The Sunk Costs of Trading

by Annie Duke

When I was in graduate school studying cognitive Psychology, I learned about an error in the human decision-making process called sunk cost. This refers to resources, whether they are time or money or anything else, which has already been spent. The decision-making error is that people tend to take sunk cost into account when making present and future decisions.

The most common example of this occurs in recognizing how we behave when we wait in line. Think about the times you have been in a line for a long time, a line that is not moving, and you have other things to do with your day. If you were to walk up to the line right then and you saw that it was going nowhere, you would decide to come back later when the wait was not so long. However, because you've already been waiting for so long, you persist. Notice the problem here. If you were to make a decision in absence of the time already spent, you would walk away. Nevertheless, you stay because of the time invested. You take into account unrecoverable resources, making a decision that is completely flawed.

Another example is commonly seen when analyzing relationships. How many times have you asked people you know why they are still in a bad relationship and the answer is: 'Because I already have so much time invested in the relationship'? If they were to rationally view the relationship without consideration for the time already invested, they would leave. Again, this is faulty decision making. The decision should be based on present circumstances and upside going forward.

The past investment should not be taken into account. When considering sunk cost, you are not just making a bad decision now; you are also incurring 'opportunity cost.' In this case, you're costing yourself the opportunity to meet the man or woman of your dreams and get into a good relationship. This applies perfectly to poker. In fact poker players are some of the worst offenders in the sunk cost department. Each decision in poker should be made based only on the math at the decision-making point. Given the information you have about your opponent's hand and what you know about your hand, you make an assessment of the probability of your hand winning (the hand odds) and then compare that to the money in the pot and to the amount of money you will have to bet at the decision point (the pot odds).

If the pot odds are greater than the hand odds, you play; if not, you fold (unless, of course, you can bluff, but the odds of the success of the bluff get taken into account anyway). The decision at that point comes down to pure math.

But poker players tend not to take math into account. Players - and you know if you are an offender - will make calls that are mathematically poor if they have money already invested in the pot. This happens most often when people make calls that are too loose from the big blind, because they want their blind back. Or they will make bad calls with draws on the turn, because they have already invested money with the draw on the flop. They want to protect their investment.

The problem is that the money you have already put in the pot doesn't belong to you anymore. The minute that money leaves your stack and goes into the middle of the table, it belongs to the pot. The decisions you make beyond that should be based on the pot size; and the pot size is relevant because it determines the the pot odds you are getting at that time. Where the money came from has no bearing on whether a call is mathematically good or bad. If you feel you have money to protect, you are much more likely to play on in situations that are mathematically disadvantageous.

And just as in the life examples above, there is opportunity cost in poker, too. If you call off a bunch of money in a bad spot because you erroneously take sunk cost into account, you are costing yourself the opportunity to earn on the money you just lost. If you are a player with an advantage, which I assume you are, then every penny you invest in a game has an earning potential.

In poker, you need to invest to make money, and reducing your bankroll by making a bad call to protect money that doesn't even belong to you anymore - well, that's just bad decision making all around.

Reinvestment decision example

Consider a project, with a projected return of $100,000 and a projected cost of $75,000. We previously determined that the project would be a good investment for us, so we funded it. Six months later, we're reviewing the financials of the project, and discover that our project manager has already spent the $75,000, has not completed the software, and wants another $50,000 to complete the project. Assume that we believe the project manager, and it really will take an additional $50,000 to finish. If we don't finish the project, the projected return is $0.

How do we make a decision about a project that is partially completed?

Financially incorrect reasoning

We now look at the project as having a total cost of $125,000 and a return of $100,000. We would lose $25,000 with this project - we should kill the project right now.

Financially sound reasoning

Unfortunately, the first $75,000 has already been "lost", so we should not include it in our analysis. The previous calculation is wrong. Financial decisions are always made about future events, not past events. No decision we make now can recover the sunk costs. We should therefore ignore those costs in any decision making.

At the beginning of the project, the projected value of the project was $25,000 ($100,000 return minus $75,000 cost). [Note: This is similar to, but not the same as expected value]. The projected value of the additional investment is $50,000 ($100,000 return minus $50,000 additional cost). The first $75,000 we spent doesn't matter any more - it's already been spent and can not be recovered.

What we are faced with now is the decision to spend $50,000 to get a return of $100,000. There are two possible scenarios: invest nothing and get nothing in return, or invest $50,000 and get $100,000 in return.

The first $75,000 is a sunk cost in that we don't get that money back just by choosing to not invest more money.

There's usually more at stake here

In another example, imagine that we've invested a million dollars to get a return of 1.5 million. We've just discovered that we will have to invest another two million dollars to complete the project. Should we do it? Financially, no. This is where the pointy-haired boss might say "We can't cancel the project - we've already invested a million dollars in it!"

However, that manager may be optimizing on his reputation, not the company's finances. The reference to previously invested funds could be a red herring. What the boss is really saying is "We can't cancel the project - the CEO knows that I'm in charge of making this happen!" It may also be that we don't have all the information. There might be other hard to quantify benefits to completing the project (like goodwill or investor-perceptions) that would justify the added expense. In other words, the return exceeds 1.5 million dollars, we just don't realize it, even if our boss does.

In cases like this - tread carefully. Those of you old enough to remember the SALT treaty will remember Reagan's famous statement - 'trust, but verify.' Take the same approach with your apparently illogical boss. And if you find out that you can't trust your boss, find another boss.

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