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Assume an investor has utility for money given by some utility function u(W), where u'(W) gt; 0, uquot;(W) lt; 0. Let R(W) denote the associated...
Assume an investor has utility for money given by some utility function u(W), where u'(W) > 0, u"(W) < 0.
Let R(W) denote the associated index of absolute risk aversion,
R(W) = -(u"(W)/u'(W))
i). Computer R(W) for the following three examples, (y = gamma)
- u(W) = W - 1/2W^2
- u(W) = -e^(y*W), y > 0
- u(W) = 1/7W^y, y > 0
ii) Now assume u(W) has the property that R(W) is constant(e.g the middle example above). If the investment opportunities consist of a single safe asset with return rF and a single risky asset with random return r^(r-hat), show that the investor with utility u(W) will always choose to invest the same amount of his/her wealth in the risky asset no matter what his/her income W is.
