Question

EEEE 1. Using the last 2 digits of your UIN, create your yield by adding 0.041 to the last 2 digits divided by 10000 (example: if last 2 digits are 26, then y= 0.041 +26/10000 = 0.0436). Create your coupon by dividing the last 2 digits by 100 and adding 4.2 to it (example continued: 26/100+ 4.2 = 4.46). Now, using your unique coupon and yield, assume your bond has 22 years to maturity and pays a semiannual coupon (assume settle date is a coupon date). Answer the following questions: (a) What is the price of the bond? (b) What is the modified duration? (c) What is the convexity measure? (d) What is the DV01 per million dollars? (e) Now consider 2 scenarios: The required yield rises 150 bps and the required yield falls 150 bps. (a) Using just duration, what is the predicted price when yields rise 150 bps and when they fall 150 bps? (b) Using both duration and the convexity measure, what is the predicted price when yields rise 150 bps and when they fall 150 bps? (c) What are the actual P/Ls that would be realized on $5 million of face if rates rise and fall by 150 bps? (Note: You will compute the actual price change in the scenarios.) source (Fixed Incomefn.r') n <- 26 y <- 0.041 + n/10000 cpn - 4.2+n/100 cy, con) ## [1] 0.0436 4.4600 T <- 22 po <- BPrice (cpn, T,y) @ @ @

Answer 1

Solution;

Now lets take the last two digits as mentioned in the example i.e. 26

So the yield becomes .041 + 26/10000 = 0.0436 = 4.36%

And the coupon becomes 26/100+4.2 = .26 + 4.2 = 4.46%

Now lets solve the parts

a) Price of the bond

using our BAII plus calculator to find the price of the bond.

PMT = 4.46% Semianual = 2.23% FV=100    n=22*2 = 44 I/Y = 4.36/2 = 2.18% PV = ??

PV = 101.40

b)Modified duration

Lets consider a 1 basis point change in the yield i.e. 1 basis point increase

Our yield becomes 4.36% + .01% = 4.37%

Our bond price becomes = 101.26 (again using the BA II plus and changing the I/Y)

we get the bond price as

We know Approx % change in bond price = -Mod Duration * Change in Yield

(101.40 - 101.26)/101.4 = - MD* .01%

.14 /101.4 = -MD * .0001

MD = (.14/101.4)/.0001 = 1.38

3) Convexity

We know that

V-> bond price

lets dec the yield by 1 basis point

New yield = 4.36% - .01% = 4.35%

Now the bond price = 101.54 (Changing the I/Y to 4.35%)

Approximate Conv = (V(dec in yield) + V(inc in yield) - 2 V) / (Change in YTM)^2 * V

= ((101.54 + 101.26) - 2* 101.4) / (.0001)^2 * 101.4

= (202.8 - 202.8)/...

=0

Annual convexity of 0

4) DVO1

Price value of a basis point(per 100$) = (Bond price(Yield dec by 1 basis point) - Bond Price(Yield inc by 1 basis) ) / 2

= (101.54 - 101.4) /2 = .07

.07 * 1million * .01 = 700

For the 1 million $ par value bond each 1 basis point change in the YTM will change the bond 's price by 700$