A major requirement in managing a fixed income portfolio using a contingent immunization policy is monitoring the relationship between the current market value of the portfolio and the required value of the floor portfolio.

Assume a $$400$ million portfolio with a time horizon of $6$ years $($so payment is due at the end of year $6).$

The available market rate at the initiation of the portfolio is $9\%,$ but the client is willing to accept $8\%$ as a floor rate to allow use of active management strategies.

The current values and current market rates at the end of year $1,2,$ and $3$ are as follow:

End of year Market Value $($$mil$)$ Market yield

$1$ $$390\mathrm{.}811\%$

$2$ $$497\mathrm{.}27\%$

$3$ $$518\mathrm{.}16\%$

Assuming semiannual compounding

a$/$ Calculate the required ending$-$wealth value for this portfolio?

b$/$ Calculate the value of the required floor portfolios at the end of year $1,2,$ and $3.$

c$/$ Compute the margin of error at the end of years $1,2,$ and $3.$

d$/$ Indicate the action that a portfolio manager utilizing a contingent immunization policy would take if the margin of error at the end of any year had been zero or negative.

e$/$ Assume that at the fourth year the manager decides to immunize. What should be the duration of the portfolio?

f$/$ If the manager chooses the duration calculated in e$/,$ what will be the value of the portfolio at year $6$ if there is an increase of interest rate at year $5?$

Show a graph.

g$/$ If the manager chooses instead a portfolio with a higher duration and if there is an increase of interest rate in year $5$ then will the fund have the correct amount, less money or more money than they should have?

Show a graph.

I only need help with d$,$ e $,$f and g