Forecasting risk premiums is a dirty business, but it’s necessary unless you’re truly a buy-and-hold investor with a very long time horizon. How many individuals fit into that category? Very few is probably a good estimate. For the rest of us, developing some intuition about expected risk premiums—the returns that are left after subtracting a risk-free rate a la Treasury bills—is useful, perhaps essential. It can be dangerous as well, but that’s the nature of toiling in risk.

In any case, it’s a constructive exercise if only to think through your assumptions and stress test them against history and the alternative methodologies for predicting risk and return, of which there are many. It’s a devilishly tricky subject, mainly because of our old nemesis… uncertainty. Accordingly, there’s no silver bullet and so it’s wise to consider several applications and compare the results.

Where to start? I like to begin with equilibrium estimates of risk premia. Why? One reason is that it’s a process that doesn’t attempt to forecast returns directly. Instead, it uses risk and correlation assumptions, which are somewhat easier to predict, as a means for considering the implied ex ante risk premia. Let me emphasize again that this is a starting point—a benchmark, if you will. With equilibrium estimates in hand, we have some context for adjusting the forecasts with any number of competing approaches. For some background and a review of how to crunch the numbers, consider Chapter 3 by Gary Brinson in The Portable MBA in Investment. I also dive into a bit of the details in Chapter 9 of my book Dynamic Asset Allocation.

For now, let’s update recent history on some of the fundamental inputs. Here’s how the annualized risk premia compare over the trailing three and 10-year periods through August 2011 for the major asset classes and my Global Market Index (GMI), an unmanaged value-weighted mix of these assets. GMI is our benchmark for “the market.”

Let’s also consider how the major asset classes and GMI stack up on a risk-adjusted-return basis in recent history via the Sharpe ratio:

Next, let’s make some assumptions for calculating equilibrium estimates of risk premia, as per the formula:

Risk premium estimate = Sharpe ratio * volatility * correlation

First, we need an estimate for the market’s price of risk. For simplicity, let’s simply use GMI’s Sharpe ratio of 0.2 for the past three years. Yes, this is naïve, but in the interest of brevity let’s take it at face value for now. On that note, 0.2 is somewhat conservative, at least relative to recent history over the past decade, and so if anything we’re probably erring on the side of caution here.

Up next are the estimates of volatility for each of the major asset classes. In this case I’ve reviewed each individually and made some assumptions, based on a mix of history and forward-looking guesstimates. Ditto for the expected correlations for each asset class and how they relate to GMI.

After plugging the estimates into the equation above, we end up with the following equilibrium risk premia forecasts:

Formally, these are the long run risk premia estimates for the infinite future for the average investor based on the assumption that in time the markets will “clear.” The value in these estimates is the process rather than the data points per se. Yes, our heroic attempt to peer into the future is likely to be wrong in some degree. But that inspires thinking about why it will be wrong and how we could improve our estimates.

One implication of assuming our predictions are subject to uncertainty is that we should be cautious in thinking that we’ll be able to beat the market portfolio easily, if at all over the long run without making sizable bets that incur a high degree of risk. The history of real world track records indicates as much, as I recently discussed here. Sure, you can make relatively dramatic changes to Mr. Market’s asset allocation by, say, overweighting stocks, leaving out a few asset classes altogether, emphasizing active management, adding “alternative” betas to the mix, etc. In fact, there are fundamental reasons for customizing the passive asset allocation mix. Depending the degree of your relative bets, you’ll either beat the market or trail it. It all boils down to how much confidence you have in your forward-looking estimates of risk premiums. Again, history suggests that most investors should be somewhat humble. For those who can tolerate a high degree of tracking error relative to GMI (or whatever benchmark you deem relevant), well, by all means, embrace your convictions.

Meantime, keep in mind that there are some enduring truths in finance—truths that don’t change no matter how much confidence you can muster. One is that in the grand scheme of investing, market-beating return (alpha) is financed solely by the losers. The benchmark ends up in the middle, as usual. And depending on trading costs, taxes and other frictions, the benchmark could very well end up in the above-average category relative to the active competition.

John HallI prefer a Black-Litterman approach to estimating implied risk premium (similar to what you do, but better). Instead multiply lambda*sigma*(w-wrf), where w-wrf is the portfolio weight minus a portfolio 100% in the risk-free, sigma is the covariance matrix, and lambda can be set as expected return of w-wrf over the variance of w-wrf.