Chapter 4: Trading Performance of Fundamental, Corporate Governance and
4.3 Corporate Governance Analysis 110
4.3.1 Model Design 110
4.3.1.1 Training Data
As discussed in the previous chapter, we employ five corporate governance variables, namely DUAL, BSIZE, INST, GOVN and BIGN, for training the corporate governance neural network (CG-NN). These variables represent board structure, ownership structure and accounting (or disclosure) quality of the firms. Table 4.9 gives the descriptive statistics of the corporate governance variables.
79 In addition, Vanstone (2006) argues that this information may also allow traders to determine whether the model is performing as expected or requires retraining.
111 Table 4.9
Descriptive Statistics of Corporate Governance Variables
Variables Min Max Mean Std Dev
DUAL 0.00 1.00 0.82 0.38
BSIZE 4.00 15.00 8.94 2.37
INST 0.01 0.76 0.27 0.22
GOVN 0.00 0.96 0.35 0.33
BIGN 0.00 1.00 0.80 0.40
The table reports descriptive statistics of corporate governance variables based on annual data synchronised daily. Following the synchronisation process, 199,205 corporate governance data points are generated—39,841 (daily observations) × 5 (corporate governance variables).
Some reflections on the statistics can be made. It can be seen that the majority of the sample firms have different persons helming the CEO and chairman positions. This shows that most firms in Malaysia comply with the MCCG (2007) Code of Best Practice for having separate top leadership. For those with role duality, we find that their decisions to combine both roles have been clearly explained in the annual reports. The minimum size of the board is four directors, while the maximum is 15. The average BSIZE, which is nine directors, is within the recommendation for an effective board as endorsed by Lipton and Lorsch (1992). Ownership by institutional investors ranges from 1% to 76%, while government holding stretches from 0% to 96%. On average, both accounted for about a third of the shareholdings, higher than the sample in Mak and Kusnadi (2005). This is not surprising, since their study includes firms from both the main and second boards. INST and GOVN are typically more prevalent in blue chip firms. In terms of audit appointments, most of our sample firms hire auditors from the Big Four (or Big Five in the earlier period) accounting firms.
To facilitate system utilisation within the constraint of RAM and time, we load every fifth row of bars as input for training the neural network, while outliers (if any) in the corporate governance information are removed. Following the sampling process, we obtain 6,776 daily observations. Table 4.10 shows the final CG-NN input variables.
112 Table 4.10
Descriptive Statistics of CG-NN Input Variables
Variables Min Max Mean Std Dev
DUAL 0.00 1.00 0.82 0.38
BSIZE 4.00 15.00 9.01 2.37
INST 0.01 0.76 0.27 0.22
GOVN 0.00 0.96 0.35 0.33
BIGN 0.00 1.00 0.80 0.40
The table reports descriptive statistics of the corporate governance variables being included for neural network training. After sampling out bars and removing outliers, there is a total of 33,880 corporate governance data points—6,776 (daily observations) × 5 (corporate governance variables).
Like financial statement analysis, the purpose of corporate governance trading strategy is long-term investment. For this reason, we utilise the CG-NN inputs (governance indicators) above to forecast annual (200-day forward) stock returns (CG-NN output). Table 4.11 reports the target output characteristics for the ANN training set.
Table 4.11
Descriptive Statistics of CG-NN Target Variable
Variables Min Max Mean Std Dev
Output -70.89 260.38 17.04 32.03
The table shows the target variable, which is the percentage return 200 days in the future. The statistics are based on the sampled data (sampling of every fifth bar), which matches the CG-NN input (i.e., 6,776 daily observations).
As can be seen from the table above, the percentage annual returns ranges from a minimum of -70.89% to a maximum of 260.38%, while the mean annual return is 17.04% with a standard deviation of 32.03%. By default, since both (traditional) fundamental and corporate governance analysis attempt to predict 200-day look-ahead returns, they produce almost identical statistics. Any distinction may be attributed to the differences in the sample set caused by the sampling of the data rows and the removal of outliers.
