Volume, Variance, and the Combined Signal Approach to Technical Analysis

Transcription

1 Journal of Money, Investment and Banking ISSN X Issue 7 (2009) EuroJournals Publishing, Inc Volume, Variance, and the Combined Signal Approach to Technical Analysis Camillo Lento Faculty of Business Administration, Lakehead University Thunder Bay, Ontario, Canada clento@lakeheadu.ca Tel: ; Fax: Abstract This paper examines the impact volume and variance on the profitability of the Combined Signal Approach (CSA) to technical analysis. The volume and variance tests are conducted on the S&P 500 and NASDAQ from January 1990 to March 2008 (n=4,558). The results suggest that the profitability of the CSA is enhanced when employing either volume or variance into the trading model. Jointly employing volume and variance was not able to provide a significant improvement in profits over the employment of volume or variance alone; this is partially the result of the correlation between volume and variance. Keywords: Technical Analysis; Combined Signal Approach; Trading Volume; Variance; S&P 500. JEL Classification Codes: C15; G11; G14 1. Introduction Technical analysis is a method of forecasting security prices by utilizing past prices, volume, and open interest. Pring (2002), a leading technical analyst researcher, provides a comprehensive definition: The technical approach to investment is essentially a reflection of the idea that prices move in trends that are determined by the changing attitudes of investors toward a variety of economic, monetary, political, and psychological forces. The art of technical analysis, for it is an art, is to identify a trend reversal at a relatively early stage and ride on that trend until the weight of the evidence shows or proves that the trend has reversed. (p. 2) Since Charles H. Dow first introduced the Dow Theory in the late 1800s, technical analysis has been extensively used among market participants such as brokers, dealers, fund managers, speculators, and individual investors in the financial industry. Technical analysis became an academic interest in the mid-1960s when Alexander (1964) and Fama and Blume (1966) began testing technical trading rules. Both of these pioneering studies suggested that excess returns could not be realized by making investment decisions based on the movements of certain sizes after adjusting for transaction costs. The number of influential studies grew in the 1990s, with many of these studies supporting the informational content of technical trading rules (Brock, LeBaron and Lakonishok (1992), Lisi and Medio (1997), Gençay (1999), Lo, Mamaysky and Wang (2000), and Lento, Gradojevic, and Wright (2007)).

2 Journal of Money, Investment and Banking - Issue 7 (2009) 76 Since its inception, various individual trading rules have emerged from technical analysis. Some of the more common trading rules include the moving average cross-over rule, the trading range break-out rule, and the filter rule. Although many individual technical trading rules have been developed, only recently has Lento and Gradojevic (2007) developed a Combined Signal Approach (CSA) to technical analysis that is based on combining individual trading rules to form a consensus buy or sell signal. The CSA has been tested in the North American markets (Lento and Gradojevic, 2007; Lento, 2008) and the Asian-Pacific equity markets (Lento, 2009) where it has been shown that the CSA approach appears to increase the profitability of the individual trading rules and also eliminates a trader s decision regarding which individual trading rule to rely upon. It is likely that the CSA performs better than individual signals alone because information related to future price moves is dispersed among various trading rules. This paper builds on the original CSA model by investigating whether the daily volume and variance, (as measured by the VIX) can be used to improve the profitability of the CSA trading signals. Profitability is defined as returns in excess of the buy-and-hold trading strategy. The volume tests are conducted on the S&P 500 and the NASDAQ for the period of January 1990 to March 2008 (n=4,558). The tests are conducted on this dataset because the VIX was introduced in the 1990s. The results suggest that both above average volume and volatility increase the strength of the CSA s buy and sell signals. For both the S&P 500 and the NASDAQ, volume and variance increased profitability in three of the five CSA variants tested. The increased profitability is significant, in many cases in excess of 3.0% per annum. The remainder of the paper is organized as follows. The next section describes the combined signal approach to technical analysis. Section 3 describes the data. Section 4 explains the methodology. Section 5 presents the results. Conclusions and recommendations for future research in Section The Combined Signal Approach, Volume, and Variance 2.1. The Combined Signal Approach Many researchers and technicians have argued that a single trading rule should not be used alone to make trading decisions (Murphy, 2000). One of the major concerns with utilizing only one trading rule is that there is no theory to guide an investor when making a decision amongst the many different types of trading rules. For example, there is no theoretical framework for choosing a filter rule over the Bollinger Band rule. Furthermore, once a rule is selected, it is not clear how to choose the underlying parameters (e.g. 1-percent filter, 3% filter, etc). This problem may be mitigated by jointly employing individual trading rules to develop a combined signal. Essentially, the CSA combines a number of individual signal s long and short forecast into a single trading rule based on the consensus of the individual signals. The CSA is based on the notion that information related to future price movements is somewhat dispersed among many trading rules. Therefore, combining trading signals may generate a more informative signal than various trading rules. It is possible that the combination of individual technical trading rules provides a synthesis whereby the whole is greater than the sum of the parts and excess profits can be generated (Lento and Gradojevic; Lento, 2008; Lento 2009). Furthermore, combining multiple signals also reduces the risk of selecting and relying on a single rule at any given time. The CSA requires an investor to buy a stock or index when there is a buy consensus among a number of different trading signals, and to sell a stock or the market when a sell consensus appears. For example, investors can use five trading rules e.g., two moving average crossovers, a percentage filter rule, moving average convergence divergence (MACD), and Bollinger Bands to develop a combined signal that triggers a long signal when three of the five rules are bullish. Or, a trader can also use a stricter version that requires four of the five signals to agree on a position.

