Trading with Market Statistics XI. HUP

[Northern boy]

interesting, thanks Jperl.

[jgotchev]

Thank you for a lovely discussion, Jperl. I find a lot of validity and usefulness to your methods. I do have one question, though. Since the skew of the volume distribution is such an important part of your analysis, why not use other methods for estimating it. Rather than rely on the position of the mode so much, one could use the median or better yet, compute it in the classical way as the third moment of the volume distribution. The reason I ask is that a lot of times in the markets we have the PVP but also another price with almost as much volume. Also, sometimes there are clusters of volume that don't neccessarily include the PVP but could also act as a HUP. The point I am trying to make is that the relative position of the PVP and the VWAP is not always a reasonable estimate for the actual volume distribution skew and I was wondering if you have looked into it.

[jperl]

	Quote:	jgotchev
	Thank you for a lovely discussion, Jperl. I find a lot of validity and usefulness to your methods. I do have one question, though. Since the skew of the volume distribution is such an important part of your analysis, why not use other methods for estimating it. Rather than rely on the position of the mode so much, one could use the median or better yet, compute it in the classical way as the third moment of the volume distribution. The reason I ask is that a lot of times in the markets we have the PVP but also another price with almost as much volume. Also, sometimes there are clusters of volume that don't neccessarily include the PVP but could also act as a HUP. The point I am trying to make is that the relative position of the PVP and the VWAP is not always a reasonable estimate for the actual volume distribution skew and I was wondering if you have looked into it.

You are perfectly correct, that the exact definition of the skew requires a computation of the 3rd moment. The problem with it is the computation is very cpu intensive. I therefore settled for the approximate value due to Pearson as discussed in the skew tag. The advantage of this is you can visualize the skew just by looking at the volume histogram with the vwap superimposed. The problem is as you point out, when you have two large volume peaks, you don't quite know what the skew is. Nevertheless since you can visualize the volume peaks in relation to the VWAP you can approach the market with caution when this occurs.

As far as HUPs go, you are correct again that peaks in the volume distribution are HUPS. Which HUPS you wish to use in your trading is of course a function of your trading style. Keep in mind that HUPS are just that, hold up prices. They are places for you to be cautious as to what to expect.

[Head2k]

	Quote:	jperl
	The problem with it is the computation is very cpu intensive.

First let me thank you for these amazing threads, being a newbie I find them very useful. Second I apologize for my poor English.
Now to the computation of the third central moment. I am not educated in statistics, so I needed to read a few articles in Wikipedia. So please correct me if I am wrong:

CM3 = sum(PROBi * (Pi - VWAP)^3),
where
i is going through all prices in range (i.e. all rows in Volume Distribution Function)
CM3 ... the 3rd Central Moment
PROBi = Vi / V ... ith price probability (Volume per ith price / Total Volume)
Pi ... ith price in the Vol. Dist. function

Then the Skew would be calculated as
Skew = CM3 / SD^3

If this is correct, the computation doesn't seem too CPU intensive to me. I programmed such a computation in AmiBroker and I plotted a line on a chart. The line is VWAP + (Skew * SD). Watching this line together with PVP-to-VWAP relation can be very useful. Now I don't have time to elaborate, but if somebody is interested I can write more later.

Ondrej

[justlurkin]

	Quote:	Head2k
	First let me thank you for these amazing threads, being a newbie I find them very useful. Second I apologize for my poor English. Now to the computation of the third central moment. I am not educated in statistics, so I needed to read a few articles in Wikipedia. So please correct me if I am wrong: CM3 = sum(PROBi * (Pi - VWAP)^3), where i is going through all prices in range (i.e. all rows in Volume Distribution Function) CM3 ... the 3rd Central Moment PROBi = Vi / V ... ith price probability (Volume per ith price / Total Volume) Pi ... ith price in the Vol. Dist. function Then the Skew would be calculated as Skew = CM3 / SD^3 If this is correct, the computation doesn't seem too CPU intensive to me. I programmed such a computation in AmiBroker and I plotted a line on a chart. The line is VWAP + (Skew * SD). Watching this line together with PVP-to-VWAP relation can be very useful. Now I don't have time to elaborate, but if somebody is interested I can write more later. Ondrej

Can you post a screenshot...
Is this Skew different from (VWAP - PVP) / SD ? More beneficial?


thanks

[jperl]

	Quote:	Head2k
	First let me thank you for these amazing threads, being a newbie I find them very useful. Second I apologize for my poor English. Now to the computation of the third central moment. I am not educated in statistics, so I needed to read a few articles in Wikipedia. So please correct me if I am wrong: CM3 = sum(PROBi * (Pi - VWAP)^3), where i is going through all prices in range (i.e. all rows in Volume Distribution Function) CM3 ... the 3rd Central Moment PROBi = Vi / V ... ith price probability (Volume per ith price / Total Volume) Pi ... ith price in the Vol. Dist. function Then the Skew would be calculated as Skew = CM3 / SD^3 If this is correct, the computation doesn't seem too CPU intensive to me. I programmed such a computation in AmiBroker and I plotted a line on a chart. The line is VWAP + (Skew * SD). Watching this line together with PVP-to-VWAP relation can be very useful. Now I don't have time to elaborate, but if somebody is interested I can write more later. Ondrej

Very good Ondrej. You have the skew computation properly weighted. What makes this computation cpu intensive is in real time you have to update the value of PROBi as you add more volume data. Should be okay for a fast machine.
Perhaps you can show us some charts with your skew computation drawn in along with the VWAP and PVP.

[Head2k]

Ok, I uploaded screenshots. These are 2min charts for ES for the last 3 business days, counting today. VWAP is the thick yellow line, PVP thick turquoise line, Skew Line (VWAP + Skew * SD) is the thin light blue line. The dark blue area is the area between the 1st SD's, the Value Area in terminology of MP.
If the Skew Line is above VWAP the skew is positive, below VWAP negative. The distance between the Skew Line and VWAP tells you how large is the skew compared to SD. To distinguish the two different methods to determine the skew, I will use terms Skew(PVP) and Skew(3CM).

While Skew(PVP) flips (or jumps), the Skew(3CM) is continuous. By the time Skew(PVP) flips the Skew(3CM) Line crosses VWAP, that means Skew(3CM) crosses zero. In other words, if the skew is positive and price action is above VWAP, Skew(PVP) rises while Skew(3CM) decreases. By the time the Skew(PVP) flips, the Skew(VWAP) crosses zero.
Hence the first use of the Skew(3CM) is to warn you before the PVP flip. Another use, surprisingly, is to determine the real statistical skew. The Skew(PVP) has the greatest absolute value right before the flip. That might lead you into some bad trades. If you look at Skew(3CM) you will recognize that the real skew is very small.
As you can see from the charts, it looks like the Skew Line is a minor HUP itself. But I have been watching this only for a couple of days, so I don't want to make any conclusions yet.