The following information relates to the Question

Melissa Clarke, a CUNY QC Adjunct Professor of Finance, is also mortgage backed securities (MBS) portfolio manager at Star Flag Fund. The fund primarily invests in Agency MBS, that is, those issued by US Agencies such as Fannie Mae and Freddie Mac. The fund also uses various interest rate products such as US Treasuries, interest rate futures and, interest rate swaps (IRS) to manage the funds duration, cash flow and, market risk.

A recent economic crisis has sharply reduced US interest rates, including fixed rates offered on conventional mortgages. The sudden drop in interest rates has sparked a re-financing boom, as US homeowners scrabble to refinance existing mortgages at lower interest rates. Clarke is worried about this development and notices that due accelerated mortgage prepayments, the portfolios average duration has contracted from 5.7 years to 4.1 years. Having a lower duration in an environment of falling interest rates will clearly hurt Star Flag Funds performance. Clarke wants to adjust the portfolios duration back to its target duration to offset the impact of increased MBS prepayments.

Fund information and market data are contained in the table below. USD IRS convention is to quote the fixed rate vs 6-month Libor. Also, assume all US IRS transactions are centrally cleared.

Fund size	$600 million
Fund target duration	5.5 years
Average duration of Agency MBS	3.7 years
Duration of 5y US Treasury	4.6 years
6m USD Libor	1.875%
5y IRS bid-offer quote	2.015% to 2.025%
7y IRS bid -offer quote	2.125% to 2.140%

2. Assuming the modified duration of the 5y and 7y swap are 4.25 a 5.75 respectively, find the swap notional needed for each tenor to return the portfolio back to its target duration.

1. $198m and $146m respectively
2. $227m and $146m respectively
3. $198m and $183m respectively