Cumulative Prospect Theory Certainty Equivalent

If you are offered a gamble, what would be a fair value for you to pay (or be paid) for the opportunity to take it? Consider a 50% chance of losing $100 and 50% chance of winning $100. The expected return is $0. But what about risk? There is no principled way of measuring risk, so let us measure it in terms of the way people actually behave. Empirical research tells us that, in practice, people frame their options, are loss averse, risk seeking and have nonlinear preferences.

I have developed a new performance measurement algorithm, which is an implementation of Tversky and Kahneman’s Cumulative Prospect Theory. The measure is known as CPTCE. Given any distribution of returns, it assigns a single value. This is the return that people, in practice, would consider equivalent in value to the distribution of returns. This measure tells us that we would wish to be paid $22.30 to take the gamble.

The Performance Measurement Calculator calculates Certainty Equivalent, along with other performance metrics.