Looking ahead: probability
After finishing all the exercises two days ago, and spending the last two days doing the review exercises they automatically assign on a daily basis, the situation looks like this:
The limited activity shown by the chart in the last two days, caused by the progress I made (there are no new exercises left), explains why I am feeling restless and looking for new tasks.
Given that I plan to resume real trading in one month (with my own very limited savings), in the next few weeks I want to do these two things:
1) stop monitoring (on the weekly update) what we would have done had we kept trading (with the investors) the previous combination, as I did until
here, and start monitoring how well I would be doing if, week after week, I were trading what seems the best combination (with the limited funds I have), which is the four systems I've kept mentioning for the past two months (2 ZN, 1 NQ, 1 GBL system). I will start doing this tonight, with the usual weekly update, which will therefore go from "previous combination we stopped trading" to "future combination I will start trading in a month". I say this to remind myself that I need to write a note explaining why the chart looks so different all of a sudden. This new weekly update will make me aware of potential new problems.
2) Since the review exercises are showing that I still have not fully understood all the material covered (I still make mistakes in about 20% of the exercises, mostly due to distraction, but also due to errors in logic and lack of complete understanding), I will keep working on khan academy, and that will require some effort, but, since it won't keep me busy all the time, I should start looking for what seems to be the next step: a course in probability and statistics.
Khan has probability videos right on his web site, but there are no exercises, so I want to find one that has exercises, and the only one that I have found so far is here:
MIT OpenCourseWare | Mathematics | 18.05 Introduction to Probability and Statistics, Spring 2005 | Home
It's not as student-friendly as Khan's material for math, so before I start doing, I'll keep looking on the web for something better. But if I don't find anything, I'll probably start with that. And even though the material is not student-friend, it will be easier to do statistics than it has been to do trigonometry and even the long division (since I started from 1+1=2 to go all the way to calculus), because it has immediate utility for me.
One question that comes to mind immediately and that I hope I'll be able to address if not answer is the following. I often think: if I trade this combination with this capital, it will be very unlikely that I blow out my account, and it will be very likely that I will make money. But how do I go about defining how likely is "very unlikely" and "very likely"? I don't expect a precise answer from a probability course, but it will probably give me a better background to address the issue. Until now I've proceeded by rule-of-thumb, and it would be nice to know how far I can go in defining risk and return.
Another example. It is clear that the fact that a system has worked for ten back-tested years and for two forward-tested years is not a guarantee that it will work in the future. However, I wonder if I can get a framework, logic, mental structure, for understanding how to go about making estimates of how reliable past statistics are in predicting future statistics (which in my case can be called "results" as well).
If at the end, nothing will still be better than rule-of-thumb and guesstimates, well, then too bad, but it was worth checking. For sure it's better to use rule-of-thumb than unreliable formulas. As they say, a little knowledge is a dangerous thing, so if I find that formulas are not effective, then I'll go back to rule-of-thumb, because the objective is to make money and not to give lectures on statistics.
Also, let's not forget that when in doubt, you can just
underbet (but then the problem is relative to what), and you will simply make less money, whereas if you overbet, then you will blow out your account, no matter how small your mistake. So it's better to be ignorant, and, knowing it, to proceed by guesstimates and underbet, than to think you've got it all figured out, push your risk too far with supposedly scientific methods, and then blow out your account, because you were slightly off. This reminds me what we did in the past year. The scientists told me what to do, a scientific method, I blindly followed them, implementing with enthusiasm their portfolio recipe, and we were all wrong. As mentioned, we used curve-fitting of historical performances, and selected an over-optimized portfolio, that delivered great returns with little losses, but worked that well only in the past. It was not an unprofitable portfolio but its drawdown was much higher in the future than what it was in the past, and this because we selected it by testing hundreds of potential portfolios (using Palisade's RiskOptimizer, which at the time I considered a great idea).
Probability might help me notice these mistakes we made recently, which I didn't even notice, maybe because I was working too hard to be thinking. But in general my handling of risk has always suffered from too much optimism. I've always pushed risk too far, whether on my own or with others. So, a course in probability can't hurt. Now I need to find something I can afford to complete. I don't want to get started doing something I will not end. I am not sure about this MIT course. It doesn't look friendly enough. On the other hand, a course is better than gathering material here and there, because in that case, I'd be missing out on things, but also I might get lazy and not finish the task and study the things I have to study.
