small company index funds. Investing in these funds is the most efficient and effective way to maximize exposure to the three risk factors that generate 95% of the market returns. For example, DFA offers investors value index funds that are structured to (1) maximize exposure to the size and price risk factors and (2) diversify that exposure as much as possible. This building block approach to building portfolios is a cleaner and more consistent way of managing money.

How a portfolio is structured for optimal exposure to the three risk factors determines how well the portfolio performs relative to other portfolios. Portfolio structure refers to the indexes the portfolio holds and in what proportions. The Fama and French findings offer guidelines to investors for effectively allocating indexes within a portfolio. The allocation decision is crucial, since the degree of exposure to the three risk factors for equities and two additional factors (term and default) for fixed income accounts for nearly all the returns earned by diversified portfolios of stocks and bonds. That’s why investors should focus on properly structuring their portfolios rather than trying to pick winning stocks or managers.

Measuring the Performance of Active Managers

Indexes such as the S&P 500 or Wilshire 5000 are often used to evaluate the performances of active money managers. Given the Fama and French findings, the use of such benchmarks is often misleading. Because these indexes are weighted heavily towards large company stocks and high priced stocks, the performances of managers investing more heavily in small company stocks or low priced stocks won’t be accurately measured by them. Instead, customized benchmarks are needed to provide accurate measurements of the contributions to performances made by active money managers.

The Fama and French Three-Factor Model is a superior way to evaluate the performances of active money managers. It shows whether a manager achieves returns in excess of index returns. After all, an active manager shouldn't’t be rewarded just for buying value stocks—that’s something that can be done inexpensively with an indexing strategy.

The place where a portfolio is positioned or structured on the cross hair map in Figure 8-18 determines the vast majority of its return. The cross hair map doesn't’t plot the market risk factor since all stock portfolios take similar market risk and are plotted relative to the stock market. So, there’s no need for a separate axis; instead, the stock market sits right at the cross hairs of the map. The cross hair map has two dimensions. The size dimension is plotted along the vertical axis, and the value (BtM) dimension is plotted along the horizontal axis. The axes represent exposure to these two risk factors. Portfolios that take on a lot of size risk appear higher along the size axis, and portfolios that take on a lot of value risk appear further along to the right on the growth/value axis.

Changing the Definition of “Alpha”

The Fama and French Three-Factor (Five Factors with bonds) Model changes the definition of alpha, as seen in Figure 8-19. According to the one-factor CAPM, alpha is the amount by which an active money manager outperforms a broad market index. The Fama and French Three-Factor Model defines alpha for equities more precisely as the return an active manager achieves above the sum of the portfolio’s expected return due to all three equity risk factors. Alpha measures a manager’s skill in earning a return that couldn't’t have been achieved by indexing the same exact risk exposure as the portfolio run by the manager. In short, did the money manager earn anything above the indexed return?

A portfolio can be plotted anywhere on the cross hair map, and it’s easy to calculate its expected return. For example, a small-cap manager may overweight value stocks relative to a benchmark, such as the Russell 2000 Small-Cap Index. As a result, the manager outperforms it. But if the extra return was simply compensation for taking additional non-diversifiable market risk, why should the manager get credit? The job of an active manager is to consistently outsmart the millions of other traders who get the same news at the same second, and through this process provide additional returns that can’t be achieved through indexing. This is exactly what the alpha is in the Three-Factor Model. Investors should insist that a manager outperforms a three factor risk adjusted benchmark before crediting him with an alpha return. After all, active manager fees are supposed to pay for predicting the future of stock prices, not for taking additional market risk from low cost index funds.

So, what “positive alpha” managers have been doing with the one-factor CAPM measurement model is just systematically subjecting their clients to two additional risk factors - size (small company) and high BtM value (distress). Thus, what’s showing up as alpha (skill) is nothing more than a measurement error. If the performances of active managers are compared between CAPM and the Fama and French model, there are radical changes in the outcomes. Any evidence of manager skill just vanishes under the Fama and French model. The formula for this type of analysis is summarized in
Figure 8-19.

