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The yield to maturity on a bond is the interest rate you earn on your investment if interest rates do not change. If you actually sell the bond before it matures, your realized return is known as the holding period yield. Suppose that today you buy a coupon bond with 9 percent annual interest for $1,000. The bond has 12 years to maturity. Three years from now, the yield to maturity has declined to 7 percent and you decide to sell. What is your holding period yield?

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Answer:

The answer is 12.83%.

Explanation:

We have the below calculations:

- Coupon payment = 1,000 x 9% = $90;

- Purchasing price = $1,000;

- Price sold after 3 years is equal to the present value of 9  annual coupon payments plus face value repayment after 9 years, discounted at YTM at the time of sell at 7%;

=> Price after 3 year = (90/0.07) x ( 1- 1.07^-9) + 1,000/1.07^9 = $1,130.3;

The holding period yield (HPY) is the discount rate that equalizes cash flow from 3 years of holding the bond to its original purchased price:

1,000 = (90/HPY) x [1 - (1+HPY)^-3] + 1,130.3/ (1+HPY)^3 <=> HPY = 12.83%.

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