We investigate the two components of the total daily return (close-to-close), the overnight return (close-to-open) and the daytime return (open-to-close), as well as the corresponding volatilities of the 2215 NYSE stocks from 1988 to 2007. The tail distribution of the volatility, the long-term memory in the sequence, and the cross-correlation between different returns are analyzed. Our results suggest that: (i) The two component returns and volatilities have similar features as that of the total return and volatility. The tail distribution follows a power law for all volatilities, and long-term correlations exist in the volatility sequences but not in the return sequences. (ii) The daytime return contributes more to the total return. Both the tail distribution and the long-term memory of the daytime volatility are more similar to that of the total volatility, compared to the overnight records. In addition, the cross-correlation between the daytime return and the total return is also stronger. (iii) The two component returns tend to be anti-correlated. Moreover, we find that the cross-correlations between the three different returns (total, overnight, and daytime) are quite stable over the entire 20-year period.
Deep Dive into Statistical analysis of the overnight and daytime return.
We investigate the two components of the total daily return (close-to-close), the overnight return (close-to-open) and the daytime return (open-to-close), as well as the corresponding volatilities of the 2215 NYSE stocks from 1988 to 2007. The tail distribution of the volatility, the long-term memory in the sequence, and the cross-correlation between different returns are analyzed. Our results suggest that: (i) The two component returns and volatilities have similar features as that of the total return and volatility. The tail distribution follows a power law for all volatilities, and long-term correlations exist in the volatility sequences but not in the return sequences. (ii) The daytime return contributes more to the total return. Both the tail distribution and the long-term memory of the daytime volatility are more similar to that of the total volatility, compared to the overnight records. In addition, the cross-correlation between the daytime return and the total return is also st
Financial markets are of great importance for economics and econophysics research [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]. A key topic of the market studies is the price dynamics, which could be measured by the price change ("return") and its magnitude ("volatility") [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20].
Especially, the volatility has important practical implications. For example, it is the key input for option pricing models such as the classic Black-Scholes model and Cox, Ross, and Rubinstein binomial models [16,17]. Usually financial markets are closed during the night, and all news or events in the night are reflected in the opening price of the next trading day.
A day (from former day closing to current day closing) therefore can be decomposed into two sessions, overnight (from former day closing to current day opening) and daytime (from current day opening to closing) sessions. The study of the returns and the volatilities during these two sessions might provide new insights towards better understanding of the financial markets. Practically, this study can help traders to improve trading strategies at the market opening and closing. It also can help investors to analyze the dually-traded equities [19].
Recently there were some studies on the returns and volatilities over sub-day sessions.
George and Hwang decomposed the daily return of 200 Japanese stocks and analyzed their volatility patterns [18]. Wang et. al. studied 15 stocks which are traded in both Hong Kong and London but in different hours [19]. However, there is still lack of a comprehensive analysis of the overnight and daytime price change for a leading market such as the New York Stock Exchange (NYSE). For the daily and high-frequency intraday data, returns and volatilities of stock prices are well studied [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]. These studies show that the return and volatility distribution decay as power laws, and the correlations in the returns disappear after few minutes while the correlations in the volatility time series can exist upto months and even longer [20,21,22,23,24,25]. It is of interest to examine whether these features persist also in the two component returns and volatilities. Obviously one can assume that the overnight price change behaves statistically different from the daytime change. What are the differences? Furthermore, the influence of the overnight price change on the daytime change is also of interest and should be examined.
In this paper we examine the daily data for all stocks traded in NYSE. First we study the fundamental features of the time series, distribution of the records and the correlations in the sequence. Three types of functions, power law, exponential, and power law with an exponential cutoff, are tested for the tail of the volatility distribution. We find that the power law function fits best for most stocks. Then we analyze the long-term memory of each stock using the detrended fluctuation analysis (DFA) method [27,28,29,30], and find that the long-term correlations persist in the volatilities of both components. We show that the distribution and the long-term memory of the daytime volatility is more similar to the total volatility, compared to the overnight volatility. Further, we study the cross-correlations between the three types of returns (total, overnight, and daytime). The two component returns are found to be weakly anti-correlated but both overnight and daytime return are strongly correlated with the total return. Interestingly, we find that this behavior is quite stable during the entire 20-year period.
We collect the daily opening and closing prices of all securities that are listed in NYSE on December 31, 2007, in total 2215 stocks [31]. The record starts from January 2, 1962, but many stocks have a much shorter history. We do not include the data before 1987 period for two reasons. First, from 1962 to 1987 there exist only very little data, about 6.5% of all the data points for these 2215 stocks. Second and more important, there was a huge market crash on October 19, 1987 (“Black Monday”), and after that the market was adapted in a great extent. Thus, to reduce the complexity of market structure, we only examine the data from 1988 to 2007, in total 20 years. The length of the 2215 stocks ranges from N = 1000 to 5000 trading days. Note that many stocks have splits in the 20-year period, which causes significant change in the price. Therefore, we adjust all prices according to the historical splits. The 2215 stocks cover all industrial sectors, a wide range of the stock market capitalization (from 6 × 10 6 to 5 × 10 11 dollars), and a wide range of the average daily volume (from 500 to 2 × 10 7 shares a day). Now we define two basic measures, return R and volatility V . The daily return is the logarithmic change of the successive daily closing prices (“total return”), R T (t) ≡ ln(p close (t)/p close (t -1));
(1) the re
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