This paper studies the profitability of the Moving Average Convergence-Divergence (MACD) trading rule under three different crossing rules: the MACD zero line, the 9-day and 14-day signal lines. It is found that the trading rules perform well in the stock markets of Germany and Hong Kong. Our research also shows that generally the major stock markets around the world have become more efficient after the millennium.

Chen Li

Ho Tin Yu

Terence Tai-Leung Chong

English

Research Papers in Economics

     
 
 
  
  
Volume 07, Issue 12 
  
Structural Change in the Stock Market Efficiency after the Millennium: The 
MACD Approach 
  
 
 
Terence Tai-Leung Chong  
The Chinese University of Hong Kong 
Chen Li  
The Chinese University of Hong Kong 
Ho Tin Yu  
The Chinese University of Hong Kong
Abstract 
This paper studies the profitability of the Moving Average Convergence-Divergence (MACD) trading rule under three 
different crossing rules: the MACD zero line, the 9-day and 14-day signal lines. It is found that the trading rules 
perform well in the stock markets of Germany and Hong Kong. Our research also shows that generally the major 
stock markets around the world have become more efficient after the millennium.
 
Citation: Terence Tai-Leung Chong and Chen Li and Ho Tin Yu, (2008) ''Structural Change in the Stock Market Efficiency after the 
Millennium: The MACD Approach'', Economics Bulletin, Vol. 7 no.12 pp. 1-6. 
Submitted: Jun 02 2008.   Published: August 29, 2008. 
 
      2
I. Introduction 
 
Technical analysis involves the study of historical prices in order to predict future 
price movements. It assumes that the information contained in historical prices is not 
correctly incorporated in current prices (Ellinger, 1971). Whether technical trading 
rules can generate excess returns has long been a controversial issue. A number of 
studies have suggested that market indicators alone cannot improve the prediction of 
the future prices (Neftci, 1991; Hudson et al., 1996; Mills, 1997). However, there are 
also studies that support technical trading rules (Treynor and Ferguson, 1985; Brock et 
al., 1992). Most of the earlier studies examine simple trading rules such as the moving 
average rule and the trading range break rule. Chong and Ng (2008) test the Moving 
Average Convergence-Divergence (MACD) rules on the London Stock Exchange 
FT30 Index and concluded that they can generate abnormal returns. Developed by 
Gerald Appel in the 1960s, the MACD is one of the simplest and most frequently 
applied trading rules in the market. In this paper, three signal lines of MACD will be 
evaluated in turn to see whether their associated trading rules are profitable in five 
major stock markets (US, Japan, UK, Germany, Hong Kong). We will also compare 
the market efficiency of these five markets before and after the millennium.   
 
 
 
II. Trading rules and Data 
 
The MACD is calculated by subtracting the long exponential moving average (EMA) 
from the short EMA. The EMA is defined as: 
 
1
22
(1 ) tt t EMA P EMA
nn
− =×+− , 
 
where EMAt is the exponential moving average at time t, n is the window bandwidth, 
Pt    is the closing price on day t. The initial EMA is the n-day simple moving average 
of the series. In this paper, we apply the 12 and 26-day EMAs, the most commonly 
used short and long-term EMAs for the MACD trading rule (Murphy, 1999).   
 
12 26 day day
tt t MACD EMA EMA
−− =−. 
 
Three different signal lines are examined in turn: 1) the MACD zero line; 2) the 9-day 
EMA of the MACD; and 3) the 14-day EMA of the MACD. A buy signal is triggered 
when the MACD crosses the signal line from below, while a sell signal is triggered 
when the MACD crosses the signal line from above. Specifically, we examine three 
trading rules: 
 
