Bonds and The Bond Market Essay Example For Students

Bonds and The Bond Market Essay DURATION, SENSITIVITY AND PLA IN BONDSIwould like to help some of you with a general explanation on how to calculatesensitivity and PLA in bonds. Many of you may know these issues, but I preferedto send a general message. Please disregard this CM if this is your case. Themarket factor (what generates the risk) in a bond, is the yield (the interestrate embedded in the investment). This means that the Position Sensitivityshould relate to changes in yields. This sensitivities, then, multiplied by thevolatility of the yields, would give us the PLA associated with the bondpositions (expected portential loss if the yield moves agains us). To calculatethe Position Sensitivity, first of all, you should know the modifiedduration of the bonds that you are holding. Duration is defined as theequivalent tenor in a bond, expressed in terms of a zero coupon bond (a bondthat has only one payment at maturity and it is traded at discount). This meansthat for example, an investor should be completely indiferent to invest in azero coupon bond of 2.25 years than in a 4 years bond (lets say with annualprincipal and interest payment) with also a 2.25 years duration. How tocalculate this duration (also known as Macaulay duration): Lets suppose thisbonds cash flow: ($100 bond with 4 equal annual principal payment and 10%interest rate on outstandings). Lets also assume that we bought at $96 (atdiscount), equivalent to a 12% yield. Coupons Disc at 12% % on price coupontenor (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% 30.66 4 25+ 2.5= 27. 5 17.49 18% 4 0.72 - - 96 100% 2.25 Theduration 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 themodified duration: Just by dividing the Macaulay duration by (1+the yield in onediscount period). In the example above, the discount period is 1 year (it wasdone on an annual basis, so we should discount the annual yield. However, if thediscount would have been done, for example, in a semi-annual basis, the discountperiod would have been 6 months, and we should divide by the semi-annual yield). Modified duration = macaulay duration divided by (1+yield) Modified duration =2.25 / (1.12) = 2.01 How to calculate Position Sensitivity: PS = Volume ofposition * 0. 01 * modified duration (unit shift = 1%) PS = Volume of position *0.0001 * modified duration (unit shift = 1bp) How to calculate PLA: PLA = PS *yield volatility * square root of days in the defeasance period Note that yieldvolatility should be expressed in terms of 1% if the unit shift is 1% or interms of 1 bp, if the unit shift is 1bp. General examples: 1) Lets assume wehave the bond of the example above ($96.000 position), the unit shift consideredis 1bp, the O/N volatility of the yield is 60 bps and the defeasance period is 4days PS = 96. 000 * 2.01 * 0.0001 = $19.3 (each time the yield changes 1bp, theposition changes $19. 3) PLA = 19.3 * 60 * square root of 4 PLA = 19.3 * 120 =$2316 (if the yield moves 120 bps in the wrong direction, the potential losswould be $2316) 1) Lets assume we have the bond of the example above ($96.000position), the unit shift considered is 1%, the O/N volatility of the yield is60 bps (0. .u904d7ecc221fabf3235b29b8daf485c1 , .u904d7ecc221fabf3235b29b8daf485c1 .postImageUrl , .u904d7ecc221fabf3235b29b8daf485c1 .centered-text-area { min-height: 80px; position: relative; } .u904d7ecc221fabf3235b29b8daf485c1 , .u904d7ecc221fabf3235b29b8daf485c1:hover , .u904d7ecc221fabf3235b29b8daf485c1:visited , .u904d7ecc221fabf3235b29b8daf485c1:active { border:0!important; } .u904d7ecc221fabf3235b29b8daf485c1 .clearfix:after { content: ""; display: table; clear: both; } .u904d7ecc221fabf3235b29b8daf485c1 { display: block; transition: background-color 250ms; webkit-transition: background-color 250ms; width: 100%; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #95A5A6; } .u904d7ecc221fabf3235b29b8daf485c1:active , .u904d7ecc221fabf3235b29b8daf485c1:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .u904d7ecc221fabf3235b29b8daf485c1 .centered-text-area { width: 100%; position: relative ; } .u904d7ecc221fabf3235b29b8daf485c1 .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .u904d7ecc221fabf3235b29b8daf485c1 .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .u904d7ecc221fabf3235b29b8daf485c1 .ctaButton { background-color: #7F8C8D!important; color: #2980B9; border: none; border-radius: 3px; box-shadow: none; font-size: 14px; font-weight: bold; line-height: 26px; moz-border-radius: 3px; text-align: center; text-decoration: none; text-shadow: none; width: 80px; min-height: 80px; background: url(https://artscolumbia.org/wp-content/plugins/intelly-related-posts/assets/images/simple-arrow.png)no-repeat; position: absolute; right: 0; top: 0; } .u904d7ecc221fabf3235b29b8daf485c1:hover .ctaButton { background-color: #34495E!important; } .u904d7ecc221fabf3235b29b8daf485c1 .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .u904d7ecc221fabf3235b29b8daf485c1 .u904d7ecc221fabf3235b29b8daf485c1-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .u904d7ecc221fabf3235b29b8daf485c1:after { content: ""; display: block; clear: both; } READ: Mindwalk: International Relations Essay6%) 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 *0. 6 * square root of 4 PLA = 1930 * 1.2 = $2316 (if the yield moves 1,20 % inthe wrong direction, the potential loss would be $2316) As you see, the PLA forboth examples is the same. By changing the unit shift, we only change the way wereport sensitivity, but the risk of the whole transaction (PLA) should be thesame.