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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.

CREDIT RISK PREMIUM: Based on the credit risk of bonds. The strategy is to take long positions in bonds with low credit quality and short positions in bonds with high credit quality.

TERM PREMIUM: Based on the riskiness of long-term bonds. The strategy is to take long positions in long-term bonds and short positions in short-term bonds.

IMPLIED VOLATILITY PREMIUM: Based on the risk premium earned by the volatility factor. The strategy is to be short the implied volatility of options (e.g., create a market-neutral position using short positions in out-of-the-money puts and short positions in stocks).

LOW VOLATILITY PREMIUM: Based on the return to low volatility stocks. The strategy is to take long positions in low volatility stocks and short positions in high volatility stocks. The same strategy can be implemented using betas.

CARRY TRADE: Based on the return to investments in high-interest-rate currencies. The strategy is to take long positions in bonds denominated in currencies with high interest rates and short positions in bonds denominated in currencies with low interest rates.

ROLL PREMIUM: Based on the return earned on commodities that are in backwardation. The strategy is to take long positions in commodities that are in backwardation and short positions in commodities that are in contango.