Professors Eugene Fama and Kenneth French and my colleague Larry Swedroe have done work highlighting the point that even premia with positive long-run expected returns can still underperform for long periods of time. Such is the nature of any strategy that has potentially attractive but modest risk-adjusted returns.

This piece addresses the same topic with one important adjustment: reducing the expected premia below their long-run averages. Both intuition and published research suggest that return premia tend to deteriorate post-publication (and, of course, some are likely entirely a result of data mining, which is a topic for another day). To get a more realistic sense of how likely underperformance truly is, such an exercise should almost certainly reduce the long-term average returns by some meaningful fraction. Here, I examine probabilities of underperformance for the U.S. market (MKT), size (SMB), value (HML) and momentum (UMD) premia after reducing their long-run averages by 35 percent. I believe this is in line with the research noted above, and one could even argue the reduction should be higher to account for transactions costs. (I’ll examine the impact of larger percentage deductions in a subsequent piece.)

The analytical side of this exercise is very similar to Fama and French’s work. I use monthly returns data from Ken French’s data library from January 1927 through April 2018 to simulate via bootstrap (BTW no idea how it got this name) premium returns over periods of three, five, 10, 20 and 25 years in length. However, in the base case, I reduce the average returns embedded in the historical data by 35 percent for each premium without changing the volatility. I then simulate 10,000 different return paths for each premium and for each horizon, and use these results to examine how frequently the premia can be expected to be negative. Figure 1 shows the results for the MKT premium via histograms of the average monthly return across each of the 10,000 simulations for all five time horizons, with each histogram representing a distinct time horizon.

**Figure 1: Simulated MKT Premia**

The top left histogram is the three-year period simulation followed by the five-, 10-, 20- and 25-year results. This same display pattern is repeated in the other figures that follow. Simulations that ended with an average premium less than zero are shaded lighter blue. The results are quantified exactly in a table further below, but visually we see that all periods have a substantial fraction of the simulations in which the realized MKT premium averaged less than zero, even the simulation horizons of 20 and 25 years. Figures 2, 3 and 4 show the results for the SMB, HML and UMD premia.

**Figure 2: Simulated SMB Premia**

**Figure 3: Simulated HML Premia**

**Figure 4: Simulated UMD Premia**

While the results are certainly better for UMD compared to SMB and HML, all three have a significant number of periods for each horizon in which the realized premium is less than zero. (We also know that, in practice, a lot of the UMD premium is lost to transactions costs, so the results are probably worse than the above graphics account for). Unfortunately, this tells us that even if various premia are indeed expected to be positive over the long term, we will observe long periods of poor performance that do not necessarily indicate the premium has disappeared. In other words, risk is ever present and none of these return premia are strong enough to avoid extremely long periods of underperformance.

Now let’s look at the precise results, comparing the results from the simulations above to the results without any reduction in the average premia.

**Table 1: Estimated Probability of Avg. Premium < 0%**

I believe the results in the grey rows reflect more realistic percentages of underperformance (if anything, possibly still understated) and the likelihoods that investors and their advisors should be prepared for when implementing any of these tilts in portfolios. I’ll further examine the potential implications of these results in a later post.

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