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We can write down the coefficient of absolute risk aversion $R_a$, or the coefficient of relative risk aversion $R_r$.

Are there intuitive interpretations of the numerical values of these coefficients? Let's say that someone has $R_a=5$ or $R_r=3$ for certain wealth level $W$, how would we interpret that number?

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Yes, there is such an interpretation in Section 3 of the original paper by Pratt:

Pratt, J. (1964). Risk Aversion in the Small and in the Large. Econometrica, 32(1/2), 122-136.

Under some regularity conditions, the coefficient of absolute risk aversion approximates the risk premium divided by half the variance for a small actuarily fair gamble. In Pratt's words, "$r(x)$ is twice the risk premium per unit of variance for infinitesimal risks". A similar interpretation holds for relative risk aversion, see Section 10.

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  • $\begingroup$ I see. So I assume that for constant absolute risk aversion, the principle holds for non-infinitessimal risks as well? Could you post the interpretation of relative risk aversion, if you want to (not if you don't want to of course)? $\endgroup$ – user56834 Nov 2 '17 at 16:50
  • $\begingroup$ I'll adress the relative risk aversion case tomorrow. One of the regularity assumptions is that the third moments become relatively negligible in comparison to the variance. So I don't think one can apply this to large gambles even under CARA. $\endgroup$ – Michael Greinecker Nov 2 '17 at 20:34

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