Law of averages

An index is a basket. On any given day some things in it rise and some fall.

Add them up with weights and the ups cancel part of the downs. So the index moves less than the things inside it.

The workbook calls this the law of averages. Because a commodity index is built as a basket of several commodities, most of the time its volatility is reduced significantly.

Now read that as two different pieces of news.

For a hedger it is good news. A price shock in one or two commodities does not knock the index about. A strategy built on index futures survives one bad warehouse or one local shortage.

For a day trader it is bad news. Low volatility means small intraday moves. A trader chasing quick gains goes to the single commodity instead.

And there is the sting. Intraday traders seldom pick the index. Hedgers cannot fill the gap alone, because they still need counterparties to trade against. So liquidity in commodity index derivatives stays thin.

The chain, as the workbook lays it out. Section 2.6 lists three challenges facing commodity index futures and options in India — liquidity, volatility and limited awareness — and the law of averages sits inside the second one. Because commodity indexes are built in the form of a basket of multiple commodities, volatility gets reduced significantly. That makes individual commodities more attractive to the majority of participants who look for greater gains in a short span, especially intraday. Those traders therefore seldom opt for a commodity index, which results in lower liquidity. Hedgers may not fill in the gap, because they do need counterparties to execute their hedge trades.

A second, separate reason for thin index liquidity. A commodity participant needs to focus on only 8 to 10 individual commodity contracts, against the hundreds of scrip-linked derivative contracts an equity participant faces. Where there are only eight or ten things to follow, an index is less necessary in the first place.

The same effect, sold as a benefit. Section 2.5, under Diversified Portfolio, says any price disruption in one or two commodities' futures does not impact traders or hedgers who use index futures. If a commodity's futures enter abnormally high backwardation because of oversupply or a quality issue in the warehouse, the index value and its futures price may not move significantly, because the underlying portfolio is diversified. The same holds where a convenience yield exists in the spot market: households preferring physical gold to a gold futures or bullion index position can push gold futures into backwardation without dragging the overall index future with them. Movements in one segment may be cushioned by opposite movements in another, and the extent depends on the weightages.

How strongly it bites depends entirely on the weights. A sectoral index barely averages anything. MCX BULLDEX for 2025 is Gold 60.119248% and Silver 39.880752% — one commodity carries three-fifths of it. NCDEX GUAREX for 2022-23 is guar seed 59.35% and guar gum 40.65%. A composite index averages far more: MCX iCOMDEX Composite has 8 commodities, and SEBI caps each constituent of a composite index at 30% with a floor of 1%, so no single commodity can dominate. MCX works inside that with its own 2% to 30% band and a 40% sectoral cap.

And because commodity indices are price-based, the weights stay fixed through the year. The averaging is a fixed-weight average, not one that drifts with market value the way an equity index does.

The sentence naming the law of averages carries no figure of its own. The figures that decide how much averaging actually happens are the constituent weights above.

Run the same trading day through a sectoral index and a composite one.

Sectoral: BULLDEX, on its 2025 weights.

Composite: an eight-commodity index. The first four weights are the workbook's iCOMDEX Composite figures for 2025; the remaining four are illustrative and sum the basket to 100%.

Look at what happened. The individual commodities moved across a spread of 8 percentage points, from -3% to +5%. The composite index moved 0.81%. The sectoral index, with only two constituents and one of them at 60%, moved 1.405% — nearly twice as much, because it averages far less.

Now price it. A commodity index future has a lot of 500 units and a tick of Rs 0.25, so one tick is worth Rs 125. From a base of 1,000, a 0.81% day is 8.1 index points:

8.1 x 500 = Rs 4,050 per lot, which is 32 ticks.

A trader who had instead bought the natural gas contract caught +5% on the day. That is the whole reason the workbook gives for intraday traders avoiding the index — and, in turn, for its thin order book.

Chapter 2 (Commodity Indices), section 2.6, in the list of challenges faced by commodity index futures and options in India, which is where the phrase appears; and section 2.5, under Diversified Portfolio, which teaches the identical effect as an advantage.

Expect a reasoning question rather than a recall one: why are commodity index derivatives less liquid in India than individual commodity contracts — reduced volatility from the law of averages, plus the availability of alternative instruments with decent liquidity and volatility. The mirror question uses the good side: why abnormally high backwardation in one constituent need not drag the index future into backwardation.

• Reduced volatility is not reduced risk of loss. An index can fall steadily. Averaging damps the size of the daily move, not its direction.
• The same effect is a benefit in one section and a drawback in another. Section 2.5 sells it as diversification; section 2.6 blames it for illiquidity. Both are the workbook's, and a question can come from either.
• A sectoral index barely averages. BULLDEX is 60.12% gold; GUAREX is 59.35% guar seed. Two constituents with one dominating is not diversification, and the 30% per-constituent cap does not apply to sectoral indices at all.
• Weights are fixed for the year. Commodity indices are price-based, so the averaging uses the year's set weights rather than today's market values — the opposite of an equity index.
• Thin liquidity has more than one cause. The workbook lists liquidity, volatility and limited awareness as three separate challenges, and separately notes that a participant follows only 8 to 10 commodity contracts against hundreds of equity scrips.
• Hedgers cannot cure the illiquidity themselves. The workbook is explicit that they need counterparties to execute their hedge trades.
• Abnormal backwardation in one constituent need not put the index future into backwardation. That is the averaging working as intended, and it is a favourite question.