**Looking At Large-Caps**

We will now turn to the data comparing the returns of large value stocks to large growth stocks and the S&P 500 Index. Large value stocks outperformed large growth stocks and the S&P 500 Index in 10—or 59%—of the 17 five-year periods. Note that whenever large value stocks outperformed large growth stocks, they also outperformed the S&P 500 Index. The reverse was also true.

In addition, the data provides us with eight nonoverlapping, 10-year periods that we can examine:

- Small value stocks outperformed large growth stocks in seven of the eight periods. The only exception was for the period 1987 through 1996, when small value underperformed by 0.31% per year.
- Small value stocks outperformed the S&P 500 Index in all eight periods.
- Small value stocks outperformed small growth stocks in all eight periods.
- Large value stocks outperformed large growth stocks in six of the eight periods, or 75% of the time.
- Large value stocks outperformed the S&P 500 Index in six of the eight periods, or 75% of the time. Large value underperformed once, and there was one tie (from 1987 through 1996, when they both returned 15.29% per year).

Even these high rates of persistence demonstrate it’s still possible you could wait out a 10-year investment horizon and have a chance that small and large value stocks won’t outperform other asset classes. If there was no possibility of this occurring, then there wouldn’t be any risk in allocating to value over growth. Knowledgeable investors shouldn’t be surprised that we’ve just experienced a 10-year period when value stocks didn’t outperform growth stocks.

**The Probability Of Underperformance**

With this in mind, my colleague, Jared Kizer, examined the likelihood of underperformance across various time horizons for the equity, size, value and momentum premiums. He begins with a demonstration of the observed historical, mean and standard deviation measures for each premium.

The data in the table above contains everything necessary to calculate probabilities of underperformance over any horizon for each of the four premiums. Of course, this all depends upon a normal distribution assumption, which is reasonable for multi-annual returns data because annual returns data is approximately normally distributed for diversified portfolios (and certainly factor portfolios meet the diversification requirement).

The graph below reports the probability of factor returns below zero for each of the four factor premiums over the one-year, three-year, five-year, 10-year and 20-year time horizons: