If you are presented with a bet, you can calculate your expected winnings (the amount you’ll earn on average each time you bet) by multiplying the probability of winning times the amount won per bet and then subtracting the probability of losing times the amount lost per bet.

Let’s say I offer you two different bets:

There is a bag of 100 marbles. One is red and 99 are green. For every dollar you bet, if you pick a green marble I’ll pay you 1.02 dollar. If you pick red you lose your dollar. The expected return works out to you earning on average 1 dollar every time you bet. Basically 99 times you’ll earn 102% and once you’ll lose 100%. So for every bet you make you will earn a 100% return on average.

There is a bag of 100 marbles. 99 are red and one is green. For every dollar you bet, if you pick a green marble I’ll pay you 199 dollar. If you pick red you lose your dollar. The expected return works out to you earning on average 1 dollar every time you bet. Basically 99 times you’ll lose 100% and once you’ll earn 19,900%. So for every bet you make you will earn a 100% return on average.

The expected return of the two bets is the same. Therefore, in theory, you should be indifferent between the two bets, especially if you’re allowed to make the bet over and over again so that the long term probabilities play out.

But what if instead you had to bet your life savings on one of these two options? Most everyone would pick bet #1. This is because if you bet everything and lose, you won’t get a chance to bet again (because you’ll be broke). You’ll never get to the long term. In other words, when deciding which bet to make, you only really care about the expected return. But if you are trying to decide how much to bet, you also need to take into account the likelihood of winning.

Interestingly, almost every Wall Street research report will address the expected return portion of the equation. “We think this stock can get to 100 dollar over the next 12-months,” “our price target for the stock is 75 dollar, ”we think the stock can double over the next three years.” But while these types of forecasts are part of every discussion of every investment opportunity, the standard stock research report makes no mention of the probability of success. For that matter, despite the industry generating an extraordinary volume of research on which stocks to buy, the literature on how much of each stock to buy is unbelievable thin. Yet how much of a stock to buy is a decision that needs to be made every single time any investor makes an investment.

How likely an investment is to pay off at or better than your estimate of its expected return must be a key input to position sizing. But estimating this probability is difficult and the best process varies depending on your investment strategy and in particular your time horizon.

For a short term oriented investment strategy in which an investor makes investments based on known catalysts such as the probability that a biotech company will have a new drug approved, most of the attributes of the company can be ignored and the investor can focus on the specifics of the catalyst in question.

But for a long term oriented strategy in which an investor makes investments based on their assessment that a particular company is superior to competitors in its ability to generate cash flow, the catalysts are mostly unknown and so the probability of success must be estimated based on an assessment of the company itself.

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