# Tag Info

16

Samuelson suggested in 1965 that the stock prices follow a martingale (see P. Samuelson “Proof That Properly Anticipated Prices Fluctuate Randomly”). Assume there is a security with a random payoff $X_T$ at date $T$. Let $..., P_{t–1}, P_t, P_{t+1},...$ be the time series of prices of a security with this payoff. Finally, define the price change $\Delta ... 14 A martingale is a random process$X(t)$which has the following properties:$ E[X(T)|\mathcal{F}_t] = X(t) $for$T > t$and$ E[|X(T)|] < \infty $where$\mathcal{F}_t$is the filtration at time$t\$. A martingale is a random walk, but not every random walk is a martingale. A Brownian random walk is a martingale if it does not have drift. Also, a ...

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Often one will find the argument that a random walk of price changes would be a proof of the efficient market hypothesis, but this is (IMO) a logical fallacy: Only because the EMH does imply random walks in the price changes, the finding of random walks does not imply automagically that the EMH is true.

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A martingale can be viewed as a fair game (a game in which there is no arbitrage strategy) A (centered) random walk is a martingale (think of it as the total Gain of the fair game) If EFH is in order, then you can think that all information is in the current price, I think this more comparable to Markov Property than to Martingale property. Hope that ...

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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 ...

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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 ...

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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 ...

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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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In the equilibrium models you can assume that there exists so called Alpha, i.e. an opportunity that can be exploited. Most of the buy side models (i.e. asset allocation, portfolio construction) are based on this idea. As a theoretical model, you can consider CAPM with heterogeneous beliefs: Hedge funds claim to generate the “Alpha”, i.e., excess ...

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