  3
Rule 1: 
Buy:  (1 )0 MACD t −< and  ( ) 0 MACD t >  
Sell:  (1 )0 MACD t −>  and  ( ) 0 MACD t <  
Rule 2: 
Buy: 
9 (1 ) (1 )
day
MACD MACD t EMA t
− −< − and 
9 () ()
day
MACD MACD t EMA t
− >  
Sell: 
9 (1 ) (1 )
day
MACD MACD t EMA t
− −> − and 
9 () ()
day
MACD MACD t EMA t
− <  
Rule 3: 
Buy: 
14 (1 ) (1 )
day
MACD MACD t EMA t
− −< − and 
14 () ()
day
MACD MACD t EMA t
− >  
Sell: 
14 (1 ) (1 )
day
MACD MACD t EMA t
− −> − and 
14 () ()
day
MACD MACD t EMA t
− <  
 
 
Short selling is not allowed in our study. A position that has been taken will not be 
reversed until the appearance of an opposite signal. For any signal at time t, we long 
or short the index at the closing price at t. Since there are about 250 trading days in a 
year, the performance is evaluated in terms of the annualized rate of return defined as: 
 
 
Annual rate of return 
250/
123 [(1 )(1 )(1 ) (1 )] 1
T
m rrr r = +++ ⋅ ⋅ ⋅ + −  
 
 
where 1+rj=S(j)/B(j); S(j) and B(j) are selling and buying prices respectively in the jth 
transaction and m is the number of transactions, and T is the sample size. We examine 
the effectiveness of the each signal line by comparing their associated returns. The 
data series under study consists of the daily closing indices of five largest stock 
markets in the world extracted from DataStream. The sample details are as follows: 
 
 
 
Table 1. The five stock market indices and their sample period 
Index Countries  From  To 
Dow Jones Industrials USA  1/1/1993  31/12/2007 
FTSE 100  United Kingdom  1/1/1993  31/12/2007 
DAX 30 Performance  Germany  1/1/1993  31/12/2007 
Nikkei 225 Stock Avg.  Japan  1/1/1993  31/12/2007 
Hang Seng Index  Hong Kong 1/1/1993  31/12/2007 
 
  4
III. Results and Conclusion 
 
Table 2 shows the annual rate of return (in percentage) generated by three trading 
rules based on the Moving Average Convergence-Divergence and the buy-and-hold 
strategies. The figures in the parentheses are the number of transactions. The 
performance of each trading rule is listed in the table. For each index, the highlighted 
figure is the highest rate of return. If there is more than one highest return, the one 
with the smallest number of transaction will be highlighted. From our findings, the 
Moving Average Convergence-Divergence rule performs well in the stock markets of 
Germany and Hong Kong. All three trading rules Hang Seng Index generate a 
double-digit annual return. The zero-line crossing is found to be the most profitable 
rule for the DAX 30, Dow Jones Industrials and FTSE 100. The rule of 9-day signal 
line is found to be most profitable for the Nikkei 225, and the rule of 14-day signal 
line is the most profitable rule for the Hang Seng Index. 
 
 
Table 2. The average rate of return for MACD and the number of transactions 
 
Index Names  MACD Zero Line  9-day Signal Line  14-day Signal Line 
Dow Jones Industrials  4.04%  (69) 2.40%  (177) 3.80%  (147) 
FTSE 100  0.97%  (73) -3.03%  (192) -3.36%  (160) 
DAX 30 Performance  12.24%  (52) 1.26%  (184) 5.06%  (153) 
Nikkei 225 Stock Avg. 1.10%  (67)  1.12%  (160) 0.60%  (133) 
Hang Seng Index  13.41%  (58)  11.99%  (162)  13.79%  (120) 
 
 
 
To investigate whether there is any change in the market efficiency, we divide the 
whole sample into two sub-samples using the year 2000 as a cut-off point. The 
millennium as the cut-off year is a nature choice for three reasons: First, it is just two 
years after the Asian Financial Crisis; Second, it is the year when the internet bubble 
started to collapse (Chong and Chan, 2008); Third, it is also close to the date of the 
911 attack. 
 
