Case 010Statistical arbitrage and event tradesCore
Stocks in the top decile of earnings surprise drift 1.8% over the next 20 days, with 30 bps round-trip cost and 120 events a year. Compute expected annual P&L at Rs 2 crore per event and discuss the risk that the drift has decayed.
1The situation
Sarvagya Quant's researcher finds that stocks in the top decile of earnings surprise in its universe earn an average of 1.8% over the market in the 20 trading days after the announcement, entering at the close after the results. There are about 120 such events a year.
Round-trip cost, including spread, impact and fees, is 30 bps. The proposal is Rs 2 crore per event, hedged with index futures, whose cost is small enough to ignore here. Individual stocks have about 2% daily idiosyncratic volatility.
2Your task
What is the expected annual P&L and return on capital, how confident should you be in it, and what is the risk that the drift has decayed?
Quick check
What is the expected net P&L per event?
Worked solution
Try it on paper, then open one step at a time.
30-second answerThe answer to give first
About Rs 3.6 crore a year: Rs 3 lakh net on each of 120 events. With about 9.6 positions open at once, capital is roughly Rs 19.2 crore, a 19% return on it, and the implied Sharpe near 1.8 is too good to take at face value. Published drifts tend to shrink once known; if this one has halved to 0.9%, the net falls to about Rs 1.44 crore. Size it as if it has decayed until live data says otherwise.
Step 1What does the trade earn on paper?
Work per event first. Net drift is 1.8% less 0.30% of cost, 1.5%, which on Rs 2 crore is Rs 3 lakh; over 120 events that is Rs 3.6 crore a year. Costs take Rs 0.72 crore of the Rs 4.32 crore gross. Capital is set by how many positions overlap: each lasts 20 of about 250 trading days, so on average 9.6 are open, about Rs 19.2 crore of long exposure, and the return on that is about 19%. This is post-earnings announcement driftThe tendency of prices to keep moving in the direction of an earnings surprise for weeks after the announcement, as if the market under-reacts at first., one of the oldest documented anomalies.
Step 2How risky is it, and does the Sharpe make sense?
Each position carries idiosyncratic risk: 2% a day over 20 days is about 8.9%, so Rs 17.9 lakh of standard deviation on each Rs 2 crore bet. Across 120 independent events that adds up to about Rs 1.96 crore a year. Rs 3.6 crore of expected P&L on Rs 1.96 crore of risk is a Sharpe near 1.8, and a number that high for a well-known anomaly is a reason to check, not to celebrate. Events cluster in results season, so they are not independent: a sector-wide surprise puts twenty correlated bets on at once, and the real Sharpe is lower.
| Rs crore a year | Backtest drift 1.8% | Drift halved, 0.9% |
|---|---|---|
| Gross | 4.32 | 2.16 |
| Costs | (0.72) | (0.72) |
| Net | 3.60 | 1.44 |
| Risk, one sd | 1.96 | 1.96 |
| Sharpe, if events were independent | 1.84 | 0.73 |
Step 3Why might the drift have decayed, and how would you tell?
A well-known pattern attracts capital, and capital trading it pulls the price move forward, closer to the announcement. Studies of published anomalies find that returns tend to shrink after publication, so treat the backtest average as an upper bound. Decay hurts more than proportionally, because costs do not shrink with it: a halved drift cuts net P&L by 60%, and at 0.3% the trade earns nothing. Test it directly. Split the sample into early and recent years and compare; fit the drift against time; check whether more of the move now happens on day 0, before you can enter.
Statistical confidence is not the constraint. Over ten years of 1,200 events, the standard error of the mean is about 0.26%, a t-statistic near 7 if the events were independent. The constraint is whether the next year looks like the average of the last ten. Run it at a fraction of the proposed size, compare live drift with the recent-years estimate every quarter, and scale up only if they agree.
Where candidates lose it
Candidates multiply gross drift by the number of events and forget costs, or subtract costs but miss that decay and costs interact: when the edge halves, the cost does not, so the net falls by more than half.
The second miss is treating the backtest average as the forecast. The interviewer wants you to name decay as the main risk and propose a test for it, not to assume the history repeats.
What the interviewer asks next
- How would you hedge the sector risk when ten banks report the same week?
- Would you exit at day 20 or earlier? How would you decide?
- The recent five years show 0.9% and the earlier five 2.7%. What do you tell the PM?
Company names and figures are illustrative.