Guest post by Emanuel Derman
Foods with equal deliciousness should sell for equal prices per ounce.
Who can argue with this? Not homo economicus. It seems completely reasonable: if that weren’t the case, gourmands would buy the cheaply delicious foods and sell the richly delicious ones until they came into equilibrium.
Now suppose I have some delicious food – call it F – which sells for f dollars per ounce and has a measured deliciousness w. Using the No Free Deliciousness Principle, it’s easy to show that if you know the price of one delicious asset, you can find the appropriate price of anyother less delicious asset. Here’s how it works.
Suppose you have access to a totally tasteless food (call it T), a food neither delicious nor disgusting, just neutral, that sells for t dollars per ounce. Think fiber, for example, or some kind of filler. You can use the totally tasteless food to dilute another food’s deliciousness. If you add some definite proportion of tasteless T to delicious F, the mixture will be less delicious. And, since you know the cost and deliciousness of the ingredients, you know the cost and deliciousness of the mixture. Then, by the No Free Deliciousness Principle, all foods with the same deliciousness as the mixture should sell for the same price per ounce, the price of the mixture. Now, by varying the amount of tasteless T in the mixture, you can figure out the fair price of foods of any level of deliciousness.
A little seventh-grade algebra turns this conclusion into the following result:
The excess cost of a delicacy over and above the cost of the tasteless food T should be proportional to the delicacy’s deliciousness ω.
In brief, more deliciousness, more cost. Or, in equation form,
f – t
______ = λ The Delicious Asset Pricing Model
ω
Here the Greek letter λ (lambda) is what my theory calls The Pleasure Premium, the extra price you must pay per unit of deliciousness ω. (If you cite this work, please refer to λ as The Derman Ratio.) You can measure the pleasure premium by sampling the tastes and prices of a range of delicacies, and it will vary over time and with economic conditions.
If you understand how humans behave, you will grasp that there are (at least) two kinds of deliciousness: realised deliciousness, which I have heretofore called ω, and, equally important, expected deliciousness (which I denote by Ω, upper case omega). Expected and realised deliciousness are not the same. People pay for expected Ω but, when they bring delicacy to lip, they experience realized ω. If ω turns out to be greater than Ω, gourmands return for more; if not, they leave and don’t return until the food becomes more delicious or the price decreases.
This, of course, is just the start of deliciousness theory, which until now has assumed the existence of only one kind of deliciousness. I am working on Multideliciousness Theory, which recognises that there is more than one kind of deliciousness, among them sweetness, tartness, smoothness, lumpiness, spiciness, blandness, etc. And deliciousness is only one kind of pleasure, purely gustatory; there are other mentionable and unmentionable pleasures to which Multideliciousness Theory can easily be extended.
This is a fundamental advance in putting behavioral finance on a sound mathematical basis. Will you be disappointed if it fails during the next gourmet food crisis?
Emanuel Derman is head of risk at Prisma Capital Partners and a professor at Columbia University. He is the author of the new book Models. Behaving. Badly: Why Confusing Illusion with Reality Can Lead to Disaster, on Wall Street and in Life.