The YTM on a bond is the interest rate you earn on your investment if interest r

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 of 4.9 percent for $930. The bond has 10 years to maturity. 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. The Coupon payment (PMT) = 4.9% of 1000 = 49, NPER = 10, FV =1000, PV =930

Yield to maturity (YTM) = rate(nper,pmt,pv,fv) =rate(10,49,-930,1000) = 5.84%

Rate of return do you expect to earn on your investment = 5.84%

b. Price of the bond after 2 years = PV(rate,nper,pmt,fv) where rate = 5.84 -1 = 4.84%,nper=8,pmt =49,fv =1000

Price of the bond = pv(0.0484,8,49,1000) = $1003.90

c. Total return = 1003.90 (sale price) + 49*2 (Coupons for 2 years) - 930 (purchase price) = 171.90

Hence total return = 171.90/930 = 0.1848

Hence HPY = (1+ 0.1848)^(1/2) -1 = 0.0885 = 8.85%

d. They are difference becuase the yield reduced by 1 percent in the holding period

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