Case 082Statistical arbitrage and event tradesWarm up
Kovidam Steel trades at Rs 1,000 and its 30-day future at Rs 1,012. Funding costs 7% a year and no dividend is due. What is the fair futures price, what is the arbitrage, and what does it earn a year?
1The situation
Kovidam Steel, an invented mid-cap steel maker, trades at Rs 1,000 in the cash market. Its stock future expiring in 30 days trades at Rs 1,012. The desk can borrow at 7% a year, simple interest, and no dividend or other corporate action falls before expiry.
The interviewer at a systematic fund asks what the future should cost, whether there is a trade, and what it is worth once you account for what the trade really ties up.
2Your task
Compute the fair futures price, describe the arbitrage step by step, give its return for the period and a year, and list what could eat into it.
Quick check
Which trade captures the mispricing?
Worked solution
Try it on paper, then open one step at a time.
30-second answerThe answer to give first
Fair value is Rs 1,005.75, so the future at Rs 1,012 is Rs 6.25 rich: sell it and buy the stock with money borrowed at 7%. At expiry the stock is delivered or the two prices converge, the loan is repaid, and Rs 6.25 a share remains whatever the price does. That is 0.625% in 30 days, about 7.6% a year above funding, before costs, margin and the capital the stock ties up.
Step 1What should the future cost?
Suppose a shop lets you collect a fridge in a month and pay then, instead of paying today. A fair shop charges you the interest it loses by waiting for its money, and nothing more. A future is the same agreement: buy now for delivery later, so its fair price is today's price plus the cost of carrying the stock until delivery, minus any income the stock pays on the way. Here that is Rs 1,000 plus 7% for 30 days, Rs 5.75, so Rs 1,005.75. With no dividend there is nothing to subtract.
| F* | fair futures price |
| S | spot price, Rs 1,000 |
| r | funding rate, 7% a year, simple |
| d | days to expiry, 30 |
| D | dividends before expiry, here zero |
Step 2How do you lock in the gap?
Do three things today: borrow Rs 1,000 at 7%, buy one share, and sell one future at Rs 1,012. At expiry the short future and the share cancel, because the future settles at the stock's price, and you owe Rs 1,005.75 on the loan. Whatever Kovidam closes at on expiry day, the stock leg plus the future leg is worth exactly Rs 1,012, so Rs 6.25 is left after repaying the loan. The table shows three closing prices; the last column does not move. This is the cash and carry trade, and it is why a future cannot drift far above spot plus carry for long.
| Price at expiry | Stock leg | Short future P&L | Loan repaid | Net |
|---|---|---|---|---|
| 900 | 900.00 | +112.00 | -1,005.75 | +6.25 |
| 1,000 | 1,000.00 | +12.00 | -1,005.75 | +6.25 |
| 1,100 | 1,100.00 | -88.00 | -1,005.75 | +6.25 |
Step 3What is it worth a year, and what eats into it?
The gap is Rs 6.25 on Rs 1,000, 0.625% for 30 days, which scales to about 7.6% a year above the funding rate. Put another way, the future prices in a carry rate of 14.6% a year when money costs 7%. That annualised figure is a rate on borrowed money, and in practice the desk also posts margin on the future and pays transaction taxes, brokerage and exchange fees on both legs. At an illustrative 10 basis points all in on each leg, costs take about Rs 2.01 a share and leave Rs 4.23. Confirm the current transaction tax and stamp duty rates before relying on any cost figure. On one lot of 5,000 shares the gross gap is Rs 31,233.
Close with the limits. The reverse trade, when a future is too cheap, needs the stock to be sold short, which in practice means borrowing it through a lending scheme at a fee, so cheap futures can persist longer than rich ones. A surprise dividend announcement before expiry would lower the fair price and shrink the gap, and the interest assumed must be the desk's real marginal funding cost, not a textbook rate. The arithmetic is exact; the edge depends on these frictions.
Where candidates lose it
The common miss is calling any future above spot mispriced and selling it. Futures should sit above spot by the cost of carry; only the excess over Rs 1,005.75 is an opportunity, and missing the carry term overstates the gap by Rs 5.75.
The second is quoting 7.6% a year as if it were free money. The trade ties up the stock purchase and the margin, pays costs on both legs, and earns its edge only because the desk can fund at 7%.
What the interviewer asks next
- A dividend of Rs 8 is announced before expiry. What is the new fair price, and is there still a trade?
- The future trades at Rs 1,002. What is the trade, and what makes it harder to do?
- How does the answer change if the desk's funding cost is 9% rather than 7%?
- Why might the futures premium widen near the end of a quarter?
Company names and figures are illustrative.