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Risk

Convexity

Convexity is the curvature of a portfolio's return profile with respect to a market factor — positive convexity means gains accelerate and losses decelerate.

Also known as: option-like payoff · positive convexity

Convexity describes how a portfolio's payoff curves with respect to a market factor. A linear payoff (e.g. cash equity exposure) has zero convexity. A long call option has positive convexity — the payoff accelerates as the market rises and decelerates as it falls. A short call has negative convexity — the payoff caps on the upside and accelerates on the downside.

Why convexity matters

Two portfolios can have the same expected return, the same volatility AND the same Sharpe yet behave very differently in extreme moves. Positive-convexity portfolios produce positive skewness and high Omega. Negative-convexity portfolios (short volatility, carry trades, short-vol ETFs) deliver beautiful Sharpe until the day they do not.

Estimating convexity

For a portfolio return R_p and a market factor R_m, fit a quadratic regression:

R_p = α + β · R_m + γ · R_m² + ε

γ > 0 indicates positive convexity, γ < 0 negative convexity. Statistical significance matters: convexity estimates require fat-tail observations to identify and 36 months of data is the bare minimum.

How MEDGE Capital uses convexity

Convexity is implicitly captured in the Omega Ratio and the Rachev Ratio reported on every backtest. Explicit quadratic convexity regression is on the roadmap — useful specifically for option-overlay strategies and trend-following sleeves where the linear regression β is misleading.

See also

Maximum Drawdown

Maximum Drawdown (MDD) is the largest peak-to-trough decline in a portfolio's cumulative value over a measurement window.

Sortino Ratio

The Sortino Ratio measures excess return per unit of downside deviation, treating only below-target volatility as risk.

Rachev Ratio

The Rachev Ratio is the expected return above the upper VaR threshold divided by the expected loss below the lower VaR threshold — a tail-to-tail performance measure.