What is the difference between upside and downside beta?

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AcadiFi · Accepted Answer

Upside and downside betas decompose total beta by sign of market return. Downside beta = Cov(r_i, r_m | r_m < 0) / Var(r_m | r_m < 0) estimates sensitivity only during market down-days. Upside beta = same but for r_m > 0 days. A stock with downside beta 1.4 and upside beta 0.8 has asymmetric systematic risk: it participates more in market declines (1.4x moves) than market rallies (0.8x moves). This is the worst of both worlds for holders and signals something like a levered defensive stock, a stock with embedded short put optionality, or one with catastrophic business risk that activates in crises. Examples: regional banks (levered to credit cycle), leveraged REITs, and some cyclicals. Pricing implications: CAPM with single beta misprices this stock - CAPM thinks the downside beta IS the beta, while fair compensation should reflect the asymmetry. Downside-beta CAPM (Bawa-Lindenberg) or dual-beta models price upside and downside betas separately. Empirically, stocks with high downside beta / low upside beta have earned premium returns over 20+ year samples, consistent with rational pricing of asymmetric systematic risk. ```mermaid graph TD A[Market up] --> B[Beta 0.8
lag rally] C[Market down] --> D[Beta 1.4
amplify drop] ```

What is the difference between upside and downside beta?

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