Question

Assuming that the expectations hypothesis is valid, compute the expected price path of the 4-year bond using the data given below as time passes. What is the rate of return of the bond in each year? (Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the "%" sign in your response.) Maturity (years) AWN Price of Bond $ 943.40 898.47 847.62 792.16 Beginning of Year Expected Price Expected Rate of Return 99

Answer 1

The forward rates can be calculated as

forward rate for year 1 = f1 = 1000/943.40 -1 = 0.06

forward rate for year 2 = f2 = 943.40/898.47 -1 = 0.05

forward rate for year 3 = f3 = 898.47/847.62 -1 = 0.06

forward rate for year 4 = f4 = 847.62/792.16 -1 = 0.07  

So, Expected Price at beginning of year 1 = 1000/((1+f1)(1+f2)(1+f3)(1+f4))

=1000/(1.06*1.05*1.06*1.07) = $792.16

Expected Rate of Return in 1st year = f1 = 6.00%

Expected Price at beginning of year 2 = 1000/((1+f2)(1+f3)(1+f4))

=1000/(1.05*1.06*1.07) = $839.69

Expected Rate of Return in 2nd year = f2 = 5.00%

Expected Price at beginning of year 3 = 1000/((1+f3)(1+f4))

=1000/(1.06*1.07) = $881.68

Expected Rate of Return in 3rd year = f3 = 6.00%

Expected Price at beginning of year 4 = 1000/(1+f4)

=1000/(1.07) = $934.58

Expected Rate of Return in 4th year = f4 = 7.00%