Your humble blogger is a vocal opponent of placing undue faith in single metrics and methodologies, like placing a lot of weight in total cholesterol as a measure of heart disease risk. One of the most troubling examples is the totemic status of discounted cash flow based analyses. It’s a weird defect of human wiring that reducing a story about the future to a spreadsheet and then discounting the resulting cash flows (which means you are now layering a second story, about what you think reasonable investment returns will be over that time period) is treated as having a solidity and weight that simply is not there, a reality of its own that manages to take precedence over the murky future it is meant to help understand.
An article by physicist Marc Buchanan in Bloomberg gives a layperson’s summary of an important paper by Yale economist John Geanakoplos, and Doyne Farmer, a physicist at the Santa Fe Institute. It shows that the conventional use of discounted cash flow models over long time periods, as is often the case when discussing environmental impacts, is fatally flawed. And this finding comes after the publication of a paper by Andrew Haldane and Richard Davies of the Bank of England, which proves what many have long surmised: that businesses use overly high discount rates, which is how you build short-termism into financial models. Needless to say, that assures underinvestment, particularly in infrastructure. Projects with paybacks beyond the 30 to 35 year time frame are treated as having no value at all. From their article:
First, there is statistically significant evidence of short-termism in the pricing of companies’ equities. This is true across all industrial sectors. Moreover, there is evidence of short-termism having increased over the recent past. Myopia is mounting.
Second, estimates of short-termism are economically as well as statistically significant.
Empirical evidence points to excess discounting of between 5% and 10% per year.
The Geanakoplos/Farmer analysis finds vastly larger distortions when NPV approaches are used over very long time frames, say over 100 years. The errors result from the convention of using a single discount rate which is meant to represent an average over the entire period. This simplification, however, is dangerous. Per Buchanan:
In calculating this average, some paths turn out to contribute far more than others. In particular, paths that descend into relatively low rates and stay there for many years have a disproportionate effect — a path at 1 percent for 50 years, for instance, counts 20 times as much as a path running along at 7 percent. Change 50 to 500 years, and the difference becomes 10 trillion times.
This demonstrates how simple thinking about the future can lead to terrific mistakes. When something fluctuates, we often suppose we can use the average rate over time. And sometimes this works. The amount of food you will eat over 20 years, for example, will be roughly equal to 20 times what you ate last year, because your appetite doesn’t fluctuate that much. But averaging to get a true effective discount rate isn’t so easy. Some of the paths of fluctuation — the lower paths — carry extraordinary weight, and hence dominate the outcome.
Not surprisingly, Geanakoplos and Farmer find that the correct formulas for discounting over long periods don’t follow the textbook exponential form. The math is tricky (I’ve put some discussion of the technical stuff on my blog). But the consequences are not. Using a standard model from finance for interest rate movements (with an average rate of 4 percent), the authors show that, for the first 100 years or so, their correct form of discounting gives results that are similar to those that come from traditional calculations. But at 500 years the standard exponential discounts the future not just a little too strongly, but a million times too strongly. And it gets worse after that.
And the flaws of using discount rates greatly exaggerate the bias we already see in practice, that of undervaluing anything beyond the next few years. Après moi, le déluge, indeed.