Is hyperbolic discounting one reason Marc is right about the DDM working for us?

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As a reminder the DDM, as copied from one of Marc’s post, is: “P=D/(R-G).”

Math aside, it is impossible to get away from the logic that a rational person will pay a little now in order to obtain a greater amount later. I know I do that—otherwise, I would just spend all of my money now. Heck, I would even spend next year’s P123 membership now if I were not discounting future returns.

So, on some level (actually many levels) the DDM has to be right: at least for many investors including, perhaps, all of us at P123.

One “loophole” or caveat for this is that this assumes a rational investor.

We all agree that not everyone is rational. For a reasonable discussion, we would want to quantitate some of this irrational behavior with a developed model.

There is a large body of literature on “hyperbolic discounting.” This is a topic of behavioral finance, I believe. And it is my understanding that many humans do use hyperbolic discounting–or close to it–in experiments. It is discussed in finance but it is also discussed as a reason why we eat too much now, get addicted to drugs etc.

A simple example would be this: Lets say I go up to the counter at McDonald’s and say I want a Big Mac and hand the person $3.99. He says: "Great I will have that in a moment but if you prefer—for the same price—I will give you 3 coupons for Big Macs that you can use any day of the week next week. I state it this way so that I would not have to eat each of the Big Macs in one sitting.

With rational discounting, I would take the deal. But my emotions (if hunger is a motion and not a drive or urge) might make me go ahead and take the burger today. If I am hungry enough, in fact, there is no question as to what I will do.

One thing that makes this interesting is that the biggest discrepancies between hyperbolic discounting and rational discounting (often modeled as exponential discounting) occurs in time-frames of weeks. Which, possibly not just by coincidence, is the time-frame that seems to yield some of the larger profits for P123 rebalancing (not the same as holding periods).

Anyway Googling “Hyperbolic Discounting” is likely to give you a more balanced, coherent understanding than what you would get if I tried to continue an explanation further. And I know, many of you have a deep understanding of this from you backgrounds.

But the basic theory would be: even if the market is well informed maybe we can make a profit by using rational discounting with the DDM while other investors–especially retail investors investing in small-caps—are using something closer to hyperbolic discounting. Or continuing the example, we end up with a few more Big Macs than the average joe. And this is because some people may be aware of the deal for more Big Macs but the deal is not getting the demand that it should in a rational market. Or more simply, most investors are too “hungry” or greedy to be rational.

So my simple question is does hyperbolic discounting explain, in part, why market participants might be well informed, on the one hand, yet we can still make a profit at P123? Or are we just more informed than the average retail investor? Or is is there another better explanation—with hyperbolic discounting playing a minor roll or no roll at all?

Personally, I think hyperbolic discounting must play some role but I promise I have not researched this enough to be critical of anyone’s opinions—if I say a lot more I will just be showing my ignorance of this subject. And I do not discount the (exhaustive?) alternatives: 1) perhaps, P123 data makes us better informed of the correct DDM price for a stock, 2) perhaps the algorithms—simple as they are—allow us to calculate a more accurate DDM. But it is one or the other: our decisions are either better informed regarding the price (relative to the BID/ASK) or we act on that price in a more rational manner (or both).

Thanks in advance for any comments.

-Jim

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This is an interesting topic which I have explored in one of my blog posts (albeit with an emphasis on reservoir engineering): http://the-world-is.com/blog/2017/03/drilling-for-value-appendix-c-discounting/

In turns out that the mathematics of hyperbolic discounting are rather simple, albeit less studied in a fiscal context. Fortunately, engineers have already figured the shorthand solutions.

Interestingly, pure harmonic discounting represents a case where only a fixed dollar amount of profits are reinvested. Exponential discounting represents the scenario where 100% of profits are continuously reinvested.

To the extent that we are able to reinvest 100% of our bankroll at given rate of return, exponential discounting is the optimal solution. However, this may be unrealistic for many people, especially retirees who need to draw on their retirement incomes and even principals. In the extreme case where negative growth is expected (i.e., negative reinvestment), the utility of short-run outcomes and risk-aversion is maximized.

To be honest, I think the right discounting rate and type curve depends on individual preferences regarding intertemporal choice. As far as maximizing market rates of return – vis-a-vis an algorithmic discounting function – I think there is far too much uncertainty in the cash-flow parameters themselves to make a whole lot of difference. But then again, assuming perfect foreknowledge of future reinvested profits, I would think a hybrid discounting function which is calibrated to match the corporation’s reinvestment policy would be the optimal solution. But then again, dividends would have to be discounting separately, according the individual’s intertemporal preferences.

In any case, I’ve experimented with both the pure exponential and pure harmonic methods, but currently just use pure exponential utility at really low rates because the differences between any two type curves is less pronounced. I also use low rates because, although I seek to maximize long-run wealth, I do not assume that I can reinvest profits at the anything greater than the risk-neutral rate.