# LO 63.4: Explain how dynamic risk factors can be used in a multifactor model of

LO 63.4: Explain how dynamic risk factors can be used in a multifactor model of asset returns, using the Fama-French model as an example.
The capital asset pricing model (CAPM) is a single-factor model. In the CAPM, the single risk factor is market risk. Stocks that have high exposure to the CAPM market factor perform well when the market performs well and poorly when the market performs poorly. Over the long run, stocks with high betas (i.e., a high market risk factor) should have higher returns than the market return. Returns are higher for high beta stocks to compensate investors for losses during bad periods.
The market portfolio can be readily traded via low-cost index funds, stock futures, and exchange-traded funds (ETFs). In general, macro factors, like political, inflation, and growth risks, are not directly traded (volatility risk is the exception). As a result, dynamic factors can be easily employed in portfolios. The best known example of a tradeable multifactor model is called the Fama and French model, introduced in 1993.2
Eugene F. Fama and Kenneth R. French, Common Risk Factors in the Returns on Stocks and Bonds, Journal of Financial Economics 33 (1993): 3-56.
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Topic 63 Cross Reference to GARP Assigned Reading – Ang, Chapter 7
Professors Note: In the academic finance literature style factors, investment factors, and dynamic factors are used interchangeably. Practitioners also refer to these factors as smart beta or alternative beta. Fama and French were the first to develop a multifactor model that captured these effects.
The Fama-French model (called the Fama-French three-factor model) explains asset returns based on three dynamic factors. The model includes: The traditional CAPM market risk factor (MKT). A factor that captures the size effect (SMB). A factor that captures the value/growth effect (HML). The Fama-French three-factor model is expressed as follows:
E(Ri) – RF + (3i>MKT x E(Rm R f ) + Pi,s mb x E(SMB) + P^h m l x E(HML)
Following the market factor, the second factor in the model is SMB. The SMB factor refers to the difference between the returns on small stocks (small market capitalization) versus big stocks (large market capitalization). In other words, the risk factor is small stock returns minus big stock returns, thus SMB. Historically, small-cap stocks have outperformed large- cap stocks. This factor captures the higher performance of small companies relative to large companies. Note, however, that the average stock only has market exposure. Every stock cannot be large, and every stock cannot be small.
The third factor in the model is HML. This factor captures the return differential of high book-to-market stocks versus low-book-to-market stocks. The ratios are calculated as book value divided by market capitalization. Recall that a value strategy consists of buying low- priced stocks (i.e., taking a long position in low-priced stocks) and selling high-priced stocks (i.e., shorting high-priced stocks), normalized by book value. Growth stocks have high stock prices relative to book values, and value stocks have low stock prices relative to book values. Historically, value stocks have outperformed growth stocks. Thus, the Fama- French factors are constructed to capture size (SMB) and value (HML) premiums (known as factor-mimicking portfolios).
A value investor, who buys stocks that are perceived as trading below their fundamental value, would have a positive HML beta. Relative to the CAPM expected return, the value investors return adjusts upward by (3j HML x E(HML). Thus, the overall risk premium increases above the single-factor CAPM risk premium. Likewise, the overall risk premium is adjusted down by HML x E(HML) for growth stocks. This is because growth stocks have negative HML betas, so expected returns are adjusted downward.
In the CAPM, both the average stock beta and the market beta equal one. In the Fama- French model, the HML and SMB betas are centered on zero. The average investor earns the market return as the average stock (or portfolio of stocks) does not have a value or size tilt. This means the investor must specifically choose a value play or a size play, to benefit from the HML and SMB factors. Also, the CAPM and Fama-French models assume betas are constant, but empirical research indicates they vary and increase during bad times.
2018 Kaplan, Inc.
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Topic 63 Cross Reference to GARP Assigned Reading – Ang, Chapter 7
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