[do NOT use Excel]

An insurance company has the liabilities with the following payment pattern, each at the end of the respective year:

Year 3: $2.5 million

Year 7: $4.2 million

Year 20: $6.0 million

There are no other liabilities for the insurance company to consider. The discount rate for the liabilities is 3%. The insurance company has the following investment opportunities in bonds and stocks:

Coupon Bonds

Maturity	Yield	Duration
4	7.0%	3
10	9.0%	7
20	10.0%	11
30	11.0%	20

Common stocks

Stock	Dividend	Duration
A	5.0%	20
B	9.3%	11
C	10.0%	10
D	14.3%	7

Zero Coupon Bonds

Maturity	Yield
3	1.5%
5	2.0%
7	2.0%
10	3.0%
15	3.5%

a. Using the information about the zero-coupon bonds, draw the yield curve and compute two forward rates of your choice.

b. Calculate the duration of the liability.

c. The insurance company desires a rate of return of 11% for its investments. Using the securities listed above, design an investment portfolio that is immunized from small interest rate changes and provides an expected return of at least 11%. If such a portfolio is impossible to achieve with the securities listed above, what return can be achieved?

d. How can the liabilities of the insurance completely immunized from all interest changes? Explain your approach and build the portfolio.