Subject: DURATION, SENSITIVITY AND PLA IN BONDS 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 but I prefered to send a general message. Please disregard this CM if 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 then, multiplied by the volatility of the yields, would give us the PLA associated with the bond positions (expected portential loss if the 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 of a zero coupon bond (a bond that has only one payment at maturity and 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 say with annual principal and interest payment) with also a 2.25 years 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 Let’s also assume that we bought at $96 (at discount), equivalent to a 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
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It goes without saying, that interest rates influence our decisions, and affect many activities in our lives. Interest rates can be expressed as a percentage of the amount borrowed or saved. People always try to be well-informed about changes in economy and finance. They say that it helps them to make better decisions about their personal finance. It is evident that interest rates affected the ...
4 25+ 2.5= 27.5 17.49 18% 4 0.72 ——- ——– ——- 96 100% 2.25 The duration of this bond is 2.25 years, even though the final maturity is 4 years, because there are some coupons that are received before the 4 years. 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 discount In the example above, the discount period is 1 year (it was done on an annual basis, so we should discount the annual yield. However, if the discount would have been done, for example, in a semi-annual basis, the discount period would have been 6 months, and we should divide by the Modified duration = macaulay duration divided by (1+yield) Modified duration = 2.25 / (1.12) = 2.01 How to calculate Position Sensitivity: PS = Volume of position * 0.01 * modified duration (unit shift = PS = Volume of position * 0.0001 * modified duration (unit shift = PLA = PS * yield volatility * square root of days in the defeasance Note that yield volatility should be expressed in terms of 1% if the shift is 1% or in terms of 1 bp, if the unit shift is 1bp.
1) Let’s assume we have the bond of the example above ($96.000 the unit shift considered is 1bp, the O/N volatility of the yield is 60 PS = 96.000 * 2.01 * 0.0001 = $19.3 (each time the yield changes 1bp, position changes $19.3) PLA = 19.3 * 120 = $2316 (if the yield moves 120 bps in the wrong the potential loss would be $2316) 1) Let’s assume we have the bond of the example above ($96.000 the unit shift considered is 1%, the O/N volatility of the yield is 60 (0.6%) and the defeasance period is 4 days PS = 96.000 * 2.01 * 0.01 = $1930 (each time the yield changes 1%, the position changes $1930) PLA = 1930 * 1.2 = $2316 (if the yield moves 1,20 % in the wrong the potential loss would be $2316) As you see, the PLA for both examples is the same. By changing the unit shift, we only change the way we report sensitivity, but the risk of the whole transaction (PLA) should be the same.
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Nokia’s website explains the goal and mission of Nokia as ‘To be technology leader in a world where everybody and everything is connected’ The website also states Nokia reinvented which explains for the fact that the company is gearing up to face the changes in the market. Change as defined in online dictionary as transfer from one to another (dictionary.com, 2014). This transfer from one to ...
