Fixed Income Homework

Extra Homework Class 3

1. The bid and ask in the secondary market for a 90 T-bill are 2.25(ask) and 2.28(bid) respectively. If I buy 1 million worth of notional, what do I pay?

I buy at the ask, so the discount is 2.25% ---2.25% is the ask. But the discount I actually use to calculate the price I pay is 1/4th of 2.25% or .5625%. So my price is (1-.005625) x (1 million) = 994,375.

2. What happens to the price of a mortgage-backed IO strip as interest rates rise and why?

As interest rates rise the pre-payment of principal slows down. Thus there is more principle from which to calculate the interest. This outweighs any reduction in present value from interest rate increases.

3. Let us do a treasury auction as we did in class to make sure we have everything straight. Assume the treasury is issuing 5 Billion USD of 10-year T-notes. The bids are given in yield terms, except the non-competitive bids which do not have a bid price(yield). Assume we have 1 Billion USD in non-competitive bids. We then have the following bids, by the following representatives of big institutions:

A. Minhui bids 1 billion at 2.80

B. Hui 1 bids 1 billion at 2.81

C. Hui 2 bids 1 billion at 2.82

D. Mr. Z 1 bids 1 billion at 2.83

E. Mr. Z 2 bids 1 billion at 2.84

F. Mr. Z 3 bids 1 billion at 2.85

G. Mr. Z 4 bids 1 billion at 2.86

What is the yield everyone who has their bids accepted receives? Who is unlucky and gets none of the auction?

The 1 billion of competitive bids and 4 more billion add up to the 5 billion in the auction. The price that everyone pays is the lowest price that clears 5 billion. Thus the yield is 2.83%. Mr. Z 2, Mr. Z 3, and Mr. Z 4 do not get any Treasury Notes in the Auction.

4. We have four Tranches of a CMO. Tranche A receives principal payments first, Tranche B second, Tranche C third, and Tranche D fourth. In...