I have recently read a lot of papers that proceeds to comment on inefficiencies in financial markets purely based on empirical evidence derived from methodologies grounded on nonlinear serial dependence. For this matter, isn't non-linearity a stylised fact across financial assets? Why and how does evidence of non-linearity disprove EMH?
Given that there can be several other non-fundamental reasons for the presence of non-linearity in an asset series (such as imperfect markets, exogenous shocks, clustered information arrivals, bubble components, active speculation, geopolitical as well as political factors among others), is it fair to conclude that a particular market is inefficient based on such evidence?
More importantly, can a theory be disproved based on the examination of real world data that does not exactly mimic/reflect the underlying assumptions against which the theory is built upon?
It would be very helpful to all if you could suggest some supporting literature that could further stimulate this discussion along with your invaluable comments.
This evidence and model need further replication to make conclusion or generalisation on the theory. But they may be possible explanation for the results depends on the economy event of that period.
EFFICIENT MARKET HYPOTHESIS had been criticized as something of an ideal that in practice is nearly not feasible to acieved. The attempts to reject EMH are mostly based on the "other reasons" which you are listed, not on the basis on non-linearity. For instance, Francis (1977), Basu (1985) and Rosenberg and Landstein (1985) showed that there is lack of support for strong-form of efficiency as predicted by the theory: weak, semi-strong and strong efficiency. They explain the failure on the basis on psychology of human behavior, i.e. herding, irrationality, over-confidence, etc.
FINANCIAL CRISES tell us that if EMH works, there would not be any financial crises. The facts say otherwise. The reasons are many, but non-linearity is not the main reason- - - it may be one of many pieces of evidence, but surely not the underlying cause.
LINKS:
Francis Nicholson. Price-Earnings Ratios in Relation to Investment Results. Financial Analysts Journal. Jan/Feb 1968:105–109.
Basu, Sanjoy (1977). "Investment Performance of Common Stocks in Relation to Their Price-Earnings Ratios: A test of the Efficient Markets Hypothesis". Journal of Finance. 32 (3): 663–682. doi:10.1111/j.1540-6261.1977.tb01979.x.
Rosenberg B, Reid K, Lanstein R. (1985). Persuasive Evidence of Market Inefficiency. Journal of Portfolio Management 13:9–17.
EMH come with some assumptions. Go through the EMH theoretical assumptions. Any irregularities from theory assumptions in relation to practices would provide evidence challenging the validity of EMH.
Dear George
I presume you are examining the EMH applying it to the CAPM. The CAPM is an ex ante model relating required return to the beta risk. Ex post (historical) results of the risk return relation that show a positive, or negative, alpha do not (dis)prove the EMH.
The EMH was originally conceived by Fama and others as a statement that market prices are martingales. This definition has been thoroughly discredited by among others, Andrew Lo, who first showed market prices are not random walks:
A Non-Random Walk Down Wall Street: Recent Advances in Financial Technology
FOUNDATIONS OF FINANCIAL BEHAVIOR AND ADAPTIVE MARKETS | 1997
Research Dialogues 52 (1997) TIAA-CREF
which was followed up by others showing they aren't martingales. Whether relationships are linear or not does not matter to this definition.
Of course, some have a more "intuitive" definition that roughly states that one cannot consistently earn above average profits. This idea is difficult to support in view of the stellar careers of a few investors and speculators like Warren Buffett and George Soros. The usual excuse for their successes is that a few investors among the millions would by chance alone, succeed. In my view, that argument fails if one analyzes the reasons for their successes.
My book "The Strategic Analysis of Financial Markets" (World Scientific, 2017) shows that even theoretically, markets should not be efficient in either of these senses, and develops another way to think about them. The book is very briefly summarized in https://ssrn.com/abstract=2925532.
In contrast to the PDE approach to pricing, martingale pricing formulae are in the form of expectations which can be efficiently solved numerically using a Monte Carlo approach. As such, Martingale pricing is preferred when valuing high-dimensional contracts such as a basket of options. On the other hand, valuing American-style contracts is troublesome and requires discretizing the problem (making it like a Bermudan option) and only in 2001 F. A. Longstaff and E. S. Schwartz developed a practical Monte Carlo method for pricing American options.
Suppose the state of the market can be represented by the filtered probability space, {\displaystyle (\Omega ,({\mathcal {F}}_{t})_{t\in [0,T]},{\tilde {\mathbb {P} }})} (\Omega ,({\mathcal {F}}_{t})_{t\in [0,T]},{\tilde {\mathbb {P} }}). Let {\displaystyle \{S(t)\}_{t\in [0,T]}} \{S(t)\}_{t\in [0,T]} be a stochastic price process on this space. One may price a derivative security, {\displaystyle V(t,S(t))} V(t,S(t)) under the philosophy of no arbitrage as,
{\displaystyle D(t)V(t,S(t))={\tilde {\mathbb {E} }}[D(T)V(T,S(T))|{\mathcal {F}}_{t}],\qquad dD(t)=-r(t)D(t)\ dt} D(t)V(t,S(t))={\tilde {\mathbb {E} }}[D(T)V(T,S(T))|{\mathcal {F}}_{t}],\qquad dD(t)=-r(t)D(t)\ dt
where {\displaystyle {\tilde {\mathbb {P} }}} {\tilde {\mathbb {P} }} is the risk-neutral measure.