3 77 Journal of Money, Investment and Banking - Issue 7 (2009) The CSA offers an opportunity to earn profits even when individual trading signals are unprofitable. The CSA was first developed by Lento and Gradojevic (2007) who tested the CSA on the Dow Jones Industrial Average (DJIA), the NASDAQ, Toronto Stock Exchange (TSX), along with the US-CAD foreign exchange rate. The CSA was profitable for the NASDAQ and TSX, whereas the results were mixed on the DJIA. The CSA was also profitable in the foreign exchange market. The Asian-Pacific equity markets provided fertile grounds for additional testing of the profitability of the CSA. The CSA was tested in eight Asian-Pacific equity markets (All Ordinaries, BSE, Hang Seng, Jakarta, KOPSI, Nikkei, Straits Times, and TSEC) and the results reveal that the CSA was profitable in all equity markets tested except for the All Ordinaries (Lento, 2009). The CSA was also extensively tested on the S&P 500 for a fifty year period (Lento, 2008). The robust results again support the profitability of the CSA. Variants of the CSA were profitable on the S&P 500 over the entire fifty-year time series even though the individual trading rules alone were not profitable. In all of the above mentioned CSA tests, the CSA has been comprised of nine trading rule variants: three moving average cross over rule variants, three filter rule variants, and three trading range break-out rule variants. Brock, Lakonishok, & LeBaron (1992) ( BLL ) discuss the potential biases that can arise from identifying and testing patterns in security returns in the same dataset. As such, the same trading rules as BLL were utilized to test the CSA, along with three common filter rules. The intention was to reduce the possibility of data snooping as the datasets were not searched for successful trading rules ex-post. These same trading rule variants will be used in this study as well to maintain consistency in comparing results Individual Trading Rules The following section describes the three trading rules, along with their variants, that are used to form the CSA. A moving average cross-over (MAC-O) rule compares a short moving average to a long moving average. The MAC-O rule tries to identify a change in a trend. The MAC-O generates a buy (sell) signal whenever the short average is above (below) the long average as follows: Equation 1 VMA Buy Signal S L R s =1 i, t R > l = 1 i, t 1 =Buy, (1) S L Equation 2 VMA Sell Signal S =1, L = R s i t R < l 1 i, t 1 =Sell, (2) S L where R i,t is the log return given the short period of S (1 or 5 days), and R i,t-1 is the log return over the long period L (50, 150 or 200 days). The following short, long combinations will be used to develop the three MAC-O variants: (1, 50), (1, 200) and (5, 150). Filter rules generate buy and sell signals based on the following logic: Buy when the price rises by ƒ per cent above the most recent trough and sell when the price falls ƒ per cent below its most recent peak. The filter size (ƒ) is the parameter that defines a filter rule. This study employs the filter rule based on three parameters to be included in the CSA. The parameters are: 1-per cent, 2-per cent, and 5-per cent. The trading range break-out (TRB-O) rule, also referred to as resistance and support levels, generates a buy signal when the price breaks-out above the resistance level and a sell signal when the price breaks below the support level. The resistance level is defined as the local maximum, and the support level is defined as the local minimum (BLL). At the resistance (support) level, intuition would suggest that many investors are willing to sell (buy). The selling (buying) pressure will create resistance (support) against the price rising (falling) above the peak (trough) level. The TRB-O rule

4 Journal of Money, Investment and Banking - Issue 7 (2009) 78 variants used to develop the CSA are based on a local maximum and minimum of 50, 150 and 200 days as defined in Equation 3. Equation 3 Trading Range Break-Out Positions Pos t+1 = Buy, if P t > Max {P t-1, P t-2,, P t-n } Pos t+1 = Pos t, if P t > Min {P t-1, P t-2,, P t-n } Pt Max {P t-1, P t-2,, P t-n } Pos t+1 = Sell, if P t < Min {P t-1, P t-2,, P t-n } (3), where P t is the stock price at time t Volume, variance and the technical trading rules Volume has been incorporated into many tests of technical analysis; however there are very few studies that incorporate the variance statistics into the trading signal to determine if excess profits are available. One of the first studies on volume was conducted by Pruitt, Tse, and White (1992) who tested the CRISMA model, which includes cumulative volume, along with relative strength and moving averages. After adjusting for transaction costs, the CRISMA model outperformed the naïve buy-and-hold trading model and earned annual mean excess returns of 1.0% to 5.2% in stock markets for Blume, Easley, and O Hara (1994) used volume more directly by developing an equilibrium model that emphasizes the informational content of volume and technical analysis. The results of the model suggest that volume provides information about the quality of traders information that price along cannot convey. A corollary from this study is that simultaneously observing both price and the volume can be more informative than analyzing solely the price. Gencay and Stengos (1998) incorporated a 10-day volume average indicator into a nonlinear feedforwad network model as an additional regressor. The nonlinear model produced an average of 12% forecast gain over a benchmark OLS model with lagged returns as regressors. The model also provided much higher correct sign predictions (an average of 62%) than other models. However, not all of the literature supports the informational content of volume. For example, Lo, Mamaysky, and Wang (2000) suggest the opposite about volume, particularly that volume trends appear to provide little incremental information with a few exceptions. Therefore, the literature appears to be