Case 079Rebalancing, implementation and costsWarm up
An index fund receives Rs 200 crore at 3 pm and cannot buy the stocks until tomorrow. How many index futures lots equitise the cash, and what does it cost?
1The situation
Prabhakiran Index Fund manages Rs 4,000 crore against a large cap index. At 3 pm a pension client invests Rs 200 crore. The dealing desk cannot buy the full basket of stocks before the close, so the money will sit as cash overnight, about 4.8% of the fund.
The index is at 24,000 and one futures lot is 25 units of the index. The near-month future, 20 days from expiry, trades 75 points above the index. The overnight rate is 6.5%, the index dividend yield is 1.2%, and round-trip trading costs on futures are about 0.02% of notional.
2Your task
How many lots do you buy, what does the trade cost, and why is it worth doing?
Quick check
How many lots equitise Rs 200 crore with the index at 24,000 and a lot of 25?
Worked solution
Try it on paper, then open one step at a time.
30-second answerThe answer to give first
Buy 3,333 lots, about Rs 199.98 crore of index exposure, for a cost of roughly Rs 8.4 lakh. Each lot is Rs 6 lakh of index. The futures trade about 5.3 points above fair value, which costs Rs 4.4 lakh, and trading costs add Rs 4.0 lakh. Against that, a 1% overnight index move on uninvested cash would put the fund Rs 2 crore off its benchmark.
Step 1Why not just leave the cash overnight?
An index fund's job is to track, not to guess. Cash sitting in the fund is a bet that the index will not rise tonight. If the index rises 1% overnight, Rs 200 crore of cash misses Rs 2 crore of gain, about 4.8 basis points on the whole fund, which is a tracking error the fund manager created. It is like booking a train for a group of forty and holding the tickets of the five latecomers in your pocket: they still need a seat on the train the moment it leaves. EquitisationUsing futures to give idle cash the same market exposure as the stocks it will buy, until the stocks are actually bought. books the seat.
Step 2How many lots, exactly?
Get the lot into rupees before dividing. One lot is 24,000 x 25 = Rs 6,00,000, which is Rs 6 lakh, so Rs 200 crore needs 3,333.3 lots: 3,333. That is Rs 199.98 crore of exposure, leaving Rs 2 lakh unhedged, which is noise. The desk also posts margin, roughly Rs 24 crore if the exchange asks for 12% of notional, out of the same cash, so the cash never leaves the fund.
Step 3What does it actually cost?
A future trades above the index by the cost of carryThe interest earned on cash over the life of a future, less the dividends given up by not holding the stocks. It sets the fair gap between futures and the index.. Fair value here is 24,000 x (6.5% - 1.2%) x 20/365 = 69.7 points. You do not lose the fair premium, because the cash earns the interest that pays for it; you lose only what you pay above fair, 5.3 points. At Rs 83,325 per index point across 3,333 lots, that is Rs 4.4 lakh, plus about Rs 4.0 lakh of trading costs on the round trip.
| Item | Working | Result |
|---|---|---|
| Lot size in rupees | 24,000 x 25 | Rs 6 lakh |
| Lots | 20,000 lakh / 6 lakh | 3,333 |
| Fair futures premium | 24,000 x 5.3% x 20/365 | 69.7 points |
| Paid above fair | 75 - 69.7 | 5.3 points |
| Cost of the richness | 5.3 x Rs 83,325 | Rs 4.4 lakh |
| Trading costs | 0.02% of Rs 199.98 crore | Rs 4.0 lakh |
| Total cost | Rs 8.4 lakh |
Tomorrow the desk buys the basket and sells the futures in the same session, ideally near the close so both sides price off the same level. Say the limit: futures track the index, not the fund's exact holdings, and a mismatch in timing between the two trades leaves a small residual. Rs 8.4 lakh to remove a Rs 2 crore swing either way is a cheap insurance premium, which is why index funds with large flows equitise as routine.
Where candidates lose it
The number that sinks candidates is the unit conversion. Rs 200 crore is 20,000 lakh; people who write 2,000 lakh get 333 lots and hedge a tenth of the cash, then defend it confidently because the arithmetic after the slip is right.
The second loss is calling the whole futures premium a cost. The fair premium is paid for by interest on the cash; only the part above fair value, and the trading costs, are true costs.
What the interviewer asks next
- The futures trade below fair value. What does that change?
- The inflow is Rs 2,000 crore on a thinly traded mid cap index. What goes wrong with this approach?
- Why might an active fund also equitise cash, and when would it choose not to?
Company names and figures are illustrative.