A Dynamic, Volume‐Weighted Average Price Approach Based on the Fast Fourier Transform Algorithm

• Date: 01 December 2013
• Author: Handong Li,Xunyu Ye
• DOI: http://doi.org/10.1111/ajfs.12037
• Published date: 01 December 2013

A Dynamic, Volume-Weighted Average Price

Approach Based on the Fast Fourier

Transform Algorithm

Handong Li*

School of Government, Beijing Normal University

Xunyu Ye

School of Government, Beijing Normal University

Received 20 August 2012; Accepted 6 September 2013

Abstract

We propose a model for decomposing a volume series based on the Fast Fourier Transform

(FFT) algorithm. By setting a threshold for the power spectrum, the model extracts the

periodic and nonperiodic components from the original volume series and then predicts

them. By analyzing samples from four major stock indices, we find that a too small thresh-

old and a too large threshold cause negative effects on the performance of the FFT model.

Appropriate thresholds are found at approximately the 93rd to 95th percentile for the four

indices studied. The out-of-sample experiment for the 50 stocks of the Shanghai 50 Com-

posite Index shows that the FFT model is superior to the classic moving average model in

terms of both volume prediction and Volume-weighted Average Price (VWAP) tracking

accuracy. Meanwhile, for almost all of the 50 stocks, the FFT model outperforms the

Bialkowski et al. (2008) model in terms of volume-prediction accuracy. The two models

perform comparably in terms of the VWAP tracking error.

Keywords Algorithmic trading; Fast Fourier Transform; Intraday volume prediction; Vol-

ume-weighted average price strategy

JEL Classification: C22,C81,G12

1. Introduction

Institutional traders are perpetually seeking ways to execute their large positions.

They could simply trade all of their positions in one transaction, but that may sig-

nificantly impact the market such that the price of an asset reverses, therefore

increasing the traders’ costs. Conversely, institutional traders could choose to divide

*Corresponding author: Handong Li, School of Government, Beijing Normal University, No.

19 Xinjiekouwai Street, 100875 Beijing, China. Tel: +8610 58809147, Fax: +8610 58808176,

email: lhd@bnu.edu.cn.

Asia-Pacific Journal of Financial Studies (2013) 42, 969–991 doi:10.1111/ajfs.12037

©2013 Korean Securities Association 969

their positions into numerous transactions to alleviate any possible market impact.

However, this strategy could also add to the traders’ opportunity costs. Thus, to

reduce their costs and manage their risks, traders make a trade-off between the

quantity of each transaction and the overall time allocated for the entire transaction

process.

Algorithmic trading is an efficient tool for solving this problem. In algorithmic

trading, various mathematical theories and advanced computer techniques are com-

bined to meet the specific needs of traders. It also enables traders to take advantage

of high-frequency information on the market. Researchers have developed many

algorithmic strategies for executing large positions. For example, the Target Volume

(TV) strategy trades a constant proportion of the real volume. It considers no his-

torical information, the volume and the duration of the order execution are

unknown before trading, and there is no benchmark the strategy tries to beat

(Fraenkle and Rachev, 2009). The Time-weighted Average Price (TWAP) strategy

tries to beat the TWAP. It divides the trading period into equal time intervals and

distributes the order volume equally over those intervals. The Volume-weighted

Average Price (VWAP) strategy tries to execute trades at a price that approximates

the VWAP, which is the strategy’s benchmark (Madhavan, 2002). Berkowitz et al.

(1988) regard the VWAP benchmark as a good approximation of price for passive

traders. The transaction costs of a large order execution mainly consist of two parts:

one is a fixed cost, such as broker commissions and exchange fees, which are gener-

ally proportional to the number of slices in the order; the other is an impact cost,

which can be caused by a large transaction. Although this cost can sometimes be

observed from the market, it is relatively hard to measure. Introductions and exam-

ples of TV, TWAP, and VWAP can be found in studies by Fraenkle and Rachev

(2009) and Palmliden (2011).

Among these strategies, VWAP is popular because of its simplicity and reliabil-

ity. This strategy hinges upon accurate predictions of intraday volume distribution.

More accurate predictions result in a better executed VWAP and thus a lower exe-

cution risk.

To illustrate this principle, we use the following example. Assume that in a

4-hour trading day, the total volume of one stock on the market is 1000 shares.

The volume and price in each hour are the following: the first-hour volume is 400

(40%), and the price is 100; the second-hour volume is 200 (20%), and the price

100.5; the third-hour volume is 100 (10%), and the price is 101; and the final-

hour volume is 300 (30%), and the price is 101.5. Thus, the market VWAP is

equal to:

100 400 þ100:5200 þ101 100 þ101:5300

1000 ¼100:7

If we need to sell 100 shares in these four hours, and we assume that we can

perfectly predict the proportion of the volume for each hour, then we can execute

X. Ye and H. Li

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