*3.10. Volume and Volatility*

Fong and Wong (2007) applied the volatility–volume regressions to the daily realized volatility of common stocks to study sources of volatility predictability. They found that unexpected volume can explain half of the variations in realized volatility and that the ARCH e ffect is robust in the presence of volume.

Xiao et al. (2009) studied the relationship between volume and volatility in the entire Australian Stock Market for di fferent firm size and trading volume. They found that daily trading volume has significant explanatory power on the variance of daily returns. Actively traded stocks having a larger number of information arrivals per day will have a larger impact of volume on the variance of daily returns. Low trading volume and small firm lead to a higher persistence of GARCH e ffects, unlike the elimination e ffect for the top most active stocks. In general, the elimination of both ARCH and GARCH e ffects by introducing the volume variable on all other stocks, on average, is not as much as that for the top most active stocks. The elimination of both ARCH and GARCH e ffects by introducing the volume variable is higher for stocks in the largest volume and/or the largest market capitalization quartile group. Their empirical findings rejected the pure random-walk hypothesis for stock returns, and they concluded that the relationship between volume and volatility is not a statistical fluke. Unlike most anomalies, the volume e ffect on volatility is not likely to be eliminated after its discovery.

#### *3.11. Trading Rules and Technical Analysis*

If investors could make significant profit when they use any tool in technical analysis, adopt any trading rule, or employ any indicator in their investment, then we will consider this is an anomaly because this shows that the market is not e fficient so that investors could have opportunity to make profit. There are many studies in this area. We list a few here.

We first discuss the adaptation of indicators and trading rules. For instance, Wong et al. (2001) introduced a new stock market indicator by using both E/P ratios and bond yields, and developed two statistics to test the following hypotheses:

#### **Hypothesis 1 (H1).** *Using the proposed indicator could make significantly good profit from the markets.*

#### **Hypothesis 2 (H2).** *Using the proposed indicator could beat the buy-and-hold (BH) strategy.*

In order to test the hypotheses, they examined the performance of their proposed indicator in five di fferent stock markets, namely the UK, USA, Japan, Germany, and Singapore stock markets. Firstly, from their empirical study, they did not reject the hypothesis H1 in (i) and concluded that their indicator could produce buy and sell signals that investors could escape from most, if not all, of the major crashes, catch many of the bull markets, and generate significantly good profit.

Thereafter, they conducted an analysis to test the hypothesis H2 in (ii), and their analysis led them not to reject the hypothesis in (ii) and to conclude that their proposed indicator performs better than the BH strategy, because using their proposed indicator enabled investors to make significant higher profit then the BH strategy.

McAleer et al. (2016) developed some new indicators, or new trading rules, that can profiteer from any main financial crisis, and they examined the applicability of their proposed indicators/trading rules on the 1997 Asian Financial Crisis (AFC), the 2000 dot-com crisis (DCC), and the 2007 Global Financial Crisis (GFC). They examined the two hypotheses H1 and H2 in (i) and (ii) with their proposed indicators.

The empirical study did not reject (i) and concluded that using the signals generated by their proposed indicators/trading rules generate significantly good profit from the markets during AFC, DCC, and GFC. Their empirical study also did not reject (ii), and they concluded that their proposed indicators/trading rules beat the BH strategy, because by using their proposed indicators/trading rules, investors could make very huge profit from the markets during AFC, DCC, and GFC; nonetheless, by adopting the BH strategy, all the profits are eaten up by the downtrend of the crisis and investors end up not having any profit or even bear big loss.

Chong et al. (2017) developed a new market sentiment index by using HIBOR, short-selling volume, money flow, the turnover ratio, the US and Japanese stock indices, and the Shanghai and Shenzhen Composite indices. Thereafter, they used the index as a threshold variable to determine di fferent states in the market and applied the threshold regression to generate buy-and-sell signals. They illustrated the applicability of their proposed trading rules on the HSI or S&P/HKEx LargeCapIndex by testing the two hypotheses H1 and H2 in (i) and (ii), with the now-proposed indicator as their proposed approach.

Their empirical study did not reject (i), and they concluded that the use of their proposed approach generated significant profit from the Hong Kong market; the study did not reject (ii), and it concluded that their proposed approaches beat the BH strategy when investors buy the stock indices when the sentiment index is smaller than the lower threshold value, and vice versa.

Using both intraday and daily data, Lam et al. (2007) examined both surges and plummets of stock price and construct momentums and five trading rules of trading in stocks. They found that all their proposed trading rules cannot ge<sup>t</sup> any significant profit in both European and American stock markets but can ge<sup>t</sup> significant profit from the Asian stock markets. Their findings accept market for European and American stock markets but reject e fficiency in the Asian stock markets, implying that the Asian stock markets are not as e fficient as American and European stock markets.

There are many trading rules. An easy one is the single lump-sum investment rule (LS) that one invests all the fund at the beginning. Another popular one is the dollar-cost averaging investment rule (DCA) in which, regardless of ups and downs in the markets, one invests a fixed amount of money periodically over a given time interval in equal installments. This approach could avoid risk and the devastating e ffect when the market crashes suddenly. The literature shows that the LS rule outperforms the DCA rule when the market is uptrend, and the DCA rule outperforms the LS rule when the market is downtrend or mean-reverted.

