Tuesday, October 29, 2013

Befuddled by expected value

In a prior post, we mused about "risk amateurs". However, even experts are often befuddled by expected value.

Questions arise:
  • What value should I plan for -- the expected value or the full face value?
  • What about the most likely value -- shouldn't it figure into the planning?
  • If I plan for the expected value, and the risk event occurs, where do I get the money to cover it? Isn't this an unmanaged exposure? And,
  • What should I pay to get someone else to take on the risk -- the expected value, or more?
There are objective answers, of course, but the objectivity often has to be tuned for domain, context, and risk attitude, and whether or not there is calibrated data to work with.

Calibrated data: data based on facts and not guesses. Of course, there is a place for estimates: facts adjusted for circumstances where adjustments are based on reasonable and customary experience.

So, the first thing is that if we have calibrated data, then we may have data good enough to estimate event probability and event impact. Multiplying these two calibrated single point estimates is valid for that one point.

We come to the second thing: my objective answers, tuning as suggested notwithstanding:
  • Make an operating plan based on expected value; to reduce exposure to an event actually happening, establish reserves (likely on possible coverage of the exposure) and alternative approaches (options) in the event of the risk event.
  • The expected value is generally more pessimistic than the most likely value, so expected value is usually a better planning metric. (reduces exposure)
  • See my first answer about where to get the money
  • Any transfer payment in excess off the expected value is a profit or bonus to the agent accepting the risk. So, if you are not bonus averse, you can pay more than expected value. See: insurance... bonus in excess of the expected value is the basic model for insurance.

Check out these books I've written in the library at Square Peg Consulting