A Sharpe Rule for Compensation? - 20 June 2009

As
we think about the extent to which compensation incentives caused the
financial mess, we might start with a basic fact: annual internal rate
of return is a bad metric for evaluating performance. The largest
problem with it is that it rewards return without punishing risk.

When firms use leverage to invest, they increase the risk they are
taking on. The value of a firm’s assets divided by its equity gives a
rough multiple of risk created by leverage.

Suppose a firm has $100 in assets, and its return in one year can be
either -$5 or $15, each with 50 percent probability. The expected
return to the firm is 5 percent, with a standard deviation of 10
percent.

Now suppose it can borrow half the money to purchase the assets at
an interest rate of 3 percent. Its expected return is now higher,
because it will expect to earn $3.50 (13.50*.5+(-6.50)*.5) on a $50
investment, or seven percent. Thus positive leverage gooses the return.

But now the standard deviation or risk) of the investment is 20
percent (the investment produces a return swing of plus or minus $10 on
a $50 investment). So while the return has improved, so too has the
risk of the investment. Compensation strategies based on return would
fail to recognize the risk.

This would not be the case if compensation were tied to a company’s
Sharpe Ratio. The Sharpe Ratio is corporate return less a risk free
rate divided by the standard deviation. In our case, in the first
instance, the sharp ratio is .2 (.05-.3)/.1. In the second case, it is
also .2 (.07-.03)/.2). If the Sharpe Ratio were used to determine
compensation, managers would not be rewarded for goosing returns via
leverage. And we could avoid all kinds of future trouble.

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