A Brief Look At Estimating Equilibrium Risk Premiums

MarketWatch’s Robert Powell reports that “two legendary investors have conflicting points of views” on stocks and bonds. Rob Arnott is cautious on the outlook for equities and Bill Gross is anxious about expected returns for bonds. Putting the two together suggests it’s time to avoid stocks and bonds.

In fact, there’s always a divergence of opinion on where asset classes are headed. Morningstar analyst Miriam Sjoblom wonders if the extra income from high yield bonds is still worth the risk. There’s also worries about REITs and commodities, which have posted exceptionally strong gains over the past year. Nonetheless, there’s no shortage of analysts who think these asset classes are still worth owning. No less is true for stocks and bonds.
In a world of endless opinions and predictions, it’s easy to lose perspective when it comes to strategic-minded investing. You’re surely asking for trouble if you let the data dump that is the Internet overwhelm the big picture. There are lots of smart analysts offering valuable insights, of course, but everyone needs a baseline to begin the critical business of estimating expected returns. But even here, the possibilities are endless and so it’s easy to get lost in a sea of numbers.
How should we begin? One possibility is estimating equilibrium risk premiums for the long haul. It’s no silver bullet, but it offers a good starting point. The basic idea is that making some assumptions about risk and correlation for the major asset classes offers some useful, if not less than flawless forecasts. One of the attractions of this approach is that it refrains from trying to predict returns directly, which is especially hazardous. Instead, the guesswork is focused on the risk side of the equation, which is somewhat more reliable when it comes to divining the future. In turn, reasonable risk estimates imply what the returns should be in the long haul. That may not sound like much, but if can be a valuable foundation for deeper analysis.
The basic idea was outlined in a 1974 paper by Professor Bill Sharpe. Over the years, a number of analysts have reviewed the concept with an eye on practical applications. For example, Gary Brinson outlines a concise explanation of the process in Chapter 3 of The Portable MBA in Investment .
The concept is one of estimating what’s known as equilibrium risk premiums. That is, the excess returns for an asset class—performance less the “risk free” rate of return as defined by, say, 3-month Treasury bills. The equilibrium reference is the assumption that markets clear eventually and so supply equals demand. That’s not all that practical as a short run assumption, but in the long run it’s a fair reading of how markets work. If it were otherwise, beating broad indices would be a breeze, which is definitely not the case.
Here’s what Robert Litterman says of equilibrium risk premium estimates in his book Modern Investment Management: An Equilibrium Approach

We need not assume that markets are always in equilibrium to find an equilibrium approach useful. Rather, we view the world as a complex, highly random system in which there is a constant barrage of new data and shocks to existing valuations that as often as not knock the system away from equilibrium. However, although we anticipate that these shocks constantly create deviations from equilibrium in financial markets, and we recognize that frictions prevent those deviations from disappearing immediately, we also assume that these deviations represent opportunities. Wise investors attempting to take advantage of these opportunities take actions that create the forces which continuously push the system back toward equilibrium. Thus, we view the financial markets as having a center of gravity that is defined by the equilibrium between supply and demand. Understanding the nature of that equilibrium helps us to understand financial markets as they constantly are shcoked around and then pushed back toward that equilibrium.

With that in mind, let’s make some assumptions about the long run future and see how estimated equilibrium risk premiums stack up. First, we need a forecast of the market price of risk. As Brinson notes, this is “the premium the market demands as compensation per unit of risk.” Based on our analysis of our proprietary Global Market Index (a benchmark that passively weights all the major asset classes), our view is that the market portfolio will have a Sharpe ratio of 0.2. Next, we need forecasts of volatility for each of the major asset classes. The third input is estimating each asset class’s correlation with the market portfolio, as per GMI. With those estimates in hand, we can deduce expected risk premiums by multiplying the forecasts for the following variables:
Sharpe ratio for the market portfolio X Standard deviation of a given asset class X The asset class’s correlation with the market portfolio
For example, we’re assuming the market portfolio’s Sharpe ratio will be 0.2 going forward. For U.S. stocks, we’re assuming a 20% annualized standard deviation for returns and a correlation of 0.95 with GMI. The imputed risk premium from these inputs is an annualized 3.8% for domestic equities for the long run future. Remember, that’s before the risk free rate. If you think T-bills will return, say, 2%, then the 3.8% U.S. equity risk premium becomes a 5.8% total return estimate (2% plus 3.8%).
Running this analysis on all the major asset classes gives us the following profile:
The risk premium estimate for GMI is simply adding up the individual estimates and weighting each based on relative market values.
With equilibrium return estimates in hand, we can now turn to the hard work of comparing them with other estimates. The goal is to figure out if our long-run forecasts differ materially with shorter term predictions. If so, we may have developed some valuable tactical information for adjusting the asset allocation for, say, the next 12 months. Any number of alternative methods for forecasting returns can be used, of course. But we can start with a simple review of realized risk premiums. Here’s how the major asset classes compare over the past 10 years:
Keep in mind that the value here is the process as opposed to any one estimate. It goes without saying that some, perhaps all of our estimates will be wrong in some degree. That’s par for the course with peering into the future, regardless of methodology. However, it’s a safe assumption that the market portfolio will randomize the errors, which is why it’s such a competitive benchmark.
The point is that by routinely estimating returns by first considering risk factors, we can develop some useful context. If, for instance, you think that the 3.8% annualized risk premium for U.S. stocks is too low, or too high, that’s an invitation to go back and rethink the underlying assumptions and run additional analysis using alternative models of return forecasting. If your outlook for stocks still radically differs from the equilibrium estimate, maybe there’s a compelling basis for overweighting or underweighting equities relative to the market portfolio, depending on your view.
In the long run, the average investor must hold the market portfolio, which means that the average investor is destined to earn the market’s return. If you’re not satisfied with the prospect of earning an average return, then you need some confidence for rethinking Mr. Market’s asset allocation. Developing that confidence isn’t easy or riskless, but estimating equilibrium risk premiums is a productive way to begin. Just don’t confuse it with an end.