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Risk Factor Investing

As the market moves, so do stocks. Stocks go up with the market and down with the market. This market effect is called “beta.” As we know, a passive market index is hard to beat, simply “betting on the market” will outperform most money managers, after fees and expenses. But not all. When a money manager beats the market it is called “Alpha.” Alpha is the unexplained profits above and beyond what the market actually delivered and is often attributed to the talents of the money manager. What allows one manager to beat the market while others don’t? Is there something only they know or is it a technique similar to beating the house in blackjack by counting cards.

Actually, a significant portion of the best money manager’s alpha can be explained by “risk factors.” The market performs along the lines of the efficient market hypothesis (EMH) over the long-term and there is a certain amount of randomness in how it moves. However, stocks don’t react immediately to new information in the market allowing an opportunity to “hedge.” This movement away from the norm is partially explained by risk factors and these risk factors explain a significant part of alpha which becomes the new Beta.


Capital Asset Pricing Model (CAPM)

The very first approach to explain the deviations from the market was the Capital Asset Pricing Model (CAP-M) introduced in the 1960’s. This early model essentially defined beta, market risk, and compared individual stocks to beta in an attempt to predict price. The difference between the predicted price and actual price is the excess market return equal to alpha plus error. For example: Suppose you have a portfolio that is 20% more volatile than the market, and the treasury bill yielded 3% (risk-free return) and the S&P 500 return was 11%. The market premium (beta) would be 11% – 3% = 8%. The portfolio’s beta is 20% MORE volatile than the markets 8% (0.2 x 8) giving the portfolio a beta of 1.6%. So, the expected return for the portfolio is the market, 11%, plus the portfolio’s beta, 1.6%, or 12.60%.

If the portfolio returned, for instance 13.20% then the unexplained difference (Alpha) is presumed to be from management skill plus random error. Obviously, the manager will claim there is no error, it was ALL his skill.

CAPM uses a single factor, market risk, to explain pricing and asset returns. It was a great breakthrough and won its creator, William Sharpe, the Nobel Prize in Economics in 1990. But, it did not explain observed returns very well, especially when a portfolio strayed from the center of the market. Small size companies and value companies persistently had higher returns than the CAP-M could explain. Managers claimed it was all Alpha. But, how can you claim Alpha for a portfolio that could potentially be indexed (small cap or value index)?

Under CAPM, here is the model:

  • Zero risk return (T-Bills)
  • Market premium (Beta)
  • Alpha
  • Random Error


Three Factor Model

The authors of the EMH, Fama and French, first postulated the three factor model in 1992. In addition to the market they added two more factors – firm size and value.

An investor’s return is related to the firm’s cost of capital. The cost of firm’s capital is best estimated by the price of their securities. Small firms pay more for capital when borrowing or issuing securities. Distressed firms (value), those with bad financial performance, irregular earnings and/or poor management must also pay more for capital. Small and distressed firms have lower stock prices to compensate investors for these risks. Fama-French found that the best measure for the value risk was the book-to-market (BTM) ratio[1].  High BTM ratio stocks are value stocks. [More commonly used today is Price to book (P/B) which is inverse of BTM. So, stocks with a P/B less than 1 is undervalued, over 1.0 is overvalued.]

Here is how Fama-French defined their risk factors. Size = difference in return between largest stocks and smallest stocks in the CRSP database[2] . Value premium is the difference in returns between the stocks with the 30% highest BTM and the 30% lowest BTM

With the three-factor model, the variables are:

  • Zero risk return (T-Bills)
  • Market premium (Beta)
  • Size premium (small size)
  • Value Premium (undervalued)
  • Alpha
  • Random error


Compared to the CAP-M, we are beginning to chip away at Alpha. Size and Value both are explainable components of alpha and can be built into a passive index.

[1] BTM = book value of firm/market value of firm. Basically speaking, above 1 is undervalued; less than 1 is overvalued.

[1] CRSP is “Center for Research in Security Prices” a comprehensive database for historical security prices since 1926.

In any particular time-frame, none of these factors is necessarily positive. However, over long periods of time they produce excess returns.

Carhart Four-Factor Model

The Carhart four-factor model is an extension of the Fama-French three-factor model which includes a momentum factor. This model comes from Carhart’s 1997 paper, “On Persistence in Mutual Fund Performance.” Carhart built upon the seminal work on momentum by Jegadeesh and Titman (1993) who defined momentum as the last 12 months of returns excluding the most recent month.

Momentum is described as the tendency for the stock price to continue rising if it is going up and to continue declining if it is going down.  Most investigators compare the price of the stock to its price 3-, 6- or 12 months ago. Some ignore the prior month in the calculation. 


How Many Factors Are There?

