Assessing Day-to-day Volatility: Does the Trading Time Matter?
| Autor | José Valentim Machado Vicente - Gustavo Silva Araujo - Paula Baião Fisher de Castro - Felipe Noronha Tavares |
| Cargo | Faculdades Ibmec-RJ, Rio de Janeiro, RJ, Brasil and Banco Central do Brasil - Central Bank of Brazil, Rio de Janeiro, RJ, Brasil - Ibmec Business School, Rio de Janeiro, RJ, Brasil - Brazilian Development Bank (BNDES) |
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Assessing Day-to-day Volatility: Does the Trading Time Matter?
(Avaliando a Volatilidade Diária dos Ativos: A Hora da Negociação Importa?)
José Valentim Machado Vicente*
Gustavo Silva Araújo**
Paula Baião Fisher de Castro*** Felipe Noronha Tavares****
Abstract
The aim of this study is to examine whether investors have distinct perceptions about the daily volatility of an asset. In order to capture the uncertainty faced by these investors, we define the volatility perceived by investors as the distribution of standard deviations of daily returns calculated from intraday prices collected randomly. We find that this distribution has a high degree of dispersion. This means that different investors may not share the same opinion regarding the variability of returns of the same asset. Moreover, the close-to-close volatility is often less than the median of the volatility distribution perceived by investors while the open-to-open volatility is greater than that statistic. From a practical point of view, our results indicate that volatilities estimated using traditional samples of daily returns
(i.e., close-to-close and open-to-open returns) may not do a good job when used as inputs in financial models since they may not properly capture the risk investors are exposed.
Keywords: volatility; risk; uncertainty.
JEL code: G1.
Submetido em 26 de novembro de 2013. Reformulado em 7 de março de 2014. Aceito em 9 de março de 2014. Publicado on-line 2 june 2014. O artigo foi avaliado segundo o processo de duplo anonimato além de ser avaliado pelo editor. Editor responsável: Ricardo
P. C. Leal. The views expressed in this paper are those of the authors and not necessarily reflect those of the Central Bank of Brazil or the Brazilian Development Bank.
*Faculdades Ibmec-RJ, Rio de Janeiro, RJ, Brasil and Banco Central do Brasil. E-mail: jose.valentim@gmail.com
**Central Bank of Brazil, Rio de Janeiro, RJ, Brasil. E-mail: gustavo.araujo@ bcb.gov.br
***Ibmec Business School, Rio de Janeiro, RJ, Brasil. E-mail: paulabfcastro@ gmail.com
****Brazilian Development Bank (BNDES). E-mail: fnoro@bndes.gov.br
Rev. Bras. Finanças (Online), Rio de Janeiro, Vol. 12, No. 1, March 2014, pp. 41–66 ISSN 1679-0731, ISSN online 1984-5146
c
[circlecopyrt]2014 Sociedade Brasileira de Finanças, under a Creative Commons Attribution 3.0 license -http://creativecommons.org/licenses/by/3.0
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Vicente, J., Araújo, G., Castro, P., Tavares, F.
Resumo
O objetivo deste estudoé examinar se investidores que negociam diariamente, mas em momentos diferentes, têm percepçôes distintas acerca do risco de um ativo. A fim de capturar as incertezas enfrentadas por esses investidores, definimos a volatilidade percebida como a distribuição de desvios-padrão de retornos diários calculados a partir de preços intradiários coletados aleatoriamente. Nós concluímos que essa distribuição tem um alto grau de dispersão. Isso quer dizer que diferentes investidores podem não ter a mesma opinião sobre a variabilidade dos retornos do mesmo ativo. Além disso, a volatilidade close-to-closeé muitas vezes menor que a mediana da distribuição de volatilidade percebida pelos investidores, enquanto a open-to-opené maior que essa estatística. De um ponto de vista prático, nossos resultados indicam que as volatilidades estimadas com o uso de amostras tradicionais de retornos diários (ou seja, retornos close-to-close e open-to-open) podem não fazer um bom trabalho quando empregadas em mode-los financeiros, já que podem não captar os riscos aos quais os investidores estão expostos.
Palavras-chave: volatilidade; risco; incerteza.
