Meyers about how a fixed-income manager would position his portfolio to capitalize on expectations of increasing interest rates. Which of the following would be the most appropriate strategy?

shorten his portfolio duration

Under the expectations hypothesis, if the yield curve is upward-sloping, the market must expect an increase in short-term interest rates.

true

Under the liquidity preference theory, if inflation is expected to be falling over the next few years, long-term interest rates will be higher than short-term rates.

uncertain

If the liquidity preference hypothesis is true, what shape should the term structure curve have in a period where interest rates are expected to be constant?

upward sloping