Random Insurance Company has liabilities equal to $400 million.  These liabilities can be modeled as long-term fixed income exposures similar to a long-term bond with a duration of 15 years.
The company has total assets worth $500 million and thus a net worth of $100 million.
Currently, the assets are all invested in a bond portfolio with a duration of 10 years.
Note:  As regulated entities, insurance companies report to their regulators using legally required statutory accounting, which is different from US GAAP.  Statutory accounting focuses on the accuracy of the balance sheet to ensure that claims can be paid.  It is much more like a liquidation analysis. GAAP, on the other hand, focuses more the accuracy of the income statement and the firm's profitability.  GAAP is concerned more with the matching principle while statutory accounting is more conservative.
The company is considering changing its asset allocation strategy, which now is 100% bonds.   However, as a highly regulated entity, it is limited in the amount of investment risk it can take on.  The company is regulated by the state insurance commission, as there is no federal regulation of insurance in the United States thanks to the McCarran-Ferguson Act.
The balance sheet looks like this:
Assets ($ millions)		Liabilities and Equity
Investments                           (100% bonds)	$500	Insurance liabilities	$400
		Equity    (Net worth)	$100
Total	$500	Total	$500
Assume that stocks and bonds have the following risk characteristics	Expected returns	Risk (std)	Correlation matrix
			Stocks	Bonds
Stocks	5%	20%	1	0.3
Bonds	2%	10%	0.3	1
a.  If interest rates increase by 1%, what will be the new equity (net worth) of the company?   (Assume that all assets and liabilities are valued at market value.) Give a numeric answer.
b.  If interest rates decrease by 1%, what will be the new equity (net worth) of the company?   (Assume that all assets and liabilities are valued at market value.) Give a numeric answer.
c)       What is are the expected rate of return and risk of the company's existing assets?	Return
	Risk (standard deviation)
d)  The company wants you to analyze its asset allocation to see if it can do better.   Construct the portfolio consisting of stocks and bonds with the highest return, but with risk no greater than the risk of their current asset allocation of 100% bonds.  Provide the weight in stocks and bonds, along with the return and risk of the resulting asset portfolio.
	Stock weight
	Bond weight
	Return
	Risk (standard deviation)