A market value balance sheet for the Carr Commercial Bank is given below in millions of dollars:

The standard deviations and correlations between returns on asset and liability categories (excepting equity) are as follows:

(a) What is the standard deviation of the equity holder's position?
(b) Suppose the bank decides to hedge by taking a position in T-bond futures contracts. You are given the following information:

Should the bank take a long or short position in T-bond futures? How many futures contracts should they buy/sell? How much is the standard deviation of equity reduced?

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Assets Liabilities Short-term U.S. government bonds Loans 100 200 700 1,000 Short-term 50 Deposts 850 100 Equity 0 1,000 STA D TUS,STL L D rSTL,D = 0. σ(STL)-02, σ(D) = 03. VB $90,000 for a $100,000 face value T-bond contract, aT B = 08, rT B.ST A = 0, rT B.L=.5, rTB,STL=0, rTB,D = .3.