Question

Suppose you purchase a 30 -year zero-coupon bond with a yield to maturity of 6.3%. You hold the bond for five years before selling it.

a. If the bond's yield to maturity is 6.3% when you sell it, what is the rate of return of your investment?
b. If the bond's yield to maturity is 7.3% when you sell it, what is the rate of return of your investment?
c. If the bond's yield to maturity is 5.3% when you sell it, what is the rate of return of your investment?
d. Even if a bond has no chance of default, is your investment risk free if you plan to sell it before it matures? Explain. a. If the bond's yield to maturity is 6.3% when you sell it, what is the rate of return of your investment? The rate of return of your investment is %. (Round to two decimal places.)

Answer 1

The rate of return for a zero-coupon bond depends on the purchase and sale prices, which fluctuate based on the yield to maturity (YTM) at the time of sale. If YTM remains at 6.3%, the rate of return is also 6.3%. Changes in YTM can lead to a higher or lower rate of return, and the investment is not risk-free due to interest rate risk.

Step-by-step explanation:

Calculating the rate of return for a zero-coupon bond requires knowledge of the purchase price, the sale price, and the holding period. Since we have the yield to maturity (YTM) and the holding period but not the actual prices, we use the following formula for zero-coupon bonds to find the purchase and sale prices:

Price = Face value / (1 + YTM)n

Where the face value is assumed to be $1,000 (a standard face value for bonds), YTM is the yield to maturity, and n is the number of periods until maturity. Assuming the bond has 25 years to maturity when sold:

1. For an unchanged YTM of 6.3%, the purchase price is calculated when n = 30 and the sale price when n = 25. Since YTM is unchanged, the rate of return is 6.3%.
2. If YTM rises to 7.3% after 5 years, the sale price is lower, reflecting the higher yield demanded by the market, which results in a rate of return that is less than 6.3%.
3. Conversely, if YTM decreases to 5.3%, the sale price is higher, leading to a rate of return greater than 6.3%.

The investment is not risk-free even if there's no default risk, due to interest rate risk; the value of the bond fluctuates with changes in market interest rates, affecting the sale price and thus the return if sold before maturity.