Question

Consider the following three zero-coupon bonds: Bond Face Value Time to Maturity (Years) Market Price 1 $1,000 1 $940 2 $1,000 2 $820 3 $1,000 3 $768 a). Calculate the one-, two-, and three-year spot rates

b). Calculate the forward rate over the second year, and the one corresponding to the third year.

c). What price of the third bond would risk-neutral investors expect to prevail at the end of the second year?

d). Now assume that investors are risk averse with a two-year investment horizon. Further assume that for every year at maturity beyond two years, investors demand a 1.5% liquidity premium. What price of the third bond would risk-averse investors expect to prevail at the end of the second year?

Answer 1

We need to calculate the 1,2,3 year spot rates.

Bond 1 is trading at $940 with face value $1000 and time to maturiy as 1 year. ENter the following in the financial calculator

FV = 1000; n=1; PV = -940; PMT = 0; calculate 1/y = 6.38%

Now for Bond 2, enter the following

FV = 1000; n=2; PV = -820; PMT = 0; calculate 1/y = 10.43% (Thsus 2 year spot rate is 10.43%)

Now for Bond 3, enter the following

FV = 1000; n=3; PV = -768; PMT = 0; calculate 1/y = 9.2% (Thus 3 year spot rate is 9.2%)

b) Let the forward rate over the second year is r, then

1.0638*(1+r) = 1.1043^2

i.e. r = 14.63%

c) Forward rate from second to third year is r (say). then

1.1043^2*(1+r) = 1.092^3

r = 6.78%

c) At the end of second year, forward rate will be 6.78%, calculated above. At this rate, the PV of the bond at that time can be caluclated by putting the following numbers in the financial calculator

FV = 1000, n=1, 1/y = 6.78%, PMT = 0; calcualte PV = $936.5