35. Holding Period Yield. The YTM on a bond is the interest rate you earn on you
ID: 2786730 • Letter: 3
Question
35. Holding Period Yield. 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 an annual coupon bond with a coupon rate of 7 percent for $875. The bond has 10 years to maturity and a par value of $1,000. What rate of return do you expect to earn on your investment? b. 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? What is the HPY on your investment? Compare this yield to the YTM when you first bought the bond. Why are they different?Explanation / Answer
a.
Initial price of the bond = P = $875
Annual coupon rate = 7%
Time to maturity = 10 years
Par value = $1000
We can find the Yield to maturity using the YIELD function of Excel
Yield to maturity (YTM) = YIELD(settlement date, maturity date, coupon rate, price, par value, frequency)
Here, frequency = 1 as its annual frequency
YTM = YIELD("11/15/2017","11/15/2027",0.07,87.5,100,1) = 8.94%
b.
If the YTM declines by 1% in 2 years, then YTM = 7.94%
Remaining maturity = 8 years
Coupon rate = 7%
Par value = $1000
We need to find the price of the bond based on the above information
We can find the price of the bond using the PRICE function of Excel
Price of the bond = PRICE(settlement date, maturity date, coupon rate, YTM,par value, frequency)
Frequency = 1 for annual payments. We calculate price per $100 face value using the price function and then multiply it by 10 to get the price per $1000 of face value
Price of the bond after 2 years = 10 * PRICE("11/15/2017","11/15/2025",0.07, 0.0794,100, 1) = 10*94.57 = $945.7
The cash flows associated with the bond are -$875 initial investment), $70 in Year 1 and 70+945.7 = $ 1015.7) after 2 years
We need to calculate the IRR for these cash flows to get the Holding period yield
Holding period yield on the investment = IRR (series of cash flows) = IRR(array(-875,70.1015.7)) = 11.81%
The HPY is different from the YTM because YTM is the expected yield if the bond is held till maturity. Since the bond is not held it maturity and is sold off after 2 years its holding period yield will be different.
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