LO 64.6: Explain how to measure time-varying factor exposures and their use in

LO 64.6: Explain how to measure time-varying factor exposures and their use in style analysis.
Style analysis is a form of factor benchmarking where the factor exposures evolve over time. To illustrate time-varying factors, consider four investments: (1) LSV Value Equity (LSVEX), (2) Fidelity Magellan (FMAGX), (3) Goldman Sachs Capital Growth (GSCGX), and (4) Berkshire Hathaway (BRK). Figure 4 shows the regression data from monthly returns on all four funds using the Fama-French three-factor model plus the UMD factor. The key difference between this information and data already presented is that the time period has been adjusted to January 2001 through December 2011.
Figure 4: Regression of Excess Returns for Multiple Funds
Alpha (a)
t-stat
Market beta ((3j MKT)
t-stat
SMB beta (3i SMB)
t-stat
HML beta (3i HML)
t-stat
UMD beta ((^u m d )
t-stat
LSVEX 0.00% 0.01 0.94 36.9 0.01 0.21 0.51 14.6 0.2 1.07
FMAGX -0.27% -2.23 1.12 38.6 -0.07 -1.44 -0.05 -1.36 0.02 1.00
GSCGX -0.14% -1.33 1.04 42.2 -0.12 -3.05 -0.17 -4.95 0.00 -0.17
BRK 0.22% 0.57 0.36 3.77 -0.15 -0.97 0.34 2.57 -0.06 -0.77
This data presents a different story about these funds than earlier. The only calculated alpha that is statistically significant is for Fidelity Magellan, but it is a 3.24% (= 0.27% x 12) in annualized terms. This was not good news for Fidelity investors, although it is time
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2018 Kaplan, Inc.
Topic 64 Cross Reference to GARP Assigned Reading – Ang, Chapter 10
constrained to a period that ended in 2011. Berkshires alpha is nicely positive, but for this time period, it is not significant. According to the HML beta factors, LSV Value Equity is indeed a value-focused investment. The data also shows that FMAGX is a leveraged play on the market with a 1.12 market beta. The UMD beta confirms that none of these four funds are momentum plays.
Style analysis tries to solve some of the problems with standard multifactor regression. Unlike Fama and Frenchs untradeable SMB and HML indices, style analysis uses tradeable assets. For example, consider three funds: (1) SPDR S&P 500 ETF (SPY), (2) SPDR S&P 500 Value ETF (SPYV), and (3) SPDR S&P 500 Growth ETF (SPYG). These three exchange-traded funds (ETFs) are hosted by State Street Global Advisors and they all belong to the SPDR (pronounced spider) family of ETFs. Style analysis also adjusts for the fact that factor loadings (betas) change over time. A possible multifactor regression could be estimated for next periods expected asset return (Rt+1) as follows:
R t+ i = <*t + (3SPY,tSPYt+ i + PsPYV.tSPYYt+i + 3sPYG,tSPYGt+i + t+i This formula has an imposed restriction that all factor loadings (i.e., factor weights) must sum to one: - 3sPY,t + 3sPYV,t + 3sPYG,t 1 - 3sPY,t + 3sPYV,t + 3sPYG,t The time-varying portion of this equation comes into play with the respective factor loadings. This process uses estimates that incorporate information up to time t. Every new month (t + 1) requires a new regression to adjust the factor loadings. This means that the beta factors will change over time to reflect changes in the real world. Is s u e s w it h Al p h a M e a s u r e m e n t f o r N o n l in e a r St r a t e g ie s

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