Journal of Money, Investment and Banking ISSN 1450-288X Issue 7 (2009) © EuroJournals Publishing, Inc. 2009 http://www.eurojournals.com/JMIB.htm
Volume, Variance, and the Combined Signal Approach to Technical Analysis Camillo Lento Faculty of Business Administration, Lakehead University Thunder Bay, Ontario, Canada E-mail:
[email protected] Tel: +1-807-343-8387; Fax: +1-807-343-8023 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)).
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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 6.
2. 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.
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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. 2.2. 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 s =1
Ri ,t
∑ >
L
l =1
Ri ,t −1
=Buy,
(1)
S L Equation 2 – VMA Sell Signal
∑
S s =1
Ri ,t
∑
Max {Pt-1, Pt-2, …, Pt-n} Post+1 = Post, if Pt > Min {Pt-1, Pt-2, …, Pt-n} ≤ Pt ≤ Max {Pt-1, Pt-2, …, Pt-n} Post+1 = Sell, if Pt < Min {Pt-1, Pt-2, …, Pt-n} (3), where Pt is the stock price at time t. 2.3. 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 1986-1990. 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. 2.4. 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: H1: 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.
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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 mth (m=1,…,M) permutation of these N returns (M=N!) is related to a unique profit measure (X[m, r]) for the rth 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.
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4. Data Description The technical trading rules are tested on the S&P 500 and the NASDAQ for the period of January 1990 to March 2008. 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 rt = log (pt) – log (pt -1)
(4)
where pt 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: Panel A:
Profitability of the Unadjusted Combined Signal Approach (CSA) Profitability of the unadjusted CSA on the S&P 500
S&P500 (N = 4,588) No Transaction Costs Annual Return Buy-and-Hold Return Over/(Under) Performance p-value S&P500 (N = 4,588) Transaction Costs Annual Return Buy-and-Hold Return Over/(Under) Performance p-value
Panel B :
CSA (Comparison) 4/9 5/9
2/9
3/9
6/9
12.8% 10.8% 2.0% 0.04
9.1% 10.8% (1.7%) 0.22
8.4% 10.8% (2.4%) 0.34
9.6% 10.8% (1.2%) 0.23
6.9% 10.8% (3.9%) 0.44
11.2% 10.8% 0.4% 0.04
7.1% 10.8% (3.7%) 0.22
6.3% 10.8% (4.5%) 0.34
7.5% 10.8% (3.2%) 0.23
3.6% 10.8% (7.2%) 0.44
Profitability of the unadjusted CSA on the NASDAQ
NASDAQ (N = 4,588) No Transaction Costs Annual Return Buy-and-Hold Return Over/(Under) Performance p-value NASDAQ (N = 4,588) Transaction Costs Annual Return Buy-and-Hold Return Over/(Under) Performance p-value
CSA (Comparison) 4/9 5/9
2/9
3/9
6/9
16.0% 12.2% 3.9% 0.05
15.5% 12.2% 3.4% 0.07
18.1% 12.2% 5.9% 0.03
17.9% 12.2% 5.8% 0.03
17.8% 12.2% 5.6% 0.06
13.1% 12.2% 1.0% 0.05
13.1% 12.2% 0.9% 0.07
15.5% 12.2% 3.3% 0.03
14.8% 12.2% 2.7% 0.03
14.2% 12.2% 2.1% 0.06
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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%. 5.2. 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
S&P500 (N = 4,588) No Transaction Costs Annual Return Buy-and-Hold Return Over/(Under) Performance p-value S&P500 (N = 4,588) Transaction Costs Annual Return Buy-and-Hold Return Over/(Under) Performance p-value
No Transaction Costs S&P500 (N = 4,588) Annual Return Buy-and-Hold Return Over/(Under) Performance p-value S&P500 (N = 4,588) Transaction Costs Annual Return Buy-and-Hold Return Over/(Under) Performance p-value
2/9
3/9
CSA with Vol. > 1 4/9
5/9
6/9
10.0% 10.8% (0.8%) 0.12
