Given a EURUSD daily chart how do you calculate volatility?
“Volatility” is kind of generic. It depends on how you want to use the measure. There is historical volatility which is your average of the change in price from one period to the next (period could be one day, one hour, one week… whatever). Then there is average true range which is the average amount of movement that happens within one period (with corrections for occasional gaps of price between periods). Finally there is implied volatility which is unique in that it is forward looking rather than based on past price behavior. Implied volatility is a function of option prices (in other words, it is based on sentiment) and can be used to project the probable range of the underlying in the next period. So yes, the first two are standard deviations of sorts and the third is something all together different.
The exact same way you’d calculate it for anything else.
Can the first two be calculated using the STDEV function in Excel or is the “true range” something else?
The easy thing to do is let your charting platform plot it out at the bottom of the screen. I can collect this data for you if you want. If you want to do it by hand, look up how to do the calculation. I’ve never actually calculated HV but for ATR there is a quirk in the calculation for the purposes of smoothing and of course there is the other quirk that accounts for gaps. Here is a link to calculating ATR
http://stockcharts.com/school/doku.php?id=chart_school:technical_indicators:average_true_range_atr
what do you need the information for? ATR may not be a good measure for your purposes anyway. I do think HV is more a strait forward calculation (maybe even just use STDEV in excel)
google “forex volatility models” and stdev aint gonna be there…
KMD, please stop replying to this thread. Like in CFA L3, spewing unnecessary information does not make the answer better.
OP, to answer your question, here is how one would calculate the standard deviation of EURUSD returns, which is *a measure* of EURUSD volatility.
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Tabulate the daily prices for EURUSD.
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Calculate the percentage return at each observation period. This is necessary so assets with larger unit prices do not produce artificially high volatility measures.
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Calculate the standard deviation of returns using the formula below, where each observation is a daily return. If your sample size is very small, consider using N-1, rather than N in the denominator to correct for sample bias.
- You will need to make a decision with regards to the period over which you intend to measure this volatility (5d, 30d, 200d, etc.). Also, depending on your objective, you might want to filter out certain periods that contain extraordinary events, like Brexit.
You can use Excel =STDEV() with the same result. However, like above, make sure you run this formula on the vector of daily returns, not daily prices.
You can also measure log returns, rather than percentage returns, if you want to assume a log-normal distribution or want to produce a more mathematically tractable result. The difference will probably be insignificant though.
There are various more complicated ways to define return volatility, like using rolling measures (i.e. the Yang Zhang model). You can read about this if you feel inspired.
OP did not specifically ask for “return volatility”. Since the inquiry on “volatility” was vague I thought I would provide the context I know on the subject. In fact, the original question read to me as “is volatility simply standard deviation, yes or no?”. The answer is no. It depends on what question it is about the underlying that you are using volatility data to answer. If you just want to know how much price has fluctuated over the course of a year so you can compare it to other underlings or to itself in other time periods then return volatility as you discussed it will work fine. However, if you wanted to know how erratic price behaviors is on a intra period level then ATR is more appropriate. The difference in these two measures could be seen in stark contrast in the example where an underlying is flat, yet the intraday action is in a large range. This example would have a small HV but a large ATR. The opposite profile would be true for an underlying that trended all over the place over the course of a year, but did so cleanly without a lot of intraday gyrations ( high HV and low ATR). Then there is IV, but you get the picture. These are all measures of volatility and they each provide different information. I did not know what kind of information OP was seeking, so I briefly discussed all three.
Well thanks for the info. I am only trying to quantify the phenomenon that happens just before news events; For example before NFP results, or Yellen speaks etc, there is great volatility (compared to an hour ago) in prices even though nothing fundamental has changed in the market yet.
I am trying to capture the major commotion in Forex markets just before expected big news events such as NFP. The volatility of prices changes drastically.
You do not have to use daily returns. You can tabulate observations at any time interval - hours, minutes, etc., and scale the result by an inverse of time^0.5 to derive a volatility measure in annualized terms. Daily returns are just a convenient convention due to market hours, but the methodology does not change if you choose a different observation frequency.
KMD is technically right that volatility is the concept, whereas standard deviation (and ATR) is just one way to quantify it.
However Ohai is right in that the standard deviation is pretty much the default measure of volatility unless you explicitly specify otherwise.
