# Tag Info

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The best explanation I have seen so far is the so-called Adaptive Market Hypothesis by Andrew Lo: The adaptive market hypothesis, as proposed by Andrew Lo, is an attempt to reconcile economic theories based on the efficient market hypothesis (which implies that markets are efficient) with behavioral economics, by applying the principles of ...

8

If one finds an anomaly relative to some asset pricing model, there are three possibilities: The anomaly you "found" actually isn't there: you're overfitting the data, found a spurious result. The efficient market hypothesis is wrong. The asset pricing model you're using is wrong. Any test of market efficiency is a joint test of market efficiency and an ...

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They are different concepts, and the relation between them can be described as a conditional: "if EMH holds (all available information about future price movements is already priced into the market), then future price movements will follow a purely random walk as new and unpredictable information emerges"

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What you describe is known as the Equity Premium Puzzle - and it really is, as the name says, a real enigma: "The equity premium puzzle (EPP) is a phenomenon that describes the anomalously higher historical real returns of stocks over government bonds." Source: https://www.investopedia.com/terms/e/epp.asp#ixzz5HlCdHS2Z A good first introduction can be ...

5

On more than a few occasions, I have attempted to extrapolate the current trend towards passive allocation to its logical conclusion: more passive allocation means more inefficiency. I am not aware of any research which directly measures the correlation between market efficiency and active versus passive allocation. In general, the level of market ...

5

Any anomaly that can be phrased as a "mispricing" or "relative value" opportunity can be expected to disappear as more people discover it and trade on it. For example, say that stock movements over the last 15 minutes of the day are found to be strongly mean-reverting. That is, stocks which decline over the last 15 minutes of the day tend to be undervalued, ...

5

Historically the RWT (Random Walk Theory) came first, as empirical observations by for example M.F.M. Osborne (1959) and others in the 1960s. The EMH came about as a result of theoretical work by Samuelson in 1965 ("Proof that properly discounted prices...") and E.Fama (1969) as a general empirical/theoretical hypothesis that guided the field for many ...

4

Generally Kurtosis measures the degree to which a distribution is more or less peaked than a normal distribution. Positive kurtosis indicates a relatively peaked distribution. Negative kurtosis indicates a relatively flat distribution. In time series we can encounter high kurtosis which is caused by "fat tails" (higher frequencies of outcomes) at the ...

4

Perhaps an answer coming from a different angle and giving you some perspective: The typical approach taken by statistics is top-down: Just looking at the data and finding patterns and stylized facts (like excess volatility, volatility clustering, fat tails, no autocorrelation in returns but significant autocorrelation in absolute returns etc.) The problem ...

4

Adding to the excellent answer of vonjd: another, more cynical interpretation is that some of these "anomalies" never would have existed ex-post and that their discovery is the inevitable result of thousands of researchers looking for patterns in the same data set. Look at ". . . and the Cross-Section of Expected Returns" by Harvey et. al. for an ...

4

First, you might find this recent paper by Israeli, Lee and Sridharan (Review of Accounting Studies, forthcoming) interesting. This is the abstract: We examine whether an increase in ETF ownership is accompanied by a decline in pricing efficiency for the underlying component securities. Our tests show an increase in ETF ownership is associated with: (1) ...

4

Suppose markets are perfectly efficient and asset prices reflect all available information. Under this assumption one expects current prices to be non-biased estimators of future prices. It is a common mistake to think that market efficiency implies $P_t = E_t[P_{t+1}]$! In general, the correct statements are: $P_t = \frac{E_t^Q[P_{t+1}]}{R_f}$ where $Q$ ...

3

We know that: $$R_{t+1} = \frac{P_{t+1} + D_{t+1}}{P_t}$$ After some algebra and taking logs we can write the returns as: $$r_{t+1} = k + \rho (p_{t+1} - d_{t+1}) - (p_t - d_t) + \Delta d_{t+1}$$ where is constant $\rho = \frac{P/D}{1+P/D}$. or: (p_t - d_t) = k + \rho (p_{t+1} - ...

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You might find this paper interesting: "Does Finance Benefit Society?" It's a very complicated question and in my opinion the above paper provides a nuanced answer.

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At what scale do you see kurtosis? Daily data? Single stocks or indices? Let us not look at single stock data, because you always find crazy stocks whose price process breaks all rules. Talking about daily data of indices: they could be thought of the sum of hourly returns or other returns of high frequency (minute returns, milliseconds ...). What are the ...

