Com 4FJ3

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Com 4FJ3

• Fixed Income Analysis
• Week 2
• Measuring yields and returns

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Current Yield

• The simplest yield measure
• Divide annual coupon payment by price
• Ignores capital gain/loss
• Time value of money also ignored
• i.e. compounding is not considered
• Why use it?

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Yield to Maturity

• Similar to IRR for capital budgeting
• The discount rate that sets the present value of
  future cash flows equal to the price
• Cannot be used to calculate future value of an
  investment due to reinvestment risk
• Usually stated on a bond equivalent basis to
  allow comparison to coupon rates

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Calculating YTM

• Easy for pure discount bonds
• face P x (1 YTM/2)t where t is in 1/2 years
• YTM 2 x (face/Price)(1/t)-1
• For Coupon paying bonds the calculation is more
  complex

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How to Calculate YTM

• Typical methods include
• Financial calculator
• Trial and error
• Spreadsheet tools goal seek or solver
• Spreadsheet function IRR

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Goal Seek
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Solver
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IRR Function
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Approximate YTM

• YTM approximation formula
• Average cash flow per perioddivided by average
  value of investment
• Gives a reasonable starting point for trial and
  error

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Yield to Call

• Sometimes a YTM may not make any sense because
  the recent trades in that bond have been priced
  to reflect a probable call.
• In those cases, it helps to solve for what the
  discount rate is that sets the price equal to the
  present value of the cash flows assuming that the
  bond will be called.
• We call this the yield to call.

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Yield to Call Example

• Consider the following bond
• 1,000 face value
• 16 coupon rate
• 5.5 years to maturity
• 1,192.31
• callable 5 years before maturity at 16 premium
• YTM 11.22

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Yield to Call Example

• Consider the following bond
• 1,000 face value
• 16 coupon rate
• 5.5 years to maturity
• 1,192.31
• callable 5 years before maturity at 16 premium
• 1,000 160 80 1,192.31(1 YTC/2)
• YTC 8

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More Yield to Call

• Most callable issues have a Call Schedule which
  lays out multiple call prices depending on when
  the issue is called
• p. 146 shows Anheuser-Bucsh call schedule for a
  30 year bond 10 premium if called in the first
  year, decreasing by 0.5 per year, to par in 2008
  or later
• Bond was non-refundable

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Other Yields to Call

• To deal with call schedules, investors can
  calculate
• Yield to first call or next call
• Yield to first par call
• Yield to refunding
• Often all possible call dates are considered for
  yield to call analysis

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Yield to Put

• Only of significant value for a discount bond
  since the company cannot force the buyer to
  exercise the put provision
• Similar to yield to call, except using the put
  schedule usually par value or below as opposed
  to a premium for calls

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Yield to Put Example

• Consider the following bond
• 1,000 face value
• 8 years to maturity
• 5 coupon rate
• Putable at par within5 years to maturity
• Current price 900
• Find YTM and YTP

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Yield to Worst

• Calculate all possible Yield to ________
• The lowest yield is called the yield to worst
• Using optional yields can give a misleading
  picture a premium bond that has just paid a
  coupon and is putable now for 95 of par you have
  a YTP of -5, though nobody is likely to use the
  put option today

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Cash Flow Yield

• Similar to YTM except for amortizing securities,
  e.g. mortgage or asset backed
• Instead of having an annuity and face value to
  find the PV, you have a stream of cash flows that
  may change over time
• Mortgage borrowers not only have an amortization
  schedule, but can prepay principal, causing
  prepayment risk

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Cash Flow Yield Example

• An asset backed security has forecast cash flows
  of 100 in six months, decreasing by 5 per
  period
• The current price is 795
• Find the cash flow yield

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Yield on Portfolio

• Given a portfolio of bonds, each with a different
  yield to maturity, how do you find the YTM of the
  portfolio
• Averages and weighted averages dont work
• Method requires summing all cash flows and then
  finding the IRR of the portfolio

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Portfolio Yield Example, p. 44
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Floating Rate Securities

• Yield spread analysis can be used.
• Calculate cash flows assuming that the reference
  rate does not change
• Find price based on required spread over the
  reference rate
• Ignores that the reference rate changes over time
  and may have cap or floor provisions

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Sources of Bond Returns

• Bond returns have 3 components
• Coupon payments
• Capital gain/loss on sale or maturity
• Reinvestment income or interest on interest
• Final component can be very important if
  investing for a significant time period

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Interest on Interest Example

• Given a par bond
• 1,000 face value
• 7 coupon rate
• 15 years to maturity
• Assume reinvestment at 7
• find the portion of future value that is interest
  on interest

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YTM and Reinvestment Risk

• From the previous example almost 27 of future
  value was dependent on reinvestment of coupon
  payments
• Reinvestment risk increases with maturity
• Reinvestment risk increases with coupon rate, no
  reinvestment risk in coupon rate is set to zero
  (pure discount bond)

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Cash Flow Yield and RR

• Reinvestment risk is greater for amortizing
  securities than for bonds
• Reinvestment is required for both interest and
  principal
• Prepayments also increase as interest rates
  decrease (refinancing) further increasing the
  reinvestment risk of amortizing securities

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Finding Total Return

• By forecasting reinvestment rates and YTM at the
  time of sale, we can calculate a total expected
  return
• Find future value of reinvested coupons and sale
  value of bond
• Return is FV/Price(1/t)-1

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Total Return Example

• Using previous bond
• 1,000 face value
• 7 coupon rate
• 15 years to maturity
• 5 year horizon
• reinvestment at 8
• YTM 7.5 in 5 years
• Find the total return

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Total Return Notes

• The total return analysis can be done with rates
  that change over time
• Accuracy of total return analysis is based on
  accuracy of forecasts used
• Total return is quite sensitive to planning
  horizon, so it is also known as horizon return

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Yields Used

• Current yield
• ignores capital gain/loss
• YTM, YTC, YTP, yield to worst, etc.
• includes capital gain/loss
• assumes reinvestment at calculated yield
• Total return or horizon return
• includes capital gain/loss and reinvestment