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I am looking for some advice for abbreviating "standard deviation" when it is used in an informal sense as a mathematical unit, especially with regard to financial usage. This often crops up when the unit of measure is measured in another quantity.

I note a previous question 1 seemed to be asking for capitalisation advice, presumably within normal text.

An example would be, "the typical bid-offer spread of Heating Degree Day futures is 0.7 [Standard Deviations]"

Standard sources (Greenbook.org or the APA style guide) favour or "sd" or "Std. Dev.". The first looks to have the right typographical features but just doesn't feel sufficiently well used to be a standard (at least in this application). The second has the drawback of punctuation within a unit, which looks undesirable. It could be further reduced to "stddev" but the double d looks not quite right. I have seen others use the Excel function name, with capitalisation, "STDEV" but this looks too accommodating to Excel users. Perhaps the most satisfactory would be the simple lowercase Greek letter, sigma, which I think would be likely understood by most relevant readers. However, this limits the text being readily electronically copied.

I would be grateful for any opinions on the subject.

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    This is a question of the jargon used in a specific topic area. – Hot Licks Apr 20 at 20:03
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    Lowercase sigma ( σ GREEK SMALL LETTER SIGMA) is standard in Unicode (U+03C3, UTF-8 CF 83), and represents standard deviation. If you're going to mention standard deviation, you have to hope your readers understand something about it, and if so, they'll recognize σ. Who knows, they may even think you understand something about it, too. – John Lawler Apr 20 at 20:19
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    @boldben an element in that set with a value 1.4 above the mean might be said to be 2 sigma above the mean. That element will be similar to elements of another set that are 2 sigma above the mean of that set. – jejorda2 May 20 at 22:44
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    No common term, but “ess-devs” would be understood by most listeners with a knowledge of statistics, especially if the full “standard deviations” had been mentioned at an earlier point. In written form, “sigma” is the easiest, as in “six-sigma” black belt. However, a financial audience might prefer an annualized percentage, as with volatility. – Global Charm May 21 at 1:47
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    @GlobalCharm “Sigma” from management-speak ‘six-sigma’ is probably as close as we’ll get to a common English term for standard deviation. It’s worth posting as an answer. – Lawrence May 21 at 2:44
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"Standard deviation" is often abbreviated as "Std Dev" or "SD" in statistics, standard deviation providing an indication of how far data deviate from the mean.

Examples:

  • So the SD(X) is the √Var(X). (citation)

  • So the Std Dev of X is the sqrt of the Var of X. (citation)

You can also use a small sigma (i.e., σ), but gauge your audience. If you are writing for an audience of mathematicians or statisticians, they'll get it, but if you're writing for an audidence of students, especially students taking finite math or statistics for the first time, you would do better to use "SD" or "Std Dev" because beginner students likely won't be knowledgeable enough or have enough of a handle on statistical jargon to be able to readily infer what "σ" means, "Std Dev" probably being the most reader-friendly abbreviation, albeit also the least brief abbreviation.

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    Thanks for the response! The audience is in general pragmatic finance folks (brokers, traders but also some actuaries) who for sure will have some statistical education (perhaps as a component of a science degree as a lowest common denominator). The use of the term comes very much as a unit (" 7.3 Std Dev" in the same way one might write "7.3 metres"). Interestingly the use of "sd" has almost no recognition factor. sigma does, but use of the greek letter often breaks in emails communication. – Tom Weston Apr 21 at 11:15
  • I also note within interest the press releases for the G-2 Muon experiments (Fermilab and elsewhere) describe the required confidence limits as "5 sigma", transliterated from the Greek. – Tom Weston Apr 21 at 11:16
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For an audience of pragmatic finance folks, writing in the style of the Investopedia would be a safe bet.

For example, in this article, there is a section on “the Greeks”,

https://www.investopedia.com/trading/getting-to-know-the-greeks/

As described by the Investopedia, the main greeks are vega, theta, delta and gamma. They are used like ordinary English words.

Volatility is represented symbolically by the Greek letter sigma. However, in finance writing, when written out, it is almost always referred to as volatility. It’s either the symbol or the word.

https://www.investopedia.com/terms/v/volatility.asp

This poses a problem for the OP’s specific need, since the “obvious” symbol for standard deviation has already been taken.

However, if the underlying need is to characterize the bid-ask spread, there are other order book metrics, such as width, breadth and depth. These are also defined on the Investopedia.

However, if there’s no alternative to using a metric based on the standard deviation of some other price variable, it might be safest to define it as the ratio between the observed price gap and reference value. It could then be referred to in the text as the “gap ratio” and denoted by whatever symbol is convenient.

Another possibility lies in the definition of the reference value as a standard deviation. It might be possible to refer to it as X-volatility, where X is a suitable descriptive term.

For a good example of how to write about these topics, the best reference is Option Volatility and Pricing by Sheldon Natenberg.

https://www.amazon.com/dp/0071818774/ref=cm_sw_r_cp_awdb_imm_7PKNPG2F2AFHFSVTM0D4

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