Risk-Neutral Pricing Measures and Risk Aversion

Summary

The document asks how risk-neutral pricing relates to the risk aversion assumed in expected utility theory. Its answer connects risk-neutral valuation to an assumption of complete markets and no arbitrage: under those conditions, a risk-neutral measure can express asset prices as discounted expectations of future values. It then describes this as if agents had linear utility and zero risk aversion under that measure.

This is a brief conceptual reply rather than a derivation or empirical analysis. The key distinction is that a pricing measure is used to value payoffs, while risk aversion describes preferences; the answer’s phrasing risks conflating the two. A risk-neutral measure does not by itself show that actual investors are risk neutral. The document offers no detailed account of how preferences, state prices, or market completeness establish the pricing measure, so readers should treat its proposed link as an intuition that needs qualification.

Key ideas

• The answer associates risk-neutral valuation with complete markets and absence of arbitrage.
• A risk-neutral measure represents asset prices through expectations of future values.
• The response describes this valuation convention as equivalent to zero risk aversion under the measure.
• A pricing measure should not be read as evidence that investors’ actual preferences are risk neutral.

Tags

# Risk neutrality coherence with risk aversion


# Risk neutrality coherence with risk aversion












I haven't been able to find an understandable explanation why the risk neutrality is coherent with the risk aversion implication of the expected utility hypothesis. I can see that when using the risk neutral measures it is independent of subjective choices, but I don't see the link why this is in line with risk aversions

## Answer by Ezy (score 1)

https://quant.stackexchange.com/a/43225

If you make the assumption that the market is complete and that there is no arbitrage then the risk neutral measure exists which allows to price each asset as an expectation of the asset’s future value. So in utility language this means that under the risk neutral measure all agents have 0 risk aversion and their utility function is purely linear (instead of a generic concave function in other measures).

Hope this clarifies.

You can also see this other related question if you want more color

Does risk-neutral measure have anything to deal with risk-neutrality in utility theory?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.