These departures from equilibrium provide strategic-minded investors with guideposts for exploiting the apparent opportunities, he continues. Financial markets have a "center of gravity" that's defined by the equilibrium between supply and demand, Litterman advises. As a result, investors should take advantage of the deviations from equilibrium. "Understanding the nature of that equilibrium helps us to understand financial markets as they constantly are shocked around and then pushed back toward that equilibrium."
The first rule in forecasting equilibrium performance for the various asset classes: Avoid the trap of trying to predict returns directly. A superior approach is inferring risk premiums from the interaction of investor risk aversion, market volatility and the correlations of returns. Developing robust estimates is still prone to error, of course, but the odds for success are better, if only slightly, by analyzing risk compared with trying to forecast returns outright. For example, financial research reveals that the ratio between any two risk premiums generally matches the ratio of correlation between those premiums. In turn, that tells us something about how to think about expected return. Simply put, reverse engineering risk premiums by measuring and analyzing risk is a more reliable way to anticipate return.
Using the formulation outlined by money manager and asset allocation expert Gary Brinson in The Portable MBA In Investment (Wiley, 1995), the equilibrium risk premium estimate for a given asset class is calculated as:
Sharpe ratio x ?i x ?im
with the variables defined as
Sharpe ratio = the price of risk, or the asset's return over the risk-free rate divided by the asset's annualized volatility (standard deviation of return). This is a proxy for the general level of risk aversion, which is derived from investors' utility functions. Higher levels of risk aversion equate with a greater demand for return per unit of risk, and vice versa. In equilibrium, this relationship is proportional across assets and applies to the market portfolio overall.
?i = standard deviation (volatility)
of asset i
?im = correlation of asset i with portfolio m
As a basic example of estimating risk premiums, imagine that the market portfolio is comprised of three assets: domestic stocks, foreign stocks in developed markets and intermediate-term U.S. Treasurys. (In practice, strategists should define the market portfolio as broadly as possible.) As proxies, we'll use the S&P 500 (U.S. equities), MSCI EAFE (foreign equities) and a five-year Treasury bond.
To keep the following example manageable, we'll simplify the analysis. Let's begin with the recent history of U.S. stock market volatility. Historical data offers a practical starting point, but the past should only be a guide. Consider that standard deviations rose sharply in 2008 amid the dramatic sell-off. That compares with relatively low volatility for equity returns during 2004-2007, a period of generally rising asset prices. During those four years, annualized monthly standard deviations of large-cap U.S. stocks in each calendar year ranged from roughly 6.5 to a bit over 10 before jumping to more than 14 for 2008, according to Ibbotson SBBI 2009 Classic Yearbook (the source for all subsequent data cited unless otherwise noted).