What is Hyperbolic Discounting?

In this article I explain the nuances of Hyperbolic discounting and some of the common misunderstandings of this concept. I later talk about how you can use this understanding to avoid making expensive mistakes and keep you on track to achieve your FIRE (Financial Independence, Retire Early) goals 

A Simple Definition

Instead of a technical definition, I will use an example to define Hyperbolic Discounting. Take some time to answer the below questions before reading any further.

Question 1 – Let’s say a friend offered you either 10$ today or 11$ next week. What will you choose?

Question 2 – Let’s say a friend offered you either 10$ one year from now or 11$ one year + a week from now. Which option would you choose?

If you chose 10$ in Question 1 and chose 11$ in Question 2, then what you did just now is Hyperbolic Discounting.

A (Slightly)Technical Definition

Hyperbolic Discounting consists of two words. ‘Hyperbolic’ and ‘Discounting’.

Hyperbolic comes from the mathematical subject area of conic sections. Think of it as a particular shape of a curve with some unique characteristics.

Here is a simple example of a Hyperbola. Notice how the graph drops steeply and stays low. If you consider the x-axis to be time and y-axis to be your perceived value of something. Then at time = 0 the value is the highest. Which makes sense as having something NOW is valuable.

However, see how the value drops steeply even if it is delayed by 1 unit of time. But as you keep going along the x-axis from left to right you notice that there is no further drop in value. So points far away in the future have no noticeable difference in value. 

‘Discounting’ comes from the world of Finance. Where discounting is a term used for the process of adjusting the future price of something to the present price. 

An example: Your Bank offers 5% interest per year  on a Savings Account. You know you need 1050$ a year from now for your vacation. How much do you need to set aside in the savings account now so that you will have 1050$ a year from now? The answer is 1000$ and the process of obtaining it is called ‘Discounting’ . Mathematically, you divide the future value of 1050$ by 1.05 (the 0.05 comes from the interest rate of 5% , i.e. 5 divided by 100 = 0.05)

My intuitive understanding

I like to think of Hyperbolic Discounting intuitively as follows. 500 feet is a considerable distance. From the place where you are sitting (or standing), you can imagine how far it is. 

Now try looking way further out of your window towards a building far away. Once you have selected this building, try to look for something ‘near’ that building. A large tree for example. Seeing from a distance you could conclude that they are quite near each other. If you had to go visit the building or the hill you would be indifferent. Even if the tree were 500 feet closer to you than the building. Because at a far enough distance it is hard to feel the difference in distance between those far off objects from where you are.

Typical Misunderstanding

Hyperbolic Discounting is not ‘A bird in hand is better than two in the bush’. I.e. choosing a certain thing over an uncertain thing. It is failing to see the difference between two outcomes when those outcomes are far into the future. 

Hyperbolic Discounting is failing to see the difference between two outcomes when those outcomes are far into the future. 

Application to FIRE

When it comes to making financial decisions on your journey towards FIRE, Hyperbolic Discounting can lead you astray. 

Here is a hypothetical scenario. You and your spouse are making an important spending decision. You are out to buy a new car. The dealer is salesy as usual and you now face a choice between, either a basic version of the car that has 300$/month payment or a fully loaded version that is 400$/month payment. The sales person says it’s only 100$ and asks you ‘what difference does it make?’.

You consider the number in your FIRE model and realize that the difference is whether you achieve FIRE in 12 years if you choose the 300$/month payment or achieve FIRE in 12.5years if you choose 400$/ month. 

If you fall for Hyperbolic Discounting you would think there is no difference between 12 and 12.5 years, after all what’s an extra half year if I can wait for 12 years anyway? and choose the 400$/month payment.

How to avoid it?

Here is a way to overcome Hyperbolic Discounting.

Imagine if you had the choice to either:

FIRE today but have a 300$/month car or 

FIRE 6 months from now but have a 400$/month car.

 Now, which one would you choose?

If you end up choosing to FIRE today and accepting the 300$/month car means that your earlier decision was influenced by Hyperbolic Discounting and you should reconsider your decision. 

Decisions like the one above are quite common when it comes to managing your personal finances and are not easy to get them right all the time. Behavioral Finance is an interesting and useful tool that can help avoid such mistakes. 

(If you liked this then check out this post on the Diderot Effect)