inconclusive on whether incorporating volume into a trading model should increase profitability. Unlike volume, there are very few studies that incorporate variance into a technical trading model. One such study was conducted by Glenn (2008) who devised a trading strategy that incorporates an index fund s variance. The method makes no use of short sales or option trading and focuses on a buy-the-market and hold strategy when measured volatility is low. When this condition is violated, a moving average look-back (MALB) algorithm is employed. The method can be used by conservative investor in equities to help harvests most of the potential gain in bull markets while avoiding most of the pain in a bear market Incorporating volume and variance into the CSA The CSA has never been tested in conjunction with volume and variance measures. All of the past CSA studies have focused on historical prices alone. However, volume and variance have been shown to have some informational content and an ability to increase the profits from technical analysis that relies on past prices alone (Pruitt, Tse, and White, 1992; Blume, Easley, and O Hara, 1994; Glenn, 2008). Therefore, incorporating volume and variance information into the determination of the CSA may be able to increase profits as in the case with the individual rules alone. This reasoning leads to the following hypothesis: H 1 : Incorporating volume and variance metrics into the determination of the Combined Signal Approach should generate a more powerful signal. The following empirical study is conducted to test the hypothesis.

5 79 Journal of Money, Investment and Banking - Issue 7 (2009) 3. Methodology Profitability is determined by comparing the returns generated by the trading signals to the buy-andhold return. The methodology relies on this relatively simple technique for analyzing the profitability of the trading rules because of the possible problems related to non-linear models such as computational expensiveness, overfitting, data snooping and difficulties interpreting the results (see White (2005) for a thorough discussion of these issues). As such, the returns are subject to sophisticated tests of significance. The returns from the buy-and-hold strategy are calculated by investing in the security at the beginning of the data set, given the trading rule parameters, and holding the security until the end of the data set. The returns from the Combined Signal Approach are calculated as follows. The CSA requires an investor to buy a stock or index when there is a buy consensus among each on the nine individual trading rules, and to sell the market when a sell consensus appears. For example, an investor is assumed to be long the market when x of the nine trading rules all agree on a long position. If x of the nine trading rules do not agree on a long position, then the investor is assumed to be out of the market. An investor s returns will be calculated based on an average, nominal interest rate of 3 percent per annum while out of the market. Therefore, various CSA models can be developed based on the parameter x. This study tests the CSA with the x consensus parameter of 2, 3, 4, 5, and 6. The CSA (2,9) is the least restrictive in that it requires that only two of the nine individual trading rules agree on a long position, while the CSA (6,9) is the most strict version of the approach in that it requires six of the nine individual trading rules to agree on a long position. It is important to note that an investor is assumed to be long the market in the day following the CSA signal agreeing upon a position. This assumption is required because the closing daily prices are used as inputs into the model. To adjust the CSA for volume and variance statistics, the buy or sell signal generated will only be acted upon if the volume or variance in the trading day that the signal is generated is in excess of 200-day historical average. Volume is measured as the number of trades per day, while volatility is measured by the VIX (Chicago Board of Trade volatility index). Similar to Gencay (1998), the returns generated from the CSA are adjusted for transaction costs. Both the bid-ask spread and brokerage trading costs are included into the total transaction cost. The bid-ask spread for the S&P 500 and NASDAQ exchange traded fund is used as a proxy for the actual index. The returns are adjusted downward when a trade is triggered. This adjustment factor approximates the average transaction costs for these securities. The significance of the results is tested by using the bootstrap approach developed by Levich and Thomas (1993). This approach, first, observes the data set of closing prices, with the sample size denoted by N+1 that corresponds to a set of N returns. The m th (m=1,,m) permutation of these N returns (M=N!) is related to a unique profit measure (X[m, r]) for the r th trading rule variant (r = 1,,R) used in this study. Thus, for each variable, a new series can be generated by randomly reshuffling the returns of the original series. From the sequence of M returns, the starting and ending points of the randomly generated time series are fixed at their original values. This maintains the distributional properties of the original data. However, the time series properties are random. In this bootstrapping simulation one can thus generate one of the various notional paths that the returns could have taken from time t (starting day) to time t+n (ending day). The notional paths are generated 100 times for each data set. Technical trading rules are then applied to each of the 100 random series and the profits X[m, r] are measured. This process generates an empirical distribution of the profits. The profits calculated on the original data sets are then compared to the profits from the randomly generated data sets. A simulated p-value is produced by computing the proportion of returns generated from the simulated series that is greater than the return computed with the actual series.

