A financial firm has acquired a portfolio of assets and liabilities. To manage the interest rate risk the portfolio managers want to follow a duration matching strategy (using the modified duration metric). The following table provides the information on their investment portfolio and bond liabilities portfolio.

Investments

Investment 1: Notes payout instrument, coupon rate of 7% payable semi-annually, 15 year term to maturity and par value is returned to investors at maturity. The current yield to maturity is 4% and a total face value of $6 million.

Investment 2: Investment to be described below.

Liabilities

Bond Payout Frequency Par Value Term to Maturity Coupon Rate YTM Face Value of Bonds

1 Annual $1000 10 8% 6% $2 million

2 Semi-annual $1,00 15 5% 5.50% $3 million

3 Semi-annual $1,000 5 2% 1.10% $4 million

Instructions

In order to execute the duration matching strategy, the above balance sheet needs to balance (market $ value), and the duration of the investments should equate to the duration of the liabilities.

Investment 1 must be held, and you cannot sell it or buy any more of it, so you will need to match the durations using only Investment 2. Calculate the $ amount (market value) needed to invest in Investment 2 and include the duration measure of Investment 2. Further, show the market value balance sheet for the investments and liabilities, including the $ amount and duration of each item as well as the total portfolios.