Perhaps the most basic principle of modern financial theory revolves around the concept that risk and expected returns are related. For example, stocks are riskier than one-month Treasury bills and because they entail more risk, the only logical explanation for purchasing stocks is that they must provide a higher expected return. However, if stocks always provided higher returns than one-month Treasury bills, then investing in them would not actually be riskier, and hence there would be no risk premium.

In fact, in 24 of the 89 calendar years from 1926 through 2014, or 27% of the time, the S&P 500 Index produced negative returns. In addition, there have been periods when the S&P 500 Index produced severe losses:

• From January 1929 through December 1932, it lost 64%.

• From January 1973 through September 1974, it lost 43%.

• From April 2000 through September 2002, it lost 44%.

• From November 2007 through February 2009, it lost 51%.

The very fact that investors have experienced such large losses leads them to price stocks with a large risk premium attached. For instance, in the period from 1927 through 2014, the S&P 500 Index provided an annual average risk premium over one-month Treasury bills of 8.2%. An indicator of how risky stocks can be is that the annual standard deviation of the equity risk premium was 20.2%, or 2.5 times as great as the premium itself.

We can extend this logic to the risks involved with investing in small-cap and value stocks.

Small companies are riskier than large companies. Therefore, the market prices small-cap stocks to provide higher returns than large-cap stocks. From 1927 through 2014, small-cap stocks provided an annual average size premium of 2.9%. However, small-cap stocks have not always outperformed large-cap stocks. If they did always outperform, there would be no risk involved with investing in them relative to large-cap stocks, and there would be no risk premium.

• From January 1969 through December 1974, small-cap stocks under-performed large-cap stocks by a total of 47%.

• From January 1986 through December 1990, small-cap stocks under-performed large-cap stocks by a total of 33%.

• From January 1994 through December 1998, small-cap stocks under-performed large-cap stocks by a total of 30%.

Further evidence of the risk associated with investing in small-cap stocks is that, while the small-cap risk premium has been 2.9%, the annual standard deviation of the premium over this period has been 12.6%, 4.3 times the premium.

From the perspective of traditional financial theory, value companies are considered riskier than growth companies. Therefore, the market prices value stocks to provide higher returns than growth stocks. From 1927 through 2014, value stocks provided an annual average value premium of 4.8%. However, value stocks have not always outperformed growth stocks. If they did, there would be no risk to investing in them relative to growth stocks, and again there would be no risk premium.

• From March 1934 through March 1935, value stocks under-performed growth stocks by a total of 43%.

• From June 1998 through February 2000, value stocks under-performed growth stocks by a total 44%.

• From April 2007 through November 2011, value stocks under-performed growth stocks by a total of 21%.

Just as with the size premium, the value premium is volatile. The annual standard deviation of the value premium, at 12.6%, historically has been roughly 2.6 times the size of the premium.

The bottom line is that the outperformance of stocks relative to Treasury bills, small-cap stocks relative to large-cap stocks, and value stocks relative to growth stocks isn’t a free lunch. There are risks involved. And it’s a virtual certainty that these risks will show up from time to time.

Unfortunately, we neither know when, or for how long, these periods of relative underperformance will last, nor how severe they will be. Therefore, having the discipline to adhere to your investment plan becomes a necessary ingredient for investment success. Ignore the noise of the market and the emotions (fear and envy in bull markets and greed and panic in bear markets) fueled by it.