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Consider a mutual fund that is currently investing only in Toyota Motor Corporations stock (Ticker: TM). The fund manager has collected information of another three stocks. The fund manager wants to combine TM with another stock and reduce the portfolios risk using diversification.

Assume that the fund manager invests 60% of the assets in TM and 40% in XOM to form the optimal risky portfolio. Then the fund manager wants to further combine the risky portfolio of two stocks (i.e., 60% in TM and 40% in XOM) with risk-free assets. However, the risk-free rates of lending and borrowing are different. The fund manager can invest in risk-free assets with 2% return. When she borrows, the risk-free rate is 5%. Suppose her risk aversion index is A=5. Then the optimal weight for the risk-free asset is _____%. (For example, if the optimal weight is 60%, then put "60" below. Keep two digits after decimal.)

What is the optimal weight for the risk-free asset?

Expected return and standard deviation TM F HPQ XOM Expected Return 82.70% 16.9% 25% 9.08% 61.74% 8.24% 13.20% Standard Deviation 146.68% Covariance Matrix TM HPO XOM TM 0.1140 HPO 0.0640 0.3044 XOM -0.0129 -0.1762 0.0008 Correlation Matrix TM F HPO XOM TM F 0.3110 HPQ 0.4147 0.3361 XOM | -0.3914 -0.9098 0.0095 Expected return and standard deviation TM F HPQ XOM Expected Return 82.70% 16.9% 25% 9.08% 61.74% 8.24% 13.20% Standard Deviation 146.68% Covariance Matrix TM HPO XOM TM 0.1140 HPO 0.0640 0.3044 XOM -0.0129 -0.1762 0.0008 Correlation Matrix TM F HPO XOM TM F 0.3110 HPQ 0.4147 0.3361 XOM | -0.3914 -0.9098 0.0095