Hedge Fund Arithmetic: Buce Clarifies Buttonwood

Buttonwood The Economist has a fine piece up in which they review some critiques of fund manager compensation.  He makes an excellent point about the role of leverage but I think I can restate it more crudely and baldly.

The subject is the so-called "two and twenty"  funds that take two percent of the gross and 20 percent of the gain.  As Buttonwood says:

Pension funds could decide to make a geared bet on equities by borrowing money and investing in the S&P 500 index. But they would understandably regard such a strategy as highly risky. Giving money to private-equity managers, who then use debt to acquire quoted companies, is viewed in an entirely different light but amounts to the same gamble.

Bingo, but  go to the tape.  Suppose the risk-free rate is 10 percent. Suppose the cohort of investors is absolutely indifferent to risk: they looks only for return.  Now, suppose a levered investment that offers "20 percent"--but with a 50 percent chance that will plotz.

The probability-weighted sun return on this investment is therefore (0.5)(0.2)+(0.5)(0)=0.1=10 percent.  Which is fine--indeed just as it should be, because the investor is indifferent to risk.  But it is not a return of 20 percent.   So, I suppose an investor might perfectly will make the investment here described, but he'd know (or ought to know) that his real return is only 10 percent.  Yet somehow when he invests with a hedge fund, he leaves his probability calculator at home.  He thinks he's getting a 20 percent return.

Why?  Because the hedge fund honcho tells him he's getting a 20 percent return.  The manager gives the investor all thee blah blah about superior analytical skills with just a nudge wink about inside information.  The greed lights begin strobing and all normal calculation gets left behind.

So, just another leveraged investment.  Well, no.  Remember 20-and-2.  The manager gets his two percent in any case; he gets his 20 on gains but never gives back the 20 on losses.  So the investor really would be better off just making his own leveraged play.

For The Economist, this is actually just the preface.  The main point of the piece is to review a couple of  new suggestions as how managers really should be compensated.  Read it here.

Addendum:  Here's a neat little example that supports the argument.