4.3 Definir la política, objetivos y plan de trabajo anual de SST
4.3.2. Objetivos de seguridad y salud en el trabajo. Para el desarrollo de los objetivos de seguridad y salud en el trabajo, se toma los lineamientos normativos del decreto 1072 de
Considering the moving average rule, when the short moving average of stock prices is above the long moving average, the traders initiate buy or hold decision relying on believe that the short term price growth surpass the long term price growth in expected time period. Oppositely, when the short moving average is below the long moving average or when they are equal, the traders make a sell or stay out decision.
A typical number of trading days in short and long term moving averages depends on research assumptions. Hence, Brock et al. (1992) are used 1 and 5 days interval for the short moving average, and from 50 to 200 trading days for the long moving averages, while Charoenwong (2012) considered that the short moving averages can range from 5 to 15 days and the long moving average from 50 to 90 days. This paper implements 1 and 5 days interval for the short, and 100, 150 and 200 trading days for the long moving average.
3. TESTING METHODOLOGY
Moving average trading rule represents unquestioned evidence of the stock price predictive ability if expected stock prices depend on available buy/sell information. To measure such a relationship it is crucial to test the difference between expected returns of buy and sell signals or returns of buy/sell signals generated from the technical trading rules and returns of buy-and-hold strategy. Evident choice for this purpose is the t–test of differences between the arithmetic means of two subsamples, presented by the following expressions in two variants:
s s b b s b N N R R t 2 2 * (2) N N R R t s b s b s b 2 / 2 / / * (3) Where the Rb and Rs are mean returns following the buy and sell signals, R is the unconditional mean,
2
b and 2
s are the variances of returns generated from buy and sell signals,
2 is the unconditional variance,
b
N and Ns are the numbers of buy and sell signals, N is the overall number of observed data. The index b/s identifies combined buy and sell signals. The results of the t–test will help either accept the null
hypothesis (there is no actual difference between mean returns) or reject it (there is an actual difference between mean returns). However, these results assume independent and stationary time series with asymptotically normal distribution.
4. DATA AND SUMMERY STATISTICS
As noted previously, implementing a well-known trading rule provides an initial test of the weak-form market efficiency hypothesis. If stock markets are efficient, one cannot achieve superior results by using technical trading rules. However, if market inefficiencies are present, profitabilityopportunities may arise.
Due to the research of moving average trading rule in the course of time, this paper work uses the period of time from January 2009 to March 2014 presented by 1301 daily stock market indices values. In analysis we use two stock market indices: the Belgrade Stock Exchange index (BELEX15) and the Zagreb Stock Exchange index (CROBEX). Both indices are recognized as indicators of average stock price movements in emerging financial markets.
Table 2: Descriptive statistics
Index BELEX15 CROBEX
Mean 0.00002 0.00002 Max 0.08250 0.08563 Min -0.07471 -0.07020 Std 0.01292 0.01173 Skewness 0.41144 0.25183 Kurtosis 8.97576 11.20887 ρ(1) 0.26031 0.11024 ρ(2) 0.10592 -0.01563 ρ(3) 0.04200 0.07012 ρ(4) 0.10409 0.02522 ρ(5) 0.04610 -0.00333
Developing stock market indices, such as BELEX15 and CROBEX, significantly alter in statistical features from developed markets. Table 2 encompasses descriptive statistics of daily returns for time series of two stock market index values. The results indicate decidedly leptokurtic characteristics of data series with some potential signs of skewness. Furthermore, the volatility, presented by standard deviation (Std), is approximately the same for both indices. Also, serial correlations ρ(i), estimated at lag i for each data series, are roughly small, except at the first lag of BELEX15. Such data provides large enough samples to generate robust trading strategies that accomplish long term excess profits.
5. EMPIRICAL ANALYSIS
The remainder of this paper considers the implementation of moving average trading strategies to the series of historical index return data. In this sense, we incorporate six different trading strategies derived from moving average trading rule. These trading strategies differ among one another in the length of short and long moving averages denoted in the parenthesis. Table 3 and 4 shows the results of applying different moving average trading rules and approve further comparison of buy and sell trade signals generated by those rules.
Table 3: Test results for moving average trading rule using BELEX15
Strategy N(buy) N(sell) Rt(buy) Rt(sell) Rt>0(buy) Rt<0(sell) t-test buy-sell. p-value uncond p-value t-test
ma(1,100) 476 662 0.00102 -0.00002 0.51185 0.49118 2.00164 0.04553 1.55948 0.11913 ma(1,150) 449 592 0.00159 -0.00142 0.54681 0.44026 6.34211 0.00000 4.56152 0.00001 ma(1,200) 420 571 0.00048 -0.00106 0.52643 0.47311 3.42192 0.00064 2.33675 0.01960 ma(5,100) 564 526 0.00121 -0.00116 0.53162 0.44332 5.10662 0.00000 3.74980 0.00018 ma(5,150) 441 597 0.00091 -0.00073 0.52216 0.46718 3.31362 0.00095 2.44021 0.01481 ma(5,200) 420 569 0.00000 -0.00071 0.47917 0.47655 1.49474 0.13522 1.00910 0.31311 First column of table 3 presents short description of applied trading strategy. Therefore, the moving average trading rule is expressed in parentheses with short and long moving averages respectively. Following two
columns N(buy) and N(sell) contain the number of buy and sell signals recorded during the sample interval of time. After those columns, the next two Rt>0(buy) and Rt>0(sell) are the fraction of buy and sell returns
greater than zero in whole sample. The t-test (buy-sell) indicates the test statistics of differences between the arithmetic means of buy and sell signals. The following column, p-value, represents the probability of obtaining test statistics. The rejection of the null hypothesis is indicated by the probability column if p-value turns out to be less than a certain significance level, for example 5%. Finally, t-test (uncond.) presents standard statistics results of testing the difference between buy and sell one-day returns and unconditional one-day mean return.
