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Game of Probability

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If you invest for long enough, people will tell you that investing is, ultimately, a game of probability. The objective is to have more winners than losers in your portfolio. So how can investors increase your win odds in investing? Before we move on, we have to understand the expectancy formula:

Expectancy = (Win Probability x Average Win) – (Loss Probability x Average Loss)

The Expectancy formula is mostly used by traders, but it can be helpful for investors to understand it well. Let me illustrate expectancy through a coin toss game:

Imagine tossing a coin. If the coin shows heads, you earn $2. If it is tails, you lose $1.

Question: After 100 tosses, what are your odds of being profitable at the end?

Take your time to think about it.

The answer is 100%. That means after 100 tosses, you will end up profitable all the time. Why?

Based on probability, your chance of getting a heads or tails is 50/50. After ten tosses, you might get eight tails and two heads. If you do the math, you’ll realize that you’re losing $4 at this point. You might even start questioning whether the odds are really 50/50 since you are losing money.

But you have to understand that in order for the odds to even out, you must have a much larger sample size. Ten tosses are too small a sample size, but after 100 tosses, the law of averages will kick in.

So let’s input the data into the expectancy ratio:

Expectancy = (50% x $2) – (50% x $1) = $0.50

This means, on average, you expect to earn fifty cents per coin toss. After 100 tosses, you will earn $50. If you don’t believe this, flip a coin a hundred times in your free time and note down the results. You will always end up profitable after 100 tosses.

The point is that the vast majority of people have a natural tendency to want to be right all the time, but from we have already seen, what truly matters is your expectancy. Even if you right only half the time, you can make money over time as long as your expectancy is positive. Hence, the goal here is to increase your overall expectancy. Here are three ways to increase the expectancy in your investing:

1. Increase Your Win Probability

In the coin toss game, the win probability for every toss is 50%. No matter how a person tosses, the odds are always 50/50. But with investing you have far more control over your win probability. You increase your win rate by simply investing in companies that are fundamentally and financially strong, have good growth prospects, and led by a team of talented managers. By investing in great companies, you increase the probability of your investments being profitable.

2. Invest in Optimal Risk/Reward Situations

The other factor that affects your expectancy is your average win and loss. In the investments you make, you always want to ensure that your average win is greater than your average loss. This links to the risk/reward ratio. If you expect a risk/reward ratio of 1:2, which means you will only invest when the reward is worth double the risk.

A great way to achieve this is to invest in a stock when its price is 50% below its intrinsic value. The cheaper you buy a stock (assuming it’s a great stock!), the higher your potential upside and the lower your potential losses.

3. Be Consistent with Your Position Sizing

In order for your expectancy to be consistent, your position sizing must also be consistent. This means if you have ten companies to invest in, you should invest 10% of your capital in each stock equally. If your win probability is 70% and your average win is greater than your average loss, you will definitely make money overall.

However, if your position sizing is inconsistent and you assign 50% of your portfolio to one stock and the rest to the remaining nine stocks, your results can now be skewed. If something disastrous happens to that one stock, it will hurt you badly and take a long time for you to recover from your losses. This is also why many investment professionals recommend investors to diversify your stock portfolio and not bet everything on a single horse. So keep your position sizing consistent.