1. [12pts] Consider the following bond (assume: credit risk free, no embedded options, pays interest semiannually):

Coupon:

9%

YTM:

8%

Term (yrs):

5

Par:

100.00

Compute the following

(a)The price value of a basis point;

(b)The exact Macaulay duration;

(c)The exact modified duration;

(d)An approximate value for the modified duration, obtained by changing the yield by 20bp. How does it compare to the exact value obtained in part (c)?

(e)The exact convexity measure;

(f)An approximate value of the convexity measure, obtained by changing the yield by 20bp. How does it compare to the exact value obtained in part (e)?

2. [8pts] For the bond in question 1,

(a)[1pt] Calculate the actual, exact price change for a 100bp increase in interest rates;

(b)[2pt] Using duration only, estimate the price of the bond for a 100bp increase in rates;

(c)[2pt] Using duration and convexity, estimate the price change of the bond for a 100bp increase in rates;

(d)[1pt] Comment on the accuracy of the approximations in (b) and (c) and explain why one is better than the other;

(e)[2pt] Without an actual calculation, indicate (explain) whether the duration of the bond would be higher or lower if the YTM were 10%, rather than 8%. Hint: recall that the price-yield curve is convex for risk- and option-free bonds.

3. [5pts] The federal housing GSEs (Fannie and Freddie) hold mortgages on balance sheet, financed by issuing debt. Their `net duration is said to be zero, while they are short convexity.

a)Explain what these two phrases mean.

b)Sketch the (book) value of their equity as a function of yield.

c)How would this diagram look if their net portfolio had positive convexity?

d)Given the markets perception that the Federal government would step in to make bondholders whole in the event of bankruptcy, why would the GSEs want negative convexity in their net portfolios?

e)Why might your answer in d) not apply to a fully private, much smaller firm that is in the exact same business as the GSEs?