Assignment 3:

Introduction

This assignment is worth 5 per cent of your final course grade.
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 years 8% 6% $2 million
2 Semi-annual $1000 15 years 5% 5.5% $3 million
3 Semi-annual $1000 5 years 2% 1.1% $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.