Here is an old version I wrote last year. Doesnt have the data I showed above unfortunately but makes the point
Effective Diversification in a Three-Factor World
Prior to the publication of the study by Professors Eugene F. Fama and Kenneth R. French the conventional wisdom was that we lived in a one-factor world—the risk and return of a portfolio is determined by its beta. Beta is a measure of equity-type risk (or market risk) of a stock, mutual fund, or portfolio, relative to the risk of the overall (U.S.) stock market. An asset with a beta above one has more equity-type risk than the overall market, while an asset with a beta below one has less equity-type risk than the overall market.
Fama and French hypothesized that we actually lived in a three-factor world—the risk and return of a portfolio is explained by not only beta, but also by its exposure to two other risk factors. Those risk factors are the risk of size (small companies) and price (value stocks). Fama and French found that while small and value stocks have higher beta (they have more equity-type risk), they also have additional risk unrelated to beta. Thus small and value stocks are riskier than large and growth stocks and thus they have higher expected returns. Studies have confirmed that the three-factor model explains well over 90 percent of the returns of diversified portfolios.
For the period the 1927–2005, the average annual returns to these three risks factors was:
·Market Factor (The return of the all equity universe minus the return on one-month Treasury bills): 8.08 percent.
·Size Factor (The return of small stocks minus the return of large stocks): 3.17 percent.
·Price Factor (The return of high book-to-market [value] stocks minus the return of low book-to-market [growth] stocks: 5.03 percent.
Independent Risk Factors
It is important to understand that size and price are independent (unique) risk factors in that they provide investors with exposure to different risks than does exposure to market risks. We can see evidence of their independence when we examine the historical correlations of the size and price factors to the market factor. If the correlations are high, the risk factors will be relatively good substitutes for each other. If that is the case then while investors can increase the expected return (and, of course, risk) of the portfolio by increasing their exposure to these risk factors, there is no real diversification benefit. On the other hand, if the correlations are low, not only will investors increase expected returns, but they will also gain a diversification benefit.
For the period 1927–2005, the correlation of the market risk factor to the size risk factor was just 0.408, and its correlation to the price risk factor was 0.091. And the correlation of the size risk factor to the price risk factor was almost zero (.026). In other words, we can effectively diversify equity risks by diversifying across the three independent risk factors. And each of the three risk factors has the potential for increasing investment returns. The following are two recent examples demonstrating that size and price are independent risk factors.
·In 2001, small stocks returned 18 percent and small value stocks returned 40.6 percent while the S&P 500 produced a negative return of 11.9 percent.
·In 1998, while the S&P rose 28.6 percent while small stocks fell 2.3 percent and small value stocks fell 10 percent.
In the one-factor world there were only two ways to increase returns—either increase the allocation to stocks or buy higher beta stocks. In either case you were taking more of the exact same type of risk you were already taking. The work by Fama and French showed investors that there are other ways to increase the expected return of a portfolio. Instead of adding more of the same type of risk, you could add different types of risk. By adding different types of risk you achieve more effective diversification (not all of your eggs are in one risk basket). The following simplified example (it ignores the diversification return) will illustrate the point.
Let’s assume that in the future we expected equities to provide an annualized return of 7 percent. And we have current bond yields of about 5 percent. Now let’s consider an investor with a portfolio that is currently 50 percent bonds and 50 percent stocks. This allocation results in an expected portfolio return of 6 percent. While developing a financial plan our investor determines that in order to achieve his objective he must achieve a return of return of 6.5 percent, greater than the 6 percent expected return of his portfolio. One way to increase the expected return to 6.5 percent is to increase his allocation to stocks from 50 percent to 75 percent.
(75% x 7%) + (25% x 5%) = 6.5%
Let’s now consider an alternative strategy; one that diversifies risk to other risk factors. For the period 1927–2005, small value stocks achieved an annualized return that was 5.4 percent above the market’s annualized return (15.5 percent versus 10.1 percent). Let’s assume that same relationship will continue in the future. (Note that since size and price are risk factors we do not know that this relationship will continue.) Thus if we are forecasting returns to the market of 7 percent, we would also forecast that small value stocks would return 12.4 percent. Using this information we can look at the expected returns for a few different portfolio allocations.
Let’s first consider a portfolio that takes one-half of the equities and allocates to small value stocks. The expected return would now be:
(25% x 7%) + (25% x 12.4%) + (50% x 5%) = 7.35%
By increasing the allocation to riskier stocks we increased the expected return. We did, however, also increase the risk of the portfolio. The result might be more risk than the investor has the ability, willingness, or need to take. So let’s consider another alternative. This time while we will shift some of the equity allocation to small value stocks (increasing risk), we will also lower the overall equity allocation to just 32 percent (lowering risk). The new allocations are 16 percent total market index, 16 percent small value stocks, and 68 percent bonds. The expected return would now be:
(16% x 7%) + (16% x 12.4%) + (68% x 5%) = 6.5%
We now have a portfolio with a 32 percent allocation to stocks that has virtually the same expected return as the portfolio that had a 75 percent allocation to stocks. Consider, however, that 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 risks of small and value stocks. Thus we diversified our equity risks across these two independent factors. We believe that this a more effective form of diversification. Again, it doesn’t place all of our eggs in one risk-factor basket—while the expected returns of the two portfolios are the same, their risks are, in fact, different.
There is another consideration that is especially important to risk averse investors (and most investors are risk averse). Since bonds are safer investments than stocks, if we were to experience a severe bear market, the maximum loss the portfolio could experience is far lower with a 32 percent equity allocation than it is with a 75 percent equity allocation. Thus while the expected returns of the two portfolios are the same, the downside risk is much less with the portfolio with the lower equity allocation. Of course, the upside potential is correspondingly lower as well. For an investor for whom the pain of a loss is greater than the benefit of an equal-sized gain, reducing downside risk as the price of reducing upside potential is a good trade-off.
There are several factors that should be given careful consideration when deciding on the appropriate portfolio mix. The first is that an investor should consider how their intellectual capital (earning power) correlates with the greater economic cycle risks that small and value stocks have as compared to large and growth stocks. Thus a tenured professor or doctor, with a low correlation to those risks, can prudently take greater small and value risks. On the other, it may not be prudent for a construction or automobile worker, with a high correlation to those risks, to increase exposure to those risk factors.
The second consideration is a psychological one. It is risk called tracking error regret. For equities 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 you take on tracking error risk. While very few investors care when tracking error is positive (their portfolio beats the benchmark), it seems that most investors care when the tracking error is negative. To have a chance for positive tracking error, you must accept the almost certainty that negative tracking error will appear from time to time (or there would be no risk). And, unfortunately, the emotions that negative tracking error can lead to causes many investors to throw their well-thought-out plans into the trash heap. And losing discipline is a recipe for failure. Thus only those investors that are willing and able to accept tracking error risk should consider diversifying across the other risk factors.
Fama and French showed us that there were two additional risk factors that we should consider when constructing portfolios. We can either use those risk factors to increase the expected return (and risk) of a portfolio, or we can maintain the expected return of the portfolio by diversifying across these independent risk factors while lowering the equity allocation. For many investors we believe that diversifying across these independent risk factors is a more effective way to diversify portfolio risk.