Suppose we make a deal. You’ll give me $1 and we’ll flip a coin. If it comes up heads, I’ll give you nothing. If it comes up tails, I’ll give you $5.
This is clearly a good deal for you. In fact, you can calculate exactly how good. 50% of the time, you get nothing. 50% of the time, you get $5. So, you are spending $1 to get something that on average is worth $2.50. The risk and reward are asymmetric–you are risking far less than you are likely to get back.
That doesn’t mean that when we make this deal, you will win. Half the time you’ll lose your dollar. But if you play this game over and over, with me or other people, you’ll win over time. Finding these sorts of asymmetric bets is one way to get rich.
Bringing it back to optionality
In life, the optionality I discussed in my last post is often closely related to asymmetric bets. You don’t want to burn bridges because the benefit of burning a bridge is often low (momentary pleasure at telling someone to get lost?), while, sometime in the future, the value of that bridge might end up being high (e.g. an acquaintance helps you find you a new, high-paying job). Not burning that bridge both maximizes optionality and is almost always an asymmetric bet because the cost is so low that almost any future gain would be larger than the cost.
When you start to apply this sort of reasoning to your finances, it suggests a simple strategy to make money. Look for opportunities where there are a variety of outcomes, but you can determine roughly what the expected value of the outcomes is. Then, pay less than that value
In poker, as in life
Poker professionals have figured this out. Texas Hold’em has four rounds of betting. In the first round, you have only two cards, and the ultimate value of your hand is very uncertain. In the second round, the ultimate value of your hand is far better defined. The third and fourth rounds can improve your hand, but more often than not, do not impact it.
This seems straightforward, but things get tricky when you actually start playing. If you look at the odds, against one opponent who has two random cards, you are over 50% likely to win with a King and a Four of different suits. You’re only 43% likely to win with a Seven and a Six of the same suit. So, with a naive strategy, you’d want to play the King/Four and fold the Seven/Six.
But among professionals, the opposite is true.
The seven/six has good potential to make powerful hands like straights and flushes, and, when it makes one of those hands, the payoff can be large. What’s more, when it doesn’t make a powerful hand, it will be a clear loser, and making it easy to cut your losses. The king/four has the opposite issue. It will win the majority of the hands, but most of the time, it won’t make a flush or straight that is an obvious winner.
So, professionals recognize that it’s worth wagering a small amount on the Seven/Six because of the optionality it provides and the asymmetric risk and reward. If they hit a great hand, they have the option to bet large amounts and win a large pot. If they don’t hit, they can just give up, costing them very little. With the king/four, even though they win most of the time, their hand will almost never be strong enough that it is worth the risk playing a large pot.
Thus, the poker pros are correctly valuing six/seven higher than the king/four because of its optionality, despite the latter being more likely to be an ultimate winner.
The valuation problem
The biggest challenge of using this strategy in real life (as opposed to gambling) is that it is often difficult to determine the value of an option, since it depends on the probability and value of all possible outcomes. Often, it’s difficult enumerating all the outcomes, let alone accurately estimating the probability of each one. If you can’t decide on how likely a single outcome is, how can you hope to ever value the aggregate of a bunch of outcomes?
For instance, suppose you’re trying to decide whether or not to invest in a start-up company. It could fail. It could succeed, but never be big. It could become big. Or it could become the next Apple. How do you know how likely each one of these possibilities is?
The answer is that it doesn’t matter.
You don’t need to be accurate, only roughly right. After you’ve come up with an estimate for the fair value of the option, build in a margin of safety by paying far less for the option than your estimate. That way, even if you’re incorrect about the probability or value of one or all of the outcomes, you are still in a good position. And, if you’re a pessimist, your valuation estimates might be on the low side rather than on the high side, leading to even greater gains.
By paying far less than the option is worth, you’re ensuring that the risk/reward is asymmetric and in your favor.
The bottom line
Optionality often leads to opportunities for asymmetric risks and rewards. People in general seem to underestimate the value of these opportunities, but if you are aware of them, you should be able to profit.
In my next blog, I’ll talk about some of the challenges in searching for these sorts of asymmetric opportunities and give examples of places where you might find them.
Deconstruction 