Correlation & Multi-Asset Volatility
Correlation measures how two assets move together. For options traders, correlation determines whether your portfolio Greeks net out or compound. A book of BTC calls and ETH puts is only a hedge if BTC and ETH actually move in opposite directions -- and they usually don't.
Correlation ranges from -1 (perfect inverse) to +1 (perfect co-movement). A correlation of 0 means no linear relationship. In crypto, most major assets are positively correlated most of the time.
What Correlation Means for Options
Correlation affects everything about a multi-asset options book:
- Delta netting: If BTC and ETH are 0.80 correlated, being long BTC delta and short ETH delta only partially hedges. The 0.20 decorrelation is residual risk.
- Vega exposure: When vol spikes, correlated assets spike together. Your vega is not diversified -- it's concentrated.
- Gamma: Correlated underlying moves cause correlated gamma P&L. A BTC crash that also crashes ETH hits both legs of your book simultaneously.
- Tail risk: The worst-case scenario for a multi-asset book is everything moving together in the wrong direction. High correlation makes this more likely.
Correlation Multiplies Risk
Two uncorrelated positions with $100k vega each give you roughly $141k portfolio vega (sqrt of sum of squares). Two perfectly correlated positions give you $200k portfolio vega -- a straight sum. The difference is whether your risks diversify or stack.
Correlation Is Not Constant
This is the critical fact that breaks most portfolio models. Correlation is a regime-dependent quantity:
The pattern is universal across all asset classes: correlation rises toward 1 in crises. This is sometimes called "correlation breakdown" -- but really, correlation doesn't break. It converges to its worst-case value precisely when you need diversification most.
Toggle between regimes to see how BTC/ETH returns cluster:
BTC/ETH Correlation Across Market Regimes
Scatter of daily returns colored by regime — correlation tightens in crises
Diversification works when you don't need it. In a crisis, everything correlates.
Implied vs Realized Correlation
Just as implied volatility can differ from realized volatility, implied correlation can differ from realized correlation.
Implied correlation is extracted from the relationship between index option prices and single-name option prices. If an index option is expensive relative to its components, implied correlation is high -- the market expects everything to move together.
Realized correlation is computed from historical returns of the component assets over a lookback window.
The pattern mirrors the volatility risk premium: implied correlation tends to exceed realized, except during the exact crises that justify the premium.
Correlation and Portfolio Greeks
Understanding how correlation affects aggregate Greeks:
| Greek | Low Correlation (< 0.5) | High Correlation (> 0.8) |
|---|---|---|
| Net Delta | Cross-asset deltas diversify well | Deltas add nearly linearly -- more directional than you think |
| Portfolio Vega | Vol shocks affect assets independently | A single vol event hits everything at once |
| Gamma P&L | Gamma gains/losses partially offset | Gamma P&L from big moves compounds across assets |
| Worst-case loss | Smaller -- unlikely everything moves against you | Larger -- correlated drawdowns are common |
The Covariance Matrix
For a multi-asset options book, the correct risk measure is not the sum of individual VaRs. It is the portfolio VaR computed from the full covariance matrix, which accounts for correlations. Using individual VaRs (assuming independence) understates risk when correlation is high and overstates it when correlation is low.
Dispersion Trading
Dispersion trading is the strategy of trading single-name volatility against index volatility to capture the correlation risk premium.
The trade: sell index options (short correlation) and buy single-name options (long individual vol). If realized correlation is lower than implied, the index options decay faster than the singles, and the trade profits.
Crypto-Specific Correlation Behavior
BTC and ETH are the most liquid and most correlated pair in crypto. Some empirical observations:
- Baseline: BTC/ETH 30-day rolling correlation typically sits between 0.70 and 0.85 in normal conditions.
- ETH Merge (Sep 2022): Correlation dropped to the 0.30-0.50 range as ETH traded on its own fundamental catalyst while BTC was directionless.
- BTC ETF approval (Jan 2024): Correlation temporarily compressed as BTC rallied on inflows while ETH initially lagged.
- Market-wide crashes (May 2021, Nov 2022, Aug 2024): Correlation spiked to 0.92-0.98. Everything sold off together. Altcoins correlated even more tightly with BTC during these events.
- Altcoin correlations: Typically 0.50-0.70 with BTC in normal markets, rising to 0.85+ in crashes. Lower market-cap assets show more idiosyncratic movement in calm markets but converge rapidly during stress.
Practical Implications
Diversification Is an Illusion in Crises
If your risk management relies on cross-asset diversification, you need to stress-test with correlation = 1. The calm-market correlation is not the number that matters for your worst-case scenario. The crash correlation is.
Cross-Asset Hedging Breaks When You Need It Most
Hedging a BTC options book with ETH perps works reasonably well in normal markets (correlation 0.80 = decent hedge). During a crash, you need it to work perfectly -- and that is exactly when it breaks down the least predictably. The residual (the 0.05-0.20 decorrelation) can produce large unexpected P&L.
Correlation Informs Position Sizing
If you run BTC and ETH options books independently, your total risk is not the sum of the two. It is higher, because the books are correlated. Correct position sizing requires adjusting for the expected correlation -- and adding a buffer for correlation spikes.
Relative Value Opportunities
The flip side: when correlation drops during idiosyncratic events, relative value trades become attractive. Long ETH vol / short BTC vol during an ETH-specific catalyst is betting on decorrelation. These trades work best when the market has not yet priced in the divergence.
💡 Tip: Try answering each question yourself before revealing the answer.
Related:
- Vol Regimes - How volatility regimes affect cross-asset behavior
- Skew - Skew dynamics across correlated assets
- Delta Hedging - How cross-asset hedging works in practice
- Basis Trades - Cross-exchange basis and correlation