What is the smartest way (having the lowest prediction errors) to estimate market beta across stocks for the purpose of portfolio construction? In their November 2017 paper entitled “How to Estimate Beta?”, Fabian Hollstein, Marcel Prokopczuk and Chardin Simen test effects of different return sampling frequencies, forecast adjustments and model combinations on market beta prediction accuracy across the universe of U.S. stocks. Their primary goal is to identify optimal choices. They focus on a beta prediction horizon of six months. They consider past beta estimation (lookback) windows of 1, 3, 6, 12, 24, 36 and 60 months for daily data, 12, 36 and 60 months for monthly data and 120 months for quarterly data. They measure beta prediction accuracy based on average root mean squared error (RMSE) across stocks. Using returns for a broad sample of U.S. stocks during January 1963 through December 2015, they find that:
- A lookback window of one year generally yields the most accurate beta predictions.
- Daily historical data generates more accurate beta predictions than monthly or quarterly data.
- Exponential weighting of past data, especially with an expanding lookback interval, materially improves beta prediction.
- Shrinking beta prediction for each stock toward the average of its industry boosts accuracy of overall raw beta predictions.
- Adjusting beta predictions by augmenting (smoothing) calculations with lagged returns to account for slow information dissemination does not improve beta prediction accuracy.
- Adjusting beta predictions to account for the state of the economy does not improve beta prediction accuracy.
- A simple combination of raw beta prediction and exponentially weighted beta prediction is the most accurate. More elaborate combinations do not work well.
- Findings are robust across beta prediction horizons of 1, 3, 6, 12 and 60 months, and for value-weighted and equal-weighted average RMSEs.
In summary, evidence indicates that the most accurate market beta predictions for individual U.S. stocks are based on: daily past returns; exponential weighting of returns with an expanding window; and, shrinkage toward associated industry historical average beta.
Cautions regarding findings include:
- Testing many approaches to beta prediction on the same data introduces data snooping bias, such that the best approach is somewhat lucky and overstates prediction accuracy.
- The authors do not address the economic value (improved smart beta portfolio performance) of better forecast accuracy.
- Findings may not hold for non-U.S. stocks or for factor betas other than market factor beta.
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