Objective:
The objective of this paper is to test whether the technical analysis indicator MACD is effective in real trading. We will use the S&P 500 Index as our samples, and our main idea is to find the average return and VaR when we buy at the time MACD shows a “golden cross” and sell at the time when there is a “death cross”.
MACD:
Before we do the test, let’s start to define the MACD as well as its components. MACD is one of the most popular indicators used in the technical analysis. And it is mainly comprised of MACD line, signal line, and the histogram. MACD line and the signal line are calculated by using the EMA (exponential moving average) function, while the histogram is the difference between the MACD line and signal line. MACD line is the difference between exponential moving averages of 12 day stock price and the exponential moving averages of 26 days stock price. The signal line is the exponential moving averages of 9 day MACD. (12, 26, 9) is the well-recognized moving average lengths used in the industry, but can be altered with other appropriate numbers.
 MACD Line = EMA [stockprice, 12] – EMA [stockprice, 26]
 Signal Line = EMA [MACD, 9]
 Histogram = MACD Line – Signal Line
In technical analysis, there is a basic rule to apply the MACD into practice, say when the MACD line up crosses the signal line, the stock price is expected to rise in the short term, while the MACD later on down crosses the signal line, the stock price may be expected to go down in short run.
So their cross points are always treated as signals to buy or sell, in which the up cross point is called “golden cross”, while the down cross is called “death cross”. Our test is to show whether MACD is helpful and how much this buy at “golden cross”, sell at “death cross” strategy can generate in real transaction.
Transaction strategy:
When the Signal Line crosses the MACD line from above, we define it as a Sell Signal. When the Signal Line crosses the MACD line from below, we define it as a Buy Signal. So when a buy signal occurs, we close our previous short position and buy 1 contract of the S&P 500 ETF. And when the sell signal occurs, we close our previous long position and sell 1 contract of the S&P 500 ETF.
Return and VaR:
We calculate 2 sets of return of our transactions. One is the transaction return. It is the return of each transaction we have made based on our transaction strategy. The other is the daily return. We ignored transaction costs in our calculation. It is the daily return during each of our transactions. In order to get a concept of the risk of this trading strategy, we also calculated the 5% VaR for both of the transaction return and the daily return. W

Code:
%retrieve data start_date = '03011950'; % a really early date will go to the first day of trading end_date = '12122012'; subject_name = '^GSPC'; subject = hist_stock_data(start_date,end_date,subject_name); sdate = subject.Date(end:-1:1); p = subject.AdjClose(end:-1:1); %calculate exponential moving average lamda=0.94; ema12=ema(p,lamda,12); ema26=ema(p,lamda,26); %define macd diff=ema12-ema26; dem=ema(diff,lamda,9); macd=diff-dem; %starting backtesting ii=0; for i=26:(length(macd)-1); a=macd(i); b=macd(i-1); if a*b0; %one transaction return for n=1:2:(l-2); m=signal(n); m1=signal(n+1); m2=signal(n+2); ret(n)=1-p(m1)/p(m); ret(n+1)=p(m2)/p(m1)-1; %daily return for u=m:m1-1; q=q+1; ret1(q)=1-p(u+1)/p(u); end for u=m1:m2-1; q=q+1; ret1(q)=p(u+1)/p(u)-1; end end ret(l-1)=1-p(signal(l))/p(signal(l-1)); for last = signal(n+2):signal(end)-1; q=q+1; ret1(q)=1-p(last+1)/p(last); end else %one transaction return for n=1:2:(l-2); m=signal(n); m1=signal(n+1); m2=signal(n+2); ret(n)=p(m1)/p(m)-1; ret(n+1)=1-p(m2)/p(m1); %daily return for u=m:m1-1; q=q+1; ret1(q)=p(u+1)/p(u)-1; end for u=m1:m2-1; q=q+1; ret1(q)=1-p(u+1)/p(u); end end ret(l-1)= p(signal(l))/p(signal(l-1))-1; for last = signal(n+2):signal(end)-1; q=q+1; ret1(last)=p(last+1)/p(last)-1; end end % identify if length() is odd or even
%if mod(l,2)==0;
% ret=[ret;lastret]; %else ret=ret;
% ret1=ret1;
%end

%total return within horizon totalret=prod((ret+1))-1 check = prod((ret1+1))-1-totalret;

%trading strategy accuracy accuracy=proportion(ret>0) %trading strategy outperformance outperformance=totalret-totalret_index %trading strategy's 1day VaR at 95% & 99%
VaR05=quantile(ret1,.05)
VaR01=quantile(ret1,.01)

%indice's 1day VaR at 95% & 99% indexVaR05=quantile(ret1_index,.05) indexVaR01=quantile(ret1_index,.01)

Results: totalret = -0.3077 accuracy = 0.4228 outperformance = -82.1771
VaR05 = -0.0146
VaR01 = -0.0263 indexVaR05 = -0.0145 indexVaR01 = -0.0259 totalret_index = 81.8694
As we can see in the result, this trading strategy is not profitable at all. The total index return during the testing period is 8187%, while the total return of our trading strategy is -30.77%.
The VaR of our trading strategy is about the same as the index VaR.