Researchers did not
have a very good idea about what sources of investment risk actually produced
higher returns until 1992. They previously only had Sharpe’s One-Factor
Model to explain how investment returns were derived as seen in Figure
8-13. Sharpe’s One-Factor Model explained only
about 70% of the returns of the stock market, but when two additional factors were considered, about 90% of the variability of returns of diversified portfolios can be explained.
Fama and French concluded that exposure to three risk factors —
market, size, and price (book-to-market) — collectively do the
best job pinpointing the sources of investment risk that account for
stock market returns. Risk factors are sources of risk that the stock
market seems to reward over the long run. Based on the Fama/French findings,
these three risk factors constitute the dimensions of stock returns.
To review the average annual returns for the 84 years from 1928 - 2011, see Figure
Here are two video clips with Kenneth French, Eugene Fama Senior and Junior, and several members of the DFA staff explaining the significance and importance of Three Factor Model for equities.
Depending on which study you review, these three risk factors
combined explain between 90% and 96% (as seen in Figure 8-14a) of the returns of the market in U.S. Studies have been completed in international markets with risk factors unique to those markets, and similar conclusions were obtained. These findings suggest that an investor’s investment
performance in comparison to the stock market or other investors depends
almost entirely on the percentage of stocks (market factor) held in a
portfolio, and more specifically, the amount of small stocks (size factor)
and high book-to-market ratio stocks (value factor) held.
Figure 8-15 illustrates the three dimensions of market, size, and value in 20 different index portfolios, as seen in Appendix A. Each colored circle represents one index portfolio, with the red button representing the highest exposure to market, small size stocks and value stocks.
The first risk factor in the Fama/French Three-Factor Model is the amount
of exposure to the overall stock market or the market risk factor. Exposure
to this factor is determined by the amount of a portfolio that’s
invested in or exposed to stocks. The greater this exposure, the higher
the return in comparison to U.S. Treasury bills.
To help you remember the concept of Market Risk versus 30 day T-Bill Risk, we created this painting.
The second risk factor in the Fama/French model is the amount of exposure
to small company stocks or the size risk factor. Exposure to this factor
is determined by the amount of a portfolio that is invested in small company
stocks. The greater this exposure, the higher the return in comparison
to large company stocks.
Small company stocks have small market capitalization. The market cap
is determined by multiplying the total number of shares times the price
per share. These stocks are generally perceived as riskier than large
company stocks because small companies have fewer financial resources
and more uncertain earnings than large companies. Small companies are
also less able to survive prolonged periods of economic downturns. Even
when small companies have good track records, these track records aren’t
very long, adding more uncertainty and greater risk to their stocks. Because
investing in small company stocks is riskier, investors demand a higher
rate of return.
It’s important to understand
that the average historical returns of small-cap company stocks have significantly
outperformed large company stocks.
8-16 plots the deciles (one-tenth buckets) of U.S. companies
sorted by size over the period from 1928 to present. Note that a fairly clear line
exists between the less risky large-cap stocks in decile 1 and the very
risky microcap stocks in decile 10. However, in shorter
time periods they don’t always outperform large company stocks.
In fact, the size risk factor fluctuates unpredictably. This is consistent
with the Random Walk Theory of changes in stock prices.
The third risk factor in the Fama/French model is the amount of exposure
to low priced stocks, which is measured by a book-to-market (BtM) value
ratio. The book value of a company is just an accounting term for its
net worth, its assets minus its liabilities. The market value of a company
is its price per share times the number of shares outstanding. This risk
factor is known by several different designations. It has been referred
to as the value factor, BtM factor, style factor and price factor. Note
that charts referring to it may have any of these designations. The most
current designation is the price factor, referring to the low prices of
these stocks compared to a company’s book value or to other stocks.
Exposure to the price factor is determined by the amount of a portfolio
exposure to high BtM stocks. In other words, when a stock’s market
price is less than its book value, the BtM ratio is greater than one.
The greater the exposure to the price factor, the higher the historic
and expected return in comparison to low BtM stocks. High BtM companies
usually have low earnings and experience other signs of financial distress.
Investors don’t like these stocks for these reasons. As a result
of their poor track records, the market drives down the prices of these
stocks. This naturally makes them riskier to investors.
Stocks with a low BtM ratio have low book values relative to their market
prices and are termed growth stocks. Investors favor growth stocks because
they’re perceived to be great companies and therefore are less risky.
They represent successful companies with strong track records and healthy
The Nobel Prize-winning contribution made by Merton Miller provides a
framework for better understanding the connection between the price risk
factor and stock returns. Miller set forth a simple but profound notion:
the cost of capital to a company equals the expected return to an investor
who holds its stock. A company’s cost of capital is equal to the
price or book value of its shares or the amount that a company must pay
in order to obtain capital from investors.The Figure below proves out Miller’s Nobel-prize winning research. The figure plots the 84-year risk and return characteristics for the entire U.S. stock market as divided by book-to-market ratios in 5 quintiles. As you can clearly see, the low-book-to-market companies (numbers 1 and 2) produced negligible returns that came with very low risk. The 20% of all U.S. companies with the highest book-to-market (number 5) were perceived to be in the greatest distress, and consequently paid a higher cost of capital (return) to their investors.