3

I think there are a few conflating ideas here. With respect to the sum of logs idea, I think you're thinking about infinitely divisible distributions (https://en.wikipedia.org/wiki/Infinite_divisibility_(probability)). These ideas are indeed used to build more complicated models (i.e. Levy processes) for asset returns. With regards to the Efficient Market ...

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There are different methodologies to detect a change in the market efficiency, both in the market and firm-specific cases. In the FIRM-SPECIFIC case, the most common procedure is the event study methodology; you can find how to construct an event-study case explained in Kothari & Warner (2006), who collected all the event study methodology implemented ...

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The subordinate return process for log returns is normal (or Gaussian). The kurtosis stems from the "activity rate" of events that move asset prices. When we measure in "clock time" we see kurtosis. However, when we measure in "event times" or "business times" the distribution is normal. The "event time" is a subordinator. Substitute "event time" for "...

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I have a paper that argues that the distribution of returns cannot have a mean. I argue that prices are data and that returns are not data. Rather, returns are transformations of data. Therefore, it is the statistical distribution of prices that must determine the distribution of returns. Since returns are $$\frac{p_{t+1}}{p_t}-1,$$ it follows that ...

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Please see the papers below: Sebastián A. Rey, Non-Arbitrage Valuation of Equities. International Journal of Financial Markets and Derivatives (2015) vol. 4, no 3/4, p. 231-245 http://www.inderscienceonline.com/doi/abs/10.1504/IJFMD.2015.073472?mobileUi=0& Sebastián A. Rey, The Valuation of Equities and the GDP Growth Effect: A Global Empirical Study. ...

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In high-frequency energy trading, it's possible for a trader to have hundreds of orders in the book, possibly on more than one exchange, e.g. ICE and NYMEX. A trader may be running dozens of algorithms simultaneously. Each of these may respond independently to the changes it detects in the market data, as well as to the timing and fill data from its own ...

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What are some indicators that a given security might be inefficiently priced? What about efficiently priced (i.e., how can we estimate the degree of information already baked into price)? You would need to get lower level data than what was used in this paper that was referenced here. The MSF data is probably fine for the paper, but if you were to ...

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There is no mathematical proof of EMH. You would need all market participants to agree on a singular pricing model for that to be possible. Without a singular, agreed-upon model, what you are asking for is proof that people's collective opinions represent people's collective opinions. This is called a tautology. Tautology There is an endless number of ...

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The assumption that the discount rate should be derived from the IRR of an alternative investment is not correct. Commonly the WACC of the company (or the WACC of the funds needed for the investment if it is standalone) is used. If this is not available, you could make use of a combination of publicly available rates and some risk-adjustments: risk-free ...

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Assuming the CAPM*, the expected return $r_i$ of stock $i$ equals $$E[r_i] = r_f + \beta(r_m - r_f)$$ with $r_f$ as the risk-less rate of interest and $r_m$ as the return of the market portfolio. The expected market return $E[r_m]$ remains unaffected by changes in $r_f$ and still equals $r_m$. The expected return of a single stock $i$ from the formula above ...

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First, the semi strong form of the EMH (prices reflect all public information) corresponds to the returns being a martingale difference; GARCH is a martingale difference, so GARCH is compliant with the EMH. Second, you can look into the stylized fact of financial returns called "leverage effect", in short it says that returns have a negative correlation ...

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The weak form of the efficient market hypothesis (EMH) just says that the market is efficient to all prior information contained within price. By definition, the weak form of EMH obeys the Markov property such that the current state contains more information about the future state than all prior states combined. Thus, the weak form EHM is alone sufficient to ...

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To take a somewhat trivial example of an underlying asset subject to arbitrage pricing, we can think of options on futures. But I think you have deeper examples in mind. Structural models, such as Merton's famous 1974 model, treat equities themselves as derivatives. In Merton's case the underlying was the economic value $A$ of the firm's assets $A$ and ...

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Arguably the top 3 anomalies for FX (at low frequencies, i.e not HFT) are Carry, Momentum and Value, which are found in some markets other than FX as well. There is a vast literature on these. For Carry I recommend a survey by Swinkels Empirical Evidence on the Currency Carry Trade, 1900-2012 For Momentum in FX this link is good Quantpedia: FX Momentum "...

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You could try Market-maker, inventory control and foreign exchange dynamics by Westerhoff and follow the references...

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