Portfolio Management: Number of Occurrences


When it comes to probabilities, we have to understand that there are winners and losers. Even if we have a 99% probability of success on a trade, one percent of those trades will still be losers over a very large pool of occurrences. Let’s say that we reach our true probability over 1000 occurrences. We could expect to see 990 winners and 10 losers. The question is - where will those 10 losers occur? Nobody knows, and that’s the importance of trading small.

Trading Small

Trading small and gathering a large number of occurrences play hand in hand. To put it simply, if we trade small relative to our portfolio size (<5%), we allow ourselves to obtain a larger number of occurrences and lower our portfolio risk per trade. If we have $100,000 and we trade very small and only deploy trades that are 1% of my portfolio, we are looking at a buying power reduction of $1000. This is very small, and puts us in a good position to thrive in the long run. Positions that go against us will not destroy our portfolio when trading this small. On the other hand, if we only have $10,000 and make trades with a buying power reduction of $1000, we’re using 10% of the portfolio per trade, which becomes problematic when we incur losses. Trading small allows us to stay alive when probabilities go against us. Over time, if we trade small we allow ourselves to reach our true probabilities of the trades we route.

Reaching True Probability

With a small number of occurrences, we would consider ourselves lucky if we actually reached our true expected probability. Let’s imagine we placed a trade with an 80% probability of success, and we only allowed ourselves 10 occurrences. To reach our true probability of success, we would have to have exactly 8 winners and 2 losers every time. With this small sample size, it’s too easy to have one trade go awry and alter our results. We could have 5 losers right from the beginning, or 10 winners in a row. Either way, it doesn’t give us a strong case for reaching our true probability.

Over a much larger number of occurrences, however, we would be very surprised if our realized results were far off from our expected probability. Taking that same trade example, if we had 10,000 occurrences, we would expect to see realized success be between 75-85%. The more occurrences we have, the closer we would expect this number to be to 80%.

We need to remember that we are trading in a random environment, and even though we have expected probabilities, it’s going to take some time to realize those results. Trading small, and eventually obtaining a large number of occurrences are two ways we can combat the random acts of the market, and ensure we maintain a proper amount of capital in our account.

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