Beta

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Hedge funds use an array of strategies to guide trading.  Most of these strategies seek to decouple returns from those of the overall market, as measured by a statistic called “beta” (β). Beta is calculated by dividing the covariance of an investment’s return by the variance of a portfolio or market return:

βi = Cov (ri, rm) / Var(rm) where i = an investment, m = market portfolio, and r = return

Market beta is, by definition, equal to 1.  A beta of zero means that an investment is uncorrelated to the overall market; a beta of -1 implies a 100% negative correlation (for example, a short position in a stock).  If you know an investment’s beta, you know how much of the investment’s return is due to market movement versus investment performance.  Another way of thinking about β is relative risk: an investment with a β of 1 should be no more risky than overall market risk. We would say that this investment has no diversifiable risk, in that all of its performance is correlated to market performance.  It is the task of a good fund manager to provide superior returns relative to investment risk.

Measuring investment risk is thus crucial in order to properly evaluate fund manager performance.  A manager can always increase risk by using leverage: borrowing capital to purchase an investment (or alternatively, putting little money down on an investment or optional investment) – in other words, buying on margin.  All things being equal, a leveraged investment should have magnified return and risk characteristics relative to the overall market.  If a leveraged investment makes money after subtracting out margin costs, then the investment is profitable, albeit riskier.

Thus, risk and return must both be considered when evaluating a fund’s performance. Let’s take a concrete example. Suppose the current risk-free rate in the market (i.e. the interest rate on 3-month T-Bills) is 2%, and the S&P 500 market index has a return for the year of 12% (10% above the risk-free rate). By definition, the beta of this return is 1. Fund Managers A and B both invest exclusively in U. S. stocks. Fund Manager A posts a return of 20% above the risk-free rate with an average beta of 2 through the use of 2:1 leverage.  While Manager A has doubled the market return, he has also doubled his risk.  He has not demonstrated any superior skill in picking investments, since all of his higher return is explained by the effects of leverage.  Manager B posts a return of 12%, but with a beta of only 0.5.  Clearly, Manager B has outperformed manager A on a risk-adjusted basis: Manager B earned market returns with only half of the market risk.

Over the long-term, it is best to seek out fund managers who consistently outperform the market on a risk-adjusted basis.  Unfortunately, this is not easy to do, and many theorists feel it cannot be done.  Nonetheless, hedge funds are extremely popular among risk-sensitive investors.  For the risk-adverse, a good hedge fund manager will using hedging techniques to lower risk relative to return. These investors are looking for steady returns in both up and down markets.  For risk-seeking investors, a hedge fund’s ability to magnify returns through the use of high leverage ratios is attractive. And, as 2008 market events demonstrated, dangerous.

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Copyright 2010 Eric Bank, Freelance Writer

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