Even though active managers focus on alpha, the amount of return due to alpha from stock picking or market timing is random, and on average is expected to be negative. It turns out that alpha is nothing more than a myth perpetuated by the improper measurement of a manager’s performance.

Higher Expected Returns of Value and Small Company Stocks

Long-term investment data makes it clear that value stocks outperform growth stocks and small company stocks outperform large company stocks, as seen in the 80 years of returns data from all over the world seen in Figure 8-20.

Figure 8-20


But there has been some debate as to what causes these stocks to outperform large company stocks. Why are there differences in the expected returns of these indexes?

In one corner of the ring are those who say that value and small company stocks outperform because investors mistakenly price the value of the future earnings of distressed companies too low. This is the “market inefficiency” view. That is, investors see the poor earnings and high risks of value and small company stocks and decide that they are worse investments than they really are. As a result, the market sets erroneously low prices for these stocks. In effect, the combination of all market participants’ opinions is wrong, and they agreed on a price that undervalues these stocks. When value and small company stocks then go up, the market is surprised. If investors guessed wrong in the past, presumably they should learn from their mistakes and guess right in the future. But, according to the market inefficiency point of view, investors will continue to repeat these mistakes in the future, thereby allowing other investors such as certain professional stock pickers to outperform them and the market. The market inefficiency view holds that the value and size risk factors turned up by Fama and French aren't’t really fundamental sources of risk, just opportunities for stock picking.

The field of behavioral finance would add that these mispriced stocks are over or under reactions of investors to market news. A study by Eugene Fama titled “Market Efficiency, Long-Term Returns, and Behavioral Finance,” indicates that this may be the case, but such reactions are random and therefore not a viable investment strategy. That paper and many other academic papers can be found on the Internet at www.ssrn.com.

Eugene Fama and other proponents of efficient markets say that the higher expected returns of small and value stocks are compensation for bearing the greater risk.

According to this “market efficiency” view, greater risk and cost of capital of these firms creates higher expected return for investors, reflected in the lower prices relative to book value for value stocks, and the lower market capitalizations of small company stocks. Quite simply, there are differences in expected returns because there are differences in risk. If value and size truly are risk factors, their expected return premiums shouldn't’t disappear, even when more investors are informed about the favorable risk/return relationships. As a result, there shouldn't’t be a predictable decline over long periods of time in the probability distributions of future returns generated by these stocks, compared to the safer overall market returns. Remember that the expected returns for these risk factors have standard deviations of about 13%, (see again Figure 8-14) so an expected return of about 4%, plus or minus 13% two-thirds of the time, is a very wide probability distribution.

Regardless of whether an investor thinks that the higher returns of value and small company stocks are a result of habitual mispricing (market inefficiency) or rational risk compensation (market efficiency), the conclusion is the same. It would behoove investors to include value and small company stock indexes in their diversified portfolios.

The Dimensions of Bond Returns

Bonds are a component of investment portfolios because they dampen the volatility of stocks due to their low correlations to movements of stock prices. Bonds also provide short-term liquidity to investors with cash needs over a two to four-year period.

There are two primary risk factors that explain bond returns. The first is the term factor, which is the difference between the returns of long-term government bonds and short-term Treasury bills. The annual average return for the term risk factor has been 1.99% for the 80 years from 1927 to 2006.

The second risk factor is the default factor. It measures the difference between long-term corporate bonds and long-term government bonds, assuming that governments are less likely to default than corporations. The annual average return for the default risk factor has been 0.31% for the 80 years from 1927 to 2006.

While the term provides higher expected returns, the excess returns diminish significantly beyond a term of five years as can be seen in Figure 8-21, so bonds with terms of more than five years should be avoided.

