Why Risk-Adjusted?
Raw returns don't tell the full story. Risk-adjusted metrics show return per unit of risk.
Key Metrics
- Sharpe Ratio: Return / Standard Deviation
- Sortino Ratio: Return / Downside Deviation
- Calmar Ratio: Return / Max Drawdown
Interpretation
- Sharpe > 1: Good
- Sharpe > 2: Excellent
- Sortino > Sharpe: Good downside management
Application
Use to compare strategies and optimize risk-reward.
Why Raw Returns Mislead You
A strategy that made 40% in a quarter may look brilliant until you realise it took a 60% drawdown to earn it. Risk-adjusted metrics divide the return by the risk taken, allowing two very different trips to the same destination to be compared honestly. In options trading, where leveraged premium structures can double the headline number while quadrupling the tail risk, this comparison is not optional; it is the only way to know whether a technique deserves more capital.
Sharpe Ratio: The Noise-Weighted Score
Sharpe divides excess return over the risk-free rate by the standard deviation of periodic returns. Its weakness is that standard deviation punishes gains as much as losses. A broken options strategy that snap-crashes throws off a huge volatility spike, and a genuine edge that produces steady small wins followed by a rare large win looks worse than it is. Use Sharpe to rank systems, never to accept or reject one alone.
Sortino: The Downside-Only Correction
Sortino replaces total volatility with downside deviation only, measuring how badly returns miss the target on the way down. For option sellers, who live on many small wins and occasional large losses, Sortino is the friendlier and more honest lens: it stops penalising the winning months for being too good. A high-Sortino credit spread portfolio is genuinely less scary than a high-Sharpe momentum system that whipsaws.
Maximum Drawdown and Its Recovery Math
Maximum drawdown is the deepest peak-to-trough decline suffered. The recovery time matters as much as the depth: a 50% drawdown requires a 100% gain to recover, while a 25% drawdown requires only 33%. Cap position sizing so the projected maximum drawdown stays under 20%; beyond that level the emotional and compounding damage becomes nearly impossible to reverse with the same rulebook.
The Calmar and Ulcer Ratios
- Calmar: annualised return divided by maximum drawdown; favours smooth, recoverable strategies.
- Ulcer index: measures time spent underwater rather than depth; catches strategies that bleed slowly for months.
- Profit factor: gross wins divided by gross losses; a robust intraday edge usually prints a profit factor of at least 1.3.
Applying Them to an Options Book
- Compute the Utfund's daily returns for the last 250 sessions, not the weekly numbers.
- Compare each strategy's Sortino and max drawdown before sizing it.
- Rebalance capital toward the highest Calmar at the start of every month.
- Trim any strategy whose 90-day rolling Sharpe drops below zero twice in a quarter.
The Final Caveat
Every ratio assumes the past distribution persists into the future. In markets, volatility clusters and tail events arrive in waves, so a ratio computed in a calm year flatters a strategy that will drown in a stressed one. Always stress-test the ratios on a recent stressful sample, such as the last high-volatility quarter, before increasing the allocation.
A Sharpe Walkthrough on an Options Book
The Sharpe ratio divides the strategy's return above the risk-free rate by its volatility of returns. Suppose the options book returns 1.2 percent per month with a monthly volatility of 2.5 percent and the risk-free benchmark sits near 0.5 percent annually; the monthly excess is about 1.1 percent and the ratio lands near 0.44 per month, which annualises by multiplying by the square root of 12, giving a Sharpe near 1.5. That one line of arithmetic explains why the strategy is only as good as its constancy: a strategy making the same money in choppy half-months and boring weeks scores far better than one making identical rupees in bursts.
Sortino: The Downside-Only Correction
Sharpe punishes upside volatility and downside volatility equally, which wrongs option sellers who deliver steady small gains punctuated by occasional ugly weeks. The Sortino ratio uses downside deviation only: how spread-out the losing returns are below a chosen target. A covered-call book with rare, sharp drawdowns scores materially better on Sortino than on Sharpe, and that gap is the honest advertisement for the style. Aim for both ratios in the write-up of any strategy, because a high Sharpe hiding a mediocre Sortino is a strategy that loses in the wrong shape.
Drawdown Math: Recovery Is Nonlinear
The single least-understood number in risk is recovery. A 20 percent drawdown requires only a 25 percent gain to claw back; a 50 percent drawdown requires a 100 percent gain; a 75 percent drawdown requires 300 percent. That nonlinearity is why position risk rules are sacred: cutting the drawdowns by a third is worth more than doubling the average win, and the ratios that reward it are Calmar (annual return divided by maximum drawdown) and the Ulcer Index, which measures how deep the pain stays drawn over time. A 30 percent drawdown with a fast recovery can be survivable; the same number with an 18-month stay is a career event.
Applying These to an Options Portfolio
Compute all three on the strategy's daily equity curve, not yearly summaries: Sharpe for the headline, Sortino for the honest shape, and Calmar for the disaster question. Normalise every strategy to the same series of daily returns before comparing, and discount the risk-free asset from each side. The final caveat never leaves the room: every ratio is computed on the past, and a single regime change can reorder all of them. Treat a ratio as a description of what was, not a prophecy of what will be.
- Annualise by the square root of trading periods per year.
- Pair every Sharpe with its Sortino and Calmar.
- Assess drawdowns by recovery time, not just depth.
- Compute on daily returns with the risk-free asset subtracted.
- Recompute monthly; ratios are weather reports, not forecasts.
Annualisation Pitfalls and Confidence in the Number
Every ratio lives in its annualisation convention, and the convention decides whether the number flatters or honestly scares. Annualising monthly numbers by the square root of twelve assumes the months are independent; annualising daily numbers by the square root of 252 assumes the same for days; both are false on option strategies whose returns cluster around expiry dates, so the honest report quotes both conventions and treats the gap between them as evidence of the strategy's calendar dependence. The second discipline is confidence: a Sharpe of 1.5 computed on six months is a different claim from the same ratio on six years. Bootstrap the daily returns to build a band around the ratio, and dismiss any point estimate wider than its own band. Pair the band with the maximum drawdown and its recovery-month count, because a beautiful Sharpe beside a sparse, brutal drawdown is a ratio selling insurance the bad quarter forfeits.
