Question

must be completed by hand

You own a $1,000-par zero-coupon bond that has 5 years of remaining maturity. You plan on selling the bond in one year and believe that the required yield next year will have the following probability distribution:

Bond Price Required Yield Probability 0.3 0.7 7% 10%

Note that the required yield can be interpreted as the discount rate.

a. What is your expected required yield when you sell the bond?

b. Calculate the variance of the required yield.

c. Calculate the bond’s price in each situation and complete the right column. (Hint: one year later, the bond has 4 years of remaining maturity.)

d. What is your expected price when you sell the bond? (This exercise shows an example that the expected price may not be equal to the price of bond with the expected required yield.)

Answer 1

a. Expected required yield = 0.3*7% + 0.7*10% = 9.10%

b. The variance on the required yield is calculated as shown below:

Probability P	Return R	R - E R	(R - E R)^2	(R - E R)^2*P
0.3	7.00%	-0.021	0.000441	0.0001323
0.7	10.00%	0.009	8.1E-05	5.67E-05
Expected Return (E R)	9.10%
Variance				0.000189

Variance = 0.000189

c. The price of the bond in each situation :

At 7%, Price of the bond = FV/(1+r)^n = 1000/(1+0.07)^4 = $762.90

At 10%, Price of the bond = 1000/(1+0.10)^4 = $683.01

Probability	Required Yield	Bond Price
0.3	7.00%	$     762.90
0.7	10.00%	$     683.01

d. Expected price is calculating the expected yield in part (a)

Expected price = 1000/(1+0.091)^4 = $705.83