FIXED INCOME FUNDAMENTALS

fall 2018

Problem Set X

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?

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

2.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?

b.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:

3.Treat the original portfolio with T and F separately.

4.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?

Need help on 7,8,9,10.