ATR Value

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MCT
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ATR Value

Post by MCT » Wed Sep 10, 2003 10:36 pm

ATR is supposed to define market volatility thus risk. But ATR is fixed dollar terms and does not take into account true market volatility. I find the atr value deceiving. An ATR of $5 for $50 stock and an ATR of $5 for $10 stock are very different. For the $50 dollar stock the ATR is 10%, where as for the $10 dollar stock the atr 50%. In general, in the conventional approach, ATR might increase or decrease to the point where the value becomes too large or too small to be a good indicator for risk management methods. A % ATR value is a better indicator of market volatility since it's is relative to price(close). In the conventional scenario, risk exposure would appear to be unequal as well as miss proper accounting of the interaction between true market volatility, equity exposure to that volatility, and time. Risk is proportional to exposure and true market volatility. Not accounting for true market volatility as it relates to equity exposure and time has unfavourable system implications. It would be interesting to hear others experience or definitions for RISK.

p.s the same could be said about SD or BB and other volatility measures.

Comments please …

MT
Last edited by MCT on Thu Sep 18, 2003 8:06 pm, edited 2 times in total.

CRM114
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Post by CRM114 » Wed Sep 10, 2003 11:09 pm

As I understand it, the use of ATR is an attempt to measure the actual dollar risk per unit traded. If I trade the same number of shares and there is a $5 move then my gain or loss is the same whether the unit price is $10 or $50. So if I am willing to risk a total of X and I will get out if the price moves against me by Y, then I will trade X/Y shares. It doesn't matter what the absolute price is. This assumes, of course, that I have sufficient funds to trade the same number of shares. It is clearer when trading futures, where the nominal value of the contract is not really at issue.

Jack (I remembered this time!)

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Post by Kiwi » Thu Sep 11, 2003 3:28 am

Hi Menelik,

It depends what you want to achieve. I have used ATR three different ways. In the first ATR was used as an element of assessing risk (a high ATR is more likely to hit your stop than a low ATR for the same stop and its relationship to absolute price is unimportant to this task). I have also used it to evaluate low volatility in preparation for a high volatility breakout so no relativity is needed. Finally I use it to set a hysteresis for some types of stop (add 0.1ATR to the recent high say).

To measure relative volatility I have done as you suggest and divided by the average price for the same period as the ATR or the option volatility. I would see this as applicable to comparing too possible vehicles for a trade.

John

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Post by Ted Annemann » Thu Sep 11, 2003 8:56 am

I think ATR is just a tool. There are some jobs it does quite well, such as measuring the amount of price motion that usually occurs during an average day. We can call that "volatility" or "Mandelbrot ergodicity" or "banana cream pie" if we want to, it doesn't change the numbers that the ATR subroutine produces.

There are some jobs that other tools do better than ATR. One obvious example is calculating "fair values" of European style equity options using Black-Scholes. This doesn't mean ATR is a crummy tool, it just means ATR is better suited to some jobs than others. It's up to us traders to choose the right tool for the right job.

I'm reasonably confident MJ made a good decision when he chose ATR to do this job:
http://traderclub.com/discus/messages/1 ... #POST14350
yet he has also produced systems that don't use ATR and do perform nicely.

It's a poor craftsman who blames his tools.

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Post by MCT » Thu Sep 11, 2003 11:03 am

If I trade the same number of shares and there is a $5 move then my gain or loss is the same whether the unit price is $10 or $50. So if I am willing to risk a total of X and I will get out if the price moves against me by Y, then I will trade X/Y shares.
(a high ATR is more likely to hit your stop than a low ATR for the same stop and its relationship to absolute price is unimportant to this task).
In my case, I found this topic important because accounting for exposure is an integral element of my risk controls. I believe that true market volatility as I calculated it is directly proportional to risk. It is my opinion that controlling exposure is an absolute foundation of risk management.

Trendfollowers equalize the volatility of each position that they take by making it a fixed percentage of their equity. It is supposed to equalize the possible market fluctuations of each element in the portfolio, to which the model is exposed. If you risk 2% of your capital on a particular trade, with an ATR of $5 for a $50 stock, it is a real risk of capital. Now, if you were to risk that same 2% of your capital on a $10 stock with an ATR of $5 is the amount risked the actual risk? In my opinion, no. Sure, the gain or loss is the same in simple atr terms but that's not the real risk. Your risk "exposure" on the $10 stock is five times greater. I believe the volatility of every element of a portfolio should not only be a fixed percentage of equity but also price(Close).

