Question

Suppose the current annualized spot rates are as follows: 6 months 2% 12 months 4% 18 months 6% Assume semi-annual compounding and semi-annual coupon payment. An investor has an investment horizon of six months. She can invest her money in three ways. First, buy a 6-month zero-coupon bond with a par of $1000 and hold it until maturity. Second, buy a 12-month zero-coupon bond with a par of $1000 and sell it 6 months later. Third, buy a 18- month zero-coupon bond with a par of $1000 and sell it 6 months later.

(a) The investor expects that the spot rates will stay the same 6 months from now. Which investment strategy would the investor choose if she prefers a high expected holding period return? (10 points)

(b) Suppose 6 months later, the annualized spot rates are as follows: 6 months 8% 12 months 10% 18 months 12% Calculate the realized holding period returns for the three investment strategies. Which strategy has the highest realized holding period return? Is it the preferred strategy in (a) and why? (20 points)

Answer 1

(a) Since the period is 6 months for all the three options, it is preferrable to chose any option as the return is same for all the three options as described below:

Option 1: buy a 6-month zero-coupon bond with a par of $1000 and hold it until maturity.

Return after 6 months= 1000 + 1000 x 2% = 1000 + 20 = 1020

Option 2: buy a 12-month zero-coupon bond with a par of $1000 and sell it 6 months later

Return after 6 months= 1000 + (1000 x 4%/2)^2 = 1000 + 20 = 1020

Option 3: buy a 18- month zero-coupon bond with a par of $1000 and sell it 6 months later

Return after 6 months= 1000 + (1000 x 4%/3)^3 = 1000 + 20 = 1020

Since compounding is semi-annual, the return is same in all options. Hence any option is preferrable.

(b) Since maturity period is only 6 months, it is not an option even if rates increase after 6 months. The period of holding is only for 6 months and not beyong.