= Solution
Indifference means equality of the risky <expected utility> and the utility of the sure reduced wealth. A second-order <Taylor expansion>, using $\mathbb E\phi=0$, gives
$$
\mathbb E U(W(1+\phi))=U(W)+\frac12W^2U''(W)\mathbb E\phi^2+o(\mathbb E\phi^2).
$$
For the sure alternative,
$$
U(W(1-\psi))=U(W)-WU'(W)\psi+O(\psi^2).
$$
Equating these and retaining the leading terms produces the <small multiplicative risk premium>
$$
\boxed{\psi\simeq-\frac12\frac{WU''(W)}{U'(W)}\operatorname{Var}(\phi).}
$$
For increasing concave <utility functions> this is positive. The approximation assumes genuinely small shocks with controlled Taylor remainders and positive final wealth; small <variance> alone would not justify it for rare large shocks.
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