Question

Prices of zero-coupon bonds reveal the following pattern of forward rates: Year Forward Rate points In addition to the zero-coupon bond, investors also may purchase a 3-year bond making annual payments of $45 with par value $1,000 eBock a. What is the price of the coupon bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Print Priceſ References b. What is the yield to maturity of the coupon bond? (Do not round Intermediate calculations. Round your answer to 2 decimal places.) Yield to maturity % 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.) Realized compound yield % d. If you forecast that the yield curve in 1 year will be flat at 8.0%, what is your forecast for the expected rate of return on the coupon bond for the 1-vear holding period? (Do not round intermediate calculations. Round vour answer to 2 decimal places.)

Answer 1

If f_i denote the forward rate for year i then,

Coupon Coupon Coupon + Par value Price=- w (1+fi) '(1+fi)(1+ f2) '(1+fi)(1+ f2)(1+f;)

Part (a)

Price = 45 / (1 + 5%) + 45 / [(1+5%)(1+7%)] + 1,045 / [(1+5%)(1+7%)(1+8%)] = 944.14

Part (b)

YTM can be found using the rate function of excel. Inputs are:

Nper = 3, PMT = Coupon = 45, PV = Current price = -944.14; FV = Par value = 1,000

Hence, YTM = Rate (Nper, PMT, PV, FV) = Rate (3, 45, -944.14, 1000) = 6.61%

Part (c)

Let the intermediate payments be reinvested at the respective forward rate. Hence, FV of all the payments received from the bond = FV = 1st coupon x (1 + f₂) x (1 + f₃) + 2nd coupon x (1 + f₃) + (3rd coupon + par value) = 45 x (1 + 7%) x (1+8%) + 45 x (1 + 8%) + (45 + 1,000) =  1,146

Hence, the expected realized compound yield = (FV / PV)^1/n - 1 = (1,146 / 944.14)^1/3 - 1 = 6.66%

Part (d)

After one year, all rates are forecast to be 8% = y

Hence, price of the coupon bond after 1 year = P1 = Coupon / (1 + y) + (Coupon + par value) / (1 + y)² = 45 / (1 + 8%) + (45 + 1,000) / (1 + 8%)² = 937.59

Current price = P0 = 944.14 (calculated in part (a))

Hence, 1 year holding period return = (P1 + Coupon - P0) / P0 = (937.59 + 45 - 944.14) / 944.14 = 4.07%