# Does an index have a currency?

Does an index like the S&P 500 (or any index for that matter) have a currency?

For example, does it make sense to say that the S&P 500 closed at \$2,132.98? Or would denoting the currency of an index be completely nonsensical?

• Index generally is a ratio. Thus it doesn't have units. Oct 16, 2016 at 3:58

From Wikipedia -

To calculate the value of the S&P 500 Index, the sum of the adjusted market capitalization of all 500 stocks is divided by a factor, usually referred to as the Divisor. For example, if the total adjusted market cap of the 500 component stocks is US\$13 trillion and the Divisor is set at 8.933 billion, then the S&P 500 Index value would be 1,455.28.

From a strictly mathematical perspective, the divisor is not canceling out the units, and the S&P index is dollar denominated even though it's never quoted that way. A case in point is that the S&P is often said to have a P/E, and especially an E, the earnings attributed to one 'unit' of S&P. And if you buy a mutual fund sporting a low expense ratio, you can invest exactly that much money (the current S&P index value) and see the dividends accrue to your account, less the fee.

• I think this is the most accurate answer. It may be worth adding that P/E has units of "years" since P has units "\$" and E has units "\$/year", so P/E has units "\$/(\$/year)" = "years". Oct 15, 2016 at 22:12
• Wow. I see that. My mind is blown. Oct 15, 2016 at 22:16
• Accepting this as the answer, although @BrenBarn has made a geat point: "Whether the index has a unit would depend on the mechanism used to compute it. I could make a new index called the Rooty-Tooty Index that is the square root of the S&P 500; its units would no longer be currency units. I could make a new index by adding together the values of other indices in different currency units, so that my new index has no definable unit." Oct 16, 2016 at 6:20
• @JoeTaxpayer: P/E can be thought of as a measure of how long it'll take to repay the capital cost of a purchase (of course with some unrealistic assumptions about cost of money being 0, earnings remaining constant, etc) Oct 16, 2016 at 11:27
• @LawrenceWagerfield - yes, agreed to that, although the quote came from a different member. I edited your comment to correct this. Oct 16, 2016 at 12:25

There's no need for an index to have a currency as its purpose is not to act as an asset but rather to signal investors about the performance of a collection of stocks. An index can be price-weighted, meaning that its value equals the (arithmetic) average of the prices of each stock in the index. With no stock splits, the return on this index is the same as the return on a portfolio composed of one share of each stock. If there is a stock split, however instead of dividing by the number of stocks, as you normally would when taking the arithmetic average, you divide it by the number that will make the value of the index pre-stock-split (arithmetic average) equal to the value post stock split. Then use that dividing number for all periods until a new stock split occurs.

An index can be value-weighted, meaning that its changes in value track the percentage changes in total market capitalization of the stocks in the index. Price weighted indexes ignore for "firm size" and percentage changes in price weighted indexes are not robust to stock-splits. Value weighted indexes take "firm size" into account and are robust to stock-splits. DJIA is price-weighted. S&P 500 is value-weighted.

• While it is true that there may be "no need" to think of an index as being a currency amount, technically an index has units and those units are currency - it is not a dimensionless number. As you say, the index measures the performance of its constituents, and that performance is measured in currency. Oct 15, 2016 at 21:55
• Also, it is incorrect to say that a price-weighted index is an equal-weighted index. A price weighted index will hold an equal number of shares for each constituent. An equal weighted index will hold an equal amount invested in each of its constituents. Oct 15, 2016 at 22:08
• your 2nd remark is correct and I will fix it and maybe add something more to it. I certainly disagree with your 1st remark :) Oct 15, 2016 at 22:26
• Actually, saying A price weighted index will hold an equal number of shares for each constituent is still technically not ok I think. If a stock split happens your index will drop due to the split. I know how to fix it though. Oct 15, 2016 at 22:30
• @NickR: Whether the index has a unit (and whether its unit is a currency) would depend on the mechanism used to compute it. I could make a new index called the Rooty-Tooty Index that is the square root of the S&P 500; its units would no longer be currency units. I could make a new index by adding together the values of other indices in different currency units, so that my new index has no definable unit. So there's a difference between saying that a given index has a given currency unit, and that all indexes must have such a unit. Oct 15, 2016 at 22:48

In practice, most (maybe all) stock indices are constructed by taking a weighted average of stock prices denominated in a single currency, and so the index implicitly does have that currency - as you suggest, US dollars for the S&P 500.

In principle you can buy one "unit" of the S&P 500 for \$2,132.98 or whatever by buying an appropriate quantity of each of its constituent stocks. Also, in a more realistic scenario where you buy an index via a tracker fund, you would typically need to buy using the underlying currency of the index and your returns will be relative to that currency - if the index goes up by 10%, your original investment in dollars is up by 10%.

More importantly, index funds are denominated in specific currencies. You can't buy or sell an index, so it can be dimensionless. Anything you actually do to track the index involves real amounts of real money.