### DURATION SENSITIVITY AND PLA IN BONDS

Subject: DURATION, SENSITIVITY AND PLA IN BONDS
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I would like to help some of you with a general explanation on how to
calculate sensitivity and PLA in bonds. Many of you may know these
issues,
but I prefered to send a general message. Please disregard this CM if
this
is your case.
The market factor (what generates the risk) in a bond, is the yield
(the interest rate embedded in the investment). This means that the
Position Sensitivity should relate to changes in yields. This
sensitivities,
then, multiplied by the volatility of the yields, would give us the PLA
associated with the bond positions (expected portential loss if the
yield
moves agains us).
To calculate the Position Sensitivity, first of all, you should know the
"modified duration" of the bonds that you are holding.
Duration is defined as the equivalent tenor in a bond, expressed in
terms
of a zero coupon bond (a bond that has only one payment at maturity and
it is traded at discount).
This means that for example, an investor should be completely indiferent
to invest in a zero coupon bond of 2.25 years than in a 4 years bond
(let's
say with annual principal and interest payment) with also a 2.25 years
duration.
How to calculate this duration (also known as Macaulay duration):
Let's suppose this bond's cash flow:
($100 bond with 4 equal annual principal payment and 10% interest rate
on
outstandings).
Let's also assume that we bought at $96 (at discount), equivalent to a
12% yield.
Coupons Disc at 12% % on price coupon tenor (1) * (2)
Ppal+ Interest in years (1) (in years)(2)
--------------------------------------------------------------------
1 25+10 = 35 31.25 33% 1 0.33
2 25+ 7.5= 32.5 25.91 27% 2 0.54
3 25+ 5 = 30 21.35 22% 3 0.66
4 25+ 2.5= 27....

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