我觉得不是由效用函数凸凹决定的，而是在于效用函数的位置，这个可以看ＳＨＡＲＰ的投资学

Here is the definition of the Arrow-Pratt risk aversion

A=-U''(W)/U'(W)

To derive this, we ask a simple question. Suppose your net wealth is W? Suppose that you are forced to take a a small fair gamble with zero expected payoff and variance of \sigma^2. How much are you willing to pay to avoid that gamble?

this implies that

E[U(W+\epsilon}]=U(W-c)

take a Taylor expansion,

we have

U(W)+U''(W)\sigma^2/2=U(W)-cU'(W)

c=(-U''(W)/U'(W))\sigma^2/2=A\sigma^2/2.

How much that you are willing to pay depends on your absolute risk aversion.

For details, see Huang and Litzenberger (1988)