13.5% 10.8% 2.7% 0.04
9.4% 10.8% (1.4%) 0.07
9.2% 10.8% (1.6%) 0.13
10.5% 10.8% (0.2%) 0.06
8.4% 11.9% 10.8% 10.8% (2.4%) 1.1% 0.12 0.04 CSA with Vol. > 2 2/9 3/9
7.5% 10.8% (3.3%) 0.07
7.2% 10.8% (3.6%) 0.13
8.5% 10.8% (2.2%) 0.06
4/9
5/9
6/9
10.6% 10.8% (0.2%) 0.13
14.1% 10.8% 3.3% 0.04
10.1% 10.8% (0.7%) 0.09
9.5% 10.8% (1.2%) 0.11
11.3% 10.8% 0.5% 0.09
9.0% 10.8% (1.8%) 0.13
12.5% 10.8% 1.8% 0.04
8.2% 10.8% (2.6%) 0.09
7.6% 10.8% (3.2%) 0.11
9.3% 10.8% (1.5%) 0.09
Journal of Money, Investment and Banking - Issue 7 (2009) Panel B:
82
Profitability of the variance-adjusted CSA
S&P500 (N = 4,588) No Transaction Costs Annual Return Buy-and-Hold Return Over/(Under) Performance p-value S&P500 (N = 4,588) Transaction Costs Annual Return Buy-and-Hold Return Over/(Under) Performance p-value
S&P500 (N = 4,588) No Transaction Costs Annual Return Buy-and-Hold Return Over/(Under) Performance p-value S&P500 (N = 4,588) Transaction Costs Annual Return Buy-and-Hold Return Over/(Under) Performance p-value
2/9
3/9
CSA with σ > 1 4/9
5/9
6/9
10.1% 10.8% (0.7%) 0.22
13.3% 10.8% 2.5% 0.05
9.6% 10.8% (1.1%) 0.08
9.0% 10.8% (1.8%) 0.19
11.0% 10.8% 0.2% 0.09
8.4% 10.8% (2.4%) 0.22
11.7% 10.8% 0.9% 0.05
6.9% 10.8% (3.8%) 0.19
8.9% 10.8% (1.9%) 0.09
2/9
3/9
7.7% 10.8% (3.1%) 0.08 CSA with σ > 2 4/9
5/9
6/9
10.6% 10.8% (0.2%) 0.25
14.1% 10.8% 3.3% 0.04
10.1% 10.8% (0.7%) 0.06
9.5% 10.8% (1.2%) 0.26
11.3% 10.8% (0.5%) 0.10
9.0% 10.8% (1.8%) 0.25
12.5% 10.8% 1.8% 0.04
8.2% 10.8% (2.6%) 0.06
7.6% 10.8% (3.2%) 0.26
9.3% 10.8% (1.5%) 0.10
Table 3:
Volume, Variance, and the profitability of the Combined Signal Approach (CSA) on the NASDAQ
Panel A:
Profitability of the volume-adjusted CSA
NASDAQ (N = 4,588) No Transaction Costs Annual Return Buy-and-Hold Return Over/(Under) Performance p-value NASDAQ (N = 4,588) Transaction Costs Annual Return Buy-and-Hold Return Over/(Under) Performance p-value NASDAQ (N = 4,588) No Transaction Costs Annual Return Buy-and-Hold Return Over/(Under) Performance p-value NASDAQ (N = 4,588) Transaction Costs Annual Return Buy-and-Hold Return Over/(Under) Performance p-value
2/9
3/9
CSA with Vol. > 1 4/9
5/9
6/9
13.2% 12.2% 1.1% 0.17
16.4% 12.2% 4.2% 0.03
16.5% 12.2% 4.3% 0.05
19.1% 12.2% 7.0% 0.13
20.0% 12.2% 7.9% 0.05
10.9% 12.2% (1.3%) 0.17
13.5% 12.2% 1.4% 0.03
14.1% 12.2% 2.0% 0.05 CSA with Vol. > 2
16.7% 12.2% 4.6% 0.13
17.1% 12.2% 4.9% 0.05
13.2% 12.2% 1.1% 0.08
16.8% 12.2% 4.7% 0.04
16.9% 12.2% 4.7% 0.03
19.1% 12.2% 7.0% 0.16
19.8% 12.2% 7.7% 0.07
10.9% 12.2% (1.9%) 0.08
14.0% 12.2% 1.8% 0.04
14.6% 12.2% 2.4% 0.03
16.7% 12.2% 4.6% 0.16
16.9% 12.2% 4.8% 0.07
Journal of Money, Investment and Banking - Issue 7 (2009)
83 Panel B:
Profitability of the variance-adjusted CSA
NASDAQ (N = 4,588) No Transaction Costs Annual Return Buy-and-Hold Return Over/(Under) Performance p-value NASDAQ (N = 4,588) Transaction Costs Annual Return Buy-and-Hold Return Over/(Under) Performance p-value
NASDAQ (N = 4,588) No Transaction Costs Annual Return Buy-and-Hold Return Over/(Under) Performance p-value NASDAQ (N = 4,588) Transaction Costs Annual Return Buy-and-Hold Return Over/(Under) Performance p-value
2/9
3/9
CSA with σ > 1 4/9
5/9
6/9
13.0% 12.2% 0.9% 0.13
16.5% 12.2% 4.3% 0.05
16.6% 12.2% 4.4% 0.02
19.1% 12.2% 6.9% 0.14
19.8% 12.2% 7.6% 0.02
10.6% 13.6% 12.2% 12.2% (1.5%) 1.4% 0.13 0.05 CSA with σ > 2 2/9 3/9
14.2% 12.2% 2.1% 0.02
16.6% 12.2% 4.5% 0.14
16.8% 12.2% 4.7% 0.02
4/9
5/9
6/9
13.2% 12.2% 1.1% 0.17
16.8% 12.2% 4.7% 0.07
16.9% 12.2% 4.7% 0.03
19.1% 12.2% 6.9% 0.12
19.8% 12.2% 7.7% 0.02
10.9% 12.2% (1.3%) 0.17
14.% 12.2% 1.8% 0.07
14.6% 12.2% 2.4% 0.03
16.7% 12.2% 4.5% 0.12
16.9% 12.2% 4.8% 0.02
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.