4.3.1.2 Training Process
Using five governance variables as inputs and future annual returns as output, the topology of CG-NN is given as 5:11:1. To be precise, the network consists of five input nodes (corporate governance indicators), 11 hidden nodes (measured as 2N+1 hidden
nodes, where N = 5 input nodes) and one output node (200-day forward returns). The
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(see Figure 4.4) shows how the MSE declines as the training progresses, with a sharp fall until about 5,000 epochs, and later flattens out when there is a small improvement to the networks. As a result, the CG-NN continues to run for a total of 30,538 epochs, after which the training stops.
Figure 4.4
CG-NN Training Error
The figure presents the training error for the ANN using the sampled data (after sampling every fifth bar and removing outliers) for the period 1 July 2002 to 30 June 2008 on each epoch. The error term denotes the average of the sum of the squared differences between the CG-NN output and the target output (MSE) and multiplied by 1,000.
It can be seen from the figure above that the final MSE obtained from the CG-NN to forecast annual returns is smaller than 0.0028. Using the trained network, we evaluate its performance on the in-sample period to identify the specific entry/exit threshold for the neurally enhanced corporate governance trading rules.
4.3.1.3 Trading Rules
Table 4.12 shows the CG-NN performance evaluation results for the entire in-sample data (1 July 2002 to 30 June 2008).
114 Table 4.12 CG-NN Performance Evaluation CG-NN Indicator Predicted Output Observations Actual Output Percentage of Average (%) Performance Bar 10-15 -21.79 48 -35.02 -305.57 15-20 -10.51 884 -6.76 -139.70 20-25 5.98 2,967 8.37 -50.86 25-30 18.05 1,773 20.19 18.51 30-35 35.10 497 40.03 135.02 35-40 51.92 443 53.35 213.19 40-45 67.94 148 77.73 356.33 45-50 83.45 97 90.72 432.62
The table shows the performance evaluation of the CG-NN using the entire in-sample period (1 July 2002 to 30 June 2008) data. CG-NN indicator presents the values generated by the ANN. When the CG-NN produces a low (high) value, it is forecasting that the output will be near the low (high) end of the output range. Predicted output shows the forecasted output value. Observations report the number of individual observations (more specifically, bars) of data within the CG-NN indicator range. We remove any outliers (any row with the observation of less than 1% of the total observations) from the analysis. Outliers (if any) provided in the table are for illustration purposes only. Actual output reports the average actual output. Percentage of average (%) displays the magnitude of the average output for that particular row compared to the average output for all observations. Performance bar provides a graphical presentation of the percentage of average (%). Note that the bar is not to scale and is provided for illustration purposes only.
The data in Table 4.12 demonstrates that the optimal point that separates the negative with positive percentage of average output is located when CG-NN = 25. That is, when CG-NN > 25, the actual output is higher than the average output for all observations. Conversely, it is apparent that when CG-NN < 25, the actual output is lower than the mean output for the entire observation. The performance bar gives the graphical illustration of this incidence. The value of 25 is also located within the range of the most number of observations (with 2,967 and 1,773 observations for the ranges of 20-25 and 25-30, respectively) for making valid analysis. Accordingly, we use this value as the demarcation point between entering and exiting a trade for programming the ANN- based governance trading rules.
Based on the CG-NN performance appraisal above, Figure 4.5 displays how we program the neural network indicator to generate trading signals. We code a buy (tomorrow) signal when CG-NN (today) > 25 and CG-NN (today) > CG-NN (yesterday), while the sell (tomorrow) signal is generated when CG-NN (today) ≤ 25 and CG-NN (today) < CG-NN (yesterday).
