# Factors Investing opportunities

The expected return of a financial asset can be modeled as a function of various theoretical factors according to three main categories: macroeconomic, statistical, and fundamental. Employing multiple factors addresses their cyclicality and increases diversification. However, there is no free lunch attached to factor investing.

Ross (1976) Arbitrage pricing theory (APT) holds that the expected return of a financial asset can be modeled as a function of various macroeconomic factors or theoretical market indexes. APT did not explicitly state what these factors should be; indeed, the number and nature of these factors were likely to change over time and vary across markets. Thus the challenge of building factor models became, and continues to be, essentially empirical in nature. Fama and French (1992, 1993) put forward a model explaining US equity market returns with three factors: the “market” (based on the traditional CAPM model), the size factor (large vs. small-capitalization stocks) and the value factor (low vs. high book to market).

**Macroeconomic factors**include measures such as surprises in inflation, surprises in GNP, surprises in the yield curve, and other measures of the macroeconomy (see Chen, Ross, and Roll (1986) for one of the first most well-known models)**Statistical factor models**identify factors using statistical techniques such as principal components analysis (PCA) where the factors are not pre-specified in advance**Fundamental factors**(Value, Growth, Size, Momentum) capture stock characteristics such as industry membership, country membership, valuation ratios, and technical indicators, to name a few

#### Factor Investing and risk sources

**Risk premia factors** (Value, Low Size, Low Volatility, High Yield, Quality, and Momentum) are factors that have earned a persistent significant premium over long periods and that clearly reflect exposure to sources of systematic risk. Instead, factors that do not explain well risk but do earn persistent premia over time are named **alpha signals** (earnings revisions or earnings momentum). All of the Fama-French factors count as risk premia factors since the aim of those original studies was to isolate asset pricing drivers. Note that the sensitivity of systematic factors to macroeconomic and market forces resulted in some long periods of underperformance; thus, because of low correlations relative to other factors, diversification across factors is fundamental in factor investing to reduce the length of such underperformance.

#### What drives factor investing returns

In general, factor returns are explained with different approaches. On one hand, factor returns reflect systematic sources of risk in (weakly) efficient markets; on the other one, factor returns derive from investors behavioral biases or constraints (e.g., time horizons, ability to use leverage, etc.).

**Systematic risk perspective**. Some risk that cannot be diversified away is paid into a premium. For instance, the small-cap premium reflects scarce liquidity (Liu, 2006), scarce transparency (Zhang, 2006), and more probable distress (Chan and Chen, 1991; Dichev, 1998). Value, Size, and Momentum are linked to country growth and inflation and are sensitive to shocks in the economy (Winkelmann et al., 2013).**Behavioral biases approach**. From behavioral finance literature, the extensive presence of specific investors traits (cognitive or emotional weaknesses) determining behavioral biases results in a prohibitively costly arbitrage, leading to such anomalies (factors). For instance, chasing winners, over-reaction, overconfidence, home bias, and myopic loss aversion.**Constraints and frictions/flows perspective**. Anomalies arise from constraints and industry practice. For instance, investors’ shorter time horizons (3- and 5-year horizons) determine a premium for stocks with low liquidity over long horizons (10 years plus). Baker et al. (2011) consider the use of institutional benchmarks, and the subsequent preference for relative returns, as one reason why the low volatility premium exists. Dasgupta, Prat, and Verardo (2011) argue that reputation concerns cause managers to move together generating momentum under certain circumstances.

Among the explanations of the returns of factor investing, the industry subscribes to the systematic risk; however, academics are more oriented towards the behavioral and constraints perspectives. However, in the latter case, factors persistence is relative to the persistence of investors’ biases and constraints.

One important critique of factor investing is that the factors that deliver premia do not always have clear economic interpretations. Although some factors, such as credit and term structure risk, are easily linked to risks which investors naturally seek to avoid or insure themselves against, others, such as momentum, are puzzling. *Unfortunately, the factors that appear to explain the most cross-sectional variation in historical stock returns are also those with the least economic intuition.*** **

#### Application: Fama-French Three Factors

The Fama-French model employs market, size (SMB), and value (HML) to calculate the expected portfolio returns. According to K. French webpage,

all returns are in U.S. dollars, include dividends and capital gains, and are not continuously compounded. To construct the SMB and HML factors, stocks in a region are sorted into two market cap and three book-to-market equity (B/M) groups at the end of each June. Big stocks are those in the top 90% of June market cap and small stocks are those in the bottom 10%. The B/M breakpoints for a region are the 30th and 70th percentiles of B/M for the big stocks.

**(Rm – Rf)**is the return on a region’s value-weight market portfolio minus the U.S. one month T-bill rate. The factor for July of year t to June of t+1 include all stocks having available market equity data for June of t**SMB**is the equal-weight average of the returns on the three small stock portfolios for the region minus the average of the returns on the three big stock portfolios. The factor for July of year t to June of t+1 include all stocks having available market equity data for December of t–1 and June of t.**HML**is the equal-weight average of the returns for the two high B/M portfolios for a region minus the average of the returns for the two low B/M portfolios. The factor for July of year t to June of t+1 include all stocks having available (positive) book equity data for t–1.