The three bond portfolios display the following characteristics: Maturities A B
ID: 2639590 • Letter: T
Question
The three bond portfolios display the following characteristics:
Maturities A B C
Under 1 year 5% 30% 7%
Over 1 under 3 years 0 30 9
Over 3 and under 5 years 0 30 9
Over 5 and under 10 years 0 10 15
Over 10 and under 15 years 30 0 15
Over 15 and under 20 years 30 0 15
Over 20 and under 25 years 30 0 15
Over 25 years 5 0 15
Total 100% 100% 100%
What outlook for changes in the level of interest rates is indicated by each of the above portfolios?
Explanation / Answer
We consider three hypothetical default risk-free bonds with the following features. The face value of bonds is
$100. We structure a cash-and neutral butterfly by selling the body and buying the wings. We compute the
level, slope and curvature $durations of the butterfly from equations (6).
Maturity Coupon Quantity Price Level D0
Slope D1 Curvature D2
Bond 1 2 years 5% 472 98.627 -192.51 -141.08 -41.28
Bond 2 7 years 5% -1,000 90.786 -545.42 -224.78 -156.73
Bond 3 15 years 5% 556 79.606 -812.61 -207.2 -172.03
Butterfly 0$ 2,744 42,987 41,041
The interpretation of these results is straightforward. For example, based on the butterfly slope $duration
D1
, one expects a 0.1% increase of the 1
b parameter to increase the value of the butterfly by 42.987$
(42,987
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