115 Figure 4.5
Pseudo Code for the CG-NN Trading Rule
1 IF CG-NNt > 25 2 AND CG-NNt > CG-NNt-1 THEN 3 BUY at OPENt+1, 4 IF CG-NN t≤ 25 5 AND CG-NN t < CG-NN t-1 THEN 6 SELL at OPENt+1
The figure demonstrates the pseudo code for signalling buy (sell) signals for the neurally enhanced corporate governance trading rule. The actual code is based on the C# programming language. The signals are emitted after the market closes at day t, while buy (sell) trades are only executed on the next day (t+1) based on the prevailing market open price (OPEN). This produces a valid trading rule, simulates a realistic trading environment and mitigates any possibility of look- ahead bias.
In summary, our in-sample results (see Table 4.12) suggest that a neural network trained with governance data is capable of predicting future (annual) stock returns. To proceed with analysing its trading performance, we include the CG-NN trading rule above within the context of a full-fledged trading system. As outlined, this comprises dynamic anti-Martingale money management strategy and risk control of 50% stop loss level. In order to provide valid empirical results, we investigate the trading performance of the neurally enhanced corporate governance trading system (CG-NNTS) against the B&H within a valid trading environment using the previously unseen, holdout sample data.
4.3.2 Empirical Results
In the table that follows, we provide the performance of the CG-NNTS against the B&H strategy using a three-year (1 July 2008 to 30 June 2011) out-of-sample period. An initial budget of RM100,000.00 is placed at the initial period, with all trades subject to a one way (round-trip) transaction cost rate of 0.83% (1.66%), realistic round lot and short selling restrictions.
116 Table 4.13
CG-NNTS Out-of-sample Performance
CG-NNTS B&H
Panel A: General Trading Metrics
Net Profit RM51,647.03 RM27,113.47 Net Profit % 51.65% 27.11% Annualised Gain % 14.91% 8.34% Number of Trades 11 30 Average Profit RM4,695.18 RM903.78 Average Profit % 42.48% 28.14% Exposure 65.03% 99.57%
Winners: Winning Trades 10 23
Winners: Win Rate 90.91% 76.67%
Winners: Average Profit % 47.32% 44.47%
Losers: Losing Trades 1 7
Losers: Loss Rate 9.09% 23.33%
Losers: Average Loss % -5.88% -25.54%
Panel B: Key Trading Metrics
Profit Factor 34.35 5.54 Payoff Ratio 8.05 1.74 Maximum Drawdown % -11.66% -26.76% Recovery Factor 2.76 1.01 Ulcer Index 3.92 9.36 Sharpe Ratio 1.27 0.65 Sortino Ratio 2.44 0.96
The table reports the performance metrics of the neurally enhanced full-fledged corporate governance trading system (CG-NNTS) compared to the benchmark B&H policy for the holdout sample, covering the period 1 July 2008 to 30 June 2011. Panel A presents the general metrics. Net profit refers to the total dollar profit generated after deducting trading costs, which includes brokerage fees, stamp duty and clearing fees, computed as 0.83% one way (or 1.66% round-trip). Net profit % indicates total net profit in terms of its percentage of initial budget (starting capital), which is RM100,000.00. Annualised gain % shows the smoothed average rate of return on the basis of compounding the starting capital annually. Exposure refers to the total area of portfolio equity exposed to the market. Number of trades shows the total round-trip trades and open positions. Average profit (profit %) is the average dollar (percentage) return per trade after trading costs. Winners: winning trades (win rate) refers to the number (ratio) of winning trades produced by the trading systems, while winners: average profit % indicates the average percentage profit of the winners. Similarly, losers: losing trades (loss rate) refers to the number (ratio) of losing trades generated by the trading systems, while losers: average loss % indicates the average percentage loss of the losing trades. Panel B presents the key metrics. Profit factor is calculated by dividing gross profit with gross loss. Payoff ratio is the system’s average percentage profit per trade divided by the average percentage loss per trade. Maximum drawdown % is the percentage decline of the largest peak to valley in the equity curve. Recovery factor is computed by dividing the absolute value of net profit by the maximum drawdown. Ulcer index is measured by square rooting the quotient of sum squared drawdowns divided by the period. Sharpe ratio conveys the risk-adjusted return for the trading systems, computed by dividing the annualised average return with its annualised standard deviation. Sortino ratio is similar to the Sharpe ratio, but utilises downside deviation instead of standard deviation in the denominator. Both ratios assume a zero risk-free rate of return.
