Efficient Market Folks believe that price follows a random walk pattern, and hence any prediction into future price is impossible. In other words you dont have an “edge” to exploit. Technical “edge” i.e. The theory extends further more into saying, that all publicly made information is fully discounted into price, which implies that fundamental investing is dead. But then, salvaging fundamental investing from the grip of Efficient Market Hypothesis is not the agenda.

The agenda, precisely put is understanding what does trend mean and how to understand more about it. Efficient Market Hypothesis claims the daily price returns are fully normally distributed. That is the price follows a log-normal distribution.

Hence, the standard deviation of a sample of size N, will have $\sigma^{2} /N$

Now, interestingly, trending nature(which can be simulated by an Ornstein-Uhlenbeck Process) is when, the return on one direction is more than the return on other. That is, if a price asset is trending, it will have more instances of positive(or negative) returns than negative(positive) returns which generates a kind of “fat tail” distribution. A distribution which is not balanced around the mean.

So, in such situations, if we are able to find a price series with its variance more than a standard gaussian variance for a sample size of say $k$, then we can confirm that indeed we do have a trending asset.

Now, consider, if we have a price series, which is lognormally distributed. Its 1-sample variance (achieved by a simple 1 period difference in closing prices divided by the previous closing price-> squaring it up-> summing it up-> dividing by Numbers of Bars-1 {its an estimator} ) is say $\sigma$ then, ideally its 4 bar standard deviation will have $\sqrt{4}*\sigma$ which equals $2*\sigma$ .

If an asset which shows an $N^{2}$ period standard deviation more than $N$ times the 1 period deviation, we have a trending asset.

Any failure to do so, will give a fair idea as it being a “counter-trend” trading price series.

Going ahead,I have coded up a MATLAB code to do the same [you can get the code if you ask me for it].

Using this, let me analyse 800 period returns for three assets. US based S&P 500 based ETF (SPYDR),India based  S&P CNX NIFTY and NSE traded price series of Larsen and Toubro. If the reader wants me to analyse any further price series,do leave me a comment.

Each data set will be presented in the following way.

Expected Ratio* Observed Ratio**

Part 2 to be followed where the data will be analysed…
* Expected as in the case of Random Walk Theory (N^2 bar variance being N times a single bar return variance)
** Observed Ratio with N^2 bar variance divided by single bar variance