Covered Call, Unmasked

Question

You buy a stock at 100 and sell the 105 call against it for 3 (rates zero). What is your maximum profit, and at what expiry price does it kick in? Then the identity question: what simpler position is "stock + short call" exactly equivalent to, and what is "stock + long put" equivalent to?

Accepted Answer

Max profit. Above 105 the shares are called away at 105; with the 3 premium banked: textmax profit = (105 - 100) + 3 = mathbf8, quad textfor all S_T ge 105. Below 105 you keep the stock and the 3: P&L = S_T - 100 + 3, breakeven S_T = 97, downside essentially the full stock risk minus three dollars of cushion. The identity. Rearranged parity (r = 0): S - C = K - P. So a covered call is a short put plus a bond paying K: same payoff in every state: capped upside, full downside. Check the premium: the synthetic short 105 put collects P = C + K - S = 3 + 105 - 100 = 8... exactly the covered call's max profit. The 8 you can make is the put premium you implicitly sold. Similarly S + P = C + K: a protective put is a call plus a bond: paying for downside insurance on stock you own leaves you holding, economically, just a call. Insurance on a thing equals an option on the thing. Why this matters beyond algebra: - No free yield. "Covered calls generate income" is the most persistent retail half-truth; parity says you are being paid to sell insurance, the income is short-put premium, compensation for keeping the crash and capping the rally. - Desk fluency: any position reduces mod-parity to a

Covered Call, Unmasked

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