Private Wealth Management puzzles, solved step by step

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All topicsCompounding and doubling8Returns arithmetic9Fee and cost drag8Inflation and real return7Tax arithmetic7Probability and risk of loss9Retirement and withdrawal8Fixed income numeracy8Behavioural traps8Estimation and sizing8Options and structured products6Leverage and borrowing6Wealth business economics8
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  1. 011A client holds a stock bought at Rs 100 and sells a one-month call option with a Rs 110 strike for a premium of Rs 3. What is his maximum gain, and what does he give up if the stock ends the month at Rs 130?Options and structured productsWarm upPrivate banking

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    The stock ends at Rs 130. What is the covered position worth, per share?

    Show the worked solution

    His maximum gain is Rs 13 a share, and at Rs 130 he gives up Rs 17. Above Rs 110 the call is exercised and the share goes at Rs 110, so the position is capped at Rs 110 plus the Rs 3 premium, Rs 113. At Rs 130 the stock alone would be worth Rs 130. The premium cushions a fall by only Rs 3: below Rs 97 he is losing money.

    What exactly has the client sold?

    Think of a landlord who takes a small non-refundable deposit from someone for the right to buy his flat at a fixed price within a month. If flat prices jump, the buyer exercises and the landlord gets only the fixed price plus the deposit. A covered call sells the upside above the strike in exchange for a small, certain fee today. The client keeps all the downside of owning the stock, less the premiumThe price the option buyer pays the seller up front, kept by the seller whatever happens next. received.

    A covered call trades the upside above 110 for Rs 3 today10011313080100110130140Stock price at expiry, Rs-17Breakeven 97Stock aloneworth 130 at 130Covered callcapped at 113= strike 110 + premium 3Below 110: 3 betterthan the stock alone
    The covered call is worth Rs 3 more than the stock below the Rs 110 strike, but it is capped at Rs 113 above it, so at a price of Rs 130 the client gives up Rs 17 against simply holding the stock.

    When does the trade help and when does it hurt?

    Walk the three regions out loud. Below Rs 110 the covered call beats the plain stock by exactly the Rs 3 premium; above Rs 113 it falls behind by every rupee the stock rises. Between Rs 110 and Rs 113 the stock alone catches up. So the trade suits a client who expects the stock to drift sideways and wants some income, and it hurts the client who is secretly hoping for a sharp rally.

    The relationship
    VT=min⁡(ST, 110)+3V130=110+3=113V_T = \min(S_T,\,110) + 3 \qquad V_{130} = 110 + 3 = 113
    S_Tthe stock price at expiry
    110the strike price of the call sold
    3the premium received up front
    V_Tthe value of the stock plus the short call, per share
    What it says in wordsThe covered position is worth the lower of the stock price and the strike, plus the premium already banked.

    Say the risk plainly, because clients hear the word income and relax. If the stock falls to Rs 70, the position is worth Rs 73: the premium barely registers. A covered call is not protection; it is a trade of upside for a small, steady fee.

    Where candidates lose it

    The trap is adding the premium on top of the full stock price and saying Rs 133. It forgets that the share is called away at the strike, which is the whole point of the option sold.

    The second loss is describing a covered call as a safe income strategy. The downside is almost entirely intact, and a wealth interviewer is listening for whether you tell a client that.

    What the interviewer asks next

    • Where is the breakeven, and what is the position worth if the stock ends at Rs 90?
    • What changes if he sells a Rs 105 call for Rs 5 instead?
    • How would you explain this trade to a client who calls it free money?