Transcript Com 4FJ3 - McMaster University

Business F723
Fixed Income Analysis
Week 2
Measuring yields and returns
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?
2
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
3
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
n
CF
P
t
t 1 1  YTM 
4
How to Calculate YTM
• Typical methods include
–
–
–
–
Financial calculator
Trial and error
Spreadsheet tools; goal seek or solver
Spreadsheet function IRR
5
Goal Seek
Rate per 1/2 year =
Period
CF
1
40
2
40
3
40
4
40
5
40
6
40
7
40
8
40
9
40
10
1040
Price =
YTM =
4.97%
PV
38.10618
36.30202
34.58327
32.94591
31.38606
29.90007
28.48444
27.13582
25.85106
640.3053
925.0001
9.940%
6
Solver
Rate per 1/2 year =
Period
CF
1
40
2
40
3
40
4
40
5
40
6
40
7
40
8
40
9
40
10
1040
Price =
YTM =
4.97%
PV
38.10618
36.30201
34.58327
32.94591
31.38606
29.90007
28.48443
27.13582
25.85106
640.3052
925
9.940%
7
IRR Function
Period
Price
1
2
3
4
5
6
7
8
9
10
IRR=
YTM=
CF
-$ 925.00
$ 40.00
$ 40.00
$ 40.00
$ 40.00
$ 40.00
$ 40.00
$ 40.00
$ 40.00
$ 40.00
$ 1,040.00
4.97%
9.94%
8
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
Face Price
Coupon
n
YTM 
Price  Face
2
9
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.
10
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%
Period
Price
1
2
3
4
5
6
7
8
9
10
11
IRR=
YTM=
CF
-1192.31
$ 80.00
$ 80.00
$ 80.00
$ 80.00
$ 80.00
$ 80.00
$ 80.00
$ 80.00
$ 80.00
$ 80.00
$ 1,080.00
5.61%
11.22%
11
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%
12
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
13
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
14
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
15
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
Period
Price
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
IRR=
YTM/P=
CF
-900
$ 25.00
$ 25.00
$ 25.00
$ 25.00
$ 25.00
$ 25.00
$ 25.00
$ 25.00
$ 25.00
$ 25.00
$ 25.00
$ 25.00
$ 25.00
$ 25.00
$ 25.00
$ 1,025.00
3.315%
6.631%
CFp
-900
$ 25.00
$ 25.00
$ 25.00
$ 25.00
$ 25.00
$ 1,025.00
4.435%
8.869%
16
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
17
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
18
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
Period
Price
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
IRR=
CFY=
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
CF
-795
100.00
95.00
90.25
85.74
81.45
77.38
73.51
69.83
66.34
63.02
59.87
56.88
54.04
51.33
48.77
46.33
5.069%
10.138%
19
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
Bond
CR
A
7.0%
B
10.5%
C
6.0%
maturity
par,000
Price
5 $ 10,000 $ 9,209
7 $ 20,000 $ 20,000
3 $ 30,000 $ 28,050
YTM
9.0%
10.5%
8.5%
WA
0.0145
0.0367
0.0416
9.28%
20
Portfolio Yield Example, p. 44
Period
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
IRR=
YTM=
A
-9,209
350
350
350
350
350
350
350
350
350
10,350
4.50%
9.00%
B
-20,000
1,050
1,050
1,050
1,050
1,050
1,050
1,050
1,050
1,050
1,050
1,050
1,050
1,050
21,050
5.25%
10.50%
C
-28,050
900
900
900
900
900
30,900
4.25%
8.50%
Portfolio
-57,259
2,300
2,300
2,300
2,300
2,300
32,300
1,400
1,400
1,400
11,400
1,050
1,050
1,050
21,050
4.77%
9.54%
21
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
22
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
23
Interest on Interest Example
• Given a par bond;
• $1,000 face value
• 7% coupon rate
• 15 years to maturity
FVcoupons
nC
Int. on int.
Face
FVall
% Int on Int
$ 1,806.79
$ 1,050.00
$ 756.79
$ 1,000.00
$ 2,806.79
26.96%
– Assume reinvestment
at 7%
– find the portion of future value that is interest
on interest
24
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)
25
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
26
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
27
Total Return Example
• Using previous bond FVcoupons
• $1,000 face value
• 7% coupon rate
• 15 years to maturity
– 5 year horizon
– reinvestment at 8%
– YTM; 7.5% in 5 years
$ 420.21
Price, t=10
$965.26
FVall
$ 1,385.47
rsemi-annual
YTM
3.314%
6.628%
• Find the total return
28
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
29
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
30