{\displaystyle (r(t))_{t\in [0,T]}} (r(t))_{{t\in [0,T]}} is an {\displaystyle {\mathcal {F}}_{t}} {\mathcal {F}}_{t}-measurable (risk-free, possibly stochastic) interest rate process.
This is accomplished through almost sure replication of the derivative's time {\displaystyle T} T payoff using only underlying securities, and the risk-free money market (MMA). These underlyings have prices that are observable and known. Specifically, one constructs a portfolio process {\displaystyle \{X(t)\}_{t\in [0,T]}} \{X(t)\}_{t\in [0,T]} in continuous time, where he holds {\displaystyle \Delta (t)} \Delta (t) shares of the underlying stock at each time {\displaystyle t} t, and {\displaystyle X(t)-\Delta (t)S(t)} X(t)-\Delta (t)S(t) cash earning the risk-free rate {\displaystyle r(t)} r(t). The portfolio obeys the stochastic differential equation
{\displaystyle dX(t)=\Delta (t)\ dS(t)+r(t)(X(t)-\Delta (t)S(t))\ dt} dX(t)=\Delta (t)\ dS(t)+r(t)(X(t)-\Delta (t)S(t))\ dt
One will then attempt to apply Girsanov theorem by first computing {\displaystyle {\frac {d{\tilde {\mathbb {P} }}}{d\mathbb {P} }}} {\frac {d{\tilde {\mathbb {P} }}}{d\mathbb {P} }}; that is, the Radon–Nikodym derivative with respect to the observed market probability distribution. This ensures that the discounted replicating portfolio process is a Martingale under risk neutral conditions.
If such a process {\displaystyle \Delta (t)} \Delta (t) can be well-defined and constructed, then choosing {\displaystyle V(0,S(0))=X(0)} V(0,S(0))=X(0) will result in {\displaystyle {\tilde {\mathbb {P} }}[X(T)=V(T)]=1} {\tilde {\mathbb {P} }}[X(T)=V(T)]=1, which immediately implies that this happens {\displaystyle \mathbb {P} } \mathbb {P} -almost surely as well, since the two measures are equivalent.
Dear Prof. Varghese,
And other readers of course, EMH is a statistical property of the market data, while linearity is a mathematical property, the two do not have the same domains in scientific fields as we have proved in our proof of the P vs. NP problem, roughly because one depends on the other for definition (Mallick, Hamburger & Mallick (2016, 2017, 2018)) hence direction of change which are based on graphs.cannot be defined without the other defining the domain of fields This applies to financial formulas and market data as they are based on the same principles of continuity (Mallick et. al.)).
Soumitra K. Mallick (CA)
for Soumitra K. Mallick, Somak Raychaudhury, Sandipan Mallick
of RHMHM School,
USA, Japan, India
Five statistical analyses are conducted in an attempt to explicate such apparently contrary convictions. An analysis of daily, weekly, monthly and annual Dow Jones Industrial Average log returns found that first-order autocorrelation is small but positive for all time periods, with the autocorrelations for daily and weekly returns closest to zero, and thus an efficient market. A standard runs test showed that the hypothesis of independence is strongly rejected for daily returns, but accepted for weekly, monthly and annual returns, whilst the results of a more sophisticated runs test showed that daily, weekly and decreasing returns are the least consistent with an efficient market. Rescaled range analysis was conducted on the same data sets, and there was no significant evidence for the existence of long memory in the returns, a result consistent with market efficiency. Finally, from an analysis of investment newsletters it may be concluded that technical analysis---as applied by practitioners---fails to outperform the market. I reconcile the fact that daily stock market log returns pass linear statistical tests of efficiency, yet non-linear forecasting methods can still generate above-average risk-adjusted returns.
Dear George Varghese,
Nonlinearity in financial data is a characteristic of the nature of financial assets (that is, a mathematical property and stylized fact).
Hence, accepting or rejecting EMH (which is a statistical property of financial data itself) depends on many factors and parameters in testing for the different kinds of market efficiencies (weak, semi-strong and strong).
Please refer to one of my coauthored research paper regarding market efficiency. It was published in International Review of Financial Analysis 19 (2010) 47–54.
Al Janabi, Mazin A. M., A., Hatemi-J, M., Irandoust, “An Empirical Investigation of the Informational Efficiency of the GCC Equity Markets: Evidence from Bootstrap Simulation”, International Review of Financial Analysis, Vol. 19, No. 1, pp. 47-54, 2010.
[Publisher: Elsevier, Inc.]
Authors: Mazin A.M. Al Janabi , Abdulnasser Hatemi-J, Manuchehr Irandoust
Best Regards
Prof. Dr. Mazin A. M. Al Janabi
Full Professor of Finance & Banking and Financial Engineering
Tecnologico de Monterrey, EGADE Business School,
Santa Fe Campus, Mexico City, Mexico.
Hi. If I may suggest George Varghese the evidence in support of stock depandance whether trend is linear or non-linear can be a possible explanation of inefficiency in the asset market. The robust the evidence is, it challenges the EMH theory in a stronger way. You may base your thought process over dependence in price data or serial correlation in asset prices. I believe EMH can be challenged along these lines. Non-linearity can be caused by other factors which are not akin to market inefficiencies. You may start here Fama, Eugene F., and Kenneth R. French. "The cross‐section of expected stock returns." the Journal of Finance 47.2 (1992): 427-465. Fama and french themselves challenged the EMH.