January 25, 2012
Estimating GMI's Ex Ante Risk Premium
Last week, I updated the Global Market Index’s (GMI) relative performance scorecard vs. actively managed asset allocation products. Now it’s time to look ahead.
For those who don’t know, GMI is an unmanaged index that holds all the major asset classes weighted by their respective market values. As such, GMI is a valuable benchmark because it reflects a broad definition of the opportunity set. Creating benchmarks is the easy part. Modeling expected risk premia is considerably more challenging, but as I noted in my previous analysis of gazing into the future via GMI: the process is "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."
There are several ways to proceed, but for now I’ll review just one approach. The goal is developing some context for considering how GMI’s expected risk premium changes through time and how it compares with the historical record. Note that I’ve calculated the implied risk premium for GMI and so there’s no attempt to forecast returns directly. (For some background on this technique, which I've modified slightly, see the "Reverse Optimization" section in Thomas Idzorek’s monograph.) Instead, I’m making some assumptions about 1) correlations for the major asset classes relative to GMI; 2) volatility for each asset class; and 3) GMI’s ex ante Sharpe ratio. After calculating expected risk premiums for each asset class, I sum the weighted estimates (weighted by current market values).
Much of what I use as assumptions comes from looking to history. The correlation assumptions are calculated based on the historical relationship between realized risk premia for each asset class and the correlation of that performance with GMI’s return. As for the volatility assumptions, those are drawn from a simple GARCH (1,1) model, which arguably provides a slightly more robust estimate of return volatility vs. standard deviation. Overall, I believe that my numbers are fairly conservative--the aim of this caution is boosting the odds that the inevitable forecasting errors will underestimate the actual return rather than overestimate it.
The graph below compares three measures of GMI’s risk premium. The red line is the rolling annualized three-year return for GMI less the risk-free rate (3-month T-bill). The other two lines are estimates of GMI’s expected risk premium through time. The two forecasts are similar in design; the main difference is the definition of the market price of risk, as proxied by the Sharpe ratio. For the strategic estimate, I’m assuming a fixed 0.2 Sharpe ratio, which history and several research studies recommend as a long-term estimate for a broadly diversified portfolio across asset classes. The tactical estimate, by contrast, uses a more sensitive estimate of the Sharpe ratio based on recent history and measuring return volatility with what’s known as a modified value-at-risk metric.
Note that the trailing 3-year realized risk premium and the tactical estimate fluctuate around the strategic forecast, which is designed to be a more stable prediction for the long run future. This isn’t terribly surprising. In the short term, GMI’s risk premium will rise and fall around a relatively long-run mean. At the moment, my estimates suggest there’s a case for thinking that GMI will generate above-average returns. In the long run, however, the numbers tell us that GMI’s expected risk premium is a relatively modest 2.3%. Remember, that’s the outlook before adding your assumption for the risk-free rate.
A 2.3% expected risk premium for GMI isn’t terribly exciting. But maybe my estimate is wrong and the true risk premium will be much higher. Alternatively, if you accept my estimate but want better results you can adjust Mr. Market's asset allocation. The sky’s the limit for possibilities on this front, but so are the risks. You could, for instance, overweight or underweight certain asset classes. Another strategy is actively managing the mix of asset classes in search of higher performance. You could also tap active managers to round out the asset allocation in a bid to earn alpha over GMI's beta.
Nonetheless, earning above-average results isn’t going to be easy. It never is, of course, as history reminds, but it appears that even stronger headwinds are blowing in the quest to mint risk premia. Unless, of course, you're willing to embrace above-average risk.
Posted by jp at January 25, 2012 12:18 PM