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Evidently, the above table shows that the corporate governance trading system yields excellent results and is a better performer compared to the B&H rule. Next we proceed with presenting the results of the related statistical tests, which confirm that our findings are statistically significant. This is followed by the summary of trading metrics.
4.3.2.1 Statistical Analysis
To determine the appropriate tests of statistical significance, we first need to verify if the returns distribution of CG-NNTS sufficiently follows the Gaussian distribution, and if there is any presence of serial dependency (in other words, if the data is not sufficiently random). Since the number of trades generated by CG-NNTS (see Table 4.13) does not exceed 20 for implementing the central limit theorem, we proceed by testing for normality using the Shapiro-Wilk test. The results from this test are displayed in Table 4.14.
Table 4.14
CG-NNTS Test for Normality
CG-NNTS
Shapiro-Wilk W Statistic 0.875
Degrees of Freedom (df) 11
p value 0.090
The table reports the Shapiro-Wilk test for normality. It tests the null hypothesis that the sample comes from a normal distribution. The value of W lies between zero and one. Normality is rejected on smaller values of W. The value of one indicates the data is normally distributed.
Based on the typical alpha value of 0.05 for testing normality, the Shapiro-Wilk statistic of 0.875 with p = 0.090 (p > 0.05) above indicates there is insufficient evidence to reject
the null hypothesis of Gaussian distribution for the CG-NNTS returns. Having passed the assumption of normality, we perform the Z score of runs test to examine the applicability of employing parametric statistical test. Table 4.15 shows the results.
118 Table 4.15
CG-NNTS Test for Serial Independence
CG-NNTS
Total Cases 11
Number of Runs 3
Z Score 1.768
The table reports the runs test analysis. Total cases indicates the total number of trades generated by the trading system. Number of runs shows the total number of runs in the sequence. Z score shows how many standard deviations the sequence of wins and losses produced by the trading system are away from the mean.
As can be seen from the table above, the Z score of CG-NNTS is 1.768, which is less than the threshold value of two. From this value, we cannot conclude that there is serial dependence among the CG-NNTS trades and thus argue that the trades are sufficiently random. The findings from both tests above validate the use of parametric tests. Table 4.16 gives the results for the one sample and independent samples t-tests.
Table 4.16
CG-NNTS Statistical Results
Panel A: One Sample t-test
Test Value = 0
Sample Mean t-statistic
Degrees of Freedom (df)
p value
(1-tailed)
CG-NNTS 4695.185 2.649 10 0.0122
Panel B: Independent Samples t-test
Levene's Test t-test for Equality of Means
F-statistic p value t-statistic
Degrees of Freedom (df)
p value
(1-tailed)
Equal Variances Assumed 29.738 0.000 3.329 39 0.0010
Equal Variances Not Assumed 2.115 10.454 0.0297
The table reports the statistical results for the hypotheses testing. Panel A presents the results from the one sample t-test (one tailed). The test is used to examine whether the mean profit from CG-NNTS is significantly greater than zero (µCG-NNTS > 0). Panel B shows the results
from the independent samples t-test. This panel provides three inferential tests. The Levene’s test is used to test the homogeneity of variances assumption. There are two types of independent samples t-tests: the equal variances assumed shows the equal variance t-test; the equal variances not assumed refers to the unequal variance (also known as Welch) t-test. These independent sample t-tests (one tailed) are used to examine if the mean return from CG-NNTS is significantly greater than the one produced by the B&H (µCG-NNTS > µB&H). The sample
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Table 4.16 (Panel A) shows that, with the sample mean of 4695.185, the t-statistic indicates that the mean return produced by CG-NNTS is significantly greater than zero, specifically t(10) = 2.649, p = 0.0122 (p < 0.05) (one tailed). Therefore, there is
sufficient evidence to accept the research hypothesis (H4a) that trading guided by the CG-NNTS can produce statistically significant return (at 95% confidence level).
