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

<blockquote>
  <p>Pratt, J. (1964). <a href="http://www.jstor.org/stable/1913738" rel="nofollow noreferrer">Risk Aversion in the Small and in the Large</a>.
  Econometrica, 32(1/2), 122-136.</p>
</blockquote>

<p>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.</p>

CC BY-SA 3.0
2017-11-02T16:50:41.740Z
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)?
user56834
CC BY-SA 3.0
2017-11-02T20:34:30.533Z
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.
Michael Greinecker
CC BY-SA 3.0
2017-11-02T12:29:34.010Z
2017-11-02T12:29:34.010Z
Michael Greinecker
<p>We can write down the <strong>coefficient of absolute risk aversion</strong> $R_a$, or the <strong>coefficient of relative risk aversion</strong> $R_r$.</p>

<p><strong>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?</strong></p>

<utility><preferences><expected-utility><risk-aversion>
Is there a natural intuitive interpretation of the **numerical value** of the coefficients of risk aversion?
user56834
# Is there a natural intuitive interpretation of the **numerical value** of the coefficients of risk aversion?

(Asked by: username_0 on 2017-11-02)

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?**

**Tags:** utility, preferences, expected-utility, risk-aversion

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## 1 answers

### Answer by username_1 on 2017-11-02. Score: 4

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](http://www.jstor.org/stable/1913738).
> 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.

> **Comments:**
> **username_0**: 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)?  
> **username_1**: 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.  

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