CalculatingTheHoldingPeriodReturnOnACouponBond

# CalculatingTheHoldingPeriodReturnOnACouponBond - \$80(1 06 2...

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Calculating the Holding Period Return on a Coupon Bond 1 For zero-coupon bonds, the holding period return (HPR) equals the yield to maturity (YTM) if the bond is held to maturity. Is the same true for coupon bonds? 1. Assume: T = 4, F = \$1000, C = \$80, and YTM = 8%. Therefore the price of the bond P = \$1000 (because C/F = YTM, the bond sells at par. The value in 4 years, V 4 , depends on the reinvestment rate for the couponds. Let’s say we reinvest the coupons at the YTM. Then: 1 2 3 4 \$80 -→ -→ -→ \$80(1 . 08) 3 = \$100 . 78 \$80 -→ -→ \$80(1 . 08) 2 = \$93 . 31 \$80 -→ \$80(1 . 08) = \$86 . 40 \$1080 \$1080 = \$1080 Total = \$1360 . 49 Therefore HPR = ± V 4 V 0 1 4 - 1 = ± \$1360 . 49 \$1000 1 4 - 1 = 0 . 08 = YTM When the coupons are reinvested at the YTM, then HPR = YTM. 2. What happens when the coupons are not reinvested at the YTM? Suppose instead that the coupons are reinvested at 6%. Then 1 2 3 4 \$80 -→ -→ -→ \$80(1 . 06) 3 = \$95 . 28 \$80 -→ -→

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Unformatted text preview: \$80(1 . 06) 2 = \$89 . 89 \$80-→ \$80(1 . 06) = \$84 . 80 \$1080 \$1080 = \$1080 Total = \$1350 1 Notes for Finance 100 (sections 301 and 302) prepared by Jessica A. Wachter. HPR = ± \$1350 \$1000 ¶ 1 4-1 = 0 . 078 < YTM Because the coupons are reinvested at a rate lower than the YTM, we achieve a lower return. 3. Suppose instead that we reinvest the coupons at a rate greater than the YTM. I leave it to you to show that HPR > YTM when the coupons are reinvested at a higher rate. What can we conclude? While YTM is a useful yardstick, it is a ﬂawed measure of returns for coupon bonds. HPR = YTM only if we can and do reinvest the coupons at the YTM. Question: Suppose we sold the coupon bond before maturity? How would we calculate the holding period return in this case?...
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CalculatingTheHoldingPeriodReturnOnACouponBond - \$80(1 06 2...

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