### The Price All Investors Pay for Benchmarking

Could the practice of measuring and evaluating manager performance by comparing it to a market index be distorting prices across the whole market? That is the conclusion reached in a recent paper entitled “Asset Management Contracts and Equilibrium Prices ,” by three academic researchers, Andrea M. Buffa of Boston University and Dimitri Vayanos and Paul Woolley of the London School of Economics.

A warning: This paper is heavily mathematical. I have spent enough time poring over it to be convinced that the math is sound and the paper is innovative and important – possibly very important.

But unfortunately, neither the non-technical article about it in the* Financial Times* nor the authors’ own non-technical explanation sent to me by one of the authors does a good job of explaining it for the layman. So, because I believe it is onto something, I will explain the core idea and why serious attention should be paid to the methodology and the conclusions.

### How benchmarking could distort the market

Let’s start with a very simplified example. Suppose the market consists of only two securities or assets. Let’s call these assets A and B. Further, suppose that the total market capitalization is 50% security A and 50% security B.

Now suppose that all investors start investing in these securities – in the market – by hiring money managers. The managers are evaluated by comparing their performance to a benchmark or index. The benchmark happens, for whatever reason, to be an index consisting of 60% security A and 40% security B.

What will happen? Let’s add some suppositions about the managers, their personal objectives and their incentives. Suppose that the managers are awarded a basic fee, but are also in effect rewarded (or penalized) for their performance by giving them (or taking away from them in the case of underperformance) a small percentage of the difference between their performance and the index.

Now, suppose these managers are loss-averse, meaning that they hate a loss in their personal incomes more than they love a gain of equivalent size.^{1}

Finally, suppose also that the managers don’t really believe they can control whether they outperform the index or underperform it. Then their utility function dictates that they will simply hug the index as closely as possible. That way, if underperformance by x is as likely as outperformance by x, they will maximize their expected utility by neither outperforming nor underperforming.

- The mathematical form of this is that their utility function U satisfies the inequality –U(-x)>U(x) for any x, that is, their utility is more negative for a loss than it is positive for an equivalent gain.