### Probability Inflation: The Risk of Ignoring Batting Average – Part 1

My company, Alpha Theory, started performing historical analysis of clients’ data about six months ago. We’ve only finished work on a dozen or so clients but one trend seems to be consistent, probability inflation. Let me explain what that means. Our clients use Alpha Theory to estimate the probability-weighted return of each investment and use that information to properly allocate capital across their portfolio. Part of estimating probability-weighted return is assigning probabilities to various potential outcomes. What we find is that clients generally have probabilities of success (scenarios where they make money) that fall in the 70-80% range. The issue is that their historical batting averages are more in the 50-60% range (batting average is how often they ACTUALLY make money on their bets).

"Of the almost 100 U.K. and U.S. fund managers in Investment Intelligence’s database, Chaban says, the best hit rate he’s seen is 64 percent; the median is just over 50 percent. " - Taras Chaban, chief executive officer of Investment Intelligence Ltd. (Bloomberg article)

Inflated probability of success causes two issues. One, the probability-weighted return is inflated. Two, the probability of loss is too low which results in an underestimation of risk. The net effect is overly optimistic assumptions and bets on assets that are too risky.

Here’s an example. Below we have three potential investments with equal 75% probabilities of success. As you can see, the return and risk characteristics vary dramatically for each asset but the probability-weighted return is a constant 30%. Imagine a portfolio manager deciding between this set of investment options with inflated probabilities and determining to weight all three positions equally.

Now imagine a portfolio manager, presented with the same investment choices, but with more realistic probabilities of success (55% instead of 75%). There is no way that these would be equally sized. In fact, #3 wouldn’t even be considered.

The return reduction for investment #1 is 8%, which is meaningful, but nothing like that for #3, which falls from 30% to -5%! Assuming a 55% probability of success creates an entirely different (and more realistic) set of investment possibilities for the portfolio manager to choose between. The complexion of the portfolio changes to lower probability of downside bets. I strongly encourage funds to use more realistic probabilities (average closer to historical batting average). If not, they will almost certainly suffer from overexposure to the #3s of the investment world.

Be on the lookout for next month’s post discussing Alpha Theory’s novel approach to calculating return and its relevance to the issue of Probability Inflation.