1. Fixed Income Analysis Week 2 Measuring yields and returns
Business F723
Fixed Income Analysis
Week 2
Measuring yields and returns

2. Current Yield The simplest yield measure Ignores capital gain/loss
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?

3. 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

4. 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

5. How to Calculate YTM Typical methods include Financial calculator
Trial and error
Spreadsheet tools; goal seek or solver
Spreadsheet function IRR

6. Goal Seek

7. Solver

8. IRR Function

9. Approximate YTM YTM approximation formula
Average cash flow per period divided by average value of investment
Gives a reasonable starting point for trial and error

10. 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.

11. Yield to Call Example Consider the following bond; YTM = 11.22%
$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%

12. 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, = $1,192.31(1 + YTC/2)
YTC = 8%

13. 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

14. 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

15. 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

16. Yield to Put Example Consider the following bond $1,000 face value
8 years to maturity
5% coupon rate
Putable at par within 5 years to maturity
Current price $900
Find YTM and YTP

17. 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

18. 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

19. 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

20. 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 don’t work
Method requires summing all cash flows and then finding the IRR of the portfolio

21. Portfolio Yield Example, p. 44

22. 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

23. 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

24. 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

25. 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)

26. 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

27. 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

28. Total Return Example Using previous bond Find the total return
$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

29. 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

30. Yields Used Current yield YTM, YTC, YTP, yield to worst, etc.
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