$1)$ Suppose that as a fixed income trader for a bank you currently are holding the following

fixed income portfolio of assets and liabilities:

Assets: $$1$ million face value, $6-$year coupon bond. $4\mathrm{.}5\%$ annual coupon payment, $3\mathrm{.}5\%$ yield

to maturity.

$$2$ million face value, $2-$year zero coupon bond. $2\%$ yield to maturity.

Liability: $$3$ million face value, $1-$year zero coupon bond. $1\mathrm{.}75\%$ yield to maturity.

a$)$ Assuming that when you set up these three positions, the total purchase price of the

two assets was exactly equal to the funding generated by the issuance of your liability,

determine the current amount of profits for this portfolio. This is its net worth.

b$)$ Determine the total Macaulay durations of your assets and your liability. Comment

on the discrepancy, specifically, what is the direction of interest rate changes that will

lead to a reduction in this portfolio$$s net worth?