Why Risk Adjustment Matters When Testing Market Efficiency
Summary
The document questions why returns must be adjusted for risk when assessing the efficient market hypothesis. It compares two shares with the same realized return but different expected returns, then considers whether a strategy that repeatedly outperforms the market could demonstrate that public information is not fully reflected in prices. It also raises the possibility that investors’ skill or circumstances change their personal exposure to risk.
The discussion distinguishes raw performance from performance relative to the risk taken: higher expected returns may compensate for greater systematic risk rather than indicate mispricing. Repeated success can be evidence relevant to market efficiency, but a short period of outperformance alone does not settle the issue. The document offers no statistical test or resolution, and its example does not specify return variability, a precise asset-pricing model, or enough observations to assess persistence. Risk adjustment remains central because a test must separate compensation for risk from abnormal returns attributable to information or skill.
Key ideas
- Equal realized returns do not imply equal risk-adjusted performance.
- Risk adjustment helps distinguish compensation for systematic risk from abnormal returns.
- Persistent outperformance may challenge market efficiency, but it requires careful statistical assessment.
- Investor skill and individual risk exposure complicate interpretation of observed returns.
- The document raises these issues without specifying a formal test or conclusive evidence.
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Full text
# Why is it that returns at the efficient market hypothesis has to be risk-adjusted?
# Why is it that returns at the efficient market hypothesis has to be risk-adjusted?
Let us assume the following situation:
- Risk-free rate: $R_F = 2\%$
- Actual return of share A after one year: $R_{A} = 15\%$
- Actual return of share B after one year: $R_{B} = 15\%$
- Expected return of share A: $E(R_A) = 11\%$
- Expected return of share B: $E(R_B) = 8\%$
$\alpha_B$ is bigger, so share $B$ would be preferable to share $A$ as it generates a higher return per unit of risk.
However, in this case it is also the case that share $A$ outperforms the average market return more strongly than share $B$, so it is more profitable than share $B$. But of course, share $B$ has a more favorable risk-return ratio. Still, I ask myself why this risk adjustment is so important to test the efficiency market hypothesis. Therefore let us now assume that the investor succeeds again and again over a longer period of time (say two years) in generating returns above the market average $R_M$ with share $A$ / strategy $A$. Then the investor would still have managed to achieve an equally good return compared to share $B$ despite the more difficult circumstances (due to the higher risk $\beta_A = 1.5$). Shouldn't one say at this point that risk also has a subjective component? This means that investors know how to use public information better and can in this way reduce their personal risk. If that would be the case, then it would represent a violation of the efficiency market hypothesis, wouldn't it? In other words: Isn't it the case that the risk adjustment loses relevance the longer a strategy is successful, since with a higher risk it should become less likely that the strategy will continue to be successful over a longer period of time, right? This means that in the long run you can not only achieve higher returns due to higher risk, but that must be due to other aspects, such as the fact that not all publicly relevant information is priced in the share price and this fact is exploited.
Is that correct or is there a mistake?
Many thanks in advance!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.