Hyperbolic Discounting and Cashflow

January 25, 2022

Hyperbolic Discounting

Back in 1970, a couple of Stanford psychologists conducted an interesting little experiment. They took young children into an empty room and showed them a treat on the table, usually a couple of animal crackers. The children were told they could eat them if they wanted, but that if they waited 15 minutes, they’d get two treats instead of just one. The idea was to see what correlations existed between the children that could delay their gratification and those who went for the immediate treat. Follow-up studies correlated the ability to delay gratification early with better SAT scores, educational achievement and even adult BMI scores. They did another followup that was famously called the Stanford Marshmallow Experiment.

The results have mostly been debunked or extremely difficult to replicate, despite the original paper picking up around 1000 citations. The effect of delayed gratification is real but very small with a correlation of r=0.05. But the idea of the power of delayed gratification has been deeply rooted in our culture.

And it should be. Delayed gratification is a powerful skill. It’s not terribly surprising that people able to delay pleasure (not eat) would be able to maintain a healthy body mass index later in life. It correlates with being able to stick to something, to double down on the same thing over and over. Sometimes this is painful, but it’s what lets us claim the power of exponential curves. As David Perell points out:

It’s okay to start small. All big things do. But they have to start somehow and with commitment comes momentum. Commitment happens in stages, and only by embracing it can you stop hugging the X-Axis and climb the compounding curve.

We’re told all the time to do this for our retirement savings. We’re told this because for so many people out there, it’s a giant step just to get them to save at all. The brilliance of the 401k/403b construct is that it correctly incentivizes everyone to take advantage of the power of compounding and accumulate a large chunk of savings for when they’re older and less able to work. But for those that can and do save, through some happy combination of foresight, high income, luck, and environment, I’ve been wondering if there’s something slightly off about this.

Go play around with one of the many 401k calculators out there; let’s try Nerdwallet. You can’t beat the name. Anyway, they all do the same thing. They take a salary and a contribution rate and show you with a pretty graph how the compounding will really take off in 20 or 30 years. Then they show you a magical figure that says “You will need about $6,650/month in retirement”. Changing the parameters doesn’t change the number, and there’s no explanation for how it’s calculated. I assume it’s some very generalized estimate of expenses for a normal 70 year old.

Poking around, a much better one is SmartAsset, wherein you can set your own estimated future financial requirements and what your tax situation will be based on where you live. They also assume an estimated drawdown of assets over time. This gets us a more realistic look at how far a 401k can go. It’s worth looking at the SSA’s estimates of benefits too, just to get an idea of how social security fits in. But don’t take that to the bank, who the hell knows what those programs will look like in the future.

The point is that for people doing a 401k, there’s a normal expected way to think about these things. There’s tons of assumptions baked in, but the one that really gets me is this: financial requirements that are the same at 60 and 70 and 80 and 90.

Economists have defined hyperbolic discounting as a way of measuring the difference in value between a dollar now and the promise of a dollar in a year. This may sound obvious but there’s some nuance to it. Most people would prefer $50 now over $100 in 6 months, but if we slide the timeframe slightly, they’d prefer $100 in 9 months over $50 in 3 months. We are naturally present-biased, where present literally means right now, just like the kids who wanted a marshmallow.

Similarly, most everyone would choose $100 in 6 years over $50 in 5 years. We expend a lot of effort to get ourselves or others to appreciate the value of compounding and saving and having money in the future, but we have a very hard time defining what is enough. This, in part, is one of the myths that overly cautious retirement planning relies on. The timeframe are so far in the future that it’s easy to just select the highest dollar amount.

And maybe that makes sense for money! We’re so present-biased that it’s a monumental effort just to delay gratification and save at all, so it’s a net win even if we don’t get it exactly right. What I’m wondering is: can we think about discounting our own time in the future as a damping effect to how we allocate money? Is a year of our life worth the same at any age?

Look: I have no idea what I’ll be doing at 90.. hopefully I’m doing more than just sitting somewhere slackjawed under a blanket. I’ve known a bunch of 90 year olds. Some of them are spry, mentally acute, and really very fun. Their lives are rich and valuable. But there’s still a very big difference between a spry 90 year old with a rich life and a spry 70 year old. Physical and mental decline is very real, and the probabalistic chances of major health issues increases dramatically with years. No matter what I’m doing, I’m quite sure that my overall desires at 90 will be significantly less than at 65. Maybe that’s not quite right; we don’t necessarily get smaller ambitions as we get older. It’s more accurate to say that the intersection of my capabilities and my desires will be smaller at 90. What I’ll be able to do is a lot different and so I think about - I care about - my year of life at 65 a lot more than I do my year of life at 90.

This is a problem of capital allocation. Capital has more value for me and for my kids and grandkids sooner rather than later. The 401K gods train us to rely on a flat income from 65 all the way to 95, which is probably just a generalization of the effects of inflation and medical expenses increasing. But it still seems wrong. To put the conclusions more plainly:

  • I plan to draw more of my 401k between 60-75 than I do beyond that. Discounting units of life suggests that there needs to be a balance between now and later.
  • My income requirements will be lower beyond that age, especially if I’m still able to live independently.

What’s doubly intriguing is where this puts me now.

I’m in my early 40s now, with kids and a mortgage and private school tuition. In other words, I have plenty of expenses. But I’ve also followed some of the compounding advice reasonably well - not great, but good enough - and I already have a nice growing pile in 401ks and IRAs. That will keep growing untouched until at least 60. And by 60, real estate will be paid off completely and most child expenses will be gone. Maintaining our current lifestyle will get drastically cheaper quickly, which we will probably offset somewhat by traveling. Again, these decades matter much more to me than my 80s or 90s, so let’s enjoy life and expend capital.

What’s the point? The point is this: since I’ve already got a nest-egg, 60 and beyond is mostly covered. My savings goals now are more focused on getting from here to 60 than from 60 to the great blue beyond.


Breaking down these years near the present is better represented as a problem of cashflow. When most people go into investing, they think about it with those long compounding curves. And that makes sense on a 30 year time horizon, because that’s where you’ll get the value. But now, I’ve broken down my problem into needing cash continuously in 2 years and in 5 years and in 12 years, which means a more constant stream of money coming in.

Again, this is a problem of capital allocation. If 60 and beyond is looking relatively good, and the focus is on a smaller time scale, where should I put my capital? Investing looks a lot different with this perspective. It’s January 2022 and the relationship between the Federal Reserve, the money supply, and the markets is front and center. The amount of money that’s been distributed has been forcing market participants to go further and further out on the risk curve because holding cash, bond, or treasury yields is a losing proposition. The further out on the risk curve, the larger the volatility. Lots of money is being lost right now, some of my own included.

My conclusion: it’s a better use of capital to start or acquire additional cashflow generating businesses than passive investment.

The last two years have been the first time I’ve taken any sort of active role in market movement. It’s been fun, but it doesn’t seem like the right focus. My wife and I have talked a lot about real estate based businesses, but this may not be the best path. Real estate is capital-intensive, so we’ll see if it makes sense. Regardless of the type, going forward I intend to focus personal capital on the accumulation of businesses.

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