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of the central concepts in finance is that returns above the risk-free rate are compensation for exposure to risks. Stocks have earned a premium above the risk-free asset because they expose their owners to their underlying risk factors. The capital asset pricing model (CAPM) can be thought of as the first theory of risk factors. According to the CAPM, the expected excess return on a risky asset is equal to the beta of the asset times the risk premium on the market portfolio. When asset returns are normally distributed, the CAPM correctly identifies the only risk factor to be the return on the market portfolio, and the measure of exposure of each stock to this factor to be its beta. By relaxing the assumptions of the CAPM, academic and industry researchers have extended the model, leading them to develop a long list of risk factors.18 Even though there is no consensus about the number of risk factors in financial markets, it is well established that the market portfolio is not the only risk factor in the market. The risk premiums earned by stocks and other traditional assets are indeed a combination of various risk premiums.

      Our discussion of factor investing begins with three important observations detailed by Ang (2014):

      1. Factors matter, not assets: The factors behind the assets matter, not the assets themselves. Assets are nothing more than means for accessing factors.

      2. Assets are bundles of factors: Most asset classes expose investors to a set of risk factors; therefore, the risk premium offered by an asset class represents a package of risk premiums offered by factor exposures. Exposures of assets and risk premiums to factors can be used to estimate the risk premium that an asset should provide.

      3. Different investors should focus on different risk factors: Asset owners differ in terms of time horizons, risk tolerances, objectives, and liabilities that should be funded. These differences require careful examination of factor exposures of a portfolio in order to ensure that the asset owners do not have too much or too little exposure to some factors.

      If we consider the risk premium earned by each asset class to be a function of exposures to several risk factors, then several important questions arise:

      

What is a risk factor?

      

Do all risk factors offer the same risk premium?

      

How do these risk premiums behave through various stages of a business cycle?

      

Are all risk factors investable?

      

How does one perform risk allocation based on risk factors?

      

Do allocations based on risk factors outperform allocations based on asset classes?

      These questions are addressed in the next six sections.

      2.5.2 How Risk Factors Are Described

      What is a risk factor? A risk factor represents a unique source of risk and risk premium in financial markets such that the observed risk and risk premium cannot be fully explained by other risk factors. In other words, risk factors are not supposed to be highly correlated with each other. In addition, risk factors should have a sound economic foundation, with rigorous academic and industry research supporting their presence. Finally, risk factors must show that their risk premiums are persistent over long periods.

      Let us examine two well-known equity risk factors: momentum and value factors. To create the momentum factor, researchers examine the performance of equity prices through time. Then two portfolios are created at the end of each period (e.g., month). One equally weighted portfolio will contain those stocks that performed well during some specific period (e.g., past 12 months), and the other equally weighted portfolio will contain those stocks that performed poorly during the same period. This procedure is repeated every period and results in two return series. If one were to go long the portfolio of winners and go short the portfolio of losers, the return to this active strategy would be the return to the momentum factor. We can ascertain that this is indeed a new factor if the return to this strategy cannot be explained by other factors, such as return to the market portfolio.

The value factor is constructed the same way except that stocks are sorted based on the ratio of their book values to their market values. Stocks with high ratios of book value to market value are considered value stocks, and those will low ratios are considered growth stocks. Two equally weighted portfolios are created each period. One will consist of those stocks with above-average book-to-market ratios, and the other one will consist of those stocks with below-average book-to-market ratios. Again, a strategy will go long the first portfolio and short the second portfolio. The return to this active strategy will represent the return to the value factor. Exhibit 2.10 displays properties of these two risk factors.

      It is important to note that the average returns reported in Exhibit 2.10 are for portfolios that, at least in theory, do not require any investment. This is because each factor consists of equal-size long and short positions. Therefore, the initial capital is available to be invested in the riskless assets, the market portfolio, or some combination of the two. For instance, if the capital were invested in the market, then the entire portfolio would earn the market portfolio plus the return on each factor. Of course, the resulting portfolio would be highly volatile because it would have a gross leverage of 300 %. Also, note that during the same period, the return on the market in excess of the riskless rate and its standard deviation were 7.72 % and 18.71 %, respectively.

EXHIBIT 2.10 Properties of Value and Momentum Factors

      Source: K. French Data Library.

      Several important observations can be made from Exhibit 2.10. First, both risk factors have generated significant positive returns over a long period. Second, both risk factors are volatile, which means they may not consistently generate positive returns, and there will be periods during which they could generate negative returns. Third, the two factors are negatively correlated (–0.41) with each other and are not highly correlated with the market risk. The fact that the two factors have been negatively correlated in the past is one of the key benefits of factor investing in the sense that two sources of returns have been discovered that are negatively correlated. This means a portfolio of the two should be far less volatile, which is confirmed by the last column of the exhibit. From Exhibit 2.10 the potential benefits of factor investing can already be seen. By isolating risk factors and investing in them, one might be able to avoid those risks that are not rewarded by the marketplace and, as a result, create portfolios that display more attractive risk-return properties.

      As was mentioned, academic and industry research has uncovered a number of risk premiums. Following is a partial list of the best-known risk factors:

      

VALUE PREMIUM: Based on the return earned by stocks with high book values relative to their market values. The strategy is to take long positions in stocks with a relatively high ratio and short positions in stocks with a relatively low ratio.

      

SIZE PREMIUM: Based on the rate of return earned by small-cap stocks. The strategy is to take long positions in small-cap stocks and short positions in large-cap stocks.

      

MOMENTUM PREMIUM: Based on past performance of stocks. The strategy is to take long positions in past winners and short positions in past losers.

      

LIQUIDITY PREMIUM: Based on the risk premium earned by illiquid assets. The strategy is to take long positions in illiquid assets and short positions in similar but otherwise liquid assets.

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