6 Journal of Money, Investment and Banking - Issue 7 (2009) Data Description The technical trading rules are tested on the S&P 500 and the NASDAQ for the period of January 1990 to March The tests are conducted on this dataset because the VIX was introduced in the 1990s. There are a total of 4,588 observations of daily stock returns. The trading rules can be calculated at various data frequencies. Investors can use highfrequency data, such as intra-day data, or longer horizons, such as weekly or yearly, when using the trading rules. The data frequency selected by a technical investor depends on many different factors and personal preferences. This research study utilizes daily closing prices. The 18 year period provides a sufficient number of daily observations to allow for the formation, recurrence and investigation of the technical trading rules. The daily returns are calculated as the holding period return of each day as follows: Equation 4 Daily Holding Period Return r t = log (p t ) log (p t -1 ) (4) where p t denotes the market price. 5. Empirical Results 5.1. The unadjusted CSA While utilizing all nine individual trading signals, the CSA was employed using the following decision rule: a long position is taken if x or more of the 9 trading rules suggest a long position. The CSA was tested for the following: (2,9), (3,9), (4,9), (5,9), and (6,9). There were not enough observations at the (7,9) or greater to allow for robust testing. Table 1 presents the returns generated by the CSA. Table 1: Profitability of the Unadjusted Combined Signal Approach (CSA) Panel A: Profitability of the unadjusted CSA on the S&P 500 CSA (Comparison) S&P500 (N = 4,588) No Transaction Costs Annual Return 12.8% 9.1% 8.4% 9.6% 6.9% Over/(Under) Performance 2.0% (1.7%) (2.4%) (1.2%) (3.9%) p-value S&P500 (N = 4,588) Transaction Costs Annual Return 11.2% 7.1% 6.3% 7.5% 3.6% Over/(Under) Performance 0.4% (3.7%) (4.5%) (3.2%) (7.2%) p-value Panel B : Profitability of the unadjusted CSA on the NASDAQ CSA (Comparison) NASDAQ (N = 4,588) No Transaction Costs Annual Return 16.0% 15.5% 18.1% 17.9% 17.8% Over/(Under) Performance 3.9% 3.4% 5.9% 5.8% 5.6% p-value NASDAQ (N = 4,588) Transaction Costs Annual Return 13.1% 13.1% 15.5% 14.8% 14.2% Over/(Under) Performance 1.0% 0.9% 3.3% 2.7% 2.1% p-value

7 81 Journal of Money, Investment and Banking - Issue 7 (2009) The results of the unadjusted CSA are consistent with prior studies on the S&P 500 (Lento, 2008) and the NASDAQ (Lento and Gradojevic, 2007). The unadjusted CSA model was more profitable on the NASDAQ than the S&P 500. Before adjusting for transaction costs, the CSA model was able earned profits of 3.9% to 5.9% on the NASDAQ. Even after adjusting for transaction costs, all five variants of the CSA model tested were able to outperform the buy and hold strategy on the NASDAQ. Although transaction costs diminish some or all of the profits, a Bayesian investor could alter his asset allocation in response to this information (Bessembinder and Chan 1998). The CSA was not as profitable on the S&P 500 as only the CSA (2,9) was able to outperform the buy-and-hold trading strategy. It is important to highlight that although the CSA did not generate profits on the S&P 500, the individual trading rules were even less profitable (note: results on the individual trading rules are not presented). The 150-day TRB-O rule was the only rule that matched the performance of the buy-and-hold trading strategy after adjusting for transaction costs. All either other trading rules were unprofitable, most by significant margins. For example, MAC-O (1, 50) lost 7.1% per annum, while 1% filter rule lost 12.1% Incorporating volume