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Measuring Yield. Chapter 3. Computing Yield. yield = interest rate that solves the following P = internal rate of return. IRR. IRR. Yields. simple annual interest rate effective annual yield EAY = (1 + periodic interest rate) m – 1 examples

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computing yield
Computing Yield
  • yield = interest rate that solves the following

P =

  • internal rate of return
  • 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
  • YTM
    • bond-equivalent 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?
    • YTM considers current coupon and capital gain/loss
  • 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 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
  • 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
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
  • Yield to Put
    • rate that makes PV of CFs to first put date equal to price plus accrued interest
    • example
  • Yield to Worst
    • 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
  • Yield (IRR) for a Portfolio
    • not simply weighted average of YTMs for all bonds in portfolio
  • 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
Spread/Margin Measures for Floating Rate Securities
  • coupon rate for floater changes periodically
  • “margin” measures
    • spread for life (simple margin)
    • 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
        • 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
      • for bond selling at par, discount margin is quoted margin in coupon reset formula
sources of bond return
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
dollar return
Dollar Return
  • coupon interest + interest on interest =
  • interest on interest =
  • example
  • Total Dollar Return
total return
Total Return
  • measure of yield that makes an assumption about the reinvestment rate
  • If all 4 have the same credit quality, which is the most attractive?
total return1
Total Return
  • 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
Yield Changes
  • absolute yield change
    • measured in basis points
    • absolute value of difference between two yields
  • percentage yield change
    • ln of the ratio of the change in yield
    • % yield change = 100 x ln(new yield / initial yield)