March 4th, 2016

Randomness in Stock Prices

Will a game with 51:49 odds still show some randomness? YES, definitely, and a lot. Even if it has a positive expected value. The same goes for a 52:48 game, there would still remain a lot of randomness. It might not matter much how the data might be distributed, it would still be mostly random-like.

Does the classification of a quasi-random game require a Gaussian distribution? NO, not at all. It could be any other type of distribution with or without fat tails.

A 52:48 game has for expected value: 0.52*$1.0 - 0.48*$1.0 = $0.04 per dollar played. Such a game is won simply by betting all the time on the built in positive edge. And in such a scenario, what comes to matter most is not the distribution, but the bet size and the number of plays: n*(0.52*10000 - 0.48*10000) = n*400. Your expected cumulative gain grows linearly. If your bet size is too big compared to your stake, you will find that variance alone can cripple your play.

Whereas for a 48:52 game, we get: 0.48*$1.0 - 0.52*$1.0 = - $0.04 per dollar played. The kind of game offered by casinos. No one should wonder why the house wins.

On average, US stocks have had a long term 8-10% CAGR, dividends included. A 10% CAGR translates to 0.00038462 (0.038%) per trading day, on average. On a $100 stock, that is an expected move of $0.0385 for the day, and $10.00 for the year.

If only 4¢ of a $100 stock can be explained by its average expected secular trend, then where does all the rest of the price movement come from? Take a stochastic representation of price movement: dp = µdt + σdW. The µdt part is 4¢ a day. The σdW part is the random-like stuff.

How much randomness is there? Technically, as much as you can't predict. If you could predict on the random-like part with some accuracy, you could do wonders playing the game.

And since you can not predict with much accuracy, then ensues plenty of randomness. Much more noise than most would want to admit. And a lot less trading "skills" than some like to advertise.

Is a bet that your next flip of a fair coin is head a prediction? Or is it simply just a guess, a bet based on assumptions gathered from the probabilities of having observed millions of tosses of the same coin. Is it still a bet if you always bet the same? How about if you throw in outliers, gaps and black swan events which will distort your distribution, doesn't the picture change?

What if the bias really is 52:48 in your favor to start with? What should be your trading strategy then? The answer seems easy: one should continuously attempt to trade on the positive bias side. You could win by default, just by playing often, with no regards to the underlying distribution since you know the game is biased in your favor.

When you design a short term trading strategy, fundamentals won't come that much to your rescue, except in the stock selection process. Even then, initial, in the short term, you will have to make a bet, but don't think that you can say: in all probability, this stock will do so and so, when in fact, whatever reason you might say might just be coincidental.

The only way to show otherwise is for your system to generate thousands of trades based on your trading principles. And a long term simulation based in your trading rules should easily demonstrate this, at the portfolio level, thereby showing the value of your trading methods.

Otherwise, whatever you put out, whatever "opinion" you may express without some kind of evidence to substantiate your claims, I will take with a very large grain of salt and might even go as far as challenge your numbers or your methodology.

Note however that if I see really great numbers, they don't need to be high, I will be the first to congratulate you on your achievement, and if your trading methods are sufficiently interesting, I will also try to design a similar trading strategy based on the same trading principles in order to extract its core components for my own use.

See recent articles, especially the trading strategy experiment series, it might give you some ideas.


Created... March 4th, 2016 © Guy R. Fleury. All rights reserved. 

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