Assume an investor has a a utility function for money, u(W), with the property t

Question

Assume an investor has a a utility function for money, u(W), with the property that u (W) > 0, u(W) < 0.

1. State the definition of the coefficient of absolute risk aversion, R(W). Compute this coefficient in the special case where u(W) = 1 W .

2. Assume that there are two possible investments, a risky asset with random return rˆ and a risk-free asset with return rf . Also assume that R(W) is an increasing function. Show that the investor will invest less of her wealth in the risky asset as her wealth increases.

Explanation / Answer

1. The coefficient of absolute risk aversion is define as the utility is a class of utility functions. It is also known as exponential utility and this is usually thought of a less plausiable description of the risk aversion as we compare with the constant relation between the risk aversion.

The formula derives as:

u(c) = -(1/a)e-ac

2. As the two possible investment that have with a risky asset with random return and a risk free asset so it is possiblity of investor to invest less of her wealth in risky as it might or might not provide the better return and also as a point of view of her random return it will provide R(w) as an increasing function.

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