Hyperbolic discounting will ruin your financial targets


Ok I might have gone a LITTLE over board with the title, but nevertheless, it is absolutely critical to understand what hyperbolic discounting is.

Ok, maybe it isn't. Actually, it most definitely is not.

BUT! It's pretty cool. I promise you'll be entertained.

In the mid 20th century some genius in the US had a heureka-moment. Some people always had trouble to find money for Christmas presents. And it was embarrassing for them that they had to use credit to pay for presents. Clearly there should be a solution, for example saving for Christmas up-front rather than having to pay interest on the credit.

The trouble of course was that these people had the problem because they were bad at saving. No-one had any illusions about them just never having thought of the obvious solution: to save throughout the year so that by December you could just dip into your savings account.

The the marvelous idea was a product they called a Christmas Club. The way it worked was as follows:

  1. You open a special savings account, usually for an opening fee
  2. You commit to saving at least a certain minimum to that savings account every paycheck. If you don't, there was a fee you had to pay.
  3. You were only allowed to withdraw the savings during December. If you needed it in any of the other 11 months, there was a fee.
  4. There was next-to-no interest paid on the principal.
So, in a nutshell, you paid so someone took away options from you. Isn't that weird? You paid, so that someone would protect your money from yourself!

Why are options dangerous?

Most people are not financial experts. Most people do not even know what discounting means. Most people don't know how to value something that isn't now, but instead is received in the future. Even us personal finance bloggers who are very savvy financially, we still are humans and we have a personal relationship with finance.

So this week I ran a small test on Twitter asking what people would choose. Have a look at this.


When you are evaluating between two rewards, both far from now, you feel like it's easy to wait the extra month for the slightly higher reward. In this case the extra 100€ for a month's wait corresponds to about 12.6% return annually. What I find interesting is that even with such a high return 45% opted for the earlier return.

I also asked a slightly different, but very similar question:


When nothing changed except 12 months had passed, 63% were eager to take the earlier reward. The sample size is too small, but this happens with larger samples as well. If you have doubts, ask your audience the question, see what happens πŸ™‚.

Now, why is this? Since only time had passed, nothing had changed, had it? Interestingly, time influences our internal discount rate.

If you like a scientific article, get your hands on "Some empirical evidence on dynamic inconsistency", by Richard Thaler, 1981 (link).

You fall victim to hyperbolic discounting all the time

Remember last week when you had that thing you were supposed to do, but instead you postponed it and watched Netflix instead?
And remember that pizza you ate the other day although you had decided to get into shape for summer?
Or how about that time when you were asked if you wanted a marshmallow now, or two a bit later, and you just had to have one right away? (Except you, reader, that time, you chose to wait, right?)

We do this all the time. It's who we are. It's being human. We can't all the time optimize for the next year. And of course we shouldn't. There is only now, and if you don't do something today, chances are you might never have another opportunity. But if we know how we behave, we can at least be conscious about it.

Hyperbolic discounting

Hyperbolic discounting in mathematical terms means that the time distance to the reward influences the discount rate. In a "normal" exponential discounting the formula is in hyperbolic discounting the form looks something like . (D is a discounting factor, k is number of periods).

A picture tells more than a thousand words, so let's imagine a hypothetical situation where you're offered to choose between 100€ in 12 months or 120€ in 13 months. In the case of exponential discounting, as time passes on, you value the choices like so:



No matter when you are asked which one you'd choose, you'd always consider waiting the extra month for the extra 20€. Only if your annual discount rate was about 650% would you think the 100€ was a better deal. With hyperbolic discounting it looks different:



You start off feeling it's worth waiting for the 120€ for the extra month, but as time goes and passes the 10 month mark, you start to feel different. "Should I just get the 100€? I could use it now. Why should I wait for the extra time, when I've waited for so long already!?".

This is how our minds work. It's not an excel sheet running on our brain, calculating the exponentially discounted present values of what's to come. We are wired for quick fixes.

But it's ok. At least now you know this cognitive bias. And you can choose to control it or not. You have a choice. Before you leave, I want you to think about the big picture.

How to relate to your hyperbolic mental discountant

(Discountant isn't an occupation. It's not even a word. I just made that up.)

Your life has a million decisions where you get to choose to delay a gratification or get it sooner. The saddest life story is that of a person who delays all gratifications until it's too late. Only the next saddest is the one who always goes for the quick fix.

There is a road in the middle in which you learn to think for a while before making a decision like that. "Is this what I really want?" or "I haven't treated myself lately, I'm doing this!" Postponing some decisions, but not all, means we will be rewarded in the long term, but we'll still enjoy the road too.

Avoid both extremes.

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