DURATION SENSITIVITY AND PLA IN BONDS
Subject: DURATION, SENSITIVITY AND PLA IN BONDSI would like to help some of you with a general explanation on how tocalculate sensitivity and PLA in bonds. Many of you may know thesebut I prefered to send a general message. Please disregard this CM ifThe market factor (what generates the risk) in a bond, is the yield(the interest rate embedded in the investment). This means that thePosition Sensitivity should relate to changes in yields. Thisthen, multiplied by the volatility of the yields, would give us the PLAassociated with the bond positions (expected portential loss if theTo 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 inof a zero coupon bond (a bond that has only one payment at maturity andThis means that for example, an investor should be completely indiferentto invest in a zero coupon bond of 2.25 years than in a 4 years bondsay with annual principal and interest payment) with also a 2.25 years
6 * square root of 4PLA = 1930 * 1. o 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 rateonoutstandings). As you see, duration is related with the current level of yiels How to calculate the modified duration: Just by dividing the Macaulay duration by (1+the yield in one discountperiod). 49 18% 4 0. 25 years, even though the final maturityis 4 years, because there are some coupons that are received before the4 years. Modified duration = macaulay duration divided by (1+yield)Modified duration = 2. However, if thediscount would have been done, for example, in a semi-annual basis, thediscount period would have been 6 months, and we should divide by thesemi-annual yield). 3 (each time the yield changes 1bp,the position changes $19. 0001 * modified duration (unit shift =1bp) How to calculate PLA: PLA = PS * yield volatility * square root of days in the defeasanceperiod Note that yield volatility should be expressed in terms of 1% if theunitshift is 1% or in terms of 1 bp, if the unit shift is 1bp. Let's also assume that we bought at $96 (at discount), equivalent to a12% yield. 01 = $1930 (each time the yield changes 1%, the position changes $1930) PLA = 1930 * 0.
Common topics in this essay:
PLA PLA,
Coupons Disc,
Position Sensitivity,
Sensitivity PS,
PLA BONDS,
unit shift,
modified duration,
pla =,
ps =,
* square root,
* square,
yield moves,
let's assume,
macaulay duration,
position sensitivity,
discount period,
4 pla =,
root 4 pla,
unit shift =,
modified duration unit,
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