Measuring Yield
Zvi Wiener
Based on Chapter 3 in Fabozzi
Bond Markets, Analysis and Strategies
Fall-02
http://pluto.mscc.huji.ac.il/~mswiener/zvi.html
EMBAF
Yield
Yield = IRR = Internal Rate of Return
T
Ct
Price  
t
(
1

y
)
t 1
T
Ct
PV  
t
(
1

r
)
t 1
t
Zvi Wiener
Fabozzi Ch 3
slide 2
FRM-98, Question 12
A fixed rate bond, currently priced at 102.9,
has one year remaining to maturity and is
paying an 8% coupon. Assuming that the
coupon is paid semiannually, what is the yield
of the bond?
A. 8%
B. 7%
C. 6%
D. 5%
Zvi Wiener
Fabozzi Ch 3
slide 3
FRM-98, Question 12
$4
$104
$102.9 

s
2
s
y


y
1
1  
2
2 

ys = 5%
Zvi Wiener
Fabozzi Ch 3
slide 4
Annualizing Yield
Effective annual yield = (1+periodic rate)m-1
examples
Effective annual yield = 1.042-1=8.16%
Effective annual yield = 1.024-1=8.24%
annualcouponrate
current yield 
price
Zvi Wiener
Fabozzi Ch 3
slide 5
Bond selling at
Relationship
Par
Coupon rate=current yield=YTM
Discount
Coupon rate<current yield<YTM
Premium
Coupon rate>current yield>YTM
Yield to call uses the first call as cashflow.
Yield of a portfolio is calculated with the total
cashflow.
Zvi Wiener
Fabozzi Ch 3
slide 6
YTM and Reinvestment Risk
YTM assumes that all coupon (and
amortizing) payments will be invested at the
same yield.
Zvi Wiener
Fabozzi Ch 3
slide 7
YTM and Reinvestment Risk
An investor has a 5 years horizon
Bond
Coupon Maturity YTM
A
5%
3
9.0%
B
6%
20
8.6%
C
11%
15
9.2%
D
8%
5
8.0%
What is the best choice?
Zvi Wiener
Fabozzi Ch 3
slide 8
Yield to Call
Yield to Put
Yield to Worst
Spread for a floater
Total return for a bond
Zvi Wiener
Fabozzi Ch 3
slide 9
IRR of a portfolio
Aggregation of all cashflows and using the
same formula.
Zvi Wiener
Fabozzi Ch 3
slide 10
Problems with yield
Many equivalent ways to measure?
Assumes reinvestment.
Does not reflect risk.
What if investment is very leveraged?
Options, Forwards, Swaps
Zvi Wiener
Fabozzi Ch 3
slide 11
Example
Cost: 101
Promised cashflow:
After 1 year
6
After 2 years
7
After 3 years
8
After 4 years
9
After 5 years
110
Zvi Wiener
Fabozzi Ch 3
slide 12
Yield calculation
6
7
8
9
110
101




2
3
4
1  y (1  y ) (1  y) (1  y) (1  y )5
y = 7.6%
Zvi Wiener
Fabozzi Ch 3
slide 13
Example 2
Cost: 101
Promised cashflow:
After 1 year
6
After 2 years
After 3 years
After 4 years
After 5 years
Zvi Wiener
7, callable at 100
8
9
110
Fabozzi Ch 3
slide 14
Yield to Call calculation
6
107
101

1  y (1  y ) 2
y = 5.94%
Zvi Wiener
Fabozzi Ch 3
slide 15
How to treat Floaters
Floater is similar to a constantly renewed loan
with fixed spread (!).
Thus the yield of a floater is equal to the yield
on the basis plus the spread.
Note that some of the Israeli government bonds
have funny linkage to other bonds.
Zvi Wiener
Fabozzi Ch 3
slide 16
Home Assignment
Chapter 3
Questions 1, 2, 5, 7, 10
Zvi Wiener
Fabozzi Ch 3
slide 17
Reverse (Inverse) Floater
USD 5 year interest rates are 5%, however short
term interest rates are Libor =2%.
Libor = London Interbank offered rate
on Bloomberg see FWCV + currency
One can construct so-called reverse floater:
Zvi Wiener
Fabozzi Ch 3
slide 18
Reverse Floater
Years
bond
loan
bond
Reverse Fl.
0
-100
+100
-100
-100
1
5
-L0
5
8
2
5
-L1
5
10-L1
3
5
-L2
5
10-L2
4
5
-L3
5
10-L3
5
105
-100- L4
105
110- L4
Zvi Wiener
Fabozzi Ch 3
slide 19