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RSM 330  Investments
Class Note 11 – Bond Portfolio
Management
August 12, 2010
Maureen Stapleton, CFA
1
RSM 330_Class 12_Summer 2010
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Plan for Today
•
Exam Review Session
– Aug 12 at
8pm in WO 35
•
Measuring Interest Rate Risk
– Duration and Convexity
•
Active Bond Portfolio Strategies
–
Barbells and Bullets
– Riding the Yield Curve
 Sector swaps

Anomaly Trading
•
Recap of the course
RSM 330_Class 12_Summer 2010
The Relationship between Bond Price & YTM is not
linear
3
RSM 330_Class 12_Summer 2010
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y
1
)
y
1
(
D
P
P
+
+
∆
⋅

=
∆
y
1
D
D
*
+
=
y
D
P
P
*
∆
⋅

=
∆
Price change of a bond is proportional to duration and not
to maturity
More precisely, if we denote D
*
= modified duration
Duration/Price Relationship:
RSM 330_Class 12_Summer 2010
5
Over time, there are three determinants of the bond price.
P = f(y, cash flow, T)
Your holding period return is impacted by a change in interest rates:
P +
P = f(y +
y)
and
∆
∆
∆
y
∆
P.
Measures of sensitivity to interest rate risk:
dP
dP
1
dy
or
dy
P
For example, suppose that dP/dy =
6000 and dP 1/dy P =
10.
−
−
Then for a
small change
y, the
∆
price change
is roughly
∆
P =
6000
−
∆
y
and
the percentage price change
is
∆
P/P =
10 y.
− ∆
RSM 330_Class 12_Summer 2010
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Duration
Macaulay Duration
:
“the average time at which you receive the cash flows from
bond”; Alternatively, it’s the time at which you receive half the PV
of cashflows
Macaulay Duration = 1 · w
1
+ 2 · w
2
+ · · · + T · w
T
where the
weights
are
and CF
t
is the cash flow at date
t
.
Note that
P
y
CF
P
CF
PV
w
t
t
t
t
1
)
1
(
)
(
+
=
=
T
t
y
CF
y
CF
y
CF
P
)
1
(
.....
)
1
(
1
2
2
1
+
+
+
+
+
+
=
RSM 330_Class 12_Summer 2010
7
8%
Bond
Time
years
Coupon
(CF)
PV of CF
(10%)
Weight
Time X
Weight
.5
40
38.095
.0395
.0198
1
40
36.281
.0376
.0376
1.5
2.0
40
1040
sum
34.553
855.611
964.540
.0358
.8871
1.000
.0537
1.7742
1.8853
Duration Calculation
2 year bond, 8% coupon, YTM =10% (semiannual
pay)
RSM 330_Class 12_Summer 2010
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0
200
400
600
800
1000
1200
1
2
3
4
5
6
7
8
Year
Cash flow
Bond Duration = 5.97 years
Example: 8year, 9% annual coupon bond
Properties of
Duration
FULCRUM = duration
What is duration of a
zerocoupon
bond?
• Holding time to maturity constant, when
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This note was uploaded on 07/16/2011 for the course COMMERCE 330 taught by Professor Stapleton during the Fall '10 term at University of Toronto Toronto.
 Fall '10
 Stapleton

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