Laws, Sausage, And Risk Premia Forecasts

Bismark Bismarck may have been misquoted when he reportedly said “laws are like sausages, it is better not to see them being made.” Whoever is the source, the observation applies to estimating expected returns. The end result is forever in high demand, but the details for generating the numbers can get messy.

The subject of looking into the quantitative grinder that spits out return forecasts was topical on these pages after yesterday’s monthly update of risk premia projections for the major asset classes and the Global Market Index (GMI). Several readers inquired about the upward drift in the estimates, the US equity forecast in particular: the expected 8.5% annualized premium (for the unadjusted estimate) looked quite high. Could that be right?

Questioning the accuracy of forecasts is always and everywhere prudent, and so the latest risk premia estimates offer a teachable moment. Let’s go down this rabbit hole a bit, if only as an excuse to review best practices for using forecasts.

Let’s start with the big-picture observation that all forecasts deserve to be treated cautiously. The monthly estimates presented here are first and foremost offered as an academic exercise, which is to say that the obvious caveats apply. The equilibrium model that’s used to generate the data is quite useful as a starting framework, but the unavoidable task of making assumptions on the data inputs can lead to a variety of outcomes. The key point: any model you use needs to be tweaked to make it useful for you. Accordingly, there are no generic solutions that apply to everyone.

Inevitably, estimating performance of asset classes and portfolios is a mix of art and science, with a greater emphasis on the former than some folks realize.

More generally, a responsible way to use forecasts, in my view, is to combine predictions from several sources, each using a different methodology. Just as you shouldn’t rely on a single market or asset class for portfolio design, it’s unnecessarily risky to use one set of forecasts for anticipating risk premia.

With that in mind, the equilibrium risk estimates published by The Capital Spectator each month represent an opening bid, so to speak, on developing a richer set of estimates. As to the question of why the US equity forecast appears high, let’s review the key points that provide the answer.

The equilibrium model requires three inputs:

  • An estimate of the overall market price of risk, which is defined here as the Sharpe ratio for GMI.
  • An estimate of volatility for each asset in the portfolio
  • The correlation of each asset with the overall portfolio

Ideally, these inputs should be ex ante numbers, but I’m using ex post data for the project as it appears on The Capital Spectator. That may not be ideal, but it serves as a reasonable baseline.

Another subjective decision has been to use a rolling 16-year historical sample of GMI’s Sharpe ratio as an input. Why 16 years? When I started publishing these estimates several years ago that was the full extent of the available data. Yes, you can find historical numbers on assets that go back much further in time, but that doesn’t help if you’re building a global market index that uses all the major asset classes, some of which have limited histories. Inflation-protected Treasuries, for instance, only date to the late-1990s.

In any case, I’ve continued to use the rolling 16-year Sharpe ratio for GMI in order to maintain consistency in comparing the current forecasts each month with the vintage history. The question is whether using a longer set of data that’s now available for this project, which begins in Jan. 1998, would offer 1) a different and 2) superior set of forecasts. On the first point the answer is clearly “yes.” As to the second point, the answer requires a deeper discussion, and one that I’ll conveniently avoid for now.

Meantime, here’s how the risk premia forecasts stack up when we use the GMI’s full history for estimating the Sharpe ratio input:

Note that the US equity risk premium forecast above is lower when we use the longer run of GMI’s Sharpe ratio vs. the estimate published yesterday. Why? The short answer is that the longer stretch of numbers includes more periods of challenged market conditions, which ultimately trims most of the forecasts. For instance, the US equity risk premium in the table above is 6.1% — more than 200 basis points below the 8.5% in yesterday’s forecast.

The larger point is that there are no standardized rules for developing risk premia forecasts. Subjectivity in choosing historical periods and making other assumptions about any given model will vary from investor to investor. The ultimate goal is to understand the assumptions of the model (or models) in an effort to develop a level of comfort and confidence in the results. That translates into finding acceptable compromises. But the compromises that you’re willing to live with will almost certainly differ from what others deem acceptable.

The bottom line: there are no one-size-fits-all models. Rather, every project for developing risk premia estimates should be and must be customized to match the expectations and objectives of a specific investment strategy. That’s certainly been true for the various consulting projects I’ve been engaged in.

With that in mind, I’ll be rethinking the format of The Capital Spectator’s monthly risk premia estimates. On that note, feel free to share your thoughts.

Meantime, let’s not forget George Box’s famous quip that “all models are wrong, but some are useful.” The goal, then, is to customize a forecasting project so that the results are useful for you (and your clients). By definition, such a project will reflect a unique set of assumptions and data choices. Perhaps, then, we should adjust Box’s observation and recognize that all models are wrong, but the one that serves your specific objectives and assumptions can be useful.

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