Another important issue would be in the placement of stops. With an ATR of $5 on both stocks, if one were to place tight stops, which stock has a higher chance of being whipsawed? I’d say the $10 stock. For the $50 dollar stock the ATR is 10%, where as for the $10 dollar stock it’s 50%. I’m of the opinion that you can only say an ATR is high or low relative to absolute price. Equalizing ATR to a fixed percentage of equity is not enough.

Everyone has a subjective opinion about what matter most; I find It enjoyable and gain insight by learning how others deal with risk.
Last edited by MCT on Wed Sep 17, 2003 2:58 pm, edited 2 times in total.

CRM114
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Post by CRM114 » Thu Sep 11, 2003 1:10 pm

Menelik,

I agree with you that a simple-minded use of ATR is probably not the final word on risk control. The thought of price fluctuations of 50% will make most folks a bit queasy, although this might be the result of an unconscious bias of using a too-long-term perspective. I just wanted to get the ball rolling by stating what I believe to be the rationale for its use.
Your risk "exposure" on the $10 stock is five times greater.
Please elaborate on your definition of "exposure" and how you arrived at the factor of five.

It's easy to imagine an extreme case where the opposite is true. Based on my previous post, suppose I go long the same number of shares, X/Y, of both stocks. The $50 stock has cost me five times as much. If the price of both suddenly goes to zero I'll find that my risk was five times greater for the more expensive stock.

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Post by Josh M. » Thu Sep 11, 2003 1:50 pm

I think the us of a straight atr for a stop is extremely useful in backtesting where a dollar stop would be useless. Converting the atr to a % is excellent for analyzing the characterstic of a market. For example the atr % for the sp increased when globex was introduced. As someone said, different tools....

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Post by MCT » Thu Sep 11, 2003 6:44 pm

CRM114,

All of the above only matters if you believe that risk is directly proportional both to exposure and volatility. For example, let’s utilize our simple portfolio example of two stocks, one for $50 and the other for $10 both with an ATR of $5. A percent volatility position-sizing model, like the turtles, would allocate the same dollar risk to both elements of the portfolio. These portfolio elements are exposed to different degrees of volatility thus risk. What I’m suggesting is the risk exposure is unequal, since the $10 stock is five times more volatile than the $50 dollar stock, regardless of time frame. The $10 stock deserves less dollar risk. To me, the risk with a 50% ATR stock is great than the risk with a stock that has 10% ATR.

For anything to be true/false or high/low, it has to be compared to a standard. For me, in the case of risk management, ATR calculated as a percentage of the closing price is the ultimate barometer. Exposure and thus risk always increases with time. For instance, if volatility remained at $5 but the same $50 stock dropped to $48, isn’t it more risky? I believe it is.
MT
Last edited by MCT on Wed Sep 17, 2003 3:00 pm, edited 2 times in total.

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Post by kmulford » Fri Sep 12, 2003 9:01 am

Menelik,

ATR is a price based gauge of volatility. It is a measure of *historical* volatility. A $5 ATR for a $10 stock has exactly the same historical volatility as a $5 ATR for a $50 stock. One is not 5 times more volatile than the other, historically speaking. The $10 stock does not have a 10% ATR - that is double counting: ATR is already related to the price of the stock, by definition. (One can debate whether it is a "good" measure of historical volatility.)

I think the confusion here is that you rightly believe that an additional layer of interpretation is necessary: which stock is more likely to continue to have a $5 ATR? You are looking to prospectively interpret (analyze, even predict) the likelihood of changing volatility. Whether ATR is a useful measure to incorporate into mechanical trading sytems (entries, exits, and position sizing) is purely a matter for historical testing. Interpreting the simulations' results requires judgment.

The question, "Which is more risky?" is a good one. I learned all about risk models in the summer of 1998, when I saw the bond book of the Wall Street firm I then worked for go from + $1.1BB to - $0.9 BB (yes that is a $2BB swing to the bad) in two months time (it was probably faster: we were a little slow to mark to market!). In this horrible time, a lot of really sophisticated models failed us. Actually, we failed ourselves. No model of risk is any good without some measure of rational interpretation.

This is where I think you intend this thread to go - interpretation. ATR, as a measure of risk/volatility, is a histoical concept and its definition is unambiguous.

Ken

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Post by damian » Fri Sep 12, 2003 10:44 am

On a related matter so I thought I would throw this into the mix.

- Take a commodity, sep02 expiry, calculate the 10 day ATR. Lets say it is 15.
- On 1st Sep 02 the close is 50.
- Divide ATR by the close of 50. 15/50=0.3
- Lets say you have a silly rule: if ATR/C<0.35 then buy.
- In real time trading of the sep02 expiry, you would buy on 1 Sep 02.

