Practice investment management pim3 ch19

CHAPTER NINETEEN

MANAGING
THE FIXED INCOME PORTFOLIO

Practical Investment Management
Robert A. Strong


Outline
 Fixed Income Security Risk
 Default Risk
 Reinvestment Rate Risk
 Interest Rate Risk

 Duration
 Duration Measures
 Applying Duration

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Outline
 Convexity





Problems with Duration
Simple Convexity
An Example
Using Convexity

 Management Strategies






Active vs. Passive Management
Classic Passive Management Strategies
The Risk of Barbells and Ladders
Indexing
Active Management

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Fixed Income Security Risk
 Default risk, or credit risk, is the possibility
that a borrower will be unable to repay
principal and interest as agreed upon in the
loan document.
 Reinvestment rate risk refers to the
possibility that the cash coupons received

will be reinvested at a rate different from
the bond’s stated rate.
 Interest rate risk refers to the chance of
loss because of adverse movements in the
general level of interest rates.
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Interest Rate Risk : Malkiel’s Theorems
 Malkiel’s theorems are a set of
relationships among bond prices, time to
maturity, and interest rates.
 Theorem One : Bond prices move inversely
with yields.
 Theorem Two : Long-term bonds have more
risk.
 Theorem Three : Higher coupon bonds
have less risk.

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Interest Rate Risk : Malkiel’s Theorems
 Theorem Four : The importance of theorem
two diminishes with time.
 Theorem Five : Capital gains from an

interest rate decline exceed the capital loss
from an equivalent interest rate increase.

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Interest Rate Risk : Malkiel’s Theorems

Insert Table 19-1 here.

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Interest Rate Risk : Malkiel’s Theorems
 Bond A : matures in 8 years, 9.5% coupon
Bond B : matures in 15 years, 11% coupon
Which price will rise more if interest rates
fall?
 Apparent contradictions can be reconciled
by computing a statistic called duration.

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Duration


For a noncallable security, duration is
the weighted average time until a
bond’s cash flows are received.

 Duration is not limited to bond analysis. It
can be determined for any cash flow stream.
 Duration is a direct measure of interest rate
risk. The higher it is, the higher is the risk.
 Thinking of duration as a measure of time
can be misleading if the life or the payments
of the bond are uncertain.
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Duration Measures
 Macaulay duration is the time-value-of-moneyweighted, average number of years necessary
to recover the initial cost of the security.
N



D

Ct

t

t 11  R 

t

P

where D = duration
      Ct = cast flow at time t
      R = yield to maturity (per period)
      P = current price of bond
      N = number of periods until maturity
      t = period in which cash flow is received

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Duration Measures
 Chua’s closed-form duration is less
cumbersome because it has no summation
requirement.
 1  R  N 1  1  R   RN 
FN


Ct 


N
N
2

1  R 
R 1  R 


D
P
where F = face value (par value) of the bond
and all other variables are as previously defined.

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Duration Measures
 Modified duration measures the percentage
change in bond value associated with a
one-point change in interest rates.
dP 1
 1  C1
2C 2
NC N  1
 

 



1
2
N 
dR P 1  R   1  R  1  R 
1  R   P

Dmodified

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DMacaulay

1+ R
2





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Duration Measures
 Effective duration is a measure of price
sensitivity calculated from actual bond
prices associated with different interest
rates. It is a close approximation of
modified duration for small yield changes.
P  P

Deffect ive
P0 R  R 



where P- = price of bond associated with a decline of x basis points
        P+ = price of bond associated with a rise of x basis points
        R- = initial yield minus x basis points
        R+ = initial yield plus x basis points
        P0 = initial price of the bond
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Duration Measures
 Dollar duration determines the dollar amount
associated with a percentage price change.
Ddollar = - modified x bond price as a
duration
percentage of par
Pnew = Pold + (Ddollar x change in yield)

 The price value of a basis point is the dollar
price change in a bond associated with a
single basis point change in the bond’s yield.

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Applying Duration
 The yield curve experiences a
parallel shift when interest rates
at each maturity change by the
same amount.
 Duration is especially useful in determining
the relative riskiness of two or more bonds
when visual inspection of their
characteristics makes it unclear which is
more vulnerable to changing interest rates.

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Applying Duration

Insert Table 19-2 here.

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price

Problems with Duration



The bond price - bond yield
relationship is not linear.

yield to maturity

 Graphically, duration is the tangent to the
current point on the price-yield curve. Its
absolute value declines as yield to maturity
rises.
 Duration is a first derivative statistic.
Hence, when the change is large, estimates
made using the derivative alone will
contain errors.
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Problems with Duration

Insert Figure 19-1 here.

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Problems with Duration

Insert Figure 19-2 here.

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Problems with Duration

Insert Figure 19-3 here.

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Convexity
 Convexity measures the difference between
the actual price and that predicted by
duration, i.e. the inaccuracy of duration.
 The more convex the bond price-YTM
curve, the greater is the convexity.

1 N t  t  1 C t N  N  1  F
Convexity  

t 2
N 2
P t 1 1  R 

1  R 

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Convexity

Insert Figure 19-4 here.

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Convexity : An Example
 Price forecasting accuracy is enhanced by
incorporating the effects of convexity.
 Suppose a bond has a 15-year life, an 11%
coupon, and a price of 93%. Macaulay
duration = 7.42, yield-to-maturity = 12.00%,
modified duration = 7.00, convexity = 97.71.
If YTM rises to 12.50%, new price= 89.95%
Actual price change = - 3.28%
Price change predicted by duration = - 3.50%
Price change predicted by duration
and convexity = - 3.38%
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bond price

Using Convexity

yield to maturity

 No matter what happens to interest rates,
the bond with the greater convexity fares
better. It dominates the competing
investment.
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Using Convexity

Insert Figure 19-6 here.

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