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Old 01-07-2014, 01:57 PM   #1

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Volatility and Position Sizing

Hello,

I thought it would be interesting to hear people's thoughts on the following . . .

Last spring I spent some time investigating volatility and position sizing. Previously I had made myself familiar with the approach of the Turtles - when volatility is high, then the same dollar movement can be achieved by holding fewer contracts; smaller positions are used in high volatility and larger positions are established in low volatility in order to normalize losses and gains.

The obvious problem with this is that 'volatility' is measured at the time the position is established. What bearing does this have on the volatility over the duration of the trade?

The first thing I did was to feed an output from my strategy - the cumulative average trade length - back into the strategy as an input (an extremely simple instance of machine learning). This meant that volatility was measured in terms of the life of an average trade, rather than using some arbitrary/optimized parameter.

At the time a position is established, however, this new adaptive measure was still only telling me something about historical volatility (albeit over a more relevant time period). What I was really interested in was anticipating the volatility that was yet to come, during the time that I would be holding a position.

Predicting volatility is obviously very difficult - I imagine quant firms involved in option pricing probably spend a lot of time working in this area.

What I found can be summarized as follows:
  • Volatility is typically cyclical and oscillates around its mean.
  • Where the time between peaks and troughs in this oscillation is roughly equal to the average trade length of a strategy, then it makes sense to do the precise opposite of what the Turtles did.
  • This means that when volatility is high, a larger position size should be used, in the anticipation that volatility will fall over the duration of the trade. Likewise, when volatility is low a smaller position size should be used.

One of the problems with this is when volatility is high and a large position is taken, but also continues to increase throughout the course of the trade.

And the solution to this problem must be that the baseline from which 'large' and 'small' position sizes are derived must not be equal to the maximum position size that is allowed by the primary money management formula. Rather, the 'large' position size should be equal to this maximum, with all lesser sizes scaled using a ratio determined by the trader.

How to do this?

Here is a simple example to begin with:
  • You are trading a single stock, with zero leverage. It is priced at $100, your account size is $100000, and you will risk no more than 10% of your account on it.
  • This means that, using fixed-fractional as your BASELINE position size, you can buy (100000*0.1)/100 shares. BASELINE=100.
  • We will assume that the TYPICAL position size is half of the BASELINE, so TYPICAL=BASELINE*0.5=50.
  • The cumulative average volatility - CAVGVOL - for the instrument is, say, 30.
  • The TYPICAL position size is aligned with the CAVGVOL. So when the predicted volatility PVOL=30, POSITIONSIZE=TYPICAL.
  • When PVOL=15, POSITIONSIZE=TYPICAL*(1/(PVOL/CAVGVOL))
  • Or . . . POSITIONSIZE=50*(1/(15/30))=100
  • This makes perfect sense - when the volatility is half the average, we need to hold twice as many shares to achieve the same gain as when volatility is average.

An obvious problem jumps out here - what happens when volatility is less than 50% of the average volatility (ie PVOL<CAVGVOL/2)?

This would require us to hold more than the BASELINE number of shares, and the BASELINE is the maximum number of shares that our underlying money management formula permits.

One solution is simply to take the lesser of the two values as a new variable - in code this might look something like:
Code:
possize=minlist(positionsize,getequity/c);
This creates a very defensive stance, whereby we will decrease the number of contracts indefinitely when we expect high volatility, but we will never increase them above the maximum our money management formula allows, no matter how low we think volatility will become.

It is of course possible to set the value for TYPICAL as a fraction of BASELINE that allows for PVOL values of 100% less than CAVGVOL. A more symmetric (though by no means better) approach is as follows:
  • Volatility cannot fall below zero, nor we will assume below 1, so the largest increase in the number shares we can ever expect is 1/(PVOL/CAVGVOL)*TYPICAL. This would require us to hold 1/(1/30)*50=1500 shares.
  • When this maximum increase occurs, we want it to be equal to the BASELINE number of shares (the maximum our underlying money management formula allows).
  • So, we want it to be possible to increase our TYPICAL position size to be 30 times greater to match the BASELINE. TYPICAL would therefore be equal to BASELINE/CAVGVOL=100/30=3.3 shares.
  • For a trade where we expect average volatility, we want to trade 0.33 times the BASELINE number of shares. In instances where volatility drops to 1, this will allow us to increase the number of shares we trade to ensure that our gain is always normalized against the gain of an average volatility trade.

