Question

Suppose you purchase 5-year annual coupon bond in the primary market. The face value of the bond is $1000. The current risk-free interest rate is 2%. The bond belongs to an asset class appropriated a 3% risk premium.

a) After a year has passed, you collect your coupon payment. At that point, a new investment becomes available to you and you decide to sell your bond in the secondary market. By the time of the sale, the economic outlook has worsened and the risk-free rate has fallen to 1%. What was your one-year rate of return for the one-year period you held the bond?

b) Now put yourself in the shoes of the buyer of the bond from part (a). The buyer holds the bond for one year and then immediately after collecting the coupon payment, she decides to sell the bond as well. By this time, although the risk-free rate remains steady at 1%, the risk-premium has increased to 4%. What was her one-year rate of return for the one-year period she held the bond?

Answer 1

Answer a:

Year of Issue:

Face value = Price of bond = $1,000

Coupon rate = yield = 2% + 3% = 5%

Annual coupon =1000 * 5% = $50

After 1 year:

Risk free rate has fallen to 1%

Yield = 1% + 3% = 4%

Time to maturity = 4 years

Sale price = PV (rate, nper, pmt, fv, type) = PV (4%, 4, -50, -1000, 0) = $1,036.30

One year return = ((Sale price - Purchase price) + annual coupon) / Purchase price

= ((1036.30 - 1000) + 50) / 1000

= 8.63%

One-year rate of return for the one-year period = 8.63%

Answer b:

Purchase price = $1036.30

After 2 year of issue:

Yield = 1% + 4% = 5%

Time to maturity = 3 years

Sale price = PV (5%, 3, -50, -1000, 0)

= $1,000

One year return = ((1000 -1036.30) + 50) / 1000

= 1.37%

One-year rate of return for the one-year period = 1.37%