# Why is it that returns at the efficient market hypothesis has to be risk-adjusted?

Let us assume the following situation:

• Average market return: $$R_M = 8\%$$
• 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: $$R_{B} = 15\%$$
• Beta of share A: $$\beta_A = 1.5$$
• Beta of share B: $$\beta_B = 1.0$$
• Expected return of share A: $$E(R_A) = 11\%$$
• Expected return of share B: $$E(R_B) = 8\%$$
• Alpha of share A: $$\alpha_A = 15 - 11 = 4$$
• Alpha of share B: $$\alpha_B = 15 - 8 = 7$$

$$\alpha_B$$ 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?