Another problem has now arisen . . . Unless we happen to be trading a very large account, our scope for reducing the number of shares is somewhat limited! This problem is not mathematical, it's caused by the 'granularity' of the share price relative to the account size, and the fact that we're trying to arrange things around a central value when the underlying input is unbounded on one side.

Here is a different way of doing things that deals with this to a reasonable extent:
  • MAXVOL is the maximum recorded volatility, and MINVOL is the minimum recorded volatility.
  • All PVOL values must exist within the space bounded by these two values.
  • This space is aligned with the space between zero and the BASELINE value.
  • So if we assume the lowest volatility recorded is 25 and the highest volatility recorded is 35, then we can locate a PVOL of 32 in terms of these values as (PVOL-MINVOL)/(MAXVOL-MINVOL)=(32-25)/(35-25)=0.7.
  • SCALEDVOL, as we shall call it, is 0.7, or 70% of the max/min range of recorded volatilities.
  • When SCALEDVOL is 0 we want to trade with our largest position size, equal to BASELINE. And when SCALEDVOL is 1 we want to trade with our smallest position size, a factor of BASELINE which we will call MINSIZE (In effect, MINSIZE*BASELINE is equivalent to TYPICAL-(BASELINE-TYPICAL) in our previous formulation, or -93.4).
  • We will set MINSIZE at 0.5.
  • So for our SCALEDVOL of 0.7, we want to trade (BASELINE-(BASELINE*MINSIZE))*(1+(1-SCALEDVOL)) . . . or . . . (100-(100*0.5))*(1+(1-0.7))=50*1.3=65 shares.
  • For a SCALEDVOL of 0.2 we want to trade (100-(100*0.5))*(1+(1-0.2))=50*1.8=90 shares.
  • For a SCALEDVOL of 1 we want to trade (100-100*0.5))*(1+(1-1))=50*1=50 shares.
  • For a SCALEDVOL of 0 we want to trade (100-100*0.5))*(1+(1-0))=50*2=100 shares.

There is just one final thing to consider, and that is how to deal with situations where the predicted volatility PVOL is greater or less than the historical MAXVOL and MINVOL. Once the strategy has a reasonable amount of data under its belt this won't happen often, but it will happen.

My solution was simply to throttle these values by passing SCALEDVOL through a sigmoid function. This is a bit of a hassle in tradestation as it only offers the hyperbolic tangent, so you need to do something like the following:

Code:
throttle=((tanh((scaledvalue*2)-1))/2)+0.5;
Note that this will also begin to compress any SCALEDVOL as it approaches MINVOL or MAXVOL, meaning that less credence is given to the reliability of extreme PVOL values - probably a good thing as all extreme values tend to revert to the mean in subsequent periods.

I am interested to know what everyone makes of this approach. Would you want to increase position size when volatility is high? Is this a good way to do so whilst maintaining control of risk within clear parameters?

Kind regards,

BlueHorseshoe
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Old 01-07-2014, 06:32 PM   #2

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Re: Volatility and Position Sizing

Hiya,

Your put a lot of effort into that post and even more effort into your research

Quite a lot of what you wrote is beyond me ....


Quote:
Originally Posted by BlueHorseshoe »
Would you want to increase position size when volatility is high?
I personally would not want to, but that is because I'm looking to trade for the duration of the high vola cycle and sit through the cycles. I'm just a short-term day trader though. My risk is defined by the structure on the chart and as a result, that is adapting to the current volatility. I know you are swing trading, so risk management is probably quite a different beast.

Many thanks for the in depth post.

