Hedge Ratio (β)
Published Last updated
Key Takeaway
Weighting coefficient determining optimal position sizing between two cryptocurrency pairs in mean-reversion trading, extracted through Engle-Granger regression analysis enabling stationary spread creation.
Learn These First
What Is Hedge Ratio (β)?
Weighting coefficient determining optimal position sizing between two cryptocurrency pairs in mean-reversion trading, extracted through Engle-Granger regression analysis enabling stationary spread creation.
How Hedge Ratio (β) Works
Frequently Asked Questions
How do I calculate hedge ratio for cryptocurrency pairs trading?
Run Engle-Granger test regressing one cryptocurrency price against another. The regression coefficient is your hedge ratio. If regressing Ethereum against Bitcoin produces coefficient 1.2, that's your hedge ratio. Interpretation: for each Bitcoin short position, long 1.2 Ethereum units. Position sizing: if you want $10,000 Ethereum long, short 1.2 × $10,000 = $12,000 Bitcoin. Most statistical software (Python, R, specialized trading platforms) calculates hedge ratio automatically during Engle-Granger testing. Recalculate quarterly: regress prices on latest rolling-window data, updating hedge ratio if significant changes occur. Dynamic updates maintain optimal spread weighting despite changing cryptocurrency relationships.
Why does hedge ratio matter if I'm already trading cointegrated pairs?
Cointegration confirms mean-reversion property exists; hedge ratio determines optimal trade execution capturing that property. A cointegrated Bitcoin-Ethereum pair with incorrect weighting (equal 1-to-1 instead of optimal 1.2) creates asymmetric spreads: positive deviations revert differently than negative deviations. This asymmetry reduces trading profitability and increases drawdowns. Proper hedge ratio ensures symmetric spread behavior where deviations above and below equilibrium revert with equal probability—essential for mean-reversion strategy success. Pairs trading with incorrect weightings leave profits on table despite sound cointegrated foundations. Professional traders verify both cointegration AND optimal hedge ratio before strategy deployment.
Should I rebalance positions when hedge ratio changes?
Yes, gradual rebalancing toward updated hedge ratios improves long-term performance. If hedge ratio shifts from 1.2 to 1.15, your existing positions become suboptimal. Rebalancing involves closing portions of positions, then re-entering at new weighting. Consider transaction costs: frequent rebalancing (monthly) incurs excessive costs; quarterly rebalancing typically balances cost against benefit. Some traders use bands: rebalance only when hedge ratio changes exceed 0.05 threshold (1.2 becomes 1.15 or 1.25). Dynamic rebalancing maintains optimal spread stationarity enabling consistent mean-reversion performance. Neglecting rebalancing causes position-weighting drift, gradually reducing strategy effectiveness as hedge ratios diverge from current coefficients.
Common Misconceptions About Hedge Ratio (β)
I can use simple 1-to-1 position weighting for any cryptocurrency pair regardless of price volatility differences.
Simple equal weighting only works if both cryptocurrencies have identical volatility and are perfectly cointegrated. Bitcoin's price changes don't necessarily predict Ethereum price changes 1:1; actual relationship might be 1.2 Bitcoin for each Ethereum (different volatility). Equal weighting on non-equally-volatile pairs creates asymmetric spreads failing to revert symmetrically. Proper hedge ratio (1.2 in example) weights positions according to actual statistical relationships. Using equal weighting instead of optimal hedge ratio reduces strategy profitability and increases drawdowns despite cointegrated foundations.
Once I calculate hedge ratio, it remains constant forever for a cryptocurrency pair.
Hedge ratios change as cryptocurrency relationships evolve. Bitcoin-Ethereum hedge ratio might be 1.2 in Q1 but 1.15 in Q2 as relative volatilities shift. Using outdated hedge ratios causes position weighting drift, reducing strategy effectiveness. Professional traders recalculate hedge ratios quarterly minimum, more frequently during volatile periods. Monitoring hedge-ratio stability reveals cointegration health: stable ratios indicate robust relationships; volatile ratios signal weakening cointegration. Dynamic hedge-ratio updates maintain optimal spread behavior essential for consistent mean-reversion performance.
Hedge ratio's only purpose is position sizing; it doesn't affect spread stationarity.
Hedge ratio directly determines spread stationarity. Correct hedge ratio creates stationary spread with mean-reversion properties; incorrect hedge ratio produces non-stationary spread lacking mean reversion. Engle-Granger testing relies on optimal hedge ratio for residuals to achieve stationarity. Using hedge ratio 1.0 when optimal is 1.2 guarantees test failure (residuals non-stationary). Hedge ratio is the mathematical solution to cointegration problem—it enables spread stationarity creation. Position sizing naturally follows from stationarity-enabling hedge ratio.