Applied moving average rule presented in table 3 for BELEX15 demonstrates the existence of a significant difference in the number of generated buy and sell signals among all six trading strategies. However, the appearance of a trading signal does not necessarily represent immediate buy or sell action. A sell signal should be a precaution for investors to avoid potential stock investment activity until another convincing trading signal emerges. Otherwise, a buy signal without making any investment action could be an unquestionable evidence of maintaining the position of given stocks in the investment portfolio. Generally, the first trading signal in potential sequence of buy or sell signals is assumed to be of most interest due to the existing stock price autocorrelation. Such a mechanism of frequent generating trading signals gathers less credibility of the investors, but at the same time inspires the growth of activity at the stock market. Moving average strategies present different average return results considering a whole sample of time interval. Meanwhile, every applied strategy obtains a positive one-day average return on generated buy signals and a negative one-day average return on sell signals. Mentioned averages on buy and sell signals are significantly different than unconditional averages presented in table 1. Because of that, t-test of difference between conditional and unconditional average returns in case of BELEX15 shows significant difference with p-value less than 5% in four of six trading strategies.
Table 4: Test results for moving average trading rule using CROBEX
Strategy N(buy) N(sell) Rt(buy) Rt(sell) Rt>0(buy) Rt<0(sell) t-test buy-sell. p-value uncond p-value t-test
ma(1,100) 627 624 0.00023 0.00007 0.49945 0.48603 0.06954 0.94457 0.03316 0.97355 ma(1,150) 537 612 0.00089 -0.00083 0.51441 0.46827 4.73631 0.00000 2.54779 0.01096 ma(1,200) 470 627 0.00054 -0.00074 0.49703 0.48620 3.85213 0.00012 1.96337 0.04982 ma(5,100) 579 620 0.00038 -0.00046 0.48264 0.49169 2.22486 0.02626 1.34446 0.17903 ma(5,150) 545 604 0.00046 -0.00054 0.48545 0.48114 2.66328 0.00783 1.49647 0.13477 ma(5,200) 471 626 0.00013 -0.00029 0.46814 0.48392 0.35697 0.72117 0.18447 0.85368 On the other hand, testing results in case of CROBEX are presented in Teble 4. First impression about results is the increasing number of trading signals compared with the case of BELEX15, although we used the same size of sample in both cases. Furthermore, the fractions of buy and sell return greater than zero are just about the same. Anyway, there are significant differences between buy signals average one-day return and sell signals average one-day return in four of six implemented moving average trading strategies. Such results provide a confirmation that trading strategies produce useful trading signals. Thus the returns made from the trading rule in case of BELEX15 and CROBEX are likely to be predictable. Leaving these inefficient trading strategies, for example ma(1,100) and ma(5,200), this paper proposes a set of moving average trading strategies with significant predictive ability and a high possibility of making profitable investment. Finding the efficient trading rule in both stock market indices supports the rejection of the weak- form efficiency hypothesis. This fact once more reminds on perception improvement of applying technical trading rules in emerging stock markets such as Serbian and Croatian stock market. Both stock market indices indicate similar stock price movement patterns, as well.
Usually, there are more sell signals in observed sample of daily returns. In overall, moving average trading strategies generate sell signals in around 55.9% (BELEX15) and 53.5% (CROBEX) of all trading signals. This epilogue shows the signs of gently to entirely reduced stock market activity and draws attraction to the lack of market capitalization. Altough Pauwels et al. (2012) consider it as a support of the efficient market hypothesis. Despite this, moving average trading rule in case of BELEX15 and CROBEX is capable to generate positive returns over a whole sample period due to the fact that the profit gained by winning trades surpass the losses from losing trades.
4. CONCLUSION
The paper attempted to provide an extensive range of possible moving average trading strategies that are capable to improve forecasting ability of stock price movements in and out of the observed sample. Overall, the results of this study contain strong support for the moving average trading strategies we have investigated and signify that almost all buy and sell differences are positive. According to previous claim, the t statistics mainly reject the null hypothesis of equality between average buy and sell returns or average trading returns and unconditional (passive buy-and-hold) returns. Strictly speaking, adequate implementation of moving average trading rule in case of Serbian and Croatian stock market leads to the rejection of the weak-form market efficiency hypothesis. Furthermore, it is inherent to the emerging stock markets that applied trading strategies generate more losing trades than winning trades.
An implementation of trading rules represents just a fragment of a comprehensive investment portfolio management analysis. As a result, complete perception of the stock price or/and return movement patterns in observed sample of time requires tools of the fundamental investment analysis, which generally rely on experience of financial experts. Nevertheless, applied trading strategies offer insight in the behaviour of the stock markets. Therefore, previously done analysis does not appear appropriate for small investors to implement. Respectively, individual case of stock trades requires analogous procedure of testing performances of moving average trading strategies referred directly to potential investment chances.
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