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Saturday, February 8, 2014

Schrödinger's Cats, An Android Game Showing the Transient Nature of Notional Profits in Individual Stocks

Here is a simple and very nice Android game which helps understand the transient nature of profits in individual stocks.

Get it for your Android device from google play store at:

The game involves selecting a radioactive element to represent your cat (for Schrodinger's cat thought experiment). To play practically, select any element and its isotope which has close to 1s half-life. 700ms is reasonable time that we take to close the box and open it.
After selecting the cat (radioactive cat :)), close the box. Then wait a 100ms and open it. You will be in for a surprise. The cat might have decayed to death or alive and going out showing you a score. If you waited for half-life time which is say 700ms, then you will get a score of 50 with a probabiliy of 50%.
That is what is half-life about. In that time period, 50% is the probability of the radio active element to decay. In other words also, if you have N number of cats, after 700ms, only N/2 will be alive.

Coming to profits from stocks as well it is an interesting thought experiment. I ended up playing it many times and had little fun while reinforcing the idea of transitory stock price movements. Especially it just happened many times in the last two years that my profits in stocks got evaporated the longer and longer I held them.

If T is defined as holding period on a specific individual stock:

When T---->infinity,

theoretically any stock will give you zero gain,

practically any stock will give you more than 50% loss

Also say, doubling the T will double the x% gain to 2x% on capital. But then it is not better than getting x% on one stock in first T time and then again same x% on another stock in same T using the entire proceeds from first trade, due to compounding. It is adjusted in this game as score which never reaches 100, which is equivalent to T=infinity or profit = unlimited % say 90000000%.

Very rarely you will hit a score above 90 for which you need to wait for T <= 4 x half-life. Most probable score is close to 50 and optimal time T ~= 1 x half-life for this score.

I will update this post soon with some more thoughts.

Update: I’m sorry for this really late update.
As we can now see, the score in this game can be increased in multiple ways but the rate of growth of score in each strategy is different. And there is an optimum one that gives fastest rate as I explain below.

To increase the score faster, you would want to maximum score per trial and also minimize the time taken per trial.

To get the score of 50, time taken is T. To get score of 75 time taken is 2T and for 88 time will be 3T. There is a trade-off here because the relationship between time and score is non-linear. If you spend T/2 time before opening the box, it doesn’t mean you will get a score of 25. However we are limited by the minimum time it takes to click the screen. We will face some limitations in stock market as well, hence we will not assume using a robot to test theoretically possible best rate of increasing score.

So taking an isotope with half-life that is close to 1s or 700ms is the best choice. In case we take higher half-life, we have to wait for more time to get even score of 50.

Now with this min. practical T, we can calculate that scoring 50 with one half-life time gives the fastest rate for score. However one more thing to note here is also that even if we were to wait for 4T to get a score above 90, there is probability issue. Probability comes down to 1/16 to get that score if we wait for time of 4T. That means 1 out of 16 trials involving a time of 4T give a score of 90 while the rest give score of 0.

This way even if were to decide to choose an isotope whose half-life is 1/4s so that 4T is 1s we still have low probability which reduces the speed of scoring. Hence we end up with the half-life of 1s and score of 50 with time of T.

Same way in stock market, we can view stocks as becoming radioactive during certain times when we say they are in uptrend. We can find uptrending stocks at any time but we cannot grow our capital fastest by trying to squeeze the profit from each uptrend. In any uptrend, there is an optimum amount of profit that comes in the least holding time. I usually find this as the time period which contains two weeks of concurrent gains of more than 10%. Beyond that whatever you may end up getting can be considered as bonus which may not practical to take in each trade. Because trends can end pretty fast sometimes.

Stock may get a bad news or broader market may get a fresh downtrend or Fed may stop Quantitative Easing etc. There are N number of things outside our control. It is best to take some profit out of a stock once it starts trending. But we need to know how much to take.

Taking too less is not good. It is not always that we will make profit in a trade. Sometimes despite our best practices we can end up with an unfortunate trade that goes very bad. I had many such experiences including Shasunpharma, Max, Mahindra Ugine etc. To cover them, we need to earn some margins. Hence we need to have a policy for optimum profits from each up cycle.

On the other hand, it can happen that we sell a stock for a handsome profit but still it continues to go up and up. It happened for me with MPSLTD that went to heaven few weeks after I sold for 50% profit. We can consider such a trade as a rare event like the 4T waiting time case that happens with 1/16 probability.

The cat you just opened alive in time T giving you a score of 50, probably may still be alive after another time of 3T while increasing your score to 90. But that is only in 1 out of 8 instances (getting 50 itself is once in 2 chances, so conditional probability of getting 90 score after knowing that cat was alive after 1T is 1/8).

This means that if I had closed a stock with a profit of 50%, and the chance that the same stock would continue to go up by another 150% is like ¼ or 1/8. That means one out of say 6 stocks may end up doing very good if I don’t take that 50% profit but continue to hold it. But in the rest of 5 stocks that I don’t book the 50% profit, I may lose all or most or some of it.

What happens with amateur traders is that they end up taking a bad lesson from it. They consider their taking 50% profit as an early mistake (actually here I waited for almost 1 year). Now making 50% profit in a stock in close to one year time a bad deal? I don’t know about you, but I don’t have a damn reason to regret about it.

There are, another class of traders who chase such stocks. After they take a profit early, they enter the same stock again at higher price than they sold seeing that it is strong and going up only. Then they sell too early thinking they can buy it again for lesser price after a “surefire” pullback which doesn’t happen. On top of that the stock flares to even higher levels catching our trader again at even higher level than they just sold recently. As the trader continues chasing game, the stock loses its steam at some point and starts some serious pullback. The trader gets trapped as he/she is habituated to trading for small profits/losses, but this one turned out to be big trap because big rises can have correspondingly big pullbacks. If the trader is lucky in the rarest of circumstances, he/she may exit at a profit again and never look at that stock again.

In the stock market, like life, there are some lessons that must be learned and some that must not be. A mistake is not decided after the fact. You can not keep learning, relearning, relearning, and relearning and so on.

Learning in the stock market is fractal in nature. What you learn in the first year of your practice you will not learn much different from it in the first 5 years or first 10 years. I can tell this from my experience. This very particular thing about learning some lessons and not some others, I had learned in my first year itself. But then the years of experience will evolve your knowledge and skills. You learning goes up in a spiral not like a straight line. After-all this world is made in a spiral. The shape of galaxies, DNA coils, kundalini charkas, etc.

If you have not learnt some of these things atleast with some little perspective in your first year of trading, then you have a long time to go in this endeavor with ups and downs. Or you can pace up by introspecting and increasing the focus on this path. I too sure had some things that I haven’t grasped in the beginning years. Certainly networking with other stock traders helped me get some new perspectives that I didn’t learn on my own.

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