New member, here. I’m trying to decide what chart speeds to try to trade from (just on a demo account, to practice) but am really stuck on a specific question of volatility and chart speed.
Various websites and search-engine attempts haven’t resolved it for me. Maybe because I don’t know enough to work out exactly what search terms to use?
Can anyone here please explain to me, in reasonably simple English (or at least in reasonably simple math) why volatility is proportional to the square root of the chart speed, and how that’s relevant to me?
This formula is used to calculate volatility from a smaller time frame (Daily) to a longer time frame (monthly, Annually). In the context of speculative trading, it’s not used.
If you’re trading options, this is how Implied Volatility is calculated to more accurately value options, based on 1 Standard Deviation (68% of the time).
Forex charts are just fractals of themselves. Price and time move the same through all charts.
I’m not trying to pick a fight with you (I don’t like taking positions in antipathy to people with green eyes), but how does this perspective fit in with the generally accepted concept that faster timeframes exhibit more “noise” and that for this reason slower timeframes tend to be more “reliable” (never quite clear exactly what people mean by “reliable,” is it?)?
You’re saying there is more ‘noise’ on smaller timeframe charts like the 1 minute compared to a Daily chart?
For the OP’s question why the square root of time is used, it pertains to how Option’s volatility is priced.
From Google:
Here’s why the square root of time is used:
Volatility Scaling: The Black-Scholes model assumes that stock price volatility increases over time.
However, the relationship isn’t linear. Standard deviation, which is a measure of volatility, grows in proportion to the square root of time.
This means that while variance (volatility squared) grows directly with time, standard deviation (a more intuitive measure of volatility) grows at a slower rate, proportional to √T.
In essence, the square root of time (√T) in the Black-Scholes formula reflects the fact that the uncertainty and potential price fluctuations of the underlying asset increase with time, but at a decreasing rate, as captured by the relationship between standard deviation and time in a Brownian motion process.
I was asking whether (“how”) what you said fitted in with the generally accepted concept that faster timeframes exhibit more “noise” and that for this reason slower timeframes tend to be more “reliable”.
The smaller time frames just look like that because the size of the moves are amplified, illiquidity and risk events seem excessive but they’re just fractals within the next higher time frame.
I don’t believe any time frame or time chart is any more reliable than another. There can’t be in the fact that market dynamics would break down if there was one. ie; if every pin bar swing low was profitable, no one would want to take the other side of the trade, so all time frame and patterns have to be equal or else the illiquidity would increase the cost of trading until it wasn’t advantageous.
My explanation may relate to what Ryan’s already said, above. It may not. I know nothing about options, or Black Scholes, or any other colour of Scholes, so I can’t tell!
Volatility, in this context, is really just another word for “standard deviation”, and in statistical terms, that’s the square root of variance, so if you’re using timed charts and looking at how volatility varies in proportion to the time-periods from which charts are constructed, it’s not going to be directly proportional to time, but proportional to the square root of time.
You can easily see this in operation. Just look at the ATR-20 (say) of a 1-minute chart (that’s a good indicator of volatility) and compare it with that of a 4-minute chart, and you’ll find the latter is almost exactly twice the size. Or compare equivalent ATR’s of a 2-hour chart with an 8-hour chart, and you’ll see the same. Because 2 squared is 4, so when the timeframe goes up by a factor of 4, the volatility doubles.
The underlying principle really isn’t any more complicated than that, and it arises, in a “fair/true market”, just because in the broadest statistical terms, standard deviation is the square root of variance. And in your question, “variance” is time, and “standard deviation” is volatility.
But there are a few other considerations, too (mostly obvious ones).
First, what I’ve said above applies perfectly only to markets with random movements (because it’s mathematically based on the same concepts as “Brownian motion”, if you know about that?). So it isn’t always quite true. It’s a slight oversimplification. But not much of one, and for forex traders, most of the time, it’s basically true (and it’s even pretty valid for trading the indices, too - and they’re certainly not random markets as they’ve had an overall unidirectional trend for centuries!).
Secondly, there are some “provisos”, of course: for example, if you compare the volatility of a 2-hour time-period when an underlying market’s open with that of an 8-hour time-period when it’s closed, it’s not going to work out exactly right. Similarly, if you compare the volatility of any 2-day period from Monday to Friday with that of any period of 8 consecutive days, that’s also not going to work out exactly as the theory says it should, because on 2 (or even 3) of those 8 days the market will have been closed, so you wouldn’t really be “comparing like with like“. There are some “common sense” limits to all of this, in other words.
If you want to read more about it, I strongly recommend a free PDF about the basics of statistics, extremely useful to traders, which you can download quite openly and legally (no copyright problems involved, because that‘s what it‘s there for!) from the University of Pennsylvania website. It’s called “Elements of Statistical Learning” and the author’s name is Hastie. Google will find it for you.
I hope my answer’s more of a help than a further confusion, anyway.
Volatility increases with the square root of time, not time itself. So, a 4-hour chart won’t show 4 times the movement of a 1-hour chart; it’ll show about 2 times. Short timeframes have more noise and faster moves; longer ones are smoother but slower. Choose your chart speed based on how fast you want to trade and how much noise you can handle.
On the first of your questions, I can’t add to the super replies of @TheodoreThring and @SallyFourthEqual above. On the second, I can maybe offer a comment.
How it’s relevant to you depends on several potential factors, but most of the important ones probably relate to the balance between (i) the common perception of slower charts being “more reliable” and faster ones exhibiting proportionally “more noise” (I don’t really believe in “noise” but many people do) and (ii) how much you can gain from the “square root principle” explained above by benefiting from the disproportionate increase in trading frequency that faster charts afford (a lot, in my opinion, if you approach everything from a risk-management and statistical perspective).
