CalculatingTheHoldingPeriodReturnOnACouponBond

CalculatingTheHoldingPeriodReturnOnACouponBond - $80(1 ....

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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 awed 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 ....

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