Essay, Research Paper: Bonds


Free Economics research papers were donated by our members/visitors and are presented free of charge for informational use only. The essay or term paper you are seeing on this page was not produced by our company and should not be considered a sample of our research/writing service. We are neither affiliated with the author of this essay nor responsible for its content. If you need high quality, fresh and competent research / writing done on the subject of Economics, use the professional writing service offered by our company.

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= 27.5 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 period). 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 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 of
position * 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 yield
volatility should be expressed in terms of 1% if the unit shift is 1% or in
terms of 1 bp, if the unit shift is 1bp. General examples: 1) Let's assume we
have the bond of the example above ($96.000 position), the unit shift considered
is 1bp, the O/N volatility of the yield is 60 bps and the defeasance period is 4
days PS = 96.000 * 2.01 * 0.0001 = $19.3 (each time the yield changes 1bp, the
position 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 loss
would be $2316) 1) Let's assume we have the bond of the example above ($96.000
position), the unit shift considered is 1%, the O/N volatility of the yield is
60 bps (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 *
0.6 * square root of 4 PLA = 1930 * 1.2 = $2316 (if the yield moves 1,20 % in
the wrong direction, 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

Good or bad? How would you rate this essay?
Help other users to find the good and worthy free term papers and trash the bad ones.
Like this term paper? Vote & Promote so that others can find it

Get a Custom Paper on Economics:

Free papers will not meet the guidelines of your specific project. If you need a custom essay on Economics: , we can write you a high quality authentic essay. While free essays can be traced by Turnitin (plagiarism detection program), our custom written papers will pass any plagiarism test, guaranteed. Our writing service will save you time and grade.

Related essays:

Economics / Brazilian Economy
An Economy Recovering From Chaos. earned the reputation of being a “miracle economy” in the late 1960s when double-digit annual growth rates were recorded and the structure of the economy underwen...
Most people think that religion and economics don’t mix. So you would think the same in the case with Buddhism and economics. But actually the there is a set of rules that go along with our modern ...
Canada has been increasing its prestige as a high-tech, industrial, society since the end of World War II. In many ways it resembles very closely its southern North American cousin, the United States....
Should the government of Canada continue to support the universality of social services by increasing the proportion of salaries given to income tax? This question hits a very touchy spot for all Cana...
Capitalism and Communism are two totally different economic systems. Capitalism is a much better economic system than Communism. Capitalism is an economic system characterized by freedom of the market...