We know too that volatility runs in cycles. That suggests that volatility will fall from 2008's lofty level in the years ahead. Let's project that domestic equity volatility will drop moderately to a standard deviation of 12 on a calendar year basis for the foreseeable future.
Foreign equities tend to exhibit even higher volatility from a U.S. dollar-investor perspective, and so we assume a standard deviation of 18, or slightly above the reported figure of roughly 17 for 1998-2008.
As for bonds, volatility for intermediate government securities has fallen in recent years, in part because interest rates dropped to record lows. But interest rates can't fall much further, if at all, and so investors should be suspicious of the recent lull in fixed-income volatility.
For 1999-2008, intermediate Treasurys posted an annualized standard deviation of 5. Yet the 8.8 volatility of the 1980s looks more reasonable going forward. Why? Interest rates were rising in the 1980s, in part because the Federal Reserve tightened monetary policy in the early part of that decade to fight inflation. Although the inflation outlook at the end of 2008 was quite low, bordering on deflation, one could reason that higher rates were coming as the economy rebounds. If so, the trend would likely elevate inflation to something approaching historically average levels. In turn, let's estimate a volatility of 7 for intermediate government bonds, or modestly higher from the reported 5 for the asset class during 1999-2008.
For correlation, consider the ten-year record through 2008 for each of the three asset classes relative to a market-cap-weighted portfolio of the trio, as determined by market values at 1998's close. The resulting correlations for 1999-2008 are 0.97 for U.S. stocks, 0.96 for foreign developed stocks and -0.29 for intermediate government bonds. Correlations tend to rise during severe periods of selling and so the reported numbers are somewhat skewed to the high side for equities in the wake of 2008's dramatic losses.
Meanwhile, due to the rush into the safe harbor of Treasurys last year, the normally low correlation for bonds relative to stocks has fallen further to a modestly negative reading. Anticipating a more conventional relationship for stocks and bonds in the years ahead, let's forecast slightly lower correlations for equities and slightly higher correlations for government bonds. As such, we estimate correlations with the market portfolio of 0.9 for both U.S. stocks and foreign stocks and 0.2 for Treasurys.
Finally, we need to make an assumption about the general level of investor risk aversion, as represented by the Sharpe ratio. This can be thought of as the market's demand for return per unit of risk (volatility). After studying history and reading the literature on risk aversion, we might anticipate a Sharpe ratio of 0.25 for the portfolio.
With the necessary estimates in hand, we can use the equation above to calculate an implied equilibrium risk premium for each asset class:
U.S. Stocks: 2.7%
Foreign Stocks: 4.1%
Intermediate Treasurys: 0.4%
Remember, these are risk premiums and so we need to add an expected risk-free rate to calculate total return estimates. For instance, if we assume that three-month Treasury bills (a common proxy for the risk-free rate) will match the long-term historical inflation rate of 3% for the foreseeable future, our equilibrium total return estimate for U.S. stocks becomes 5.7% (a 2.7% risk premium plus a 3.0% risk-free rate).