The results presented in Table 4.13 earlier clearly show the dominance of our corporate governance strategy over the B&H, in terms of the trading metrics. Table 4.16 (Panel B) confirms that the difference in mean returns is statistically significant. As can be seen, the assumption of homogeneity of variances is violated, where the Levene’s test shows that F = 29.738, p = 0.000 (p < 0.05). Since the variances for CG-NNTS and B&H are
not equal, the result is reported using the Welch t-test. The result verifies that FA-NNTS is indeed significantly superior to the B&H, with t’ = 2.115, df = 10.454, p = 0.0297 (p
< 0.05) (one tailed). This allows us to accept the alternative hypothesis, H4b, at 95% confidence level.
4.3.2.2 Trading Metrics
As with our neurally enhanced trading system trained with financial statement data, we find that our corporate governance strategy is superior to the B&H approach. The results in Table 4.13 (Panel A) show that the corporate governance trading system produces greater net profit with RM51,647.03, which is almost twice the return produced by the B&H strategy with RM27,113.47, and yields higher annualised gain (14.91%) compared to the B&H (8.34%). The governance trading system also has lower exposure (65.03%), higher win rate (90.91%) and average profit (47.32%) when the trade is winning, and lower average loss (-5.88%) when the trade is losing, compared to the B&H (99.57%, 76.67%, 44.47% and -25.54%, respectively).
The more crucial aspects of performance measures as reported in Panel B (Table 4.13) further confirm the outperformance of CG-NNTS. Briefly stated, it has a greater profit factor (34.35), payoff ratio (8.05) and recovery factor (2.76), and lower maximum percentage drawdown (-11.66%) and ulcer index (3.92), compared to the B&H approach (with 5.54, 1.74, 1.01, -26.76% and 9.36, respectively). Figure 4.6 exhibits the
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underwater equity curve, which pinpoints the location of CG-NNTS maximum percentage drawdown on 11 March 2011.
Figure 4.6
CG-NNTS Drawdown Curve (Underwater Equity Curve)
The figure illustrates the percentage decline of peak to valley in the CG-NNTS equity curve for the period 1 July 2008 to 30 June 2011, presented on a daily basis. It shows the period and magnitude of the drawdown. The curve is measured on a walk-forward basis. Specifically, the percentage of drawdown at a point is determined from the maximum equity obtained until that specific time.
Results reported for the metrics on risk-return tradeoffs (see Panel B of Table 4.13) validate the fact that CG-NNTS is indeed a superior trading strategy. More specifically, the non-financial fundamental strategy yields greater Sharpe and Sortino ratios with 1.27 and 2.44, respectively, compared to the B&H with only 0.65 and 0.96. This indicates that for a unit of risk, the corporate governance trading system produces better returns. In a nutshell, based on the overall metrics as outlined above, it is apparent that our neurally enhanced full-fledged corporate governance trading system clearly dominates the B&H policy. For expositional purposes only, we give the graphical presentations of the CG-NNTS return distributions for multiple periods (daily, weekly and monthly) from 1 July 2008 to 30 June 2011 (see Appendix II).
4.4 Technical Analysis
Thus far we have examined the performance of both traditional and new fundamental trading systems. Both results are excellent, yielding superior risk-return profiles over the B&H benchmark. We now investigate the outcome from trading using historical market data. Supported by technical theory, our technical trading system (TA-NNTS) uses technical information as inputs to the neural network to predict short-term returns.