Taking Advantage of Hyperbolic Discounting

2 January 2019 | by Todd Wenning, CFA

After reading psychologist Robert Cialdini’s book Influence, Warren Buffett’s investing partner, Charlie Munger said that it, “filled in a lot of holes in my crude system.”

In other words, Munger may have intuitively understood the principles of influence, but Cialdini’s book provided the blueprints. Munger and Buffett apparently made so much money from Cialdini’s book that they sent Cialdini one Berkshire Hathaway Class A share, currently valued over $300,000.

Never underestimate the potential return on investment from reading books. Or from writing them, apparently.

Instant gratification

In a similar vein, I’ve learned through experience and study that investors often overreact to negative news. They sell first, ask questions later. I learned from Michael Mauboussin, for example, that stress from volatility shrinks investors’ time horizons. And because we feel losses more than we feel equivalent gains, there’s pain relief in selling.

You don’t need to be an investing genius to conclude these moments tend to be good long-term buying opportunities. If you can hold your own nerve, that is.

My crude but important understanding of the subject was enhanced when I recently came across the concept of “hyperbolic discounting.”

That’s a $5 word

Hyperbolic discounting is a fancy way of saying that people discount the near future more than the distant future. In Willpower: Rediscovering the Greatest Human Strength, Roy Baumeister writes, “as we approach a short-term temptation, our tendency to discount the future follows the steep curve of a hyperbola…As you devalue the future, you lose your concern about a hangover tomorrow, and you’re not focused on your vow to go through the rest of your life sober.”

A rational actor will discount future rewards at an exponential rate, as illustrated by the present value formula most investors will recognize:

PV = Cash Flow / (1 + r)t

Here, the “reward” is the cash flow, “r” is the discount rate, and “t” is time. For example, the present value of $100 received in three years’ time with an 8% discount rate is $79.

This rational formula becomes irrational under hyperbolic discounting. Here’s an illustration of how it might look, with “t” now magnifying the denominator.

PV = Cash Flow / [(1 + r*t]

Using the previous example, rather than present value being $79, it’s now $23. Note: nothing about the cash flow or the discount rate has changed – only the impact from time.

Putting it into practice

Now, let’s assume we’re determining the present value of an asset with cash flows of $100 per year for 10 years. We’ll stick with an 8% discount rate.

The rational actor using exponential discounting would assume a fair value for the asset at $671. On the other hand, the irrational actor using hyperbolic discounting would assume the fair value is less than half that amount at $271.

Exponential Hyperbolic
1  $          93  $          93
2  $          86  $          46
3  $          79  $          31
4  $          74  $          23
5  $          68  $          19
6  $          63  $          15
7  $          58  $          13
8  $          54  $          12
9  $          50  $          10
10  $          46  $            9
SUM  $        671  $        271

Here’s how the cash flows look graphically.

The above table illustrates how the market can dramatically undervalue strong businesses when it goes into panic mode.

Assuming no change to the long-term cash flow outlook or riskiness of the business, hyperbolic discounting by market participants will alone drive its share price lower.

This is the mercurial Mr. Market that Benjamin Graham famously described in The Intelligent Investor: “Often…Mr. Market lets his enthusiasm or his fears run away with him, and the value he proposes seems to you a little short of silly.” Herein lies the opportunity for long-term investors.

To be fair, it’s hard to know before the fact if the market is panicking or if it’s making rational adjustments. Maybe your own cash flow projections are wildly off, or maybe you’ve underestimated the business risk.

We believe that the better you understand the business, the drivers of its fundamental performance, and its moat sources, the more likely you’ll be prepared to take advantage of the market’s emotional swings.


During the fourth quarter, for example, we added to our position in Broadridge Financial Solutions, a provider of investor communications, trade processing, and wealth management technology, as the stock fell nearly 30% from its September highs. From our perspective, there was little news that directly impacted the underlying business. Even if we are about to enter a recession, most of Broadridge’s revenue is recurring and their services are mission-critical to its customers. Further, the board recently boosted the dividend by 33%, suggesting long-term confidence in cash flow growth.

Though we acknowledge that our cash flow projections will be wrong to some degree, we think Broadridge is one of the more intrinsically-forecastable businesses we own. Despite the stock’s decline, we made no changes to our cash flow outlook and affirmed our discount rates.

It could very well be that hyperbolic discounting took over with Broadridge. Amid rising concerns about the financial markets, Broadridge may have become a “sell first, ask questions later” target by association.

Or at least we think so. Time will tell if our assessment was correct.

Bottom line

Right after he introduces Mr. Market in The Intelligent Investor, Graham added: “Basically, price fluctuations have only one significant meaning for the true investor. They provide him with an opportunity to buy wisely when prices fall sharply and to sell wisely when they advance a great deal.”

Ultimately, this is what we’re after at Ensemble. We aim to pay good prices for great companies and then be patient with them. That said, we want to be ready to both buy and sell when market participants underprice and overprice stocks for emotional reasons.

We don’t always get it right, but by remaining fundamentally-focused on the businesses we own and not getting caught up in the madness ourselves, we believe we have a good shot of taking advantage of price fluctuations driven by hyperbolic discounting as well as euphoria.

As of the date of the post, clients invested in Ensemble Capital Management’s core equity strategy own shares of Broadridge Financial Solutions (BR). This company represents only a percentage of the full strategy. As a result of client-specific circumstances, individual clients may hold positions that are not part of Ensemble Capital’s core equity strategy. Ensemble is a fully discretionary advisor and may exit a portfolio position at any time without notice, in its own discretion.

For more information about positions owned by Ensemble Capital on behalf of clients as well as additional disclosure information related to this post, please CLICK HERE.

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