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  1. 084You own a stock bought at Rs 500 and sell a call struck at Rs 550 for a premium of Rs 12. At expiry, what is your maximum profit and where is your breakeven?Options and payoffsWarm upVolatility and relative value fundsProp and quant trading firms

    Try it first

    What is the most you can make?

    Show the worked solution

    Maximum profit is Rs 62 and the breakeven is Rs 488. Above the Rs 550 strike the stock is called away, so you keep the Rs 50 rise from 500 to 550 plus the Rs 12 premium. Below 550 the call expires worthless and you keep the premium, which cushions the first Rs 12 of any fall. You lose money only below 500 minus 12, which is Rs 488.

    What have you actually sold?

    Think of renting out a flat you own with an agreement that the tenant may buy it at a fixed price within the year. You collect rent now, but if flat prices soar, the tenant buys at the agreed price and the extra gain is theirs. A covered call swaps the upside above the strike for cash today: the premium is the rent, and the strike is the agreed sale price.

    The premium lifts the line by Rs 12 and the strike flattens it at Rs 62-50+50+1000450500550600Stock price at expiry, RsProfit, Rsbreakeven 488cap: +62 at 550 and aboveabove 562 the plainstock does betterstock onlycovered callbelow 550 the gap between the linesis the Rs 12 premium
    The covered call earns Rs 12 more than the plain stock at every price up to Rs 550, is capped at a profit of Rs 62 from Rs 550 upwards, breaks even at Rs 488, and falls behind the plain stock above Rs 562.

    How do you find the two numbers quickly?

    Take the two regions separately. At or above Rs 550 the position is worth 550 plus the 12 kept, against 500 paid, so Rs 62 whatever the stock does. Below 550 the call is worthless and the position is just the stock plus 12, so it loses money only once the stock falls more than 12 below the purchase price, at Rs 488. At a stock price of 520 you make 32: 20 on the stock and 12 of premium. At 450 you lose 38 instead of 50.

    The relationship
    profit=min⁡(ST,K)−S0+cmax⁡=550−500+12=62breakeven=500−12=488\text{profit} = \min(S_T, K) - S_0 + c \qquad \max = 550 - 500 + 12 = 62 \qquad \text{breakeven} = 500 - 12 = 488
    S_Tthe stock price at expiry
    Kthe strike of the call sold, Rs 550
    S_0the price paid for the stock, Rs 500
    cthe premium received, Rs 12
    What it says in wordsYou keep the stock's value up to the strike, plus the premium, minus what you paid for the stock.

    What is the trade-off in plain terms?

    The premium improves every outcome below Rs 562 and worsens every outcome above it. Above Rs 562 the plain stock position beats the covered call, because the gain you gave away exceeds the premium you took in. On the downside the cushion is thin: the stock can fall all the way from 500 and the premium covers only 12 of it. That is the limitation to state: a covered call is income with a cap, not protection.

    Where candidates lose it

    The common slip is quoting the premium, Rs 12, as the maximum profit, which forgets that you still own the stock and keep its rise up to the strike. The opposite slip is saying unlimited, which forgets the call you sold.

    For the breakeven, candidates often add the premium to the purchase price and say Rs 512. The premium is money received, so it lowers the breakeven, to Rs 488.

    What the interviewer asks next

    • At what stock price are the covered call and the plain stock worth the same at expiry?
    • Why might the same call fetch more than Rs 12 just before a results announcement?
    • Which position gives the same payoff at expiry as a covered call without owning the stock?