What is conversion arbitrage, and how does it exploit violations of put-call parity?

Conversion arbitrage exploits a violation of put-call parity by constructing a synthetic position that differs in price from the equivalent cash position. When the synthetic is cheaper than the actual, you buy the synthetic and sell the actual (or vice versa) for a riskless profit.\n\nPut-Call Parity:\n\nC - P = S - K x e^{-rT}\n\nIf this equation doesn't hold, arbitrage exists.\n\nConversion Trade (when the stock is overpriced relative to synthetic):\n\n`mermaid\ngraph TD\n A[\"Detect Mispricing
C - P < S - PV(K)\"] --> B[\"Buy the Synthetic Short\"]\n B --> C[\"Buy Put\"]\n B --> D[\"Sell Call\"]\n B --> E[\"Buy Stock\"]\n C --> F[\"Riskless Combined Position\"]\n D --> F\n E --> F\n F --> G[\"Payoff at Expiry = K
regardless of stock price\"]\n G --> H[\"Profit = K - Cost of Position\"]\n`\n\nThe conversion combines: Long Stock + Long Put + Short Call (all same strike and expiry).\n\nAt expiration, regardless of the stock price:\n- If S > K: the short call is assigned, you deliver stock at K. Put expires worthless. Receive K.\n- If S < K: exercise the put, sell stock at K. Call expires worthless. Receive K.\n- If S = K: both options expire worthless, sell stock at K. Receive K.\n\nPayoff is always K. If your initial cost is less than PV(K), you earn risk-free profit.\n\nNumerical Example:\n\nWestbrook Energy: S = $62.00, K = $60, T = 60 days, r = 5%\n- Call (60-strike, 60-day): C = $4.80\n- Put (60-strike, 60-day): P = $2.30\n- PV(K) = $60 x e^{-0.05 x 60/365} = $59.51\n\nParity check: C - P = $4.80 - $2.30 = $2.50\nS - PV(K) = $62.00 - $59.51 = $2.49\n\nViolation: $2.50 > $2.49 (call is slightly overpriced relative to put).\n\nConversion trade:\n- Buy stock: -$62.00\n- Buy put: -$2.30\n- Sell call: +$4.80\n- Net outlay: $62.00 + $2.30 - $4.80 = $59.50\n- Receive at expiry: $60.00\n- Profit: $60.00 - $59.50 = $0.50 (riskless, before transaction costs)\n\nAnnualized return: ($0.50 / $59.50) x (365/60) = 5.11% (above risk-free rate of 5%)\n\nReversal Arbitrage is the mirror image: if C - P < S - PV(K), you short the stock, sell the put, and buy the call.\n\nPractical Risks:\n- Transaction costs and bid-ask spreads often consume the small profit\n- Pin risk near expiration (stock closing exactly at the strike)\n- Early exercise risk on American options\n- Dividend timing can invalidate the parity relationship\n\nExplore arbitrage strategies in our CFA Derivatives course.