Does the LS rule really outperform the DCA rule when the market is uptrend? Lu et al. (2020) conjectured that the DCA rule could still outperform the LS rule when the market is uptrend. To show that their conjecture could hold true, they applied both Sharpe Ratio (SR) and economic performance measure (EPM) and compared the performance of both LS and DCA rules in both accumulative and disaccumulative situations. They showed that, when the trend is not too upward, the DCA rule performs better than the LS rule in almost all the situations. In addition, when the market is uptrend, the DCA rule could still outperforms the LS rule in many situations, especially when volatility is high and when longer investment horizon is chosen.

Thus, the authors concluded that their conjecture hold true that the DCA rule could outperform the LS rule in many situations even in the situation the market is in the uptrend. Together with the findings in the literature that the DCA rule outperforms the LS rule when the market is downtrend or mean-reverted, the authors recommended that investors not choose the LS rule but use the DCA rule in their investment.

We note that one could apply the rules in the above papers to make good profit in their studying periods. If this is the case, then we will consider this is an anomaly, because this shows that the market is not e fficient so that investors could have opportunity to make profit. However, there is a chance that the rules may not be able to make money after the rules released. If this is the case, then the market is still e fficient and the anomaly disappears. Now, we turn to discuss using technical analysis (TA) to generate profit.

There are many studies that show that technical analysis can be used to generate profit. For example, to examine whether TA is profitable, Wong et al. (2003) used two popular technical tools—moving average (MA) and relative strength index (RSI)—and introduced two statistics to test the two hypotheses, H1 and H2, in (i) and (ii), with the now-proposed indicators MA and RSI. Using the data from the Singapore stock market, they accepted both H1 and H2 and concluded that both MA and RSI could be used to make significantly positive profit and both MA and RSI beat the BH strategy significantly.

In addition, to examine whether TA is profitable, Wong et al. (2005) examined the performance of di fferent MAs in the Taiwan, Shanghai, and Hong Kong stock markets and tested the hypotheses H1 and H2 in (i) and (ii) with the now-proposed indicators, are MA rules from MA family, by using the Greater China data. Their empirical findings did not reject H1, and they concluded that, in general, all MAs from the entire MA family can generate significantly positive profit and accept H2, and conclude that, in general, all MAs from the entire MA family generate significantly higher profit than the BH strategy in the two subperiods before and after the 1997 AFC, and in the entire period, as well as in all the bull, bear, and mixed markets.

Moreover, they conducted a wealth analysis and examined how much more wealth one can ge<sup>t</sup> by using all the MA rules from the entire MA family and concluded that di fferent MA rules could yield di fferent cumulative wealth, which could be as much as hundreds of times more than that obtained by choosing the BH strategy, when transaction costs have been considered. Without considering transaction costs, the cumulative wealth is much higher. Their findings and observations imply that the MA family is useful in investment that can create significant higher wealth so that we can reject market e fficiency in the Greater China markets.

Like many other studies in TA rules, the above studies conclude that the TA rules are useful and can generate higher profit so that we can consider this is an anomaly. Nonetheless, not all studies make the same conclusions. Some could conclude that TA rules are not useful or at least not useful in some periods or in some markets. For example, to test the hypotheses H1 and H2 in (i) and (ii), Kung and Wong (2009a) made the following conjecture:

#### **Conjecture 1.** *Using TA rules may not be able to generate significant profit recently and the anomaly is disappearing.*

In order to test whether their conjecture holds true, they applied three most commonly used MA rules and tested whether using these three MAs rules could enable investors to make a significant profit in all the periods they studied in the Singapore stock market. From their empirical study, they did accept H1 in (i) and concluded that using the three MAs did generate significantly higher profit in the 1988–1996 period, but they reject H1 in (i), and they concluded that the three MAs did not generate significantly higher profit in the 1999–2007 periods.

In addition, their analysis led them to accept H2 in (ii) and conclude that using the three MAs did generate significantly higher profit than adopting the BH strategy in the 1988–1996 period, but they rejected H2 in (ii) and concluded that the three MAs did not generate significantly higher profit than adopting the BH strategy in the 1999–2007 periods. Based on their findings, market e fficiency was rejected before the 1997 AFC, but was rejected for the period after the 1997 AFC in the Singapore stock market. This could mean that the anomaly is disappearing after the trading rules being introduced.

In addition, to test the hypotheses H1 and H2 in (i) and (ii) and test whether Conjecture 1 holds true, Kung and Wong (2009b) conducted a similar analysis in the Taiwan market. From their analysis, H1 in (i) was strongly accepted, and they concluded that the two popular TA rules could be used to generate significant profit in the 1983–1990 period. However, H1 in (i) was not so strongly accepted in the 1991–1997 period, and they concluded that the two popular TA rules could be used to generate only marginally significant profit in the 1991–1997 period.

Moreover, H1 in (i) was strongly rejected in the 1998–2005 period, and they concluded that the two popular TA rules could not be used to generate any significant profit in the 1998–2005 period. Based on their findings, market e fficiency was strongly rejected in the 1983–1990 period, weakly rejected in the 1991–1997 period, and strongly accepted in the 1985–2005 period for the Taiwan stock market. Thus, the empirical findings from Kung and Wong (2009a, 2009b) support their conjecture that using TA rules could be useful in the past, but it may not be able to generate significant profit recently, and the anomaly is disappearing. Readers may refer to Chan et al. (2014) for further information.
