{"id":217055,"date":"2025-01-07T10:58:04","date_gmt":"2025-01-07T15:58:04","guid":{"rendered":"https:\/\/ibkrcampus.com\/campus\/?p=217055"},"modified":"2025-01-07T10:58:13","modified_gmt":"2025-01-07T15:58:13","slug":"trading-101-understanding-the-expected-value-of-uncertain-bets","status":"publish","type":"post","link":"https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/trading-101-understanding-the-expected-value-of-uncertain-bets\/","title":{"rendered":"Trading 101: Understanding the Expected Value of Uncertain Bets"},"content":{"rendered":"\n

The post \u201cTrading 101: Understanding the Expected Value of Uncertain Bets\u201d first appeared on Robot Wealth<\/a> blog.<\/em><\/p>\n\n\n\n

Industry veterans sometimes remark that successful gamblers tend to make good traders, and engineers tend to make lousy traders.<\/p>\n\n\n\n

This is a gross generalisation, of course, but one reason is that trading, at the most fundamental level, is a game of pricing uncertain outcomes. This requires probabilistic thinking, and engineers tend to be trained to think deterministically.<\/p>\n\n\n\n

Indeed, thinking probabilistically is hard for most people.<\/p>\n\n\n\n

That\u2019s why so much retail trading tends to involve buying when the news is good and the price is increasing, and selling when the news is bad and the price is decreasing.<\/p>\n\n\n\n

That\u2019s deterministic thinking, and we\u2019re good at that because we evolved that way \u2013 there isn\u2019t much need to think probabilistically when you are trying to avoid being eaten by a bear.<\/p>\n\n\n\n

On the other hand, a more thoughtful assessment of probabilities is hard. If you like money, however, you\u2019re going to need to learn to think probabilistically.<\/p>\n\n\n\n

How do we \u201cthink probabilistically\u201d?<\/em><\/strong><\/p>\n\n\n\n

Let\u2019s go through the basics.<\/p>\n\n\n\n

Imagine someone is offering you a game. You roll a dice. If you roll 5 or 6 then you get $1,000. If you roll any other number you get nothing.
<\/p>\n\n\n\n

What would you pay to play this dice game?<\/em><\/strong><\/p>\n\n\n\n

Well, this is a risky game, and most people don\u2019t like playing games in which they can lose money. But, to start with, at least, let\u2019s assume that you don\u2019t mind taking risks and you are only interested in maximising the expected value of the bets you take.<\/p>\n\n\n\n

First, you must work out the price at which you are indifferent to playing the game.<\/strong><\/p>\n\n\n\n

If you don\u2019t mind taking the risk, then the price at which you are indifferent to playing the game is the price at which you break even over the long term playing it. You want to play the game if it\u2019s cheaper than this value, and you want to pass if it\u2019s more expensive.<\/p>\n\n\n\n

How do I calculate that?<\/em><\/strong><\/p>\n\n\n\n

It\u2019s simple (in this toy example, anyway.)<\/p>\n\n\n\n

You write down all possible outcomes of the game, and for each possible outcome you write down:<\/p>\n\n\n\n