Question

The YTM on a bond is the interest rate you earn on your investment if interest rates don’t change. If you actually sell the bond before it matures, your realized return is known as the holding period yield (HPY).

a.	Suppose that today you buy a bond with an annual coupon rate of 10 percent for $1,050. The bond has 19 years to maturity. What rate of return do you expect to earn on your investment? Assume a par value of $1,000. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
b-1.	Two years from now, the YTM on your bond has declined by 1 percent, and you decide to sell. What price will your bond sell for? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b-2.	What is the HPY on your investment? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Part a)

Holding Period Return = (Coupons + Face Value - Cost price of the bond) / Cost price of the bond

• Coupon = 10% * $1,000 * 19 = $1,900
• Face Value = $1,000
• Cost Price of the bond = $1,050
• Holding Period Return = ($1,900 + $1,000 - $1,050) / $1,050 = 176.19%

Part b) 1)

Yield to Maturity (YTM) =(Coupon +((Face Value-Price)/Years to maturity)) / ((Face Value+Price)/2)

YTM = (100 + ((1000 - 1050)/19))/(1000+1050)/2)

YTM = (100 + (-2.6316))/(1025)

YTM = 9.50%

After 2 years, decline in YTM --> 1%

Change in price = -Price * duration (as %) * change in yield (in %)

= -1050 * 2% *-1%

= $21

Price at which the bond can sold for is = $1,050 + $21 = $1,071

Part b) 2)

Coupon Earned = 10% * $1,000 * 2 = $200

Capital Appreciation = $21

Total Income = $221

Holding Period Yield=(((Total Income / Cost Price)+1)^1/years held)-1

HPY = (((221/1050)+1)^1/2)-1

HPY = 10.02%