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# Trading With Market Statistics.II The Volume Weighted Average Price (VWAP)

posted in: Order Flow Analysis |

In a previous thread, I introduced the Volume Distribution Function in the form of a volume histogram plotted along the price axis (see figure 1 of that thread). The length of the bars extending out to the right represent the amount of volume traded at that price during the day. The distribution has a peak which I call the peak volume price or PVP ( also known as the Point of Control in Market Profile Analysis, but I won’t use that term here in order to avoid any confusion). . The volume distribution is a probability function, thus trading occurs less often in the low volume regions of the distribution compared to the high volume regions. However I also stated that the distribution function is dynamic and that the shape of the distribution changes during the day such that the PVP may change abruptly as the trading day progresses. As such, if price action is in the low volume region, it does not mean that there will be a reversal back to the high volume region. The distribution function could simply expand itself and continue moving in the same direction with an eventual abrupt change in the PVP. This was shown by the price action in figures 2 and 3 of the previous thread.

In order to shed more light on this, I want to introduce the concept of the volume weighted average price or VWAP. The VWAP is a well known quantity used by institutional traders to gauge there trading performance. It’s use as a day trading tool however has not been fully explored. The VWAP is simply the average of the Volume Distribution Function. The figures below show examples. The red line is the PVP of the distribution and the light blue line is the VWAP for the distribution. To compute it, take the volume Vi for each bar i in the distribution, multiply it by the bars price, Pi, compute the sum, SUM(PiVi) and divide by the total volume, Vtotal, for the whole distribution:

VWAP = [SUM (PiVi)]/Vtotal

The VWAP has the following characteristics:

1) Being the average for the entire distribution, Volume traded above the VWAP is identical to volume traded below the VWAP.

In terms of the distribution function as a probability function, it means that when price action is at the VWAP, there is equal probability for price to move up as there is for price to move down.

As corollaries then we have:

2) if the VWAP is above the PVP, then more volume has traded above the PVP than below it. The distribution function is thus skewed to the upside and the expectation is that at the PVP, price action should move up.
Take a look at the figure below, the ER2 for June 28,2007. At the end of the day, the VWAP (light blue line) is at 847.98 and the PVP at 846.60. The VWAP > PVP hence more volume was traded above the PVP than below.

3) Conversely, if the VWAP is below the PVP, then more volume has traded below the PVP than above it; the distribution function is skewed to the downside and the expectation is that when price is at the PVP, price action should move down. You see this in the following figure for ES on June 11, 2007. The VWAP is at 1525.32 and the PVP is at 1528.75. VWAP < PVP. Clearly the amount of the skew will be a function of the difference between the VWAP and the PVP.

4) If the VWAP approximately equals the PVP, then the distribution function is symmetric. In this case when price touches the PVP, there is no expectation of price movement in either direction. Instead, expect to see small oscillations about the VWAP. The next image shows this for ER2 on June 22, 2007. VWAP = 840.44 and PVP = 840.20. Oscillations about the VWAP occured for most of the afternoon starting at 13:30.

5)The VWAP and its relation to price also determines the trend of the market as follows:

a)If Price >> VWAP, the trend is up
b)If Price << VWAP, the trend is down.
.

6) Finally it doesn’t matter on what time scale you plot the distribution functions and its associated VWAP. The chart could be a 1, 2 ,3 minute etc time chart, or a tick chart, or a range bar chart or a volume bar chart. The distibution and hence the PVP and VWAP are all the same. You need only take a quick glance at the VWAP and its relation to price, to decide the trend of the market.

In future threads I will present some examples of how to use this information for entering a trade. In part III we will start with the newbies, since they need the most help. After that we will look at more complex situations using only the distribution function and the VWAP.

There is a lot here to digest, so I will stop for now.