With kind regards for the new years,
MK
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Old 01-08-2014, 03:09 AM   #3
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Re: Volatility and Position Sizing

Quote:
Originally Posted by BlueHorseshoe »
I am interested to know what everyone makes of this approach. Would you want to increase position size when volatility is high? Is this a good way to do so whilst maintaining control of risk within clear parameters?
Much the same as MidKnight - well done, and although I dont wish to run through all the exact maths, I think you hit upon the problems inherent with any of these methods. There are trade offs involved in each, and ultimately a lot will depend on what you are trying to achieve.
Do you want steady, lower risk, less volatile returns, or maximum returns with more risk higher drawdowns etc. Then you also introduce the issues of how this works within a diversified portfolio of non correlated assets, v a diversified portfolio of correlated assets, v what happens when they are meant to be diversified but turns out correlation might go to 1 for a few months!

Regards what I have seen for trend followers who largely deal with this, some research I have seen elsewhere suggests (in a general manner) apart from the choosing the tradeoffs that best suit you, that less risk and hence smaller sizes when trading is volatile is a better approach.
They then go on to summarise that over the long term, a simple rule, or even a simple non mathematical set of rules work out much the same as anything too precise. Rule such as - excessive vol means half current position, or if we have too many similar assets already on as a trade we wont accept more. eg; long dow, long nikkei, long Nasdaq, so we wont take anymore long equity positions.

If however, you have enough patience, or discretion or whatever and your trading style is such that in volatile market conditions you are able to pick levels/turning points well, then your risk can still be quite small for large positions and the resulting payoff can be much bigger. As Zdo rightly reminds us - system specific.

.......
Personally - I am conservative and adopt the approach - if the volatility is occuring because I dont know whats happening then stay out. If the volatility is occuring and I know the reason and the ducks line up - load up. (Liquidity not being an issue for most of us, but for others it is)
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Old 01-08-2014, 09:56 AM   #4

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Re: Volatility and Position Sizing

Quote:
Originally Posted by MidKnight »
I know you are swing trading, so risk management is probably quite a different beast.
Hi MidKnight,

Glad you found the post interesting!

As far as any of it goes, this relies on being able to work out where you are within a volatility cycle, and how well your strategy's typical trade length is aligned to the cycle. For daytraders the cycles generally seem to be more erratic - volatility tends to increase sharply during the first few minutes of trading, completely regardless of how it was unfolding up to that point - no simple geometric projection model is going to predict this.

So I would agree that it is probably significantly easier to find an application for this as a swing trader.

Best wishes to you for the New Year also!

Kind regards,

BlueHorseshoe
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Old 01-08-2014, 10:39 AM   #5

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Understanding Weighting

Quote:
Originally Posted by SIUYA »
Do you want steady, lower risk, less volatile returns, or maximum returns with more risk higher drawdowns etc.
The goal for me was to try and smooth the equity curve without significantly reducing the number of trading opportunities and hence the net profit. In other words, I wanted to strike a balance between the two. The answer seems to be to adjust the position size down rather than throw a trade out all together when some condition such as volatility doesn't look the way you want it to.
Quote:
Then you also introduce the issues of how this works within a diversified portfolio of non correlated assets, v a diversified portfolio of correlated assets, v what happens when they are meant to be diversified but turns out correlation might go to 1 for a few months!
Yep - it only ever gets more complicated! But remember, with any of the approaches above, your maximum position size will still be no greater than what you would have used anyway.

Quote:
Regards what I have seen for trend followers who largely deal with this, some research I have seen elsewhere suggests (in a general manner) apart from the choosing the tradeoffs that best suit you, that less risk and hence smaller sizes when trading is volatile is a better approach.
For a trend follower, though, my OP would be of no value for the following reason: as a trend follower most of your profits come from outliers, and these trades will typically be many multiples of the average trade in duration (the average trade will be a loser), and also span numerous volatility cycles. It's also safe to say that the further out you go, the less accurate your prediction of volatility is likely to be.

The best predictor of future volatility over a longer time period is almost always . . . current volatility. Which is exactly what the Turtle method uses And, I'm guessing, the simpler option pricing models?

