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072

Case 072Short sellingHard

You want to short Pravit Gaming at Rs 500. Borrow costs 12% a year. You think there is a 60% chance it falls to Rs 350 within a year and a 40% chance it rises to Rs 700. Is the short worth doing, and what borrow cost would make it work?

1The situation

Pravit Gaming, a listed online gaming company, trades at Rs 500. Your research says its user growth is slowing and a regulatory change will hit revenue; you give a 60% chance the stock falls to Rs 350 within a year. If the market ignores the change and a new product takes off, you see it at Rs 700, with 40% chance.

The stock is heavily shorted. Your prime broker quotes a borrow fee of 12% a year on the value borrowed. Assume the position is held for a year and ignore dividends and financing on the proceeds.

2Your task

Work out the expected P&L per share before and after borrow cost, the borrow rate at which the short breaks even, and how confident you would need to be. Then say how you might still express the view.

Quick check

Before borrow costs, what is the expected gain per share on the short?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

No: a good thesis, a bad short. The expected gain is only Rs 10 a share, and a year of borrow at 12% costs Rs 60, so the trade expects to lose Rs 50. It breaks even only if borrow is below 2% a year, or if the fall comes within about 2 months. You would need to be 74% sure of the fall, not 60%. Express the view through puts, a pair or a smaller, catalyst-timed short instead.

Step 1What does the short earn before costs?

Lay out the tree. A fall to Rs 350 earns Rs 150 a share with 60% chance; a rise to Rs 700 loses Rs 200 with 40% chance; the expected gain is Rs 10, 2% of the price. Notice the asymmetry. The downside for a short is larger than the upside here, because the stock can rise further than it can fall, and a short that goes against you grows as a share of the book, which is why shorts are usually sized smaller than longs with the same conviction.

Step 2What does borrow do to the trade?

It comes off both branches, whatever happens. 12% a year on Rs 500 is Rs 60 a share, six times the Rs 10 expected gain, so the short now expects to lose Rs 50. It is like renting a shop for a year at Rs 60,000 to sell stock you expect to make Rs 10,000 on: the idea can be right and the rent still loses you money. Crowded shorts are exactly the names where borrow costThe fee paid to the lender of shares that are sold short, quoted as a yearly percentage of their value; it rises when many investors want to short the same stock. is highest, because many funds share your thesis.

The same thesis, before and after paying to borrow the sharesBefore borrow costShort atRs 50060%40%Falls to Rs 350+150 a shareRises to Rs 700-200 a shareExpected: 0.6 x 150 - 0.4 x 200 = +10After Rs 60 of borrow a shareShort atRs 50060%40%Falls to Rs 350+90 a shareRises to Rs 700-260 a shareExpected: 0.6 x 90 - 0.4 x 260 = -50
Before borrow the Pravit short expects to make Rs 10 a share, 0.6 x 150 less 0.4 x 200, but a year of 12% borrow costs Rs 60 a share and turns the expected result into a loss of Rs 50.
Step 3What would make the short work?

Solve for each lever. Borrow must be below 2% a year, Rs 10 on Rs 500, for the trade to break even over a year. Or the fall must come faster: at Rs 5 a month of borrow, the Rs 10 of edge pays for about 2 months, so a short around a result or a regulatory decision due in weeks can work where a year-long hold cannot. Or you must be more confident: breakeven probability rises from 57.1% without borrow to 74.3% with it.

The relationship
E[P&L]=0.6(150)−0.4(200)−60=−50p∗=200+60150+200=74.3%E[\text{P\&L}] = 0.6(150) - 0.4(200) - 60 = -50 \qquad p^* = \frac{200 + 60}{150 + 200} = 74.3\%
150gain per share if Pravit falls to Rs 350
200loss per share if it rises to Rs 700
60a year of borrow at 12% on Rs 500
What it says in wordsAfter borrow the short loses Rs 50 a share on your odds, and would need a 74.3% chance of the fall just to break even.
How confident must you be? Breakeven moves from 57% to 74%-150-100-500+50+100+15040%50%60%70%80%90%100%Chance the stock falls to Rs 350 within the yearno borrow cost12% a year of borrow, Rs 60your view, 60%57.1%74.3%
The Pravit short breaks even at a 57.1% chance of the fall before borrow but needs 74.3% after a year of 12% borrow, well above your 60% view.
Step 4How else could you express the view?

Three ways, each with its own cost. A put option caps the loss if the stock rises to Rs 700, but on a crowded short the puts are expensive for the same reason the borrow is. A pair, short Pravit against a long in a gaming peer that the regulation does not hit, keeps the thesis and may be cheaper to carry, though the borrow on Pravit remains. Or a smaller short timed to the catalyst, held for weeks rather than a year. The answer the PM wants is that the view can be right and still not pay for its own carry.

Where candidates lose it

The frequent mistake is judging the short on the thesis alone: 60% chance it falls, so short it. The expected gain is only Rs 10 a share because the loss if wrong is larger than the gain if right.

The second is forgetting borrow entirely or treating it as small. On crowded shorts, borrow can be the largest number in the trade.

What the interviewer asks next

  • Borrow is recalled after six months and you must cover at the market. How does that change the risk?
  • How big would you make this short in a Rs 500 crore book?
  • What would a one-year Rs 450 put need to cost for it to beat the short?
← Case 071A pod holds three longs of 4% of NAV each, Kalinda Paints, Rasvi Tyres and Orbel Chemicals, all helped by falling crude, with pairwise correlation of 0.8 and 30% volatility each. How many independent bets is that really, and what is the combined risk?Case 073 →How would you make money from social media data on Fizzora Beverages? You have three years of daily brand mentions and sentiment, and quarterly sales. Design the signal, the test and the trade, and say how you would know it is not noise.

Company names and figures are illustrative.

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