There are LOTS of factors. The Barra Risk Factor Analysis is a multi-factor model which incorporates over 40 data metrics. The finance journals have “discovered” some 250 factors. Luckily, not all factors are statistically significant in predicting stock returns. Most are not persistent.

A factor is any characteristic relating a group of securities that is important in explaining their returns and risk. The market itself can be viewed as the first and most import factor. Beyond the market, researchers look for factors that are persistent over time and have strong explanatory power over a broad range of stocks.

There are three main categories of factors: macroeconomic, statistical, and fundamental.

  • Macroeconomic include surprises in inflation, surprises in GNP, surprises in the yield curve, etc.
  • Statistical factor models identify factors with statistical techniques such as principal components analysis (PCA) where the factors are not pre-specified in advance.
  • Fundamental factors are the most widely used and capture characteristics such as industry membership, valuation ratios, and technical indicators. The most popular and important four factors are: Value, Growth, Size, and Momentum. Recently, two more factors have been added, Dividend Yield and Quality.


Those factors that have consistently shown larger returns and are called risk premia. 

Risk Premia Defined

Let’s further define the four main risk premia researchers have studied.


The Value factor captures the link between low prices relative to their fundamental value. This strategy consists of buying stocks with low prices normalized by some indicator of company fundamentals (price/book value, price/sales, price/earnings, PEG ratio, or dividends, etc.) and sell stocks with high prices. Graham and Dodd first wrote about it in 1934 (“Security Analysis”). Basu, in 1977, identified price to earnings ratios as predictors of subsequent performance.

 Low Size

In 1981, Banz discovered that smaller firms grow more than larger firms. Fama and French hypothesized that small caps have higher systematic risk which earns them a premium. Other researchers suggest that size may represent other unobservable risk factors such as liquidity (Amihud, 2002), information uncertainty (Zhang, 2006), financial distress (Chan and Chen, 1991) and default risk (Vassalou and Xing, 2004). The size anomaly has been found to exist even when other factors are controlled: beta, value, momentum, liquidity, leverage, etc. It has also been identified across the world in developed and emerging markets (Rizova 2006).


Winners continue to win and losers continue to lose. One of the first papers was published by Jegadeesh and Titman (1993) studying the US market from 1965 to 1989. Rowenhorst (1998) found a similar result in Europe and Carhart (1997) added momentum to the Fama and French model.

How is momentum measured by these researchers? Depending on the author they looked at price over a three to twelve-month period.

Low Volatility

Stocks with lower average volatility, beta, or risk have excess returns. This factor represents a quandary. One of the most basic principles is that high volatility equals high returns (Blitz and Vliet, 2007). The CAPM model states that riskier assets should earn higher premiums. However, research shows that low volatility stocks outperform the market!

The first researchers to document this relationship was Haugen and Baker in 1991. Other researchers to document this includes Chan, Karceski and Lakonishok (1999), Schwartz (2000), Jagannathan and Ma (2003) and Clarke, DaSilva and Thorley (2006). Many other investigators showed the same effect in global markets. The definition of low volatility used varied amongst the investigators as well as the time frame.


EW = Equal weighted portfolio; VM = value plus momentum

Risk Premia Timing

Unfortunately, there is never a free lunch. You cannot just find stocks with a risk factor, buy it and forget it. There is timing involved. Risk premia undergo cycles including multi-year periods of underperformance.

As the table below shows there are long periods when a risk factor may not outperform the market.


Two of the most important factors, value and momentum, usually move opposite of each other. A momentum stock is rising in price (market value) relative to its book value which means that over time it is less “value-like” and low momentum stocks tend to become more “value-like.” However, even this simple rule can exhibit periods of decoupling.


In fact, one factor can even morph into another factor. If a momentum stock loses its momentum and the price plunges it can become a value stock.

Quality And Dividend Yield

While the above four factors (value, size, volatility, momentum) are the strongest and most studied risk premia, two newer ones have entered the stage – quality and yield.


Different than Value (P/earnings, EPS, PEG ratio), there is no single definition of quality. Throughout the academic papers there are numerous factors mentioned; here are 10 popular quality factors:

  • Profitability
  • Margins
  • Growth in profitability
  • Growth in margins
  • Leverage
  • Financial constraints and distress
  • Earnings stability
  • Net payout/issuance
  • Growth activities (R&D, advertising expenses, etc.)
  • Accounting quality

Levi and Welch (2014) examined the literature and reported that among 600 factors that worked in-sample, 51% work after publication and 49% fail.

The Nifty Fifty. In the late 1960s and early 1970s institutional investors were enamored with 50 large, stable, fast-growing companies such as: General Electric, Xerox, Polaroid, and IBM. In 1973 – 1974 the S&P fell by 39% while the Nifty Fifty fell 47%. By the end of 1976 the S&P 500 was back to breakeven but it took nearly a decade for the Nifty Fifty to recoup their losses.