Now, 1 year later and you are building a continuous back adjusted series.

- There is a 10 point gap between sep02 and dec02.
- Dec is 10 points below sep.
- The splice requires the sep02 series to have 10 points deducted from all data points so as to align with the dec02 relative level.
- Remember that the actual historical close of the Sep02 contract on 1 Sep was 50. However the back adjustment changes it to 40.
- 1 Sep 02 ATR would not have changed as a result of the back adjustment.
- Now on 1 Sep 02, we have ATR/C = 15/40 = 0.375
- in backtesting on this adjusted series you would no longer get a buy signal on 1 Sep 02.

The only difference is the close.

I used a silly rule, yet it is not so hard to think of a realistic rule that would be influenced by the magnitude of the close relative to ATR.

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Post by Mark Johnson » Fri Sep 12, 2003 11:30 am

It seems to me you could formalize damian's suggestion and turn it into a new test of trading systems:
  1. Run system S on price dataset D, record entry/exit dates and per trade profits
  2. Create modified price dataset M: add 100.0 to all prices (O,H,L,C) in dataset D
  3. Run system S on price dataset M, record entry/exit dates and per trade profits
  4. Compare the entry/exit dates and the per trade profits of steps 1 and 3
  5. If they are not identical, abandon system S

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Post by Josh M. » Fri Sep 12, 2003 11:39 am

I would think it extremely rare, though, for the difference between one contract and another in any market be 20% of the underlying. In which case under most circumstances change of atr/c would be rather small.

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Post by MCT » Fri Sep 12, 2003 11:58 am

Hi Ken,

No model of risk is any good without some measure of rational interpretation. This is where I think you intend this thread to go - interpretation. ATR, as a measure of risk/volatility, is a histoical concept and its definition is unambiguous.


Precisely my point. You are correct; there is simply no way to analyze data in a way that is theoretically neutral.

The average true range allows the study of distribution of ranges through time. ATR basically measure the noise level in a given market. It's a rough and simple measure; are the markets calm or turbulent? This is the variability of price or noise. Noise(let's call it N) is a measure of the effects of the variance of volatility relative to price.

It is wise for risk management models not to allow for unusual amounts of noise or huge moves in the opposite direction of the trend. To do so would be to take more risk than is necessary. But in order to account for the true market volatility, we have to account not only for the variance of volatility itself but also for the variance of volatility relative to price. It is my opionion, for instance, that risk is greater when volatility remains at $5ATR but the same $50 stock drops to $48. It is now much more volatile and thus more risky. Even though the ATR hasn't budged, volatility relative to price has. $5ATR no longer represents the same degree of volatility, however you define it.

As far as prediction goes, it is much easier to forecast volatility than price. Market phenomena, such as breakaway gaps, and reversal gaps (volatility expansions) are all illustrative of increases in volatility that accompany changes in market direction. And if one were to look at a summary stat that includes variance of volatility relative to price, for the purposes of trade generation and statistical inference, there would be more there than meets the eye. Just a thought. :P

MT
Last edited by MCT on Sun Sep 21, 2003 1:27 pm, edited 3 times in total.

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Post by Chuck B » Fri Sep 12, 2003 12:59 pm

damian wrote:- in backtesting on this adjusted series you would no longer get a buy signal on 1 Sep 02.

The only difference is the close.

I used a silly rule, yet it is not so hard to think of a realistic rule that would be influenced by the magnitude of the close relative to ATR.
This just illustrates the fact that using almost any math that produces a percentage derivative of price in an absolute fashion (i.e. Close/ATR used as a measure in absolute terms, i.e. >0.40 or whatever) is always going to produce an "error" in back adjusted continuous contracts. Now if you used Close/ATR today versus 5 days ago, you may get by ok using this division as long as you don't lookback too far for the comparison.

Mark's suggestion is a good tool to use when testing against continuous contracts.

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price, volitility %

Post by Nathan » Fri Sep 12, 2003 9:12 pm

If you risk 2% of your capital on a particular trade, with an ATR of $5 for a $50 stock, it is a real risk of capital. Now, if you were to risk that same 2% of your capital on a $10 stock with an ATR of $5 is the amount risked the actual risk? In my opinion, no. Sure, the gain or loss is the same but that's not the real risk. Your risk "exposure" on the $10 stock is five times greater. I believe the volatility of every element of a portfolio should not only be a fixed percentage of equity but also price.
Either I am misunderstanding what you are saying, or I have the complete opposite view. In my view, all else equal (using % risk model) the position taken in the $50 stock is much more risky. I base this not on intended risk or % adjustments, but total dollar commitment and therefore max theoretical risk. Following the money...

