bond T F S Z P M

maturity, yrs 2 5 7 5 3 months

price 100 99.5 99

duration 1.9 4.0 5.7

yield, % 2.5 3 3.3 3.1 3.9 2

All securities above have face value 100.

The durations above are not Modified.

1) A portfolio consists of 10 T and 5 F. Whats the portfolios Modified Duration?

2) If the portfolio starts with 10 of T how many F are necessary to produce a target modified duration of 3 years?

3) Same question, but target duration is 0? What is the hedge ratio of F for T (how many F are needed to hedge one of T)? T for F?

4) Return to the original portfolio of 10 T and 5 F. How many S are needed to bring the portfolios Modified Duration to 5? Do this two ways:

a) Treat the original portfolio with T and F separately.

b) Consider the original portfolio as a combination of the T & F with one value and one modified duration.

5) Repeat #4 but target duration of 0.

6) What is the hedge ratio of F for Z? Remember you need to calculate Zs modified duration first.

7) What is the hedge ratio of P for Z? Assume Ps coupon is 6. Here you need to calculate Ps modified duration indirectly, by first finding its dv01. (Note: If you change Ps coupon, youll get a different dv01. But as long as the yield is the same, no matter what the coupon is, modified duration is the same! Try it.)

8) What is the hedge ratio of T for M? M has a single cash flow of 100.

9) An overnight repurchase agreement, of course, has a duration of 0. Suppose a portfolio contains 5 of T and 500 in a repurchase agreement. What is its modified duration?

10) Again a portfolio has 5 of T. How much does the investor need to lend with a repo in order to bring the portfolio duration to 1?