To help you remember the concept of Value Risk, referring to the difference between growth companies and value companies, we created this painting. The painting illustrates the difference in the allure of hot products like the early days of cell phones from Motorola to the bland appeal of a can of Spam from Hormel. Over the long haul, stocks that sell closer to their book values have had higher returns as shown in the Figure above.
For an explanation of Book Value versus Market Value, watch this video from the Khan Academy.
Suppose that a value company and a growth company each approach
a bank for a loan. Which company will have to pay the higher cost of capital
(the higher interest rate) on its loan? The value company will pay the
higher cost because its future is less certain and the bank will need
to charge extra interest for taking the extra risk that the company won’t
be able to pay back its loan. Thus, the riskier the company’s stock,
the higher the cost of capital paid by a company.
Because the market perceives a value stock to be riskier, it drives down
their price so that the expected return is high enough to make it worthwhile
for investors to hold, despite the extra risk they take when buying
it. In this way, stock prices adjust, (the market sets the price at a
discount, so its expected return is higher) to reflect the perceived riskiness
of the stock. This ensures that the stock will be purchased, even though
growth companies have better earnings prospects and generally seem safer.
The key to understanding the connection between the price risk factor
and stock returns lies in focusing on the market price of a stock. A high
BtM ratio suggests that the market values the stock less than the stock’s
accountants. This is usually because the stock has poor earnings as well
as other indications of financial distress. This makes the stock riskier.
As a result, investors demand a higher rate of return to compensate them
for the risk that a high BtM stock will do worse than expected, go bankrupt,
and end up as one of the “stocks in a box.”
A 1987 study compared the investment performance of a portfolio of 29
growth stocks to one with 29 value stocks. The growth stocks represented
companies that were stronger and healthier than value stocks by every
economic measure, including return on total capital, return on equity,
and return on sales. The value stocks represented companies that had little
profitability, terrible management, and a bad image. Yet, the study found
that the value stocks outperformed the growth stocks, 298% to 182%, over
the five-year period of 1981 to 1985.
This means that investors earned higher returns by owning the stocks of
companies that did poorly. That seems counterintuitive to most investors,
since they tend to think that healthy stocks are better investments than
distressed stocks. After all, if investors ask for a stock tip, they want
to hear the name of the next Microsoft, not a stock with poor earnings.
The fact is that investors should be interested in great investments (value
stocks), not great companies (growth stocks).
Figure 8-17 illustrates the relationship between expected return and the three factors
of market, size, and value. Since we are only discussing stocks, the market
exposure is not shown on this plot. The higher the investment plots in
the top right quadrant, the higher the expected return. The full page Figure 8-18 actually puts values of average expected
returns of various indexes over the market return. The blue circles on
the plot represent various indexes. The total market index is plotted
at the center of the cross hatch, which is a 0,0 on the scale of size
and value. The return in the top right corner is the highest return on
the plot. The dotted diagonal line represents indexes that would have
the same return as the market return. Also note that large growth stocks
have negative average returns relative to the total market return, with
the bottom left corner value being -4.71%. Large and safe companies have
lower risk associated with them and therefore have lower returns compared
to smaller companies. Note that a portfolio similar to IFA Index Portfolio
90 plots with an expected average return of about 3%
over the total market return. Because Index Portfolio 90 has international
indexes in the mix, this is not entirely accurate, but it does give us an
idea of how this type of analysis works.
Most investors are
really only guessing which managers or asset classes will outperform
the market. They encounter vast inefficiencies in trying to pick winners
from among thousands of money managers and mutual funds. However, with
the introduction of the Fama and French model, these costly efforts can
be entirely eliminated by investing in Fama and French designed index funds.
Some mutual fund
companies such as Dimensional Fund Advisors (DFA) have taken advantage
of the Fama and French research by offering a full assortment of index funds,
including low price and small company index
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
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.
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 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.
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 U.S and Non-U.S. returns data in 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 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 disappear, even when more investors are informed
about the favorable risk/return relationships. As a result, there shouldn'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 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.
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 five-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 2.48% for the 85 years from 1928 to
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 value risk factors of stocks.
Figure 8-21A below shows six different allocations of Long-Term Government Bonds and 30-Day T-Bills and the differences in risk and return of those various allocations. Since the period from 1928, there has been a clear relationship between the risk and return among these allocations.
To help you remember the concept of Term Risk, referring to the difference between short duration 30-day US T-Bills and long duration US government bonds, we created this painting.
The second risk factor for Fixed Income is the default risk factor, which
is associated with the credit quality of bonds. Instruments of lower credit
quality are riskier than those of higher credit quality, thus yielding higher
expected returns. Despite the August 2011 downgrade of U.S. Government debt by
Standard & Poors, the market still assigns a higher default risk to corporations
over the U.S. Government. The default risk factor refers to the additional expected
return of corporate bonds over government bonds. Figure 8-21B shows the strong
relationship between risk and return as the probability of default increases.
To help you remember the concept of Default Risk, referring to the difference between Long Term Corporate Bonds and Long Term Government Bonds, we created this painting.
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.
Once we adjust the returns of equity mutual fund managers for their average exposure to the three risk factors, we discover that the factors explain almost all of the returns, leaving little, if any, alpha (skill).
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