Do the large trend-following funds get around this by constantly rebalancing against shorter term volatility predictions? I don't know the answer to this.
Quote:
They then go on to summarise that over the long term, a simple rule, or even a simple non mathematical set of rules work out much the same as anything too precise.
Shhh! That's meant to be a secret - otherwise what will all those PhDs do for a living?

Quote:
Personally - I am conservative and adopt the approach - if the volatility is occuring because I dont know whats happening then stay out.
You're clearly talking about a discretionary element here, based on your fundamental understanding of a market. If you have this then it probably makes life much easier, but if you don't then can someone quantify your statement?

Assuming you expect volatility to follow a predictive model, and the further from the model it strays the less confidence you have in understanding what's happening, then you could do something like the following:
  • A market's volatility is increasing by 5 per day.
  • Your model makes a simple linear projection and expects that it will continue to increase by 5 tomorrow. As long as it does this then you "understand" the increase and can trade with perfect confidence at the end of tomorrow with your default size of 100 units.
  • At the end of tomorrow you obtain your "Understanding Weighting" by calculating the deviation from the expected volatility, where a 100% deviation (ie 10 or 0 increase) gives a zero weight and a 0% deviation (ie 5 increase) gives a weight of 1.
  • When volatility at the end of tomorrow turns out to have increased by 3.68%, your Understanding Weighting = 3.68/5 = 0.736, so you trade with 0.736 * 100 = 73 units.
  • If volatility at the end of tomorrow increased by 6.32% then Understanding Weighting = 1-((6.32-5)/5) = 0.736, so you trade with 0.736 * 100 = 73 units.

Before anyone points it out - yes, I am consumed by an unhealthy need to quantify and control everything!

Regards,

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Old 01-08-2014, 11:52 AM   #6
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Re: Understanding Weighting

Quote:
Originally Posted by BlueHorseshoe »
For a trend follower, though, my OP would be of no value for the following reason: as a trend follower most of your profits come from outliers, and these trades will typically be many multiples of the average trade in duration (the average trade will be a loser), and also span numerous volatility cycles. It's also safe to say that the further out you go, the less accurate your prediction of volatility is likely to be.

The best predictor of future volatility over a longer time period is almost always . . . current volatility. Which is exactly what the Turtle method uses And, I'm guessing, the simpler option pricing models?
I would imagine the best predictor for future vol is more some reversion to the mean of something. Particularly when using options....eg in periods where there is wild volatility then while some short term options trade close to what is happening, others will trade at big discounts as when the volatility stops the implieds collapse. Alternatively when vols are below averages, people still tend to pay up for them as it only takes one good move....when traders are burning with time decay its depressing, and can kill some accounts. Plus with options there are different series and 30, 60,90 day vols differ in expectations as well as measurements.

For trend followers - assuming you are not having the additional issues of rebalancing due to subscriptions an redemptions, I gather most only really care about their initial risk at entry. After that they are either stopped out, or if it moves many multiples in their favour its not such an issue...they will only wish they had larger size on. The killer is volatility at entry and if they use trailing stops then that should take into account future volatility?
Thats not to say you can have a trend and not still get chopped up. They are mainly worried about portfolio concentration I would imagine.
There is also the other little issue in some trends - the marginal value of each tick depends on where the entry is....usually not an issue but i could imagine it could be.
(There was one little tick which seemed to work pretty well. exit a trade when Vol was 2x your vol at entry.) Does it matter that most of the volatility issues affecting these guys and their use of the ATRs generally were designed to standardize each trade, given they had the same entry triggers. in which case if thats all you want to do then current vol is a good measure.
To be honest I have not given it much more thought than that.
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Old 01-09-2014, 06:03 AM   #7

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Re: Volatility and Position Sizing

Enter small in a volatile market but get big as soon as possible if the trade is moving in the right direction. Getting big right away just because volatility is high increases your risk of ruin. Starting out with a large position when there is high volatility doesn't make sense to me unless we are only talking about winning trades.
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