and variance into the CSA The volume adjusted CSA returns and variance adjusted returns for the S&P 500 and NASDAQ are presented in Table 2 and Table 3, respectively. The variance and volume were used to adjust the signal such that a buy(sell) signal was only triggered if the volume or variance was in excess of the 200-day moving average (denoted by the number 1) or two times greater than the 200-day moving average (denoted by the number 2). Table 2: Volume, Variance, and the profitability of the Combined Signal Approach (CSA) on the S&P 500 Panel A: Profitability of the volume-adjusted CSA CSA with Vol. > 1 S&P500 (N = 4,588) No Transaction Costs Annual Return 10.0% 13.5% 9.4% 9.2% 10.5% Over/(Under) Performance (0.8%) 2.7% (1.4%) (1.6%) (0.2%) p-value S&P500 (N = 4,588) Transaction Costs Annual Return 8.4% 11.9% 7.5% 7.2% 8.5% Over/(Under) Performance (2.4%) 1.1% (3.3%) (3.6%) (2.2%) p-value CSA with Vol. > 2 No Transaction Costs S&P500 (N = 4,588) Annual Return 10.6% 14.1% 10.1% 9.5% 11.3% Over/(Under) Performance (0.2%) 3.3% (0.7%) (1.2%) 0.5% p-value S&P500 (N = 4,588) Transaction Costs Annual Return 9.0% 12.5% 8.2% 7.6% 9.3% Over/(Under) Performance (1.8%) 1.8% (2.6%) (3.2%) (1.5%) p-value

8 Journal of Money, Investment and Banking - Issue 7 (2009) 82 Panel B: Profitability of the variance-adjusted CSA CSA with σ > 1 S&P500 (N = 4,588) No Transaction Costs Annual Return 10.1% 13.3% 9.6% 9.0% 11.0% Over/(Under) Performance (0.7%) 2.5% (1.1%) (1.8%) 0.2% p-value S&P500 (N = 4,588) Transaction Costs Annual Return 8.4% 11.7% 7.7% 6.9% 8.9% Over/(Under) Performance (2.4%) 0.9% (3.1%) (3.8%) (1.9%) p-value CSA with σ > 2 S&P500 (N = 4,588) No Transaction Costs Annual Return 10.6% 14.1% 10.1% 9.5% 11.3% Over/(Under) Performance (0.2%) 3.3% (0.7%) (1.2%) (0.5%) p-value S&P500 (N = 4,588) Transaction Costs Annual Return 9.0% 12.5% 8.2% 7.6% 9.3% Over/(Under) Performance (1.8%) 1.8% (2.6%) (3.2%) (1.5%) p-value Table 3: Panel A: Volume, Variance, and the profitability of the Combined Signal Approach (CSA) on the NASDAQ Profitability of the volume-adjusted CSA CSA with Vol. > 1 NASDAQ (N = 4,588) No Transaction Costs Annual Return 13.2% 16.4% 16.5% 19.1% 20.0% Over/(Under) Performance 1.1% 4.2% 4.3% 7.0% 7.9% p-value NASDAQ (N = 4,588) Transaction Costs Annual Return 10.9% 13.5% 14.1% 16.7% 17.1% Over/(Under) Performance (1.3%) 1.4% 2.0% 4.6% 4.9% p-value CSA with Vol. > 2 NASDAQ (N = 4,588) No Transaction Costs Annual Return 13.2% 16.8% 16.9% 19.1% 19.8% Over/(Under) Performance 1.1% 4.7% 4.7% 7.0% 7.7% p-value NASDAQ (N = 4,588) Transaction Costs Annual Return 10.9% 14.0% 14.6% 16.7% 16.9% Over/(Under) Performance (1.9%) 1.8% 2.4% 4.6% 4.8% p-value

9 83 Journal of Money, Investment and Banking - Issue 7 (2009) Panel B: Profitability of the variance-adjusted CSA CSA with σ > 1 NASDAQ (N = 4,588) No Transaction Costs Annual Return 13.0% 16.5% 16.6% 19.1% 19.8% Over/(Under) Performance 0.9% 4.3% 4.4% 6.9% 7.6% p-value NASDAQ (N = 4,588) Transaction Costs Annual Return 10.6% 13.6% 14.2% 16.6% 16.8% Over/(Under) Performance (1.5%) 1.4% 2.1% 4.5% 4.7% p-value CSA with σ > 2 NASDAQ (N = 4,588) No Transaction Costs Annual Return 13.2% 16.8% 16.9% 19.1% 19.8% Over/(Under) Performance 1.1% 4.7% 4.7% 6.9% 7.7% p-value NASDAQ (N = 4,588) Transaction Costs Annual Return 10.9% 14.% 14.6% 16.7% 16.9% Over/(Under) Performance (1.3%) 1.8% 2.4% 4.5% 4.8% p-value The marginal contribution of volume and variance to the CSA s ability to generate profits was summarized and is presented in Table 4. Table 4 compares the unadjusted CSA returns (Table 1) with the adjusted returns (Table 2 & 3) to determine if volume or variance is able to improve the CSA.