Table 3a and 3b show the returns of the MACD rules before and after the millennium. 
For the stock market of the Germany and the United Kingdom, the zero-line crossing 
rule is the most profitable rule in both periods. In other stock markets, there is no 
trading rule that can consistently outperform others in both subsamples. As the market 
develops, it should become more efficient. Note that the returns after the year 2000 
are generally smaller than those before the year 2000. This implies that the market has 
become more efficient. In a nutshell, we find that the Moving Average  5
Convergence-Divergence perform well in the stock markets of Germany and Hong 
Kong. Our research also shows that generally the major stock markets have become 
more efficient after the millennium. 
 
 
Table 3a: The average rate of return for Period I: 1/1/1993 - 31/12/1999 
Index Names  MACD Zero Line  9-day Signal Line  14-day Signal Line 
Dow Jones Industrials  10.65%  4.37%  7.28% 
FTSE 100  3.83%  0.51%  -0.55% 
DAX 30 Performance  15.27%  4.22%  9.19% 
Nikkei 225 Stock Avg.  1.69%  0.28%  3.49% 
Hang Seng Index  15.67%  20.97%  23.76% 
 
Table 3b: The average rate of return for Period II: 1/1/2000 - 31/12/2007 
Index Names  MACD Zero Line  9-day Signal Line  14-day Signal Line 
Dow Jones Industrials  -1.99%  1.09%  1.20% 
FTSE 100  -2.13%  -5.73%  -5.29% 
DAX 30 Performance  5.27%  -1.84%  0.85% 
Nikkei 225 Stock Avg.  0.19%  2.17%  -1.48% 
Hang Seng Index  9.32%  5.56%  5.70% 
 
 
 
 
References 
 
Brock, W., J. Lakonishok and B. Lebaron (1992). Simple Technical Trading Rules and 
the Stochastic Properties of Stock Returns. Journal of Finance 47, pp.1731–1764. 
 
Chong, T.T.L. and W.K. Ng (2008).  Technical Analysis and the London Stock 
Exchange: Testing the MACD and RSI rules using the FT30. Applied Economics 
Letters, forthcoming. 
 
Chong, T.T.L. and  S.T. Chan (2008). Structural Change in the Efficiency of the 
Japanese Stock Market after the Millennium. Economics Bulletin 7, No. 7, pp. 1-7. 
 
Ellinger, A.G. (1971). The art of Investment, 3
rd ed, Bowes and Bowes, London. 
 
Hudson, R., M. Dempsey, and K. Keasey (1996). A Note on the Weak Form  6
Efficiency of Capital Markets: The Application of Simple Technical Trading Rules 
to UK Stock Prices – 1935 to 1994. Journal of Banking and Finance 20, 
pp.1121-1132.  
 
Mills, T.C. (1997). Technical Analysis and the London Stock Exchange: Testing 
Trading Rules using the FT30. International Journal of Financial Economics 2, 
pp. 319-331.   
 
Murphy, J. J. (1999) Technical Analysis of the Financial Markets. New York Institutes 
of Finance. 
 
Netftci, S.N. (1991). Naïve Trading Rules in Financial Markets and 
Wiener-Kolmogorov Prediction Theory: A Study of Technical Analysis. Journal of 
Business 64, pp. 549-571. 
 
Treynor, J.L. and R. Ferguson (1985). In Defense of Technical Analysis. Journal of 
Finance 40, pp. 757-773. 

A Note on the Weak Form 6 Efficiency of Capital Markets: The Application of Simple Technical Trading Rules

In Defense of Technical Analysis.

Naïve Trading Rules in Financial Markets and Wiener-Kolmogorov Prediction Theory: A Study of Technical Analysis.

Simple Technical Trading Rules and the Stochastic Properties of Stock Returns.

Technical Analysis and the London Stock Exchange: Testing the MACD and RSI rules using the FT30. Applied Economics Letters, forthcoming.

Technical Analysis and the London Stock Exchange: Testing Trading Rules using the FT30.

Technical Analysis of the Financial Markets. New York Institutes of Finance.

Structural Change in the Stock Market Efficiency after the Millennium: The MACD Approach

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Structural Change in the Stock Market Efficiency after the Millennium: The MACD Approach

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