Question

a. Assuming that the expectations hypothesis is valid, compute the price of the four-year bond shown below at the end of () the first year; (i) the second year; (ii) the third year; (iv) the fourth year. (Do not round intermediate calculations. Round your answers to 2 decimal places.) Beginning of Year Expected Price Price of Bond $ 955.90 1 916.47 2 $ 834.12 3 $ 766.39 4 b. What is the rate of return of the bond in years 1, 2, 3, and 4? Conclude that the expected return equals the forward rate for each year. (Do not round intermediate calculations. Round your answers to 2 decimal places.) Expected Rate of Return Beginning of Year 1 % 2 % 3 Next> 2 of 9 <Prev AM 24

Answer 1

a. Computation of Expected Price

Year	Bond Price	Forward Rate	Expected Price
1	955.90	4.61%	766.39
2	916.47	4.30%	801.76
3	834.12	9.87%	836.24
4	766.39	8.84%	918.77

We need to calculate Forward rate in order to calculate expected price of Bond

Forward Rate for 1st Year = ( 1000 / 955.90 ) -1 = 4.61 %

Forward Rate for 2nd Year = ( 955.90 / 916.47 ) -1 = 4.30 %

  Forward Rate for 3rd Year = ( 916.47 / 834.12 ) - 1 = 9.87 %

  Forward Rate for 4th Year = ( 834.12 / 766.39 ) -1 = 8.84 %

Calculation of Expected Price

Expected Price of 4th year = 1000 / ( 1 + 0.0884 ) = $918.77

  Expected Price of 3rd year = 918.77 / ( 1 + 0.0987 ) = $836.24

Expected Price of 2nd year = 836.24 / ( 1 + 0.0430 ) = $801.76

  Expected Price of 1st year = 801.76 / ( 1 + 0.0461 ) = $766.39

b. Calculation of Expected Rate of Return

Year	Amount	Calculation	Rate of Return
1	955.90	[(1000 - 955.90 ) /955.90 ]*100	4.61
2	916.47	[(955.90 - 916.47 ) /916.47 ]*100	4.30
3	834.12	[(916.47 - 834.12 ) /834.12 ]*100	9.87
4	766.39	[(834.12 - 766.39) /766.39 ]*100	8.84