10 Journal of Money, Investment and Banking - Issue 7 (2009) 84 Table 4: Marginal contribution of volume and variance S&P 500 No Transaction Costs S&P 500 No Transaction Costs CSA CSA Marginal CSA Marginal CSA Marginal CSA Marginal Volume 1 Impact Variance 1 Impact Volume 2 Impact Variance 2 Impact CSA (2,9) 2.00% -0.80% -2.80% -0.70% -2.70% -0.20% -2.20% -0.20% -2.20% CSA (3,9) -1.70% 2.70% 4.40% 2.50% 4.20% 2.20% 3.90% 3.30% 5.00% CSA (4,9) -2.40% -1.40% 1.00% -1.10% 1.30% -0.70% 1.70% -0.70% 1.70% CSA (5,9) -1.20% -1.60% -0.40% -1.80% -0.60% -1.20% 0.00% -1.20% 0.00% CSA (6,9) -3.90% -0.20% 3.70% 0.20% 4.10% -0.50% 3.40% -0.50% 3.40% S&P 500 Transaction Costs CSA CSA Marginal CSA Marginal CSA Marginal CSA Marginal Volume 1 Impact Variance 1 Impact Volume 2 Impact Variance 2 Impact CSA (2,9) 0.40% -2.40% -2.80% -2.40% -2.80% -1.80% -2.20% -1.80% -2.20% CSA (3,9) -3.70% 1.10% 4.80% 0.90% 4.60% 1.80% 5.50% 1.80% 5.50% CSA (4,9) -4.50% -3.30% 1.20% -3.10% 1.40% -2.60% 1.90% -2.60% 1.90% CSA (5,9) -3.20% -3.60% -0.40% -3.80% -0.60% -3.20% 0.00% -3.20% 0.00% CSA (6,9) -7.20% -2.20% 5.00% -1.90% 5.30% -1.50% 5.70% -1.50% 5.70% NASDAQ No Transaction Costs CSA CSA Marginal CSA Marginal CSA Marginal CSA Marginal Volume 1 Impact Variance 1 Impact Volume 2 Impact Variance 2 Impact CSA (2,9) 3.90% 1.10% -2.80% 0.90% -3.00% 1.10% -2.80% 1.10% -2.80% CSA (3,9) 3.40% 4.20% 0.80% 4.30% 0.90% 4.70% 1.30% 4.70% 1.30% CSA (4,9) 5.90% 4.30% -1.60% 4.40% -1.50% 4.70% -1.20% 4.70% -1.20% CSA (5,9) 5.80% 7.00% 1.20% 6.90% 1.10% 7.00% 1.20% 6.90% 1.10% CSA (6,9) 5.60% 7.90% 2.30% 7.60% 2.00% 7.70% 2.10% 7.70% 2.10% NASDAQ Transaction Costs CSA CSA Marginal CSA Marginal CSA Marginal CSA Marginal Volume 1 Impact Variance 1 Impact Volume 2 Impact Variance 2 Impact CSA (2,9) 1.00% -1.30% -2.30% -1.50% -2.50% -1.90% -2.90% -1.30% (-2.3%) CSA (3,9) 0.90% 1.40% 0.50% 1.40% 0.50% 1.80% 0.90% 1.80% 0.90% CSA (4,9) 3.30% 2.00% -1.30% 2.10% -1.20% 2.40% -0.90% 2.40% -0.90% CSA (5,9) 2.70% 4.60% 1.90% 4.50% 1.80% 4.60% 1.90% 4.50% 1.80% CSA (6,9) 2.10% 4.90% 2.80% 4.70% 2.60% 4.80% 2.70% 4.80% 2.70% Table 4 reveals that both volume and variance appear to be able to improve the CSA s profitability for both the S&P 500 and the NASDAQ. For the S&P 500, volume and variance increased profitability in three of the five CSA variants tested for both volume and variance metrics. The results are similar for the NASDAQ, where both volume and variance were able to improve the CSA s profits in three of the five variants. The increased profitability is significant, in many cases in excess of 3.0% per annum. It is interesting to note that both volume and variance improved profits for the same three variants of the CSA model CSA (3,9), CSA (4,9), and CSA (6,9) on both the S&P and the NASDAQ. It appears that both volume and variance did not improve the CSA (2,9) and CSA (5,9) profits. Currently, it is unclear exactly why periods of increased variance would results in excess profits from technical trading rules. It could be that periods of higher variance are associated with time-series dependencies, such that a price increase (decrease) is followed by another price increase (decrease), thereby creating a trend reinforcing patterns that can be exploited by technical trading rules. To test this possible explanation, the Hurst Exponent can be used to determine whether periods of high volatility are associated with trend reinforcing patterns. The Hurst statistic (H) (Hurst, 1951) has emerged in economics research as a measure of classifying a time series based on its long-term dependencies (Bender et al., 2006) whereby a H of 0.50 indicates a series is random. A 0<H<0.5 indicates an anti-persistent series (mean reverting tendencies). A 0.5<H<1 indicates a persistent series (trend reinforcing). The strength of the trend increases as H approaches 1. The H is estimated through a rescaled range analysis.