If investors keep terms or maturities short and default risk relatively low, they have more opportunity to capture the much higher expected returns from the size and price risk factors of stocks.

Figure 8-21

The Five Dimensions of Risk Exposure

Now that we have the three risk factors of stocks and the two risk factors of bonds, we can look at the explanation of returns for balanced portfolios that include stocks and bonds. Take another look at Figure 8-19 for a verbal equation that explains all five of the risk factors of stocks and bonds. The chart below summarizes all 5 Risk Factors.




The Trade-offs between Risk and Return

Risk and return are inseparable. This means that investors must often face bedeviling trade-offs between risk and return. There’s no way around these decisions, since they’re required in order to build portfolios. For example, sometimes investors look at short-term CD rates. They like the certainty and stability of CD returns, but they feel they need to obtain higher returns. So, these investors turn to stocks. But, when they focus on the years of negative returns, they become uncomfortable because of their aversion to losses.

The result of all this is the “eat well/sleep well dilemma.” That is, if investors want to eat well and earn higher returns with stocks, they need to be prepared to take more risk and go through the volatile roller coaster ride of fluctuations in the value of their portfolio. But if they want to sleep well, they must take less risk; that is invest in fixed-income investments such as bonds, and accept that they’ll earn lower returns. Thus, the price of obtaining greater long-term accumulation of wealth with stocks is frightening fluctuations in the value of a portfolio. There really is no free lunch in investing. It’s the same old story of risk and return trade-offs identified by Markowitz.

Investors can select from a wide array of risk and return combinations when building efficient portfolios. Figure 8-22 shows the risk and return trade-offs for various Fama and French indexes over about an 81-year period from January 1928 to December 2009.

Figure 8-22

High risk exposure is like a scream inducing roller coaster with soaring highs and stomach churning lows. Investors should hop on a milder ride if they don’t like the extreme rush of the one they’re on. The same concept applies to investing. However, not everybody has the capacity for such exposure to risk. Figure 8-23 shows the roller coaster like returns of five different index portfolios. The gold colored Index Portfolio 90 has higher highs and lower lows than the other lower risk portfolios. Also, note that the growth of $100,000 over 35 years is higher for the higher risk Index Portfolio 90. Figure 8-24 shows what the one index of small value stocks looks like on the same scale. These graphs provide a vivid illustration of the concepts of risk, return, and time. They are available in dynamic versions that allow movement and selection options, see below.

Figure 8-23

Figure 8-24

8.2.9 Time Diversification of Risk

Charles D. Ellis said, “The average long-term experience in investing is never surprising, but the short-term experience is always surprising.”

Figures 8-25 through 8-29 illustrate this famous quote by Ellis, one of the first proponents of indexing. These charts show 50 years of returns on monthly, quarterly, annual, five-year, and ten-year periods, and will help investors better understand the time element of riskese. These are clear indicators of the reversion to the mean concept already described. Does time reduce risk? For many years, this question has generated a hot debate among academic researchers and investment professionals.

On one side are those who believe that the risk involved in holding stocks is reduced the longer the investment time horizon. This belief is based on two facts.

First, as the investment time horizon lengthens, the actual average annual compound return achieved by a stock portfolio converges to its expected returns. As the period of measurement changes from monthly to every seven years, the volatility of returns reduces, and the existence of a losing period diminishes.

Figures 8-25 through 8-29 show that the chance of incurring a negative return declines as the time horizon lengthens. In these studies, the chance of negative returns virtually disappeared when returns were graphed every five years. This long-term horizon phenomenon occurs because the risk or standard deviation of holding an all equity portfolio drops by 67% (from 19.2% to 6.4%%) when extending the investment time horizon from one year to five years. After 10 years, 78%% of the risk (now down to 4.2%) has been eliminated.

Figure 8-25

Figure 8-26

Figure 8-27a

Figure 8-27b

Figure 8-28

Figure 8-29