Tim Olson
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3.6 KiB
description, tags
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| Overweights ETFs with high selectivity (low R-squared against factor model) and high alpha, and underweights ETFs with low selectivity (high R-squared), using a two-dimensional sort on R-squared and alpha. |
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R-Squared
Section: 4.3 | Asset Class: ETFs | Type: Factor-Based / Selectivity
Overview
Empirical studies suggest that augmenting Jensen's alpha with an indicator based on R-squared from a factor model regression adds predictive value for future ETF returns. R-squared measures how much of an ETF's return variance is explained by common factors; low R-squared (high "selectivity") combined with high alpha predicts strong future performance. High R-squared (low selectivity) combined with low alpha predicts weak future performance.
Construction / Signal
Run a serial regression of ETF returns R_i(t) on 4 factors (Fama-French 3 + Carhart momentum):
R_i(t) = alpha_i + beta_{1,i} MKT(t) + beta_{2,i} SMB(t) + beta_{3,i} HML(t) + beta_{4,i} MOM(t) + epsilon_i(t) (365)
Compute regression R-squared:
R^2 = 1 - SS_res / SS_tot (366)
SS_res = sum_{i=1}^{N} epsilon_i(t)^2 (367)
SS_tot = sum_{i=1}^{N} (R_i(t) - R_bar(t))^2 (368)
R_bar(t) = (1/N) * sum_{i=1}^{N} R_i(t) (369)
Selectivity = 1 - R^2 [Amihud and Goyenko, 2013]. High selectivity = low R-squared = returns less explained by common factors.
Two-dimensional sort strategy:
- Sort ETFs into quintiles by R-squared (5 groups).
- Within each R-squared quintile, sort ETFs into sub-quintiles by alpha (5 sub-groups).
- This creates 25 groups of ETFs.
- Buy ETFs in the group with lowest R-squared quintile and highest alpha sub-quintile.
- Sell ETFs in the group with highest R-squared quintile and lowest alpha sub-quintile.
Entry / Exit Rules
- Entry: At rebalance, run regression, compute R-squared and alpha for each ETF, perform 5×5 sort, enter long/short positions.
- Exit: Hold for estimation period or holding period; rebalance periodically.
- Estimation period: Same as alpha rotation (typically 1 year); longer estimation periods can be used, especially for monthly returns.
Key Parameters
- Factor model: 4-factor (Fama-French 3 + Carhart MOM); 3-factor also usable
- Estimation period: Typically 1 year; can be longer for monthly return data
- Sort dimensions: R-squared quintiles × alpha sub-quintiles (5×5 = 25 groups)
- Holding period: Similar to alpha rotation strategy (1–3 months)
- Selectivity definition:
1 - R^2
Variations
- 3-factor model: Use Fama-French 3 factors without momentum factor MOM
- Different quintile splits: Use deciles instead of quintiles for finer grouping
- R-squared only: Sort purely by R-squared without the alpha sub-sort
- Estimation period alignment: Use same estimation period as alpha rotation strategy (Section 4.2) for consistency
Notes
- R-squared as a measure of active management: in Amihud and Goyenko (2013), R-squared is applied to mutual funds; Garyn-Tal (2014a, 2014b) applies it to actively managed ETFs.
- Low R-squared means the ETF has high "active share" — its returns are driven more by the manager's specific bets than by passive factor exposure.
- The estimation period and return frequency for R-squared can be the same as for alpha rotation (see Section 4.2 and fn. 77).
- Longer estimation periods are particularly appropriate if R_i(t) are monthly returns.
- Can be combined with the MA filter (Section 4.1.1) as an additional condition.