How does theta decay vary across different times to expiration, and why does it accelerate near expiry?

Theta measures the rate at which an option's time value erodes per day. The key insight is that theta is not constant; it follows a square-root-of-time relationship that causes dramatic acceleration as expiration approaches.\n\nThe Square Root Rule:\n\nTime value of an ATM option is approximately proportional to sqrt(T). Therefore:\n\n- An option with 64 days has time value proportional to sqrt(64) = 8\n- At 16 days: sqrt(16) = 4 (half the time value, though only 48 days have passed)\n- At 4 days: sqrt(4) = 2 (quarter of initial time value)\n- At 1 day: sqrt(1) = 1 (one-eighth of initial time value)\n\nThis means the option loses more value per day as expiration nears.\n\n`mermaid\ngraph TD\n A[\"90 Days to Expiry
Theta = -$0.03/day\"] --> B[\"60 Days
Theta = -$0.04/day\"]\n B --> C[\"30 Days
Theta = -$0.06/day\"]\n C --> D[\"14 Days
Theta = -$0.09/day\"]\n D --> E[\"7 Days
Theta = -$0.13/day\"]\n E --> F[\"1 Day
Theta = -$0.35/day\"]\n style D fill:#f59e0b,color:#000\n style E fill:#ef4444,color:#fff\n style F fill:#dc2626,color:#fff\n`\n\nNumerical Example:\n\nMeridian Corp stock is at $100. Consider ATM calls at various expirations (risk-free rate 5%, vol 25%):\n\n| Days to Expiry | Call Price | Daily Theta |\n|---|---|---|\n| 90 | $6.42 | -$0.033 |\n| 60 | $5.28 | -$0.041 |\n| 30 | $3.74 | -$0.058 |\n| 14 | $2.56 | -$0.085 |\n| 7 | $1.81 | -$0.120 |\n| 1 | $0.69 | -$0.345 |\n\nStrategy Implications:\n\nCovered call sellers benefit from writing short-dated options (30-45 DTE) because theta decay is steepest per day in that range, while gamma risk is still manageable.\n\nIron condor traders target the same window: sell options at 30-45 DTE, buy them back when theta has extracted 50-70% of the premium (around 14-21 DTE), avoiding the final week when gamma explodes.\n\nCalendar spread buyers exploit the differential decay between front-month and back-month options: the short near-term leg decays faster than the long far-term leg.\n\nOTM vs ATM Theta: ATM options have the highest absolute theta, but OTM options have a flatter decay curve. Deep OTM options lose most of their value early and have very little left to decay near expiry.\n\nExplore theta strategies with our CFA Derivatives practice questions.