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  1. 076Your stop-loss on a new long position sits 25% below your entry price, and the desk rule caps the loss on any one idea at 1% of the book. What is the largest position you can take?Betting and sizingWarm upMulti-manager platformsProp and quant trading firms

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    Before you work it: how big can the position be, as a share of the book?

    Show the worked solution

    4% of the book. If the stop is hit you lose 25% of the position, and that loss must not exceed 1% of the book. So the position times 25% equals 1%, and the position is 1% divided by 0.25, which is 4%. On a Rs 1,000 crore book that is a Rs 40 crore position and a Rs 10 crore loss at the stop.

    Why is the answer not simply 1%?

    Think of lending a friend money for a trip when you know the worst case is that a quarter of it never comes back. If you can stand to lose Rs 1,000, you can lend Rs 4,000, because only a quarter of the loan is at risk. The loss cap limits what you can lose, and the stop decides what fraction of the position you can lose, so the size is the cap divided by the stop distance. A trader who puts on 1% because the cap is 1% has confused the bet with the damage.

    Every position on the curve loses exactly 1% of the book at its stop0%2%4%6%8%10%10%25%50%0Position size, % of bookStop distance below entry2% x 50% = 1%4% x 25% = 1%10% x 10% = 1%each point loses 1% at its stopLoss at the stop= size x stop distance1% = size x 25%size = 4% of bookOn a Rs 1,000 crore bookPosition: Rs 40 croreLoss at the stop: Rs 10 crore
    A 4% position with a 25% stop, a 2% position with a 50% stop and a 10% position with a 10% stop all lose exactly 1% of the book at the stop; on a Rs 1,000 crore book the 4% position is Rs 40 crore and loses Rs 10 crore.
    The relationship
    size=loss capstop distance=1%25%=4% of the book\text{size} = \frac{\text{loss cap}}{\text{stop distance}} = \frac{1\%}{25\%} = 4\%\ \text{of the book}
    loss capthe most the desk lets one idea lose, as a share of the book, here 1%
    stop distancehow far below entry the stop sits, as a share of the entry price, here 25%
    What it says in wordsThe position is as large as it can be while still losing no more than the cap when the stop is hit.

    What happens to the size as the stop moves?

    Tighten the stop and the position can grow; widen it and the position must shrink. With a 10% stop the same 1% cap allows a 10% position, and with a 50% stop only 2%. Every pair on the curve loses exactly 1% of the book when the stop is hit. This is why a trader whose thesis needs room to breathe, say through an earnings print, carries a smaller position than one working to a tight technical level.

    What does the stop not protect you against?

    The arithmetic assumes you get out at the stop price. A stock that gaps through the stop overnight, on results or a regulatory order, fills below it, and the loss exceeds the cap. If the stock opens 40% down, the 4% position loses 1.6% of the book, not 1%. Risk managers therefore size to the stop and then check the gap risk separately, often capping single-name positions whatever the stop says. Give that limitation straight after the number.

    Where candidates lose it

    The quick wrong answer is 1%: candidates hear the loss cap and repeat it as the position size. That position would lose only 0.25% of the book at the stop, so the trader is using a quarter of the risk the desk allowed.

    The second loss is stopping at 4% without saying that a stop is not a guarantee. One sentence on gap risk shows you know the rule sizes the planned loss, not the worst loss.

    What the interviewer asks next

    • The stock gaps 40% below your entry overnight. What did you lose as a share of the book?
    • You want the same 1% cap across ten ideas with different stops. How do you set each size?
    • How would you size the position from the stock's volatility instead of a fixed stop?