11 85 Journal of Money, Investment and Banking - Issue 7 (2009) As a test of this proposition, the H was estimated for the longest period of above average (high) and below (low) average volatility for both the NASDAQ and S&P 500 data sets. The resulting H exponent estimations are presented in Table 5. Table 5: Long-term dependency estimation of periods of high and low variance N Date Hurst Exponent Rescaled Range Slope Std. Error NASDAQ High Variance 266 2/27/2007-3/17/ Low Variance 248 3/14/2003-3/9/ S&P 500 High Variance 228 4/23/2007-3/17/ Low Variance 204 1/23/ /14/ The results suggest that periods of high volatility are indeed associated with trend reinforcing tendencies in the time series, while periods of low volatility exhibit anti-persistent tendencies. These results corroborate the results obtained that suggest additional profits can be earned by the CSA by incorporating variance into the model. In addition to variance, volume also appears to be able to provide informational content that amplifies the CSA model s ability to generate profits. These results of this study are consistent with past studies (Pruitt et al., 1992) as the increased profits suggest that volume provides information about the quality of traders information that price along cannot convey (Blume et al., 1994). This study reveals that the CSA profitability increased by using high volume levels to amplify the strength of a buy/sell signal generated by the CSA model. This is consistent with the extant literature. Volume has been shown to be higher than normal during weeks when a stock s price exceeds its 52-week high (Huddart, Lang, and Yetman, 2002). Higher prices appear to be interpreted as a psychological reference point used by investors to make decisions. This is consistent with the CSA model tested in this paper because all of the trading rule are momentum based (i.e. buy into strength and sell into weakness). Therefore, it is possible that as prices increase, so too does volume as more traders pile into the stock, further driving prices higher. This notion is corroborated by literature that reveals that periods of high volume are associated with increases in persistence (i.e. trend reinforcement). For example, Brock (1992) documented increased persistence in the Dow Jones Industrial Average on rising volume. This is similar to the results found in Table 5 for variance Joint-employment of volume and variance into the CSA Additional tests were conducted on profitability of the CSA when both volume and variance are used simultaneously to adjust the signal. For example, both volume and variance would have to exceed their 200-day historical averages to generate a signal. The results of the joint-employment of volume and variance into the CSA on the NASDAQ were not significantly different from the CSA based on volume or variance alone. The results are presented in Table 6. Table 6: Joint-employment of volume and variance into the CSA Average Volume & Variance 1 CSA Volume & Variance 1 Marginal Impact Average Volume & Variance 2 CSA Volume & Variance 2 Marginal Impact CSA (2,9) (1.4%) (1.4%) 0.00% (1.6%) (1.3%) 0.30% CSA (3,9) 1.4% 1.4% 0.00% 1.8% 1.8% 0.00% CSA (4,9) 2.05% 2.1% 0.05% 2.4% 2.4% 0.00% CSA (5,9) 4.55% 4.6% 0.05% 4.55% 4.6% 0.05% CSA (6,9) 4.8% 5.1% 0.30% 4.8% 4.8% 0.00%

12 Journal of Money, Investment and Banking - Issue 7 (2009) 86 The results of the joint-employment of variance and volume on the S&P 500 are also not significantly different than the results of incorporating volume and variance individually (and therefore have not been presented in a table). A potential explanation for the joint-employment s lack of additional power maybe because the variance and volume measures are closely related. That is, periods of high volatility maybe accompanied by periods of high volume, and vice versa. Pearson correlation analysis was performed on the volume and variance measures to investigate this possible explanation. The resulting ρ of 21.7% suggests that there is some correlation between volume and variance. 