1. Introduction
Since the seminal work of Markowitz (1952), the volatility of asset returns has played an important role in modern financial theory, particularly in pricing models, portfolio selection and risk management. Volatility is an unobservable variable that reflects the degree of variation in prices of a given asset at a certain time period. Undoubtedly, it is the simplest way to quantify the uncertainty of an asset payoff.1Several studies propose models to estimate volatility.2 In general, when these volatility models are used in practical applications they are estimated with daily data, commonly using the closing price, as noted by Goodhart & O´Hara (1997). However, this procedure has some drawbacks. For example, Parkinson (1980) shows that the volatility estimated using the highest and lowest prices of the days is superior to the close-to-close volatility. Wood et al. (1985) and Lockwood & Linn (1990) show that higher stan-1There is no consensus on what risk and uncertainty mean. Several definitions of these concepts have been proposed. For instance, Knight (1921) distinguishes risk and uncertainty. Knightian uncertainty is risk that is immeasurable. Bekaert et al. (2009) define uncertainty as changes in the fundamentals. In this work we follow a more casual approach. The terms risk and uncertainty are used interchangeably. Risk and uncertainty just mean the dispersion of an asset’s payoff.
2Among others, we can cite the works of Engle (1982) and Bollerslev (1986), which led to the development of the GARCH model and its variants.
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Assessing Day-to-day Volatility: Does the Trading Time Matter?
dard deviations are observed at the beginning and at the end of the trading session, i.e., volatility has a U-shaped pattern throughout the day. Brown (1990) argues against the use of the closing prices since they can be influenced by the lack of trading at the close or by “marked on the close” orders. Guillaume et al. (1994) and Andersen & Bollerslev (1998) observe that the series of intraday returns have different characteristics for different periods of the day. They warn that this intraday seasonality should be corrected to avoid distortions in the volatility estimation.
In this paper we revisit these criticisms from a different point of view. As in other studies, we calculate volatility from a series of daily prices. Therefore, we have the same amount of information used by models which estimate volatility from closing or opening prices. However, instead of prices being collected at a fixed time, we randomly select the time that it is observed each day. With these prices, we calculate the realized volatility of the asset return in a given period (set as one month in the empirical exercise of Section 3).3 Next we repeat this experiment, i.e., we draw another sequence of random daily prices and calculate a new volatility for the same period. From a sequence of draws, we build a probability distribution of volatility. We call this distribution the volatility distribution perceived by investors (VDPI). This distribution is the focus of our paper.
Note that the selection procedure described in the previous paragraph better approximates the daily volatility perceived by investors. An investor does not trade (or look at the market) only at the beginning or at the end of the trading session. In fact, there is no reason for the buying and selling decisions to occur at a specific time. In this sense, we believe the volatility calculated from a random sampling of daily prices as the real volatility perceived by investors.
A tale may shed some light on the reason why the volatility calculated with prices collected at random moments represents the volatility perceived by an investor. Suppose an investor negotiates a single share over a month once a day. The time of the trade is determined, for example, when the price reaches thresholds (above an upper limit she sells and below a lower limit she buys). If at the end of this month we ask the investor what the perceived asset volatility is, the answer will be the standard deviation of daily returns calculated based on the prices actually negotiated. In other words, her perception of uncertainty is one draw from VDPI. If this volatility is
3The realized volatility of the asset return in a given period is the standard deviation of the series of returns observed in this period.
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Vicente, J., Araújo, G., Castro, P., Tavares, F.
much higher or much lower than the close-to-close volatility, the investor’s perception of the uncertainty of this share is undoubtedly different from that calculated by a market analyst who uses closing prices.
Let’s look at a more realistic example. Suppose a hedge fund evaluates its risk by the Value-at-Risk (VaR) metric. Suppose further that VaR is estimated from a parametric model in which the volatility of the portfolio is obtained from the closing prices. However, the hedge fund does not necessarily negotiate assets at the close of the market. The trades are conducted according to the manager’s strategy and can happen at any time during the session. Therefore, the VaR model may not do a good job, i.e., it may not adequately capture the uncertainty faced by the hedge fund.
Our goal in this paper is to study the dispersion of the distribution of the daily volatility perceived by investors. Additionally, we compare the volatility calculated from daily prices randomly selected with the volatility calculated from opening and closing prices. More specifically, we investigate the location of the open-to-open and the close-to-close volatilities on the VDPI. This allows us to evaluate whether these volatilities can be a good representation of the uncertainty perceived by an arbitrary investor.
Harris (1986), Amihud & Mendelson (1987), Lockwood & Linn (1990), Hong & Wang (2000), among others, present comparisons between the open-to-open and close-to-close volatilities. They show that the open-to-open returns are more volatile than close-to-close returns. Besides replicating this result our study extends these works since the...
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