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Unformatted text preview: Measuring Yield
Chapter 3 Computing Yield
yield = interest rate that solves the following CF CF P = CF + CF + + . . .+ 1 2 3 N (1 +y ) 1 (1 +y ) 2 (1 +y ) 3 (1 +y ) N internal rate of return
Years from Now 1 2 3 4 Promised Annual Payments (Cash Flow to Investor) $100 100 100 1,000 IRR
Years from Now 1 2 3 4 Years from Now Promised Annual Payments (Cash Flow to Investor) $100 100 100 1,000 Promised Annual Payments Present Value of Cash (Cash Flow to Investor) Flow at 10% 1 $100 $90.91 2 100 82.64 3 100 75.13 4 1,000 683.01 Present value = $931.69 IRR
Years from Now Promised Annual PaymentsPresent Value of Cash (Cash Flow to Investor) Flow at 12% 1 $100 $89.29 2 100 79.72 3 100 71.18 4 1,000 635.52 Present value = $875.71 Years from Now Promised Annual Payments ) Present Value of Cash (Cash Flow to Investor) Flow at 11% 1 $100 $90.09 2 100 81.16 3 100 73.12 4 1,000 658.73 Present value = $903.10 Yields simple annual interest rate effective annual yield EAY = (1 + periodic interest rate)m 1 examples current yield = (annual $ coupon int.) / price only considers coupon interest not capital gain/loss if selling at discount/premium Yields YTM bondequivalent yield convention in bond market to move from semiannual yield to an annual yield by doubling the semiannual yield
Why is practice of doubling a semiannual yield followed? Wouldn't it be more appropriate to compute EAY by compounding? factors affecting reinvestment risk YTM considers current coupon and capital gain/loss for a given YTM and a given nonzero coupon rate, the longer the maturity, the more the bond's total dollar return depends on reinvestment income to realize the YTM at time of purchase (ie, the larger the reinvestment risk) for a coupon paying bond, for a given maturity and a given YTM, the higher the coupon rate, the more dependent the bond's total dollar return will be on the reinvestment of the coupon payments in order to produce the YTM at time of purchase Yields Yield to Call in practice, YTM and YTC calculated for callable bonds to calculate, find PV of all coupons until bond is called and then use call price as final value convention is to calculate yield to first call (or yield to next call), yield to first par call, and yield to refunding Yield to Call
Annual Interest Semiannual Rate Present Value of 6 PV of $103 PV of CFs Rate (%) y (%) Payments of $3.5 6 Periods from Now 5 2.5 $19.28 $88.82 108.10 5.2 2.6 19.21 88.30 107.51 5.4 2.7 19.15 87.78 106.93 5.6 2.8 19.09 87.27 106.36 8 year 7% coupon bond with maturity value of $100 first call date is end of year 3 call price of $103 note that YTC assumes that all CFs can be reinvested at YTC until assumed call date may not be true Yields Yield to Put Yield to Worst rate that makes PV of CFs to first put date equal to price plus accrued interest example calculate yield to call/put for all possible dates and YTM and then pick minimum of all of these does not mean much since problem with all yield measures are they do not identify potential return over investment period Yields Yield (IRR) for a Portfolio Bond A B C not simply weighted average of YTMs for all bonds in portfolio
