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A risk-averse investor who makes an investment choice based on the expected utility of the return on his investment portfolio is equivalently making investment choices based on the expected return and variance of the portfolio

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A risk-averse investor who makes an investment choice based on the expected utility of the return on his investment portfolio is equivalently making investment choices based on the expected return and variance of the portfolio." Prove or disprove this statement.

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SOLUTION:-

The above statement is very much relevant.

The statement can be proved by considering the equation of utility fuction given below:-

$U= E(r) -\frac{1}{2}A\sigma ^{2}$

where,

U = Utility

E(r) = Expected return on the asset or portfolio

$\sigma ^{2}$ = Variance of returns

$\frac{1}{2} = Scaling factor$

A = Cofficient of risk aversion, or the investor's degree of risk aversion

The larger values of A, the investor will penalize risky investments more severly.

As we can see above in the formula that " A risk- averse investor who makes an investment choice based on the expected utility of the return on his investment portfolio is equivalently making investment choices based on the expected return and variance of the portfolio".

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A risk-averse investor who makes an investment choice based on the expected utility of the return on his investment portfolio is equivalently making investment choices based on the expected return and variance of the portfolio

Finance