100,000 portfolio. 2% risk, or $2000. 2atr stop

stock A.
$50 stock. 5atr = $10 stop. 200 shares to risk $2000.
dollar commitment on trade = 50 * 200 = $10,000.
Max theoretical loss = $10,000

Stock B.
$10 stock 5atr = $10 stop. 200 shares to risk $2000
dollar commitment to trade = 10 * 200 = $2000
Max theoretical loss = $2000

This second position appears (from traders perspective) to be like a call option with no time decay. your intended risk is your maximum theoretical risk. In my view, this makes it much less risky. I don't see how stock B is 5x risker. If anything, i think it may be the opposite. True exposure is 5x greater for stock A. Of course this will only matter when the rare event strikes. One other possibility is that I am not correctly understanding the % risk model used, or am misunderstanding something else. Both these possibilities are quite likely. if that is the case I apologize. :D If I am applying it correctly, Then I question if the % adjustments you suggest reflect the realities.

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Post by MCT » Sat Sep 13, 2003 4:42 am

Hi Nathan, Good post
To quote you:
-Your intended risk is your maximum theoretical risk. In my view, this makes it much less risky.
-I don't see how stock B is 5x risker. If anything, i think it may be the opposite. True exposure is 5x greater for stock A. Of course this will only matter when the rare event strikes.
-One other possibility is that I am not correctly understanding the % risk model used, or am misunderstanding something else.
Unless I’m misunderstanding your point in your example, your actual risk per trade ‘now’ is $2000 in both A & B. But your dollar commitment on trade-A and your dollar commitment to trade-B work just as well in equalizing exposure if you accept the dollar commitments as the actual risk to trade now, until you accept the trade as such your exposure is unequal. I am not referring to your intended risk. When we start intending and supposing we bring in discretionary elements into our risk controls, which we don’t want. With $2ooo risks per trade for both A & B, your portfolio is displays 5x greater dependence on the performance of B because of the greater true market volatility exposure-or atr relative to price. (A) has a .10atr.2000=$200 risk exposure, where as (B) has .50atr.2000= $500 risk exposure. These are different volatility units in dollar terms.

If you look closely, I made no mention of stops/exits or any model… I feel exits such as 2atr are 1) arbitrary for the purposes of sizing positions and defining risk… 2) and your exposure could vary depending on where your stop is placed.. thus skewing the exposure conundrum further, I utilize other methods but that’s another subject all together. What I had in mind was even simpler, suppose: $100,000 account. Risk=2% or 2000. atr-value=$5. $2000/$5=400shares or 2 percent allowed equity volatility. The allowable equity volatility remains constant by fixing it to true market volatility or 1ATR relative to price. Since risk control methods are highly personal and psychological, the ideas are open to disagreements. The main point I was trying to hit home was simple atr measure seems to provide missing structural information when looked at relative to price.

What I’ve attempted to do is equalize the possible exposure and true market fluctuations of each element in my portfolio. Without getting into the intricate details, I use a simple risk control model that resembles a cross between the percent-volatility-risk model, 1-unit-per-fixed-amount-of-money model and Percent-Exposure model, it’s much simpler than it seems-and some would say it is naïve. It equalizes true market volatility to allowable portfolio equity fluctuation.

In all, the purpose is to equalize exposure to true market volatility. It’s not perfect, but it gets the job done. :P

Cheers,

MT
Last edited by MCT on Wed Sep 17, 2003 3:12 pm, edited 3 times in total.

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Post by MCT » Sat Sep 13, 2003 1:49 pm

… and oh yes, if you accept your dollar commitment of trade right away, to maintain the same level of risk, to use your example, you have to:

100,000 portfolio. 2% risk, or $2000. 2atr stop

stock A.
$50 stock. 5atr = $50stock.40 shares to risk $2000. $10 stop.
dollar commitment on trade = 50 * 40 = $2,000.
Risk per trade = $2,000

Stock B.
$10 stock 5atr = $10stock.40 shares to risk $400. $10 stop.
dollar commitment to trade = 10 * 40 = $400
Risk per trade = $400

The exposure is still unequal, but it is much better than before.
:P

I’m not sure if the thread belongs here any further; I’ve posted it here nonetheless.

