Price formation on stock exchanges has been the center of attention of many researchers for several decades now. As a result, there is an abundance of theories, models, and empirical evidence on the price, and although there are always new aspects to discover, we believe that the financial knowledge is fairly comprehensive on the subject. We understand the dynamics of the price reasonably well, and most of us agree that it is rather difficult to forecast.
In contrast, the trading volume, which is another fundamental measure of the trading process on stock exchanges, has been much less researched. The most common equilibrium models on price do not even include volume in their framework of explaining trading activities. It is only recently that researchers appear to be paying increasing attention to volume, and they have already found that its stylized facts allow for much better forecasts compared to price.
This chapter aims to introduce an intra-day forecasting model selected from the available literature, and to provide its implementation in R.
The motivation behind gaining a better understanding of volume is not merely theoretical, but it equally has a great practical relevance. On order-driven markets, if a submitted buy (sell) market order is relatively large compared to the market, it will possibly swipe out several price levels; thus, the achieved average price on the entire trade will be higher (lower) than the best price level at the moment of order submission, and the submitter loses money. This phenomenon is often referred to as price impact, and it is well worth making an effort to avoid or at least minimize it.
One way to do this is to perform order splitting, that is, splitting a market order into smaller chunks and submitting them gradually. Among the numerous logics behind splitting, a popular one is the volume weighted average price (VWAP) strategy that aims to obtain the daily weighted average price where weights are determined by the volume transacted relative to the total daily volume. Long-term investors would happily settle for an average execution price equal to the daily VWAP, which is considered to be a neutral trading result. However, some investors find it tricky to split their trades throughout the day in a fashion that results in reaching the VWAP, which can only be calculated at the end of the day, so they delegate the problem to brokers. Brokers guarantee to trade on the VWAP, and are paid a fee for this service. This fee also serves as a buffer for tracking errors, which means that the broker that has the most precise forecast of the daily volumes will be the one who can charge the clients the least, because all they have to do is split their trades in similar proportions to their forecasts, and then (assuming the forecasts are perfect) the VWAP will be reached regardless of the price evolution. For brokers, therefore, accurate volume forecasts are considered a valuable business asset that directly affects their profits.