To calculate the equilibrium risk premium for our simple three-asset class portfolio, we add up the weight-adjusted return estimates. Using relative market cap weights as of September 2009, we project an expected risk premium of roughly 3.1% for this portfolio. If we add a 3% risk-free rate, the portfolio's projected total return becomes 6.1%.
How can we use these equilibrium estimates of risk premiums to build a portfolio? One option is running the forecasts for each asset class through portfolio optimization software to determine the optimal asset mix. But this approach has pitfalls and shouldn't be used in isolation. In particular, small changes in assumptions can lead to extreme results in the standard mean-variance model. One solution is using what's known as the Black-Litterman model for taming extreme outputs by integrating an investor's views with equilibrium estimates.
We can use our forward-looking equilibrium forecasts as neutral views of the future. A long-term investor with no particular outlook, or one who deems himself average, should consider the equilibrium projections as the basis for asset allocation.
Alternatively, if you have definite expectations about one or more of the asset classes, those forecasts are the inspiration for altering the neutral weights.
For instance, let's say you're quite a bit more bullish on U.S. stocks for the next three to five years compared to the equilibrium risk premium projection. Adapting that view into the asset allocation in the example above translates into raising the U.S. equity allocation over the passive market cap weight of roughly 41% (as of September 2009) of the total portfolio. A more bearish outlook suggests a below-41% asset allocation for U.S. stocks.
Inevitably, different investors will come to different conclusions about the future. Even your own view on what's coming will change over time as new information arrives. In short, no one forecast should be considered definitive. What seems reasonable today may look unrealistic tomorrow. We should also assume that our forecasts, no matter how thoroughly researched, will be less than perfect. That suggests holding a multi-asset-class portfolio to hedge this risk. As our confidence in our projections increases, so too might our willingness to deviate from the passive asset allocation implied by market capitalization.
We also need to think about the real-world implications if we're expecting, say, a 3% risk premium for the portfolio and end up with less or even a small loss over some period of time. If that possibility is unacceptable, perhaps it's time to go back to the drawing board and reassess expectations, risk tolerance and the asset allocation choices. Indeed, the example above is only a simple illustration of projecting risk premiums, and a deeper analysis may yield different results.
Nonetheless, the future is still uncertain and projecting equilibrium risk premiums won't change that fundamental obstacle. But routinely performing the analysis for the major asset classes and the portfolio overall promotes a deeper level of insight when it comes to changing Mr. Market's asset allocation to match your client's needs. That's hardly the last word on anticipating the future, but it's a reasonable place to start.