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To quote Wikipedia:

In hyperbolic discounting, valuations fall very rapidly for small delay periods, but then fall slowly for longer delay periods. This contrasts with exponential discounting, in which valuation falls by a constant factor per unit delay, regardless of the total length of the delay.

Hyperbolic Discounting

This concept has been viewed as a possible structure for the construction of utility functions, but I'm interested in its application to security valuation. As you may know, asset valuation - at least for equities - is dominated by discounted cash flow (DCF) analysis, which is a time-consistent method of valuation.

Do any models exist to value securities using hyperbolic discounting? If not, how would one go about creating such a model?

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4 Answers

up vote 3 down vote accepted

A paper by Gong, Smith, and Zou (2007) addresses your question exactly. From the abstract:

This paper explores the implications of hyperbolic discounting for asset prices and rates of return. Hyperbolic discounting has no effect on the equity premium. However, by making people less patient, causes stock prices to be lower, and interest rates higher, than with exponential discounting. In addition, hyperbolic discounting dampens the marginal effect of risk on stock prices, relative to the exponential case.

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Hyberbolic discounting seems to be operative in "bear" or panicked markets. That's when utilities, and other companies with heavily "front ended" earnings do relatively well, while cyclicals do poorly. People "know" that the cyclicals will (probably) do well some day, but they discount "delayed" earnings that will follow poor near term ones more heavily than usual.

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This is definitely not my field of expertise, so you can take my answer with a grain of salt.

That said, you might want to check out some research by Robert Woodford. I know some people who are taking a class of his and a lot of papers that he reviews discuss imperfect rationality and their effect on macro models. His CV may be a good starting point. Andrei Shleifer is also a prolific researcher in the field and studies behavioral questions.

Hope that helps!

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To create such a model, you'd start with some data, and then start fitting curves to it.

For example, let's take a company where there are reasonable consensus forecasts about the next few years' earnings; and let's assume you've got some time-series data on changes in those consensus forecasts, and changed in the price. You could then fit a model based on a set of constraints where your discount value decreased year on year, and where (for example), the ratio of your nth year discount rate to n+1th year discount rate is, say, greater than 1.3 (to pluck a factor out of the air). So a 1st-year discount rate of 26% would imply a second-year discount rate of less than 20% ... and so on.

The problem is that here, your cost of carry would not reflect your discount rate. So you've got an assumption that your market price is arrived at by a systemic flawed valuation method, which suggests that a new entrant could come into the market with a discount rate that reflected cost of carry, and reap excess profits.

There is an argument for higher discounts on earnings forecasts for years 2-5 than on next years earnings, to reflect the greater uncertainties in far-ahead forecasts. To calibrate a model on that, might require some assumptions about consensus over how those uncertainties differ over time. Getting data on that might be hard.

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