MBS and Futures Contracts

Lecture 8 - Mortgages and MBS

Consider the following fixed-rate level-payment mortgage pass-through security:

Total principal outstanding = $5,000,000

Weighted average mortgage (Note) rate = 8.25%

Weighted average remaining maturity = 30 years (360 months)

Pass-through rate=7.5%

a. What is the scheduled monthly mortgage payment if there is no prepayment?

b. Assume that you are an investor in the pass-through security. Assume 150 PSA pre-payment. Calculate the interest and scheduled principal repayment received by you for the sixth month.

c. What is the amount of prepayment in the sixth month?

Lecture 9 - Interest Rate Futures

1. It is August 2 and a fund manager invested in $10 million government bonds (trading at par) is concerned about an increase in interest rates over the next 3 months. The manager decides to use the T-bond futures contract to hedge the portfolio. Current futures price is 93-02.

The modified duration on the bond portfolio is 6.80 years. The CTD issue has a modified duration of 9.2 years. Devise a hedge for the manager?

(Hint: You need to find the PVBP of the portfolio and the futures contract using the following formula: PVBP = - Modified Duration * P * 0.01%.).

2. Now suppose a financial institution has a duration gap of -4 years and $5 million in assets. The cheapest to deliver bond for Treasury futures contracts has a duration of 3 years. How will the manager hedge this interest rate risk? Assume the cheapest to deliver bond is trading at par.