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I came to the conclusion that in literature Markowitz' Portfolio Theory is believed to be compliant with the Efficient Market Hypothesis. The weakest form states that the current price fully incorporates information contained in the past history of prices only. That is, nobody can detect mispriced securities and “beat” the market by analyzing past prices.

I understand this means that future price movements are independent from what happened until now. In MPT though, to allocate funds between assets, we estimate the expected return and covariances from past prices. If we want to be compliant with EMH, shouldn't we believe that those estimates make no sense?

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Hi Karol Przybylak, welcome to quant.SE! Thank you for asking your question here. –  Bob Jansen Jul 20 at 7:40

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EMH says that one can not earn excess return using some information. This is known as joint-hypothesis problem: to test for market efficiency one have to determine first what is "normal" market return, i.e. what type of information is normally priced by the market. Usually to test for EMH they use CAPM or 3-factor Fama-French model (which is a kind of CAPM-on-crutches), or 4-factor Carhart, of Stambaugh, of 5-factor Fama-French. CAPM, in turn, is a model for asset price in the world where everyone is using Markowitz-style optimization. Other models are built on CAPM. Authors who created it tried to overcome CAPM inconsistencies with empirical evidence.

Now back to Markowitz. Markowitz just recommends what you have to do, if you (1) want to be optimal, (2) have some expectations of return and risk. It EMH holds, your expectations wouldn't earn you excess return (but would earn you some normal). If not, then you'll earn "normal" + excess return. That's why Markowitz had won his Nobel prize: his theory is good both for efficient and non-efficient market, whatever you define "efficiency".

Now back to your question. "If we want to be compliant with EMH, shouldn't we believe that those estimates make no sense?" EMH doesn't stop you from having your own views. It just says that whatever your views would be, you can not use it and earn return in excess of return predicted by some market model (CAPM, FF3F, etc.) But if you have views, you have to organise portfolio according to Markowitz.

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The weak EMH states that it is impossible to earn an excess return given publicly known information such as past prices. Clearly, different securities have different expected returns. For example: the bond and the stock of one company or a security that generates twice the return of another one.

This difference in expected return is explained by a difference in the amount of risk taken which is compensated by a risk premium. The amount of risk is persistent over time (the nature of the securities in the previous examples doesn't suddenly change), thus future price fluctuations are related to past prices. The EMH merely states that we can't predict these fluctuations better than other market participants.

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The Efficient Market Hypothesis (EMH) states that you cannot beat the market on a risk-adjusted basis by looking at past prices. You can certainly earn higher returns than the market if you take on more risk (by leveraging, for example).

Modern Portfolio Theory allows you to construct portfolios that are efficient. According to this theory, you still cannot beat the market portfolio on a risk-adjusted basis.

So, using estimates with past prices with MPT does not contradict EMH.

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I agree with your answer, but could you please rephrase "better returns than the market"? I think you mean "higher" returns at the cost of more risk and lower Sharpe ratio. –  emcor Jul 20 at 22:05
    
Well the Sharpe ratio could be the same as the market -- it is not necessariliy lower -- but yeah higher returns for higher risk. –  SRKX Jul 21 at 12:07

MPT uses expected values for its parameters.

How these expected (future) parameters are estimated, is another question.

Usually one takes historic averages when its the only information available, but one could for example also use analysts forecasts or other advanced estimation methods.

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