Question

Problem #5: The derivative is dP/di=[(-182/365)(90000)]/[(1+I(182/365)]^2 where i=11.09%.

Problem #4: What is the price P today of a S90 ,000 182-day Canadian T-Bill if its quoted yield is 11.09%? Problem #4: 85283.96 Answer correct to 2 decimals. Just Save Your work has been saved! (Back to Admin Page) Submit Problem #4 for Grading Problem #4 | Attempt #1 Your Answer: 85283.96 Your Mark: 2/2 Attempt #2 | Attempt #3 | Attempt #4 Attempt #5 Problem #5: Find the derivative of the previous result from Problem #4 above, with respect to the quoted yield i Use this derivative to approximate the change in the price of the T-Bill if the yield were to have decreased by 0.002 (ie di 0.2%) immediately after the T-Bill was purchased. Problem #5: 80.59 Answer correct to 2 decimals Just Save Your work has been saved! (Back to Admin Page) Submit Problem #5 for Grading Problem #5 | Attempt #1 Your Answer: 80.39 Attempt #2 Attempt #3 Attempt #4 | Attempt #5 80.59 Your Mark: O/2% 2/2 em #6: For the T-Bill in question 4 above, what value does di approach as one gets closer and closer to the maturity date?

dP/di=-40296.81627(-0.002) --> bc of the yield decrease

= 80.593

Problem #6 is where I'm having problems. I'm not sure what it is asking us to and I don't know how to attempt it. Thanks.

Answer 1

The price of Zero coupon bond is given by;

$P=\frac{90000}{(1+i)^{\frac{t}{365}}}$

$\therefore \frac{\mathrm{d} P}{\mathrm{d} i}=-90000\times \frac{t}{365}\times (1+i)^{-\frac{t}{365}-1}$

Here, t is the days to maturity.

Now, as per the question four, bond approaches the maturity. I.e. t is tending to 0.

Hence, question four is nothing but finding derivative when t tends to 0.

In this case it will be 0.