Journal of Money, Investment and Banking - Issue 7 (2009) Table 4:
Marginal contribution of volume and variance S&P 500 No Transaction Costs
CSA CSA (2,9) CSA (3,9) CSA (4,9) CSA (5,9) CSA (6,9)
2.00% -1.70% -2.40% -1.20% -3.90% CSA
CSA (2,9) CSA (3,9) CSA (4,9) CSA (5,9) CSA (6,9)
0.40% -3.70% -4.50% -3.20% -7.20% CSA
CSA (2,9) CSA (3,9) CSA (4,9) CSA (5,9) CSA (6,9)
3.90% 3.40% 5.90% 5.80% 5.60% CSA
CSA (2,9) CSA (3,9) CSA (4,9) CSA (5,9) CSA (6,9)
84
1.00% 0.90% 3.30% 2.70% 2.10%
CSA Volume 1 -0.80% 2.70% -1.40% -1.60% -0.20% CSA Volume 1 -2.40% 1.10% -3.30% -3.60% -2.20% CSA Volume 1 1.10% 4.20% 4.30% 7.00% 7.90% CSA Volume 1 -1.30% 1.40% 2.00% 4.60% 4.90%
S&P 500 No Transaction Costs CSA Marginal CSA Variance 1 Impact Volume 2 -0.70% -2.70% -0.20% 2.50% 4.20% 2.20% -1.10% 1.30% -0.70% -1.80% -0.60% -1.20% 0.20% 4.10% -0.50% S&P 500 Transaction Costs Marginal CSA Marginal CSA Impact Variance 1 Impact Volume 2 -2.80% -2.40% -2.80% -1.80% 4.80% 0.90% 4.60% 1.80% 1.20% -3.10% 1.40% -2.60% -0.40% -3.80% -0.60% -3.20% 5.00% -1.90% 5.30% -1.50% NASDAQ No Transaction Costs Marginal CSA Marginal CSA Impact Variance 1 Impact Volume 2 -2.80% 0.90% -3.00% 1.10% 0.80% 4.30% 0.90% 4.70% -1.60% 4.40% -1.50% 4.70% 1.20% 6.90% 1.10% 7.00% 2.30% 7.60% 2.00% 7.70% NASDAQ Transaction Costs Marginal CSA Marginal CSA Impact Variance 1 Impact Volume 2 -2.30% -1.50% -2.50% -1.90% 0.50% 1.40% 0.50% 1.80% -1.30% 2.10% -1.20% 2.40% 1.90% 4.50% 1.80% 4.60% 2.80% 4.70% 2.60% 4.80% Marginal Impact -2.80% 4.40% 1.00% -0.40% 3.70%
Marginal Impact -2.20% 3.90% 1.70% 0.00% 3.40%
CSA Variance 2 -0.20% 3.30% -0.70% -1.20% -0.50%
Marginal Impact -2.20% 5.00% 1.70% 0.00% 3.40%
Marginal Impact -2.20% 5.50% 1.90% 0.00% 5.70%
CSA Variance 2 -1.80% 1.80% -2.60% -3.20% -1.50%
Marginal Impact -2.20% 5.50% 1.90% 0.00% 5.70%
Marginal Impact -2.80% 1.30% -1.20% 1.20% 2.10%
CSA Variance 2 1.10% 4.70% 4.70% 6.90% 7.70%
Marginal Impact -2.80% 1.30% -1.20% 1.10% 2.10%
Marginal Impact -2.90% 0.90% -0.90% 1.90% 2.70%
CSA Variance 2 -1.30% 1.80% 2.40% 4.50% 4.80%
Marginal Impact (-2.3%) 0.90% -0.90% 1.80% 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