Buying quality stocks at high prices is a bad investment idea.

Although “quality” by itself does not produce a return, Research Affiliates compared Low- and High-quality “value” stocks. For value they used the companies’ combined book-, dividends-, earnings-, and sales-to-price ratios to select 400 value stocks from 1000 large-cap stocks. For “quality” they used return on equity (ROE) to reflect growth and profitability; debt coverage ratio for likelihood of default; and accruals-to-average-total-assets to quantify possible accounting red flags.

Then they sorted into two groups: low-quality and high-quality.


While “quality” alone is not a premia factor, it can be a good filter and lowers portfolio volatility.

Dividend Yield

chart11Low interest rates are enticing investors to seek income in high-yielding stocks. A slow economy, market volatility, and aging baby-boomers are seeking the steady income of dividend payers. Over the 88-year period ended July 2015, high dividend-paying stocks have outperformed the market by 1.5% per year.

Current interest rates make a difference in yield investing after controlling for market, size, value and momentum. Contrary to conventional wisdom that investors should hunt for yield in a declining or low interest rate environment, the yield-factor does well during low and rising interest rate times.

From January, 2011 to September, 2012, the FTSE High Dividend Yield Index of U.S. stocks returned 26% compared to 19% for the S&P 500. However, when other factors are controlled, the dividend yield actually subtracted 1.02% from the total yield (Dividend Investing: A Value Tilt in Disguise? By Gregg S. Fisher). It turns out that dividend yield is actually a tilt towards value (book value to price ratio) and earnings yield (stock earnings per share divided by price per share). The high-dividend portfolio also has low volatility.

Why would the dividend factor be negative? Two possible explanations. One, the dividend is a lagging indicator due to delayed actions by management. The market adjusts the price of a company’s stock. The management, however, takes longer to adjust the dividend policy. A decrease in stock price raises the dividend to a high dividend stock.

The second possibility is momentum. Once the stock begins a price decline it will continue to decline giving it a higher dividend yield.

The bottom line is that dividend is not an isolated risk premia. It can act as a proxy for value.

Can Alpha Be Captured?

A handful of risk-premia indices can account for as much as 80% of alpha.  There is a strong case for replacing a portion of alpha with risk premia. Alpha is expensive and difficult to find. It is difficult for active managers to earn alpha (Malkiel [1995], Gruber [1996], Wermers [2003], Jones and Wermers [2011]). Even the small subset of those that outperform the market do so for an average of 36 months.

Traditionally, portfolio returns were considered a combination of passive market exposure (beta) and active portfolio management (alpha). Certain returns once considered alpha are now recognized as newly isolated forms of beta.

Risk-premia strategies can be classified into two categories: 1) risk-based strategies that aim to lower risk (equal weighted, low volatility), and 2) return-based strategies that aim to tilt towards a specific factor (value, momentum).

Melas et al. (2011), showed that tilting toward any one fundamental factor does not guarantee long-term out-performance. There are periods of over- and under-performance.  Some factors (Value, Momentum, and Size) are pro-cyclical, performing well when economy growth, inflation and interest rates are rising. Quality and Low Volatility have historically been defensive doing well when the environment was falling or weak. This is the role of active management, determining which factors should be relied upon at any point in time and for how long.



If, in theory, we could identify ALL risk-premia, active management still plays a roll with respect to market timing (asset class, country, style, size, sector), risk-premia timing (factor timing), or stock selection (timing individual stocks). An index can never capture the returns from timing.


*ACWI IMI is the world index by MSCI and captures large, mid and small cap representation across 23 Developed Markets and 23 Emerging Markets countries. With 8,609 constituents, the index is comprehensive, covering approximately 99% of the global equity market. *ESG Beliefs and Constraints = environmental, social and governance principles.


In this exhibit “Passive Investing” is simply the market, i.e. S&P 500 or DJI or Russell 2000. This is the Beta that we want to beat. Next, we add “Factor Investing.” This means filtering the market to isolate stocks which exhibit a single or combination of strategic factors. Finally, is the “Active Management” component. Active management determines which stocks from the filtered market will be incorporated, when to enter and exit, and what portion of your portfolio each stock represents.



Before the 60’s, any money your broker made was chalked up to his wonderful skill and learning, his Alpha. Then in the 60’s we learned that the market itself is a factor and market indexes were developed. You could just invest in the market and outperform most investors.

Investing is rapidly changing from the 60’s and the original CAP-M. Since then, academicians have started explaining how and why some managers can outperform the market. Over 250 such factors have been found, but just a handful represent the majority (80%) of alpha. The factors are cyclical and can underperform during certain market conditions underscoring the importance of active management.

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