Expected Value: Upgrading Your Decision-making

31 March, 2021
Investing; Decision-making

What if I told you that I thought Bitcoin had an 85% chance of going to zero. And what if I also said that I was investing in Bitcoin.

In a similar vein, what if I told you I was bullish and yet short on the market.

Would you think I was crazy?

If so, then you’ve fallen for a trap that beguiles even the best investors.

The key is the difference between expectation vs probability.

To illustrate, let’s look at an example:

  1. Say a stock is $100.
  2. I think it has an 75% chance of going to $80 ($20 loss).
  3. I think it has a 25% chance of going to $300 ($200 gain).
  4. Expected value = 75%*-$20 + 25%*$200 = $35 profit.

I profit on average even if a stock has a 75% chance of decreasing.

This thinking motivates my investments in startups and early-stage cryptocurrencies.

Bullish or bearish are terms used by people who do not engage in practicing uncertainty … Accordingly, it is not how likely an event is to happen that matters, it is how much is made when it happens that should be the consideration - Nassim Taleb

Good Outcome ≠ Good Decision

The outcome is not indicative of the quality of the decision.

If you make money it doesn’t mean you made a good decision.

If you lose money it doesn’t mean you made a bad decision.

This is a counterintuitive but fundamental idea.

Let me explain.

I like to think of it like Russian Roulette.

If you play Russian Roulette and win, did you make a good decision? What if you play again and win?

Playing Russian Roulette is a bad decision, even if the outcome is favourable.

Investing is the same. You might invest in a $200 stock to see it go up by $100.

Was it a good decision to invest?

Not necessarily. You might have just been on the lucky end of a bad decision.

For example, let’s say the:

  1. Probability of the stock going up $100 was 5%.
  2. Probability of the stock going down $100 was 95%.
  3. Expected profit was -$90.

But in actuality, the 5% chance of going up is what materialised. Here you make money off a bad decision.

It’s a bad decision because making the same decision multiple times would lose money.

In a single decision you can be lucky. But over infinitely many decisions, luck disappears and the odds weigh in.

So for any single decision, a good outcome does not mean that it was a good decision.

The Paradox of Expected Value is that it's hard to know whether a good outcome was merely just the lucky end of a bad decision. Only in the long term can we 'know'.