Otherwise, it’s just like answering the question “How do I get the average?” by saying “rank all numbers from high to low, and choose the middle one.” Yes, the median is also a way to measure an average. And in certain contexts, it can be more useful. But it’s not what 99% of people mean when they say “what is the average,” and so you need to warn them that you’re giving a nonstandard answer so they don’t look like an idiot when they use it.
So generally, volatility is measured as standard deviation of percent changes in price (or yields, if FI). If you are trading daily charts or intraday charts, sometimes ATR is a more useful measure of risk, particularly over short periods, when it jumps around, and if there is a lot of movement between the close and the open prices. However, if I am labeling something for other people to read, I would pretty much always use standard deviation for a “volatility” column, since that is what they will assume, and simply label an ATR column with the title “ATR” (perhaps grouping it next to standard deviation so that measures of volatility are all grouped together).
The one thing I might do for currencies, since there is a numerator and a denominator and it is a bit uncertain whether people are going to be thinking of X/Y currency or Y/X currency, is take the natural log of the exchange rate and calculate the standard deviation of the logs, then reexpress it as a percent. This creates a volatility figure that is the same for X/Y and Y/X. For small changes in rates, the number is almost identical to the ordinary standard deviation, and is nicely symmetrical for large changes (i.e. won’t depend on which currency is the numerator currency). That modification would warrant an asterisk on the volatility column to disclaim the calculation.
I was just reading this thread and thinking, this poor guy is going to think there’s actually debate on this matter. In options pricing, interest rate models, and so on, the Greek lower case sigma represents standard deviation. When we back out sigma to solve for “implied volatility,” we automatically equate volatility with standard deviation. It would be extremely uncommon to talk to someone who mentions volatility and isn’t talking about standard deviation.
Ohai’s post is spot on.
Well yes, volatility can always be interpreted as a measure of standard deviation (even IV). However, it certainly is not always calculated through the method of a standard deviation calculation. The derivation of IV has nothing to do with standard deviation. It is purely based on how inflated the price of options are. This thread is about the origination of volatility measures, not their interpretation.
No, this thread is about someone asking how to calculate the volatility of an exchange rate. Now, I don’t know if you have to deal with institutional currency traders in your job, as I regularly do, but I would say approximately zero percent of them would respond to this question with anything other than advice on how to calculate the standard deviation of the series in question.
The only debate would center around defining data window length, frequency, whether a weighted approach should be used as opposed to 1/n with one degree of freedom, etc. But it would still be standard deviation.
Now, don’t get me wrong…SD almost always sucks as a measure of dispersion, but the OP didn’t ask my philosophy on the accuracy of a Gaussian distribution as a measure of dispersion. The fact is, when industry people speak of volatility (I’m talking, the people that go and work in the industry every day…not students, not “day traders,” etc.), you can bet your bottom dollar they almost certainly are talking about standard deviation.
Also, your comment on IV is somewhat valid re: pricing bloat…where it misses the mark is that it’s still comparing it to other measures of standard deviation to determine mispricing. Six one way, a half dozen the other, as they say.
this is an extension of the truth. you would never see a report where an FX rate is discussed and a number quoted as the (realised) volatility. there is always a table of cross rates and the volatilities ranked.
most likely you are looking at a fit to a laplacian or similar distribution, not gaussian.
I guess I’m missing your point. The statements “you would never see a report where an FX rate is discussed and a number quoted as the (realised) volatility. there is always a table of cross rates and the volatilities ranked,” even if true, do not disprove my assertion that the default measure people are generally thinking about when they say volatility is indeed standard deviation. The fact that you have pointed out cross rates could have different properties (at least, I think that is what you’re trying to say) than the original series logically adds nothing to your argument here, I’m sorry.
Further, the question OP posed is not asking what the best-fit probability density function is for various FX time series. If that was the question, I would agree that Gaussian is almost certainly not the best for most financial time series (see my statement earlier that it “sucks.”). However, whether the best-fit for a given series is Laplacian, Cauchy or any other of the myriad families of distributions is irrelevant to the original question.
here is my point.
If I read in a report something like “EURUSD volatility was 0.05% in 2015” wtf does that tell me`? and you want to scale that by 250^0.5?
^ No, this is really simple. I wouldn’t scale a figure in this chart by the square root of time because I can plainly see the metric that the graph is showing is “average absolute percentage change.”
But I think you’re actually missing my point. When you speak to most people in the industry about volatility, do you believe that they are thinking of average absolute percentage change?