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Risk-Neutral Expectations and Comparing Asset Volatility

Article Quant Q&A · Author: Lei
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Summary

The document poses a question about how expected asset prices can be equal under the physical probability measure, while the expected value of the more volatile asset is lower under the risk-neutral measure. It asks whether this relationship can be proved or disproved, given two assets whose physical expected prices match but whose volatilities differ. The topic concerns how changing probability measures affects expected values in asset pricing.

No answer, derivation, model assumptions, or supporting evidence is included. In particular, the text does not specify how the risk-neutral measure is constructed, what market setting applies, or whether the assets have any relationship beyond their stated means and volatilities. Those omissions prevent the question alone from establishing a general ordering of risk-neutral expectations. The document is useful as a prompt for examining measure changes and asset pricing, but it does not provide a conclusion or method for resolving the claim.

Key ideas

  • The question compares two assets with equal expected prices under the physical measure and different volatilities.
  • It asks whether the more volatile asset must have a lower expectation under the risk-neutral measure.
  • The document provides no proof, counterexample, or answer to the question.
  • The relationship cannot be assessed from the stated information alone because the model and measure construction are unspecified.

Tags

Derivatives pricingStatisticsVolatility
Full text
# Why price with lower volatility yield higher expectation under risk neutral measure


# Why price with lower volatility yield higher expectation under risk neutral measure












Suppose $S_1$ and $S_2$ are two asset prices, such that, E[$S_1$] = E[$S_2$] under physical measure and $\sigma(S_1)$ > $\sigma(S_2)$. Then why E[$S_1$] < E[$S_2$] under the risk neutral probability measure? How can we prove or disprove this?

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