The equity risk premium stands at the heart of the asset allocation decision. Wharton professor Jeremy Siegel, who popularized the concept for many investors, once noted that if it was less than 3%, than it wasn’t worth the risk. This at a time when long Treasuries were yielding 3% and Robert Arnott and Peter L. Bernstein were arguing for a going-forward (aka ex ante) risk premium of 0. That was 2003, when 30-year Treasuries had been discontinued thanks to the prospects of government surpluses that stretched out ad infinitum.
Siegel was so backward (aka ex post). So what to count on: the past we know but can’t repeat, or the future we can’t know but hope to cheat. Along comes one of those useful meta-analyses, useful not for their accuracy – because they’re already three steps removed from the original data – but for their impact on hubris.
Casper van Ewijk, Henri L.F. de Groot, and Coos Santing, researchers at the University of Amsterdam, the Tinbergen Institute and the Dutch Ministry of Finance suggest that “meta-analysis provides us with a toolkit of statistical techniques enabling a quantitative review of the existing literature. As such, it complements narrative reviews.” (Your narrator has been warned.)
In an engaging paper, they treat a number of issues:
“- First, the equity premium as measured from ex post stock returns proves to be quite sensitive to the observation period….
“- A second, and related, controversy concerns the question whether the equity premium is constant over time.
“- Third, the equity premium may vary across space. There is no strict need that the equity premium should be identical across countries and regions.”
Let’s take them up seriatim.
Ex post, the equity risk premium looks substantial. But there’s no guarantee history recurs (not on conditions of the investors’ choosing). Secondly, if one were to insert oneself into history that ex post premium is considerably higher than what would have been expected ex ante – thanks to rising price/equity ratios. At very least, the equity risk premium has bounced around.
Thirdly, there may be survivorship bias in ex post analyses, not only survivors among companies, but among stock markets. Taking global markets as the benchmark rather than the U.S., then the historical risk premium declines to 0.29% instead of a robust 4.3%. Hardly worth the effort to getting the stock screens fired up.
So what does the meta-data say? Well, there’s 24 studies, with 535 observations. The result is reproduced below:
While the researchers slice and dice the premium across time,with little indication of any consistency (the 1920s and the post-war era had high equity risk premiums, with huge gaps before, in between, and possibly after, once we assess the impact of the Great Liquidity Crunch), across space there’s an interesting conclusion: “We find that the equity premium is relatively high in emerging countries. The lowest average equity premium is found in Canada, and the highest is found for the Asian Tigers. The mean of the equity premium for these groups of countries varies from 3.95 percent in Canada to 13.14 in the Asian Tigers.”
There are other useful findings, to wit: “the equity premium tends to be higher in studies that use the arithmetic mean, the ex post method and the short term interest rate.” That’s opposed to studies using a geometric rate, ex ante anticipations and long-term bonds as the measure of the “risk-free” rate.
Remember, with meta-analysis we are now at least three steps away from the original data. Now comes the fourth step: meta-regression. Canada still comes out badly, compared to the U.S., while the Asian Tigers race ahead.
Why would that be?
“Going one step beyond the standard meta-analysis we will also explore some underlying economic fundamentals of the equity premium…. Specifically, we look at the impact of volatility of income, the stage of development of the country, the interest rate and inflation. Both the stage of economic development and income volatility can influence the price of risk underlying the equity premium.”
Upon meta-reflection, don’t blame Canada. The vagaries of the investment calculation “can easily add up to 3.5% points between the extremes of ex ante/geometric/bond rate on the one hand and ex post/arithmetic/Tbill rate.”