Measuring Yield Chapter 3

Computing Yield yield = interest rate that solves the following yield = interest rate that solves the following P = internal rate of return internal rate of return Years from Now Promised Annual Payments (Cash Flow to Investor) 1$ ,000

IRR

IRR

Yields simple annual interest rate simple annual interest rate effective annual yield EAY = (1 + periodic interest rate) m – 1 examples examples current yield = (annual $ coupon int.) / price current yield = (annual $ coupon int.) / price only considers coupon interest not capital gain/loss if selling at discount/premium only considers coupon interest not capital gain/loss if selling at discount/premium

Yields YTM YTM bond-equivalent yield bond-equivalent yield convention in bond market to move from semiannual yield to an annual yield by doubling the semiannual 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? Why is practice of doubling a semiannual yield followed? Wouldn’t it be more appropriate to compute EAY by compounding? Wouldn’t it be more appropriate to compute EAY by compounding? YTM considers current coupon and capital gain/loss YTM considers current coupon and capital gain/loss factors affecting reinvestment risk factors affecting reinvestment risk for a given YTM and a given non-zero 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 given YTM and a given non-zero 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 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 Yield to Call in practice, YTM and YTC calculated for callable bonds 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 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 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 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 Put rate that makes PV of CFs to first put date equal to price plus accrued interest rate that makes PV of CFs to first put date equal to price plus accrued interest example example Yield to Worst Yield to Worst calculate yield to call/put for all possible dates and YTM and then pick minimum of all of these 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 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 Yield (IRR) for a Portfolio not simply weighted average of YTMs for all bonds in portfolio not simply weighted average of YTMs for all bonds in portfolio

Yields Cash Flow Yield Cash Flow Yield MBS and ABS have CFs that include interest and principal – amortizing securities MBS and ABS have CFs that include interest and principal – amortizing securities prepayment speed must be assumed to project CFs needed to calculate yield prepayment speed must be assumed to project CFs needed to calculate yield yield calculated using assumed prepayment rate is cash flow yield ** yield calculated using assumed prepayment rate is cash flow yield ** example example limitations limitations projected CFs assumed to be reinvested at CF yield 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 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 coupon rate for floater changes periodically “margin” measures “margin” measures spread for life (simple margin) spread for life (simple margin) discount margin discount margin determine CFs assuming reference rate does not change over life determine CFs assuming reference rate does not change over life select a margin select a margin discount CFs in step 1 by current value of reference rate plus 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 compare PV of CFs in step 3 to price plus accrued interest if PV = security’s price + acc. int., discount margin is margin assumed in step 2 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 if PV does not equal, go back to step 2 and try another margin for bond selling at par, discount margin is quoted margin in coupon reset formula for bond selling at par, discount margin is quoted margin in coupon reset formula

Discount Margin

Sources of Bond Return coupon payments coupon payments capital gain/loss on sale of bond (or when called) capital gain/loss on sale of bond (or when called) reinvestment of coupon payments – interest on interest reinvestment of coupon payments – interest on interest yields yields current current YTM YTM CF Yield CF Yield

Dollar Return coupon interest + interest on interest = coupon interest + interest on interest = interest on interest = interest on interest = example example Total Dollar Return Total Dollar Return

Total Return measure of yield that makes an assumption about the reinvestment rate measure of yield that makes an assumption about the reinvestment rate If all 4 have the same credit quality, which is the most attractive? If all 4 have the same credit quality, which is the most attractive?

Total Return 1. Compute the total coupon payments plus the interest on interest based on the assumed reinvestment rate. 2. Determine the projected sale price at the end of the planned investment horizon. 3. Sum the values computed in steps 1 and To obtain the semiannual total return, use {total future $ / purchase price} 1/h Double the interest rate in step 4 (as interest is assumed to be paid semiannually.)

Yield Changes absolute yield change absolute yield change measured in basis points measured in basis points absolute value of difference between two yields absolute value of difference between two yields percentage yield change percentage yield change ln of the ratio of the change in yield ln of the ratio of the change in yield % yield change = 100 x ln(new yield / initial yield) % yield change = 100 x ln(new yield / initial yield)