Expected Return

How much an investor thinks they will likely make from an investment.

It may seem like a guess. Like...a lotto player's expected return might be $300 million. Their likely return is a loss of $1. But they expect a lot more. That's expected return.

For savvy investors, the process for determining expected return is more rigorous. It's not "hoped-for return" or "wouldn't-mom-be-proud-if-I-earned-this-much-and-finally-moved-out-of-the-basement return."

Basically, the investor figures the possible outcomes of an investment and the likely return. Situation 1, you make a 10% return. Situation 2, you double your money. Situation 3, you lose everything.

The investor then calculates the likelihoods for each outcome. Situation 1 is 70% likely. Situation 2 is 20% likely. Situation 3 is 10% likely.

They multiply the various likelihoods by the corresponding returns for those events. Situation 1 becomes 0.07% return. Situation 2 becomes a 0.2% return. Situation 3 becomes a -0.1% return.

Add that all together (0.07 + 0.2 + (-0.1)) and it gives the expected return for a particular investment. In this case, the expected return would be about 17%.

Think about roulette. Each number has a 1/38 chance to come up. The numbers pay 35 to 1 if you hit. You put $5 on number 22.

You've got a 2.63% chance of making $175. Meanwhile, you've got a 97.37% chance of losing $5. So multiply 0.9737 by -5...that's the situation where you lose. The figure you get is -4.8685.

Now, look at the winning situation. That's 0.0263 times $175. You get $4.6025.

Now add the two together. $4.6025 + (-4.8685). The answer is -0.266. Your expected return is a loss of about 27 cents each spin.

Not a great investment. Unless you're the casino, of course, in which case you reverse the signs on all those cases and run the math again. The casino gets an expected profit of about 27 cents on each $5 bet on an individual roulette number.

Figuring out these chances for a real-life investment can take some estimation and guesswork. The numbers in roulette are easy to figure out because there are a fixed number of outcomes that have easily discernible odds. A real life investment (buying shares of a biotech startup, or going short on Swiss franc-denominated bonds) are less straightforward.

But then, that's why mutual funds and hedge funds have Stanford/CalTech/MIT League-Caliber mathematicians and statisticians to get as close as they can.