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Chapter 3 Measuring YieldsYield-to-maturity is rate that equates CFs to PriceP = C/(1 + r) + C/(1 + r)2 + C/(1 + r)3 + … + (C + M)/(1 + r)nP = Σnt=1 C/(1 + r)t + M/(1 + r)nSimilar to NPV:NPV = Σnt=0 CF/(1 + r)t Where CF0 = priceAnnual Yield vs Periodic Yield:APR = (Periodic Rate)(m)APR = m[(1 + EAR)1/m – 1]EAY = [1 + (APR / m)]m – 1Yield Measures:YTMToday is January 22, 2019Bond Matures on March 22, 2025Pays 5.125% couponPriced at 102.56% of parGo to Excel =Price() and =Yield() FunctionsCurrent YieldAnnual Coupon Dollars/PriceRecalculate YTM and CY if price is discount (98.00%)Relationship between YTM, Current Yield (CY) and Coupon RateYield to CallAssume Bond is callable on:3/22/2021 at 102.003/22/2022 at 101.503/22/2023 at 101.003/22/2024 at 100.50This is the call ScheduleRecalc Yield at each maturity date at each redemption valueYield to WorstThe lowest of all the YTCs and YTM Go to YTM, YTC, YTW CalculatorCash Flow YieldSame thing applied to an amortizing security3 CFs:InterestScheduled Principal RepaymentsEstimated PrepaymentsBond Portfolio YieldThe one IRR for all the bonds in the portfolioNOT the weighted average YTMYield on a FloaterCalled Discount MarginIt is a yield spread measureIt is equal to the YTM (if it were a regular bond) - SpreadBut sine CFs are unknown, can’t calculate YTMExample:6 year Floater80 bps spread to the reference rate (LIBOR)Ref rate 10%Price = 99.3098Calc YTM as if a regular coupon bond:HINT: Exactly 6 years to maturity – no dates given – so use =RATE() function.N = 6 x 2 = 12PMT = .108/2 x 100 = 5.4PV = -99.3098FV = 100Rate = 5.48YTM = 5.48 x 2 = 10.96Yield Spread = 10.96 – 10 = 0.96Sources of a Bonds ReturnWhat do you actually earn from holding a bond?Maybe not the YTMDo you earn the dividend from holding a stock?Example:3 year, 8% $1,000 bond priced at 949.24N = 6PMT = 40PV = 949.24FV = 1000RATE = 5 YTM = 10%So what is the FV of 949.24 over 6 periods at 5% per period?949.24(1 + 0.05)^6 = 1272.08But the sum of the CFS = 6 x 40 + 1000 = 1240 < 1272.0832.08 difference is Interest on interest (I on I)FV of an annuity formula FVA = C{[(1 + r)N – 1]/r} = 40{[(1 + 0.05)6 – 1]/0.05} = 272.0Since Coupons = 6 x 40 = 240I on I = 272.08 – 240 = 32.08So only get YTM ifBond held to maturityCoups reinvested at YTMInstead calc Total Return from holding the bondAlso called Horizon ReturnAssume:Investment horizon (year’s bond held)Reinvestment rate for coupons (rate of I on I)YTM of bond at horizon (this give sale price of the bond if bond doesn’t mature) Compute total Future dollarsCoupons + I on ISale price of bondCompute total return in BEY terms (APR S-A)r = (Total Future Dollars/Price)1/h – 1 h = # number of S-A periods in horizonTotal Return = 2 x rExample:20 year 8% bond priced at $828.40YTM = 10% (check this.)Assumptions:3 year horizonReinvestment rate = 6%YTM in 3 years for 17-year bonds = 7%Compute total Future dollarsCoup + I on I = FVA = C{[(1 + r)N – 1]/r} = 40{[(1 + 0.03)6 – 1]/0.03} = $258.74Sale price in 3 years of 17 year bond with YTM = 7%N = (20 – 3) x 2 = 34; PMT = 40; Rate = 0.07/2 = 0.035; FV = 1000 PV = $1,098.50Total Future Dollars = $1,098.50 + $258.74 = $1,357.25Compute total return in BEY terms (APR S-A)r = (Total Future Dollars/Price)1/h – 1 = (1,357.25/828.40)1/6 – 1 = (1.6384) 1/6 – 1 = 0.0858Total Return = 2 x 0.0858 = 17.16% How do you earn 17.16% from a bond with an 8% coupon?YTM went from 10% to 7% while you held the bond.A common bond portfolio strategy is to try to identify bonds that will be upgradedCalled credit analysis ................
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