Do you believe in market efficiency?
No. Perfectly constructed markets reflect the dollar-weighted opinions of participants with perfect efficiency. Even perfect markets do not predict the future perfectly. 1/ Perfect markets are an abstract ideal. Actual markets are sociological phenomena emerging from political, cultural, economic, ideological, religious and other institutions formed by individual and collective dialectics. All market constructs, whether bottom up or top down, have intended and unintended biases reflecting the values of the society they emerge from. 2/ Opinions are the explicit or implicit forecasts that motivate buyers and sellers. Opinions are similar to to utilities in economic theory, but distinct in that people actually have and use opinions.Routine transactions are essentially automatic. Standing in line at the grocery checkout you might overhear "ooh I love chocolate, this is so worth a trip to the gym!" However, unless you live on the south side of Chicago, you'll never hear "the utility of eating this chocolate bar right now exceeds the present value of the utility I'd derive from investing this dollar now and consuming more chocolate later." Actually, you wouldn't likely hear it there either because the utility curve for getting the snot beat out of you is slightly flatter among academics than the aggregate. Empirical studies of stock market anomalies began piling up as soon as the Efficient Market Hypothesis was introduced. These so-called "anomalies" are more accurately called empirical evidence that the stock market is not information efficient. The causes are partly institutional structures, inherent complexity, and intractable uncertainty. High value transactions are normally rigorously scrutinized. As often as not the decision process is identical to a small impulse buy except that once made, it is then supported with detailed charts, surveys and formal math. 3/ Market construction prevents perfect incorporation of opinions. Some example distortions include borrowing and lending restrictions, inside information laws and tax laws.IMHO
In which of the following markets should we expect efficient outcomes?
None of the above. It used to be thought that the financial markets, such as the stock markets (plural, there are many of them), were almost perfectly efficient. Clearly, as the current recession has shown, they too are far from efficient. http://en.wikipedia.org/wiki/Efficient-m...
What are some mathematical methods which are used to predict stock price movement?
To actually predict stock price movement, you are referring majorly to the Technical analysis part of investing domain. At a very basic level, you can use a large number of technical indicators which can be easily found by googling. Some of the popular ones are Bollinger bands, MACD, EMA(Exponential Moving Average), RSI (Relative Strength Index),Stochastic Oscillators etc. A complete list can be found at Simply the Web's Best Financial Charts One should keep in mind that these are applicable for a specific time frame. There are different models for HFT ,intra day or long term trading. If you are looking for more complex indicators to capture the price in a more precise manner, you can employ regression analysis, Autocorrelation function, GARCH Models, Regime shifting models like ANOVA, Markov Chains or any other Stochastic model etc. These tools require a better mathematical grasp of concepts of probability, stochastics and programming skills. Going deeper into prediction of stock price, for HFT, sentiment analysis, random forest, granger and kelly information criterion etc can be implemented. A lot of ML algorithms are being and have been tested by a number of hedge funds. Note : I believe that market is efficient to a large extent, hence it is quite probable the any of the existing mathematical models might not work if they have been tested by anyone before you. However it has been seen that tweaking the existing algorithm logically can lead to tremendous results. Hence, its always good to innovate on existing models rather than using them as it is.A blog by E. P Chan Quantitative Trading can also help you.