Coupon Rate (%) Maturity (years) Par Value Price YTM (%) 7 5 $10,000,000 $9,209,000 9 10.5 7 20,000,000 20,000,000 10.5 6 3 30,000,000 28,050,000 8.5 Period CF Received Bond A Bond B Bond C Portfolio 1 $350,000 $1,050,000 $900,000 $2,300,000 2 350,000 1,050,000 900,000 2,300,000 3 350,000 1,050,000 900,000 2,300,000 4 350,000 1,050,000 900,000 2,300,000 5 350,000 1,050,000 900,000 2,300,000 6 350,000 1,050,000 30,900,000 32,300,000 7 350,000 1,050,000  1,400,000 8 350,000 1,050,000  1,400,000 9 350,000 1,050,000  1,400,000 10 10,350,000 1,050,000  11,400,000 11  1,050,000  1,050,000 12  1,050,000  1,050,000 13  1,050,000  1,050,000 14  21,050,000  21,050,000 Yields Cash Flow Yield MBS and ABS have CFs that include interest and principal amortizing securities prepayment speed must be assumed to project CFs needed to calculate yield yield calculated using assumed prepayment rate is cash flow yield ** example limitations projected CFs assumed to be reinvested at CF yield MBS or ABS is assumed to be held until final payoff of all loans based on a prepayment assumption Spread/Margin Measures for Floating Rate Securities coupon rate for floater changes periodically "margin" measures spread for life (simple margin) SpreadForLife = [ 100(100  Pr ice) 100 + QuotedM arg in] * ( ) Maturity Pr ice discount margin determine CFs assuming reference rate does not change over life select a margin discount CFs in step 1 by current value of reference rate plus margin compare PV of CFs in step 3 to price plus accrued interest for bond selling at par, discount margin is quoted margin in coupon reset formula if PV = security's price + acc. int., discount margin is margin assumed in step 2 if PV does not equal, go back to step 2 and try another margin Exhibit 31. Calculation of the Discount Margin for a FloatingRate Security Floatingrate security: Maturity: six years Coupon rate: reference rate + 80 basis points Reset every six months PV of CF at Assumed Annual Margin (bp) Reference Cash Period Rate Flow 80 84 88 96 100 1 10% 5.4 5.1233 5.1224 5.1214 5.1195 5.1185 2 10 5.4 4.8609 4.859 4.8572 4.8535 4.8516 3 10 5.4 4.6118 4.6092 4.6066 4.6013 4.5987 4 10 5.4 4.3755 4.3722 4.3689 4.3623 4.359 5 10 5.4 4.1514 4.1474 4.1435 4.1356 4.1317 6 10 5.4 3.9387 3.9342 3.9297 3.9208 3.9163 7 10 5.4 3.7369 3.7319 3.727 3.7171 3.7122 8 10 5.4 3.5454 3.5401 3.5347 3.524 3.5186 9 10 5.4 3.3638 3.358 3.3523 3.3409 3.3352 10 10 5.4 3.1914 3.1854 3.1794 3.1673 3.1613 11 10 5.4 3.0279 3.0216 3.0153 3.0028 2.9965 12 10 105.4 56.0729 55.9454 55.8182 55.5647 55.4385 Present Value = 100 99.8269 99.6541 99.3098 99.1381 Discount Margin Sources of Bond Return coupon payments capital gain/loss on sale of bond (or when called) reinvestment of coupon payments interest on interest yields
current YTM CF Yield + r ) n  1 (1 C  nC r Dollar Return coupon interest + interest on interest = + r ) n  1 (1 C r interest on interest = + r ) n  1 (1 C  nC r example Total Dollar Return Total Return measure of yield that makes an assumption about the reinvestment rate
bond A B C D coupon 5 6 11 8 maturity 3 20 15 5 YTM 9 8.6 9.2 8 If all 4 have the same credit quality, which is the most attractive? Total Return
1. 2. 3. 4. 5. Compute the total coupon payments plus the interest on interest based on the assumed reinvestment rate. Determine the projected sale price at the end of the planned investment horizon. Sum the values computed in steps 1 and 2. To obtain the semiannual total return, use {total future $ / purchase price}1/h 1 Double the interest rate in step 4 (as interest is assumed to be paid semiannually.) Yield Changes absolute yield change measured in basis points absolute value of difference between two yields ln of the ratio of the change in yield % yield change = 100 x ln(new yield / initial yield) percentage yield change ...
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This note was uploaded on 09/22/2008 for the course HKIT 211 taught by Professor Wang during the Spring '08 term at Hong Kong Institute of Vocational Education.
 Spring '08
 WANG

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