Table of Contents

VWAP

Definition of Volume Weighted Average Price

Volume-Weighted Average Price (VWAP) is a trading algorithm based on a pre-computed schedule that is used in the execution of a bigger order to minimize the impact on the market price.

In the book “Algorithmic & Trading DMA” we can read about VWAP that “As a benchmark, it rapidly became ubiquitous since it gives a fair reflection of market conditions throughout the day and is simple to calculate. This led to algorithms that tracked the VWAP benchmark becoming extremely popular.”

Before diving into the details of VWAP calulations and its appliance as a trading strategy, let’s look at this interesting short video on algorithmic trading in general.

VWAP as an Indicator and Its Formula

The schedule is the heart of a algorithmic trading strategy. To compute the schedule, the strategy should first look into historical data. As an input user defines $n$ the Number of Intervals and delay between each two of them. This gives us a partition of the period since Start Time until End Time into intervals $I_1, ldots I_n$ . Using the historical data strategy have to estimate how a big fraction of a volume traded between Start Time and End Time is traded in each time interval – these values are denoted by $u_j$ for each time interval $I_j$ .

Notice that the following holds:

$sum_{j = 1}^{n} u_j = 1$
$u_j geq 0$ for each value of $j in {1, 2, ldots n}$

On a base of the above considerations, the strategy can estimate the size of a trade that should be traded at the end of each time interval to minimize the market price strategy’s self-impact. For a $i$ -th time interval it is defined as follows:

$x_j = u_j times Target~quantity.$

Larger market participation does more impact on a market asset’s price weighted by volume, which is expressed by the formula:

$VWAP = frac{sum_i v_i p_i}{sum_i v_i},$

where $i$ is every trade. Therefore strategy tries to keep steady market participation in each of intervals.

If, defined above, predictions of volume fractions in each interval are proper then the algorithm works perfectly, otherwise it can cause a considerable impact on a market price. To prevent this bad situation more advanced versions of this algorithm take into the account also actual volume and modify their schedule to fit the market conditions.

VWAP as a Trading Strategy

Market Data

Last trade
Best quote
Order book
Statistics
Historical market data

Algorithm Parameters

PARAMETER NAME	DESCRIPTION	ESSENTIAL
Target Quantity	Overall quantity to be realized by strategy	Yes
Number of Intervals	Number of intervals to be used	Yes
Delay Table	Delay times between following orders	Yes
Start Time	A time when strategy begins to submit orders	Yes
End Time	A time when strategy stops working	No
Side	Market side for orders	Yes

Algorithm Conditions

Open position

Side Defined by Side parameter
Amount Proper step size ( defined in the Description)
Price Last market price
Type Limit or Market Order

The strategy opens positions every time the delay value is reached.

Close position

The strategy does not close its opened positions.

Termination

Strategy ends when the declared orders’ quantity has been realized. By design around defined End Time.

Time frame

This strategy is dedicated to being used in a short period of time like one day.

Calculations used in trading strategy

Calculation of VWAP it’s relatively simple and was described at the begging of the article. In mathematical approach VWAP is represented by the equation below:

wzor 1.jpg

where P is the price of i-th trade and V is the size related to i-th trade. In fact, it takes five steps to calculate your first VWAP. First, only if we use intraday data for examination, we need to calculate the typical price for our intervals. Then multiply the price by period’s volume and create a running total of these values for future trades. Fourthly we create cumulative volume and in the end, we divide cumulative multiplication of price and volume by running a total of volume to obtain VWAP. Even simpler, VWAP is a turnover divided by total volume.

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Let’s take a look at example results calculated using these five steps on 1-minute interval intraday Morgan Stanley’s data.

Time	Close	High	Low	Open	Volume	Typical Price	Price*Volume	Total PV	Total Volume	VWAP
09:30:00	38.90	38.96	38.90	38.96	69550	38.93	2707581.50	2707581.50	69550.00	38.930
09:31:00	38.94	38.97	38.86	38.92	27617	38.92	1074922.68	3782504.18	97167.00	38.928
09:32:00	38.91	38.96	38.91	38.94	11441	38.93	445398.13	4227902.31	108608.00	38.928
09:33:00	38.89	38.94	38.88	38.92	23587	38.91	917710.61	5145612.93	132195.00	38.924
09:34:00	38.90	38.94	38.90	38.90	10771	38.91	419099.61	5564712.54	142966.00	38.923
09:35:00	38.97	38.97	38.90	38.90	12721	38.93	495276.23	6059988.77	155687.00	38.924
09:36:00	38.92	38.96	38.92	38.96	16471	38.94	641384.86	6701373.63	172158.00	38.926
09:37:00	38.90	38.93	38.86	38.93	23788	38.91	925472.14	7626845.77	195946.00	38.923
09:38:00	38.90	38.92	38.89	38.89	9170	38.90	356701.54	7983547.30	205116.00	38.922
09:39:00	38.92	38.92	38.88	38.91	4644	38.91	180682.02	8164229.32	209760.00	38.922
09:40:00	38.90	38.92	38.88	38.91	4917	38.90	191283.59	8355512.92	214677.00	38.921

All calculations are pretty straightforward, but let us take a look at one interesting element. When you look at typical prices more than half of them (7/11) is below the last VWAP At the same time mean equals 38.917. So where does the difference come from? Volume is the culprit. In our case, a period with the higher typical price also has a bigger Volume, thus bigger market impact and VWAP calculations indicate that.

Intraday or tick

The most classical VWAP approach is based on tick-by-tick data. But as the market grows and the frequency of trades increases more resources are required to keep all calculations up-to-date. Nowadays it is nothing extraordinary for stock to have over a hundred trades per minute (true or false?). When multiplied by minutes in a trading day and number of stocks it develops into numbers that might cause some performance troubles.

With help arrives intraday data, i.e. tick-by-tick data aggregated in time periods e.g. 1-minute, 5-minute or 15-minute that contains the close, high, low and open price. As in VWAP calculations, only one price is required we have to somehow average available prices. For this task exist typical price:

typical

Also, there is a second version of typical price that includes Open Price and it’s divided by 4.

Strategy

Most likely we can point out two different strategies of reading VWAP. The first one used especially by short-term traders relies on waiting for VWAP to cross above the market price and then enter long position as they interpret price to be bullish. On the other hand, are Institutions looking to sell at this moment because they consider it a good opportunity for that day’s price.