Principle of least error

Ask twenty traders across the country what a commodity is selling for today and you get twenty answers.

Which one is the price?

The exchange does not simply take the average, the median or the mode. It runs an algorithm, and the principle of least error is what the algorithm is trying to satisfy.

The rule is one line. The final polled price figure should have the least standard deviation with the set of polled prices.

The workbook says this is based on the principle of least error, or similar to the least square method of regression.

So the chosen price is the one sitting closest to the whole set, measured across every poll rather than against any single one.

When the polls are tightly clustered the answer lands near the average, the median or the mode anyway. The method only really matters when they are spread out.

Where it sits in the polling sequence. Spot prices are collected from empanelled polling participants comprising traders and users of the particular commodity across centres, and the panel is reviewed regularly, adding active participants and removing inactive ones. Because there are many participants across mandis for agricultural products, polling may produce multiple price quotations for the same product.

Then two steps run in order.

Step one, bootstrapping. From among the various prices polled, a bootstrapping methodology removes the extreme prices. A median is arrived at, and outlier prices are ignored for further bootstrapping.

Step two, the least-error algorithm. An algorithm is then run across the balance of polled prices, on these principles:

1. the final polled price figure should have the least standard deviation with the set of polled prices — based on the principle of least error, or similar to the least square method of regression;
2. the standard deviation is worked out for the polled data against a random price selection, and the same procedure is repeated after selecting another random price;
3. the random price whose standard deviation is higher is ignored, and another random price is considered;
4. the process repeats until a final number is arrived at, from the set of polled prices, which has the least standard deviation against the polled data.

That number is the spot polling price at that time on that trading day. Note where the candidates come from: they are drawn from the polled prices themselves, so the output is one trader's quote, not a computed average.

What happens to it. The spot polling price is declared daily by the exchanges on their websites and broadcast on the trading screen. On NCDEX the details of prices given by different participants for each commodity are disclosed twice daily, at around 1:30 pm and again at around 4:00 to 5:00 pm. For agricultural products the polls are ex-warehouse prices inclusive of Mandi Cess but exclusive of GST. Three such daily prices — for E, E-1 and E-2 — are then simple-averaged into the Final Settlement Price.

One loose sentence in the source, flagged rather than fixed. The workbook says the polling price may be almost similar to the arithmetic average, median or mode if the polled data are highly polarized with a low level of deviation between highest and lowest, and then glosses that in brackets as the polled prices being in a tight range. Polarised and tight range pull in opposite directions in ordinary usage; the bracket is the definition, so read the condition as a tight range.

The least-error passage itself attaches no threshold — no maximum permitted standard deviation, no minimum number of polls, no tolerance band.

Nine polled prices survive bootstrapping for a commodity, in rupees per quintal:

5,940 · 5,960 · 5,975 · 5,980 · 5,985 · 5,990 · 6,000 · 6,010 · 6,040

Their sum is Rs 53,880, so the arithmetic mean is Rs 5,986.67.

The algorithm now takes candidates from the set itself and measures the standard deviation of all nine polls about each candidate:

Rs 5,985 wins, with the lowest figure at Rs 27.23. Rs 6,040 is worst at Rs 59.86, which is why a candidate whose standard deviation is higher gets ignored and another is tried.

Compare the three shortcuts. The mean is Rs 5,986.67, the median is Rs 5,985 and there is no mode. Here the least-error answer and the median coincide — exactly the case the workbook flags, because these nine polls sit in a tight range of Rs 100.

Now break the range. Suppose one participant had quoted Rs 6,400 instead of Rs 6,040. The arithmetic mean would jump to Rs 6,026.67 — Rs 40 higher — dragged by a single outlier. The least-error pick from within the surviving set would stay near the cluster. And in practice that quote would never reach the algorithm at all, because bootstrapping strips extremes first. The ordering of the two steps is the point.

Why Rs 40 matters. The FSP is the simple average of the polled prices on E, E-1 and E-2, and it invoices every delivery. On a 10 MT lot — 100 quintals — a Rs 40 per quintal difference in the polled price is Rs 4,000 per lot, and it lands on every open position in the contract, not just on one trader's.

Chapter 3 (Commodity Futures), section 3.10 on spot price polling and the final settlement price of futures, in the list of principles on which the polling algorithm arrives at the final polled price.

Expect a definition question: the final polled price is the figure with the least standard deviation against the set of polled prices, and the workbook likens the method to the least square method of regression. A second question tests the order of operations — bootstrapping removes extremes around the median first, and the least-error algorithm then runs across the balance. A third tests the consequence: the result may resemble the average, median or mode only when the polled prices sit in a tight range.

• It is not the average, the median or the mode. Those coincide with the answer only when the polls sit in a tight range, and the workbook says so explicitly.
• Least standard deviation against the set, not against any one poll. The measure is taken across the whole balance of polled data.
• The workbook likens it to the least square method of regression. It does not say it is a regression, and an answer calling it one overstates the source.
• Bootstrapping comes first. Extreme prices are removed and a median arrived at before the least-error algorithm runs. The two are sequential steps, not alternatives.
• The candidates are polled prices. The workbook describes repeatedly selecting a random price and keeping the one with the lower standard deviation, so the output is a quote from the set, not a computed figure.
• No threshold attaches to it. There is no maximum permitted standard deviation and no minimum number of polls in this paper.
• The workbook's wording is loose in one place — it says the result may resemble the average, median or mode if the polled data are highly polarized with a low level of deviation between highest and lowest. The bracketed gloss settles it: the condition is the polled prices being in a tight range.
• The output is one day's spot polling price, not the FSP. The FSP is the simple average of the polled prices of E, E-1 and E-2.