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Risk-adjusted return

Any measure of return per unit of risk taken, which is the only fair way to compare results produced with different amounts of leverage.

Raw return is uninformative on its own. A 60% year at 5x leverage and a 12% year unlevered can be the same skill expressed at different sizes - and the levered version is one bad week from being a minus 60% year.

The family of measures differs only in what goes in the denominator: total volatility for the sharpe-ratio, downside volatility for the sortino-ratio, maximum drawdown for the calmar-ratio, depth and duration of drawdown for the ulcer-index. Each encodes a different definition of what counts as risk, and a strategy can look excellent under one and poor under another. Compute at least two.

The practical use is allocation. Between two strategies, the higher risk-adjusted return can be levered up to match the other's volatility and will still win; raw return comparisons cannot tell you that. What none of them capture is the tail, so a high ratio from selling options is not the same as a high ratio from trend following. See return-skew.

Related: sharpe-ratio, sortino-ratio, calmar-ratio, return-skew

See it drawn

Original diagrams for the ideas on this page. Illustrative, not real market data.

An equity curve and its drawdownAn account balance rising over a year, falling from a peak to a trough, then climbing back to the old peak.ACCOUNT EQUITY$20k$12k$8k024681012TIME (MONTHS)PEAK $16,000TROUGH $12,000DRAWDOWN−25%RECOVERY
Equity curve and drawdown. An account balance plotted month by month. The fall from the $16,000 peak to the $12,000 trough is a 25% drawdown, and the shaded area lasts until the balance climbs back to the old peak.
The volatility smile across strikesImplied volatility plotted against strike, dipping near the money and turning up at both ends, more steeply on the downside.Implied volatility32%28%24%20%8090110120Puts below the money cost moreFar calls cost more tooLowest IV near the moneyATM 100Strike price
The volatility smile. Options on the same stock and the same expiry are not priced off one volatility. Strikes near the money carry the lowest implied volatility, and it rises towards both ends — usually faster on the downside, which tilts the smile into a skew.

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