Hyperbolic Discounting in Security Valuation
Summary
The discussion asks whether security prices can be modeled with hyperbolic rather than exponential discounting. It points to academic work examining the asset-pricing consequences: less patient investors may produce lower stock prices and higher interest rates, while the equity premium remains unchanged; risk also has a weaker marginal effect on stock prices in that framework.
A practical calibration idea is to fit a declining schedule of discount values to earnings forecasts and observed price changes. The schedule could impose faster discounting across near-term periods, but choosing its shape requires assumptions and evidence about how forecast uncertainty changes with horizon. A key tension is that a discount schedule detached from the cost of carry could imply a pricing inefficiency that other investors might exploit. One response is that investors may discount distant earnings more heavily when those forecasts are especially uncertain. The text also suggests that panic in falling markets can resemble heightened discounting of profits expected later. These proposals are exploratory; no fitted model, empirical test, or demonstrated trading performance is provided.
Key ideas
- Hyperbolic discounting reduces the value of near-term delayed rewards more sharply than it reduces the value of distant rewards.
- Research discussed here associates the approach with lower stock prices and higher interest rates, while leaving the equity premium unchanged.
- A possible empirical model would fit a declining discount schedule to earnings expectations and price movements.
- Model calibration depends on assumptions about how forecast uncertainty grows with time horizon.
- Discount rates that diverge from carrying costs could create an apparent arbitrage opportunity.
- Panic markets may amplify the discount investors apply to earnings expected further in the future.
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Full text
# Are there any valuation models of securities that use hyperbolic discounting? # Are there any valuation models of securities that use hyperbolic discounting? 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? ## Answer by Tal Fishman (score 3, accepted) https://quant.stackexchange.com/a/3432 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. ## Answer by 410 gone (score 4) https://quant.stackexchange.com/a/3430 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. ## Answer by dchandler (score 2) https://quant.stackexchange.com/a/3431 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! ## Answer by Tom Au (score 1) https://quant.stackexchange.com/a/3433 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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