6. Conclusions and Discussion An empirical study was conducted to determine if the profitability of the CSA could be improved by incorporating volume and variance measures into the model. Profitability was defined as returns in excess of the buy-and-hold trading strategy. The results demonstrate that, on average, both volume and variance levels appear to have some information content to improve the profitability of the CSA. For both the S&P 500 and the NASDAQ, volume and variance increased profitability in three of the five CSA variants tested. The increased profitability is significant, in many cases in excess of 3.0% per annum. This study confirms the results obtained in Lento and Gradojevic (2007) and Lento (2008), whereby, the CSA was profitable. The results also support the notion that a synergy is created by the CSA, and that combining the individual signals creates a more powerful, and profitable trading signal. The results of this study provide a different approach to testing the CSA model by utilizing both volume and variance as additional variables to improve the strength of the model s signal. Therefore, the results of this study contribute to our overall understanding of the profitability of the CSA. The results of the CSA thus far are impressive, and indicate that further research in this area is warranted. Future researchers are encouraged to further develop the CSA. Future researchers are encouraged to learn more about what alternative weighting schemes and trading rules are likely to be more successful and in what circumstances. Moreover, it may be possible to determine the optimal number of rules for the decision-making mechanism using a more complex methodology. Developing a fully artificial intelligence-based combined signal may be a promising and challenging direction for future research. References [1] Alexander, S. (1964). Price Movements in Speculative Markets: Trends or Random Walks, No. 2 in P. Cootnered (ed.), The Random Character of Stock Market Prices (MIT Press, Cambridge, MA). [2] Bender, C., Sottinen, T., and Valkeila, E. 2006, Arbitrage with fractional Brownian motion, Theory of Stochastic Processes, 12(28), pp [3] Bessembinder, H. & K. Chan, (1998). Market efficiency and the returns to technical analysis. Financial Management, 27 (2), [4] Blume, L., Easley, D. and O Hara (1994). Market statistics and technical analysis: The role of volume. Journal of Finance, 49(1), [5] Brock, W. (1992). Persistence of the Dow Jones Index on rising volume. Working paper [6] Brock, W., J. Lakonishok, & B. LeBaron (1992). Simple Technical Trading Rules and the Stochastic Properties of Stock Returns. Journal of Finance, 47, [7] Fama, E. & M. Blume Filter Tests and Stock Market Trading. Journal of Business, Vol. 39, pp [8] Gençay, R The Predictability of Security Returns with Simple Technical Trading Rules. Journal of Empirical Finance, 5 (1998)

13 87 Journal of Money, Investment and Banking - Issue 7 (2009) [9] Gençay, R., and T. Stengos Moving Average Rules, Volume and the Predictability of Security Returns with Feedforward Networks. Journal of Forecasting, 17(1998), [10] Glenn, L Beat the Market - A Strategy for Conservative Investors. SSRN Working Paper. Available at: [11] Huddart, S., Lang, M. and Yetman, M Psychological factors, stock price paths, and trading volume. Working Paper. [12] Hurst, H Long-term Storage of Reservoirs: An Experimental Study, Transactions of the American Society of Civil Engineers, 116, [13] Lento, C Combined Signal Approach: Further Evidence from the Asian-Pacific Equity Markets. Applied Economics Letters, 16(7), [14] Lento, C A Combined Signal Approach to Technical Analysis on the S&P 500. Journal of Business & Economics Research, Vol. 6, No. 8, pp [15] Lento, C. and Gradojevic, N The Profitability of Technical Trading Rules: A Combined Signal Approach. Journal of Applied Business Research 23(1), [16] Lento, C., Gradojevic, N. and Wright, C.S Investment Information Content in Bollinger Bands? Applied Financial Economics Letters 3(4), [17] Levich, R. and L. Thomas The Significance of Technical Trading Rules Profits in the Foreign Exchange Market: A Bootstrap Approach. Journal of International Money and Finance, 12, [18] Lisi, F. & A. Medio Is a random walk the best exchange rate predictor? International Journal of Forecasting, 13, [19] Lo, A. W., H. Mamaysky, & J. Wang Foundations of Technical Analysis: Computational Algorithms, Statistical Inference, and Empirical Implementation. The Journal of Finance 55 (4), [20] Murphy, J Charting Made Easy. Marketplace Books, 2000 [21] Pring, M. J Technical Analysis Explained. New York, NY: McGraw-Hill. [22] Pruitt, S. W., K. S. Maurice Tse, and R. E. White The CRISMA Trading System: The Next Five Years. Journal of Portfolio Management, (Spring), [23] White, H Approximate Nonlinear Forecasting Methods. G. Elliot, C.W.J. Gragner, and A. Timmerman, eds., Handbook of Economics Forecasting.