Question

Suppose you purchase a 30​-year, zero-coupon bond with a yield to maturity of 5.8 %. You hold the bond for five years before selling it.

a. If the​ bond's yield to maturity is 5.8 % when you sell​ it, what is the annualized rate of return of your​ investment?

b. If the​ bond's yield to maturity is 6.8 % when you sell​ it, what is the annualized rate of return of your​ investment?

c. If the​ bond's yield to maturity is 4.8 % when you sell​ it, what is the annualized 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.

Answer 1

Price of zero coupon bond = face value / (1 + yield to maturity)years to maturity

sale price of bond = purchase price * (1 + r)n

where r = annualized rate of return

n = number of years the bond is held

From this equation, r is calculated as :

r = (sale price / purchase price)1/n - 1

Let us assume the face value is $1,000.

Price of zero coupon bond = face value / (1 + yield to maturity)years to maturity

Purchase price of bond = $1,000 / (1 + 5.8%)30 = $184.26

After 5 years, the bond will have 25 years left to maturity

a]

sale price of bond = face value / (1 + yield to maturity)years to maturity

sale price of bond = $1,000 / (1 + 5.8%)25

sale price of bond = $244.26

r = (sale price / purchase price)1/n - 1

r = ($244.26 / $184.26)1/5 - 1

r = 5.80%

b]

sale price of bond = face value / (1 + yield to maturity)years to maturity

sale price of bond = $1,000 / (1 + 6.8%)25

sale price of bond = $193.07

r = (sale price / purchase price)1/n - 1

r = ($193.07 / $184.26)1/5 - 1

r = 0.94%

c]

sale price of bond = face value / (1 + yield to maturity)years to maturity

sale price of bond = $1,000 / (1 + 4.8%)25

sale price of bond = $309.72

r = (sale price / purchase price)1/n - 1

r = ($309.72 / $184.26)1/5 - 1

r = 10.94%

d]

No,  even if a bond has no chance of​ default, your investment is not risk free if you plan to sell it before it​ matures.

This is because even though default risk is zero, interest rate risk still exists. Interest rate risk is the risk that the price of the bond will change due a change in interest rates. If interest rates rise high enough, the price of the bond may decrease so much that your realized return may be negative.