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Post by CRM114 » Sat Sep 13, 2003 4:03 pm

I'm still trying to get a feel for this problem so I've been playing around with some stock data. I'm hoping to get some idea of what nasty surprises might be out there by looking at tomorrow's true range vs. today's atr (10-day average). Following Menelik's suggestion, I normalized both by today's close. Here's an example using CSCO. It's pretty much consistent with the few other examples I've looked at.

The grid size on the vertical axis is twice as big as on the horizontal, so the simple 2-atr stop corresponds (sort of) to the diagonal passing through the origin. It looks like the big relative moves are more likely to happen when the volatility is low. Sounds familiar.

I'll be the first to say that this is only a simple first step.

Jack
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Different systems require different back-adjusting methods

Post by TK » Sat Sep 13, 2003 5:08 pm

damian wrote: [...] Now, 1 year later and you are building a continuous back adjusted series.

- There is a 10 point gap between sep02 and dec02.
- Dec is 10 points below sep.
- The splice requires the sep02 series to have 10 points deducted from all data points so as to align with the dec02 relative level.
- Remember that the actual historical close of the Sep02 contract on 1 Sep was 50. However the back adjustment changes it to 40.
- 1 Sep 02 ATR would not have changed as a result of the back adjustment.
- Now on 1 Sep 02, we have ATR/C = 15/40 = 0.375
- in backtesting on this adjusted series you would no longer get a buy signal on 1 Sep 02.
One important piece of information that is missing from Damian’s example is the type of back-adjusted data that is used. The error that Damian got is due to the use of point-based back-adjusted data and this is the wrong type of data to use with that kind of system. Let me explain.

We must differentiate between two types of systems:

A. Point-based systems that rely on absolute point-based differences between two prices, e.g. if TodayClose – YesterdayClose > 0 then go long
B. Ratio-based systems that rely on the ratio of two prices, e.g. if TodayClose / YesterdayClose > 1.2 then go long

Point-based systems (PGO and Thirteen fall into this category) test well on point-based back-adjusted data. If you add any value to all the prices (as Mark Johnson suggests), test results will not change. But if you do the same with ratio-based systems, your results will get distorted in the way shown by Damian above.

Does it mean that you should reject all ratio-based systems as untestable? Well, I don’t think so. One solution to the problem was proposed by Thomas Stridsman (see Trading Systems That Work, page 37) and this is ratio-adjusted data. At the rollover, all the prices should be adjusted by the percentage rather than point difference between the prices of the old and new series. You can use the following formulas:

Ratio = New Series Price on Rollover Date / Old Series Price on Rollover Date
New Price = Old Price * Ratio

If Damian used this type of data to test his example on, he should find that his entry/exit dates remained intact. This, however, leads to another problem: while percentage-based changes will be the same, all dollar-based calculations (such as the calculation of your equity used in position sizing models) will be wrong. One solution that I see is this: test ratio-based systems on ratio-adjusted data for your entry/exit dates but then use point-based back-adjusted data to trade them and to calculate your equity and all kinds of performance ratios.
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How to define low and high volatility?

Post by TK » Sat Sep 13, 2003 5:17 pm

In testing different systems for the Polish FW20 stock index future, I liked to use the 2*ATR stop loss and 5% risk per trade to determine my position size. This is the standard % risk model by which your position is bigger when the volatility is low, and it is lower when the volatility rises. Then I came up with the idea of making my model even more dynamic by tightening my stop and increasing risk per trade when the volatility was low, and widening my stop and reducing risk per trade when the volatility was high. This boiled down to the following set of rules:

If ATR is low, then use 1.8 * ATR stop loss and 7.5% risk per trade
If ATR is normal, then use 2 * ATR stop loss and 5% risk per trade
If ATR is high, then use 2.2 * ATR stop loss and 2.5% risk per trade

The problem that I had to solve was how to define low and high volatility? The ATR of 30 may be considered low volatility at the price level of 2000, but it may be viewed as high at the price level of 1000. I knew that the high and low could not be defined in absolute terms. What I did was calculate 14-period FastATR and 100-period SlowATR and compare the two. Then I decided that:

If ATR(14) <= 0.8 * ATR(100), then volatility is low
If 0.8 * ATR(100) < ATR(14) <= 1.2 * ATR(100), then volatility is normal
If ATR(14) > 1.2 * ATR(100), then volatility is high

This way, the ATR of 30 could be considered either low, or normal, or high no matter what the current price level is, depending only on the volatility levels in the fairly recent past. This solution worked for me. You may test it to see whether or not it does the job for you.

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