Embrace risk, but only over the long haul

Since the 1992 publication of "The Cross-Section of Expected Stock Returns," the Fama-French three-factor model has been the dominant conceptual framework used in financial research. Put simply, the model's premise is that the returns of well-diversified portfolios are explained by their exposure to three factors:

• Beta -- the exposure to stock-market risks
• Size -- the risk of small-cap stocks
• Value -- the risk of value stocks

The first thing we need to discuss is how the premiums are calculated. The equity premium is calculated as the return on the total stock market minus the return on the riskless asset, one-month Treasury bills. The size premium is calculated as the return on small-cap stocks (CRSP 6-10) minus the return on large-cap stocks (CRSP 1-5). The value premium is calculated as the return on value stocks (deciles 8-10 ranked by book-to-market) minus the return on growth stocks (deciles 1-3 ranked by book-to-market).

Now let's look at the size and persistence of the premiums. First, it's important to note that risk premiums are calculated as annual averages. The table below shows the size of the annual premiums. as well as their standard deviations. The period is 1927-2011.

Note how volatile the premiums are: The standard deviations are multiples of the risk premiums. This is a good indication that they're risk premiums, not free lunches.

Next, we will look at the persistence of the premiums. The table below presents the data for the same 1927-2011 period. The data shows the percent of the rolling periods the realized premiums were positive.

There are a few important observations we can make, although not before some caveats. The above data is based only on U.S. investment history. There is also no guarantee that history had to play out the way it did -- events could have been profoundly different. Meanwhile, this data is based on rolling periods; we have very few non-overlapping (independent) 10- and 20-year periods.

With those qualifications in mind, here is what we can infer from these figures. First, the likeliness for the risk premium to be positive increases as the horizon increases. The fact that the equity premium was positive 100 percent of the time when the horizon was 20 years leads many to the incorrect conclusion that stocks are only risky if your horizon is short. As stated earlier, alternative histories could have played out. For example, Japanese investors have certainly had a very different experience since 1990. Stocks are risky no matter how long the horizon.

Second, once we extend the investment horizon to beyond five years, the value premium becomes more persistent than the equity premium. This is an important reminder, as the value premium has been negative for four of the past five years. Looking at the table above, we can see that this is nothing new. This pattern has actually occurred about 15 percent of the time.

Third, the size premium is less persistent than the value premium. However, it's important to note that this is to some degree explained by how the premiums are measured. Value stocks are considered the top 30 percent when ranked by book-to-market. On the other hand, small stocks are considered the bottom 50 percent when ranked by market cap. If they were considered the bottom 30 percent, not only would the premium have been larger, but it also would have been more persistent.

There's one more important point we need to cover. As another demonstration that the risk premiums aren't free lunches, consider the following:

• The equity premium was negative for the period September 1929-January 1945
• The size premium was negative for the period May 1981-July 2003
• The value premium was negative for the period May 1988-October 2000

The data clearly shows that you can wait a long time to be rewarded for taking incremental risks. The lesson is that you should only invest in risky assets if you have the patience and discipline to adhere to your plan. If you're going to be tempted to abandon your plan when there are the inevitable long periods of underperformance, you should avoid the risks in the first place.

Otherwise, you will likely end up like most investors -- buying only after periods of strong performance (when expected returns are now low), and selling after periods of poor performance (just when expected returns are now high). You'll also likely be reciting this unhappy refrain: I own last year's top-performing asset classes, only I bought them this year!