Size and price are independent (unique) risk factors in that they provide investors with exposure to different risks than those provided by exposure to market risks. Evidence of this independence can be seen when we examine the historical correlations of the size and price factors to the market factor. High correlations would mean the risk factors would be relatively good substitutes for each other. If that were the case, while investors could increase the expected return (and risk) of the portfolio by increasing their exposure to these risk factors, there would be no real diversification benefit. If the correlations are low, investors could both increase expected returns for a given level of risk and gain a diversification benefit.

For the period 1927–2008, the correlation of the market risk factor to the size risk factor was .38, and its correlation to the price risk factor .11. The correlation of the size risk factor to the price risk factor was almost zero (.04). In other words, one can effectively diversify equity risks by diversifying across the three independent risk factors. Each risk factor has the potential for increasing investment returns. Two recent examples demonstrate that size and price are independent risk factors.

In the one-factor world, there seemed to be only two ways to increase returns: increase the allocation to stocks or buy higher beta stocks. In either case, investors were taking more of exactly the same type of risk they were already taking. The Fama and French research indicated other ways to increase the expected return of a portfolio. Instead of adding more of the same type of risk, investors could add different types of risk to achieve more effective diversification. The following simplified example (which ignores the diversification return) will illustrate this point.

Assume we expect equities to provide a future annualized return of 7 percent, and we have current bond yields of about 5 percent. Consider a portfolio that is 50 percent bonds and 50 percent stocks. This allocation results in an expected portfolio return of 6 percent. If the portfolio's objective is to achieve a return of 6.5 percent, one way to increase the expected return is to increase the allocation to stocks from 50 percent to 75 percent.

Now consider an alternative strategy, one diversifying risk to other risk factors. For the period 1927–2008, small-cap value stocks achieved an annualized return of 13.0 percent, 3.5 percent higher than the market's annualized return of 9.5 percent. Further assume that same relationship will continue in the future. If we hypothetically forecast market returns of 7 percent, we would also forecast that small-cap value stocks would return 10.5 percent. Using this information, we can look at the expected returns for a few different portfolio allocations.

First, consider a portfolio taking half of the equities and allocating them to small-cap value stocks. The expected return would now be:

By increasing the allocation to riskier stocks we increased the expected return—and the risk of the portfolio. As the result might be more risk than the investor has the ability, willingness, or need to take, let's consider another alternative. This time, while shifting some of the equity allocation to small-cap value stocks (increasing risk), we also lower the overall equity allocation to just 40 percent (lowering risk). The new allocations are 20 percent total market index, 20 percent small-cap value stocks, and 60 percent bonds. The expected return would now be:

We now have a portfolio with a 40 percent allocation to stocks with the same expected return as the portfolio having a 75 percent allocation to stocks. But in this case, instead of increasing the expected return by taking more of the same type of risk (market risk), we increased returns by adding different types of risk: the risk factors of small-cap and value stocks. We diversified our equity risks across these two independent factors. This is a more effective form of diversification. While the expected returns of the two portfolios are the same, their risks are different.

There is another consideration especially important to risk-averse investors (which most are). Since bonds are safer investments than stocks in a severe bear market the portfolio's maximum loss would likely be far lower with a 40 percent equity allocation than with a 75 percent one. Thus, while the expected returns of the two portfolios are the same, the portfolio with the lower equity allocation has less downside risk. Of course, the upside potential during a strong bull market is correspondingly lower. For an investor for whom the pain of a loss is greater than the benefit of an equal-sized gain, reducing downside risk at the price of reducing upside potential is a good trade-off.

Several factors should be given careful consideration when deciding on the appropriate portfolio mix. First, as discussed in Chapter 3, an investor should consider how his or her labor capital correlates with the greater economic cycle risks of small-cap and value stocks compared to large-cap and growth stocks.

The second consideration is a psychological one: tracking error regret. Recall, tracking error is the amount by which the performance of a portfolio varies from that of the total market or other broad market benchmark, such as the S&P 500 Index. By diversifying across risk factors, investors take on increased tracking error risk. While very few investors care when tracking error is positive (their portfolio beats the benchmark), many care when it's negative.

To have a chance for positive tracking error, investors must accept the likelihood negative tracking error will appear from time to time, or there would be no risk. Emotions associated with negative tracking error can lead many investors to abandon carefully developed investment plans. Only those investors willing and able to accept tracking error risk should consider diversifying across the other risk factors.