Why did my P&L move? Greek attribution, explained

Greeks · 6 min read

Greek attribution splits a day of options P&L into Delta, Gamma, Theta and Vega, showing which forces actually produced the number your broker reports.

Yesterday your iron condor made $12. Was that a good day? You genuinely cannot answer that question from the number alone. Maybe time decay earned you $85 and everything else was quiet. That is a great day for a premium-selling position. Or maybe time decay earned $85, a volatility spike cost you $310, and a favorable price drift clawed back $237. Same $12. Completely different story, and completely different implications for what you should do tomorrow.

Greek attribution is the discipline of splitting a day's profit and loss into the forces that produced it. It is the difference between watching your account balance and understanding your position. Once you see your P&L decomposed a few times, you will never trust a raw daily number again.

Figure: The quiet +$12.00 day from the opening paragraph: Theta +$85.00, Vega −$310.00, and the favorable +$237.00 drift split into its Delta (+$289.00) and Gamma (−$52.00) parts.

The four forces acting on every option

An option's price responds to a handful of inputs, and each Greek measures sensitivity to one of them. Attribution simply multiplies each sensitivity by how much its input actually moved.

  • Delta: profit or loss from the underlying's price change. A Delta of 40 means roughly $40 of P&L per $1 move in the underlying.
  • Gamma: the correction to Delta for larger moves. Delta itself changes as price moves, and Gamma captures the P&L from that curvature, roughly one half of Gamma times the move squared.
  • Theta: profit or loss from the passage of one day, everything else frozen. Short premium positions collect it; long premium positions pay it.
  • Vega: profit or loss from a change in implied volatility. A Vega of 30 means roughly $30 of P&L per one-point change in implied volatility.

A day's P&L is approximately the sum of these four contributions, plus a residual for what the linear model misses. When the residual is small, you understand your position. When it is persistently large, something in your model, usually your volatility inputs, is wrong, and that itself is valuable information.

A worked example: the day that looked like nothing happened

Say you are short a 30-day at-the-money straddle on an index product trading at 560. Your position Greeks at the open: Delta −8, Gamma −22, Theta +$95 per day, Vega −$120 per volatility point.

During the day, the underlying rallies $2.40 and implied volatility drops 0.9 points. At the close, your P&L reads +$18. Flat day, right? Here is the attribution:

  • Delta: −8 × $2.40 = −$19.20. Your small short lean cost you a little on the rally.
  • Gamma: 0.5 × (−22) × (2.40)² ≈ −$63.36. The move itself hurt, because short Gamma always pays for realized movement.
  • Theta: +$95.00. One day of decay collected.
  • Vega: −$120 × (−0.9) = +$108.00. The volatility drop was your biggest earner.
  • Sum: −$19.20 − $63.36 + $95.00 + $108.00 = +$120.44. Residual versus the actual +$18: −$102.44.

Two lessons jump out. First, your quiet +$18 day was actually a $200-plus tug of war: Theta and Vega earned $203 while price movement cost $82 and the residual absorbed another $102. Second, that residual is too big to ignore. In practice a residual like this often traces to cross-effects: Delta changing as volatility fell, or marks moving from bid-ask noise rather than model-fair prices. A good attribution engine breaks those out explicitly instead of letting them contaminate your read of each Greek.

The daily number tells you what happened to your money. The attribution tells you whether your thesis is true.

Why cancellation is the dangerous case

The scariest positions are the ones whose net P&L stays calm while enormous forces cancel underneath. In the example above, imagine the same day but with implied volatility rising 0.9 points instead of falling. Vega flips to −$108, and your day becomes roughly −$95 before residual, from the identical price path. The calm was never structural; it was two large exposures happening to offset. Attribution makes the size of each exposure visible before the day they stop offsetting.

This is the single most common blind spot in retail options accounts: a trader believes a position is 'working' because the equity curve is smooth, when in fact one Greek is quietly financing losses in another. A short-Vega book bleeding Gamma losses in a rising market looks fine right up until realized movement and implied volatility spike together.

Figure: One reported number, four drivers: a +$412.00 result earned by Delta while the volatility thesis quietly bled. The headline cannot tell you which anatomy you have. Attribution can.

Reading an attribution report

When you look at a decomposed day, ask three questions in order. First: did the P&L come from the driver you intended? If you sold the straddle to harvest Theta and your profit came from a lucky Vega crush, you were paid for a risk you did not mean to take. Second: which single Greek was your largest gross exposure, regardless of sign? That is your real risk, whatever the net said. Third: how big is the unexplained residual relative to the explained buckets? Under about 10% of gross movement, trust the read. Persistently above that, audit your volatility marks before trusting anything else.

Attribution over time is where the edge shows up

One day of attribution is diagnostic. Thirty days of attribution is a verdict on your strategy. Sum each bucket across a month of trading and you learn what your approach actually monetizes. A trader who believes they are selling time decay may discover that 80% of their cumulative profit came from Vega during a falling-volatility regime, profit that a rising-volatility regime will take back with interest. Another may find that path-dependent Gamma losses consistently consume most of the Theta they collect, meaning the strategy only appears profitable because of a directional tailwind.

This is why serious desks run attribution on every book, every day. The daily number tells you what happened to your money. The attribution tells you whether your thesis is true. Only one of those helps you make the next decision.

Educational content, not investment advice. Options involve substantial risk.

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