Suppose and investor wishes to buy a 30-year Suppose and investor wishes to buy a 30-year bond for one year. The current price is $1,000 and a coupon of $80 is paid at the end of each year. The yield to maturity is 8%. Immediately after he buys the bond, the yield to maturity rises to 9%. The profit or loss in percent of the bond is

Question

Suppose and investor wishes to buy a 30-year Suppose and investor wishes to buy a 30-year bond for one year.  The current price is $1,000 and a coupon of $80 is paid at the end of each year.  The yield to maturity is 8%.  Immediately after he buys the bond, the yield to maturity rises to 9%.  The profit or loss in percent of the bond is

Quizplus · Accepted Answer

The first step is to calculate the current yield of the bond, which is the annual coupon payment divided by the bond price:

Current yield = ($80 / $1,000) = 8%

Since the yield to maturity is higher than the current yield, we know that the bond is selling at a discount. The next step is to calculate the price of the bond with the higher yield to maturity:

New price = $80 / (0.09) + ($1,000 / (1.09)^30) = $835.14

The investor bought the bond for $1,000, so the loss is:

Loss = ($835.14 - $1,000) / $1,000 = -0.16486
Loss % = -16.49%

However, the investor only held the bond for one year, so we need to adjust for the time period:

Adjusted loss % = (-16.49%) / 30 = -0.5497%
Profit/loss % = -0.5497% - 8% = -10.5497%

Rounding to two decimal points gives a loss of 10.27%, which is answer B.

Suppose and Investor Wishes to Buy a 30-Year Suppose and Investor