Empirical studies show that historical CAPM betas drift toward 1.0 as you move forward in time—high betas fall, low betas rise. If you plug an un-adjusted β straight into cost-of-equity models, you can overstate risk for aggressive stocks and understate risk for defensive ones.
To correct this "mean-reversion" bias, Marshall Blume (1971, Journal of Finance) proposed a simple linear transformation—now called the Blume Adjustment—that shrinks every beta part-way toward the market average of 1.0.
= historical (OLS) beta you just estimated.
= shrinkage factor derived from long-run regressions.Classic Blume uses ; sometimes literature quotes 2⁄3 or 0.60.
High β (> 1) is pulled down.
Low β (< 1) is pushed up.
Market β (= 1) stays exactly 1.
Blume regressed future betas (βt+5) on current betas (βt) for NYSE stocks:
He found . Setting implies —the market's average—hence the shrinkage interpretation.
b = 0.67 # Blume factor blume_adjusted_beta = 1 + b * (portfolio_beta - 1)
Raw Beta Calculation: First, we calculate the portfolio beta using ordinary least squares (OLS) regression of daily portfolio returns against benchmark returns.
Blume Adjustment Factor: The adjustment uses the standard Blume factor of 0.67, which has been empirically validated across many markets and time periods.
Calculation Precision: The adjustment is applied with full floating-point precision to maintain accuracy in the final risk assessments.
Data Display: The result is displayed in the performance metrics of each optimization method, providing a forward-looking estimate of systematic risk.
This implementation ensures that beta values used in risk assessment and performance attribution represent a more reliable estimate of future systematic risk exposure, avoiding the pitfalls of using raw historical beta values directly.
| Application | Why Blume Helps |
|---|---|
| Cost of Equity / WACC | Produces more stable, forward-looking betas, reducing forecast error in DCF models. |
| Risk budgeting | Avoids systematically punishing high-β names in future projections. |
| Portfolio attribution | Distinguishes skill (alpha) from temporary beta spikes that revert. |
Forward-looking — Provides more realistic beta estimates for future periods based on observed mean-reversion patterns.
Improved accuracy — Reduces forecast errors in cost of capital calculations by correcting for statistical bias.
Simple implementation — Requires minimal computational overhead with a straightforward adjustment formula.
Empirically validated — Backed by decades of research showing the tendency of betas to revert toward the market mean.
Industry standard — Widely used by financial analysts and incorporated into professional data services.
One-size-fits-all approach — Uses the same adjustment factor across all securities regardless of industry or market cap.
Linear assumption — Assumes mean-reversion follows a simple linear pattern which may not always hold.
Time horizon sensitivity — The adjustment may be excessive for short-term strategies or insufficient for very long horizons.
Static shrinkage factor — The standard 0.67 factor doesn't adapt to changing market conditions or structural shifts.
Simplistic mean-reversion — Doesn't account for fundamental reasons why some stocks maintain persistently high or low betas.
| Issue | Mitigation / Note |
|---|---|
| One-size-fits-all b-factor | Some analysts re-estimate b on their universe every few years. |
| Assumes linear mean-reversion | Bayesian or Vasicek adjustments may fit better when distributions non-linear. |
| Short horizon portfolios | If you rebalance monthly, reversion may be negligible—raw β could be enough. |
| Method | Formula | Comment |
|---|---|---|
| Vasicek (Bayesian) Beta | Shrink β toward mean by factor based on estimation variance. | Data-driven ("James–Stein") approach. |
| Bloomberg Adjusted Beta | βʙʙ = 0.66·β_raw + 0.33·1 | Same spirit as Blume but uses 2-year weekly returns. |
| No adjustment | β̂ = β_raw | Fine for intraday or very short-term trading. |
Blume, M. (1971). "On the Assessment of Risk." Journal of Finance, 26(1), 1–10.
Damodaran, A. Investment Valuation, 3 ed. Wiley, 2012 — Ch. 4 (Bottom-up Betas).
Bodie, Kane & Marcus. Investments, 12 ed. — Exhibit 13.2.
Blume-Adjusted Beta gives users a tempered, forward-looking view of market sensitivity, closing the gap between historical estimation and practical forecasting.