Matlab for backtesting Best practice advise wanted. Examples provided

Hey guys any help on the below would be much appreciated.

Summary

I am reading a book that come with examples. The subject matter is quantitative trading. The examples provides are are quite old therefore I am working to reqork them as best as I can.

Question - I have Pair trading example below however my result doesn't match the result of the original. If someone can show me the right way great if not advise would be great too.

• My results - sharpeTrainset = NaN, sharpeTestset = 0.9917
• Expected result - sharpeTrainset = should be about 2.3, sharpeTestset = should be about 1.5

Some lines I found a real challenge to rework that are probably leading to my result

results = fitlm(t1,t2);

hedgeRatio = results.Coefficients{2, "Estimate"};

positions=fillmissing(positions, "previous");

train1 = cl1(trainset, "Adj Close");
train2 = cl2(trainset, "Adj Close");
t1 = table2array(train1);
t2 = table2array(train2);

% combine the 2 price series
ccl1 = table2array(cl1); 
ccl2 = table2array(cl2);
ccl = [ccl1, ccl2];

Here is the out of date code

clear; % make sure previously defined variables are erased.

[num, txt]=xlsread('GLD'); % read a spreadsheet named "GLD.xls" into MATLAB. 

tday1=txt(2:end, 1); % the first column (starting from the second row) is the trading days in format mm/dd/yyyy.

tday1=datestr(datenum(tday1, 'mm/dd/yyyy'), 'yyyymmdd'); % convert the format into yyyymmdd.

tday1=str2double(cellstr(tday1)); % convert the date strings first into cell arrays and then into numeric format.

adjcls1=num(:, end); % the last column contains the adjusted close prices.

[num, txt]=xlsread('GDX'); % read a spreadsheet named "GDX.xls" into MATLAB. 

tday2=txt(2:end, 1); % the first column (starting from the second row) is the trading days in format mm/dd/yyyy.

tday2=datestr(datenum(tday2, 'mm/dd/yyyy'), 'yyyymmdd'); % convert the format into yyyymmdd.

tday2=str2double(cellstr(tday2)); % convert the date strings first into cell arrays and then into numeric format.

adjcls2=num(:, end); % the last column contains the adjusted close prices.

[tday, idx1, idx2]=intersect(tday1, tday2); % find the intersection of the two data sets, and sort them in ascending order

cl1=adjcls1(idx1); 

cl2=adjcls2(idx2);  

trainset=1:252; % define indices for training set

testset=trainset(end)+1:length(tday); % define indices for test set

% determines the hedge ratio on the trainset
results=ols(cl1(trainset), cl2(trainset)); % use regression function 
hedgeRatio=results.beta;

spread=cl1-hedgeRatio*cl2; % spread = GLD - hedgeRatio*GDX

plot(spread(trainset));

figure;

plot(spread(testset));

figure;

spreadMean=mean(spread(trainset)); % mean  of spread on trainset

spreadStd=std(spread(trainset)); % standard deviation of spread on trainset

zscore=(spread - spreadMean)./spreadStd; % z-score of spread

longs=zscore<=-2; % buy spread when its value drops below 2 standard deviations.

shorts=zscore>=2; % short spread when its value rises above 2 standard deviations.

exits=abs(zscore)<=1; % exit any spread position when its value is within 1 standard deviation of its mean.

positions=NaN(length(tday), 2); % initialize positions array

positions(shorts, :)=repmat([-1 1], [length(find(shorts)) 1]); % long entries

positions(longs,  :)=repmat([1 -1], [length(find(longs)) 1]); % short entries

positions(exits,  :)=zeros(length(find(exits)), 2); % exit positions

positions=fillMissingData(positions); % ensure existing positions are carried forward unless there is an exit signal

cl=[cl1 cl2]; % combine the 2 price series

dailyret=(cl - lag1(cl))./lag1(cl);

pnl=sum(lag1(positions).*dailyret, 2);

sharpeTrainset=sqrt(252)*mean(pnl(trainset(2:end)))./std(pnl(trainset(2:end))) % the Sharpe ratio on the training set should be about 2.3

sharpeTestset=sqrt(252)*mean(pnl(testset))./std(pnl(testset)) % the Sharpe ratio on the test set should be about 1.5

plot(cumsum(pnl(testset)));

Here is my code (trial and error rework)

T = readtable("Backtesting/GLD.xls", "VariableNamingRule","preserve"); % read a spreadsheet named "GLD.xls" into MATLAB. 
tday1=T{1:end, 1}; % the first column (starting from the second row) is the trading days in format mm/dd/yyyy.
tday1.Format = 'yyyy-MMM-dd'; % convert the format into yyyymmdd.
adjcls1=T(:, end); % the last column contains the adjusted close prices.
G = readtable("Backtesting/GDX.xls", "VariableNamingRule","preserve"); % read a spreadsheet named "GDX.xls" into MATLAB.
tday2=G{1:end, 1}; % the first column (starting from the second row) is the trading days in format mm/dd/yyyy.
tday2.Format = 'yyyy-MMM-dd'; % convert the format into yyyymmdd.
adjcls2=G(:, end); % the last column contains the adjusted close prices.
[tday, idx1, idx2]=intersect(tday1, tday2); % find the intersection of the two data sets, and sort them in ascending order
cl1=adjcls1(idx1,"Adj Close"); 
cl2=adjcls2(idx2,"Adj Close");
trainset=1:252; % define indices for training set
testset=trainset(end)+1:length(tday); % define indices for test set from the 253 to 385
% determines the hedge ratio on the trainset
train1 = cl1(trainset, "Adj Close");
train2 = cl2(trainset, "Adj Close");
t1 = table2array(train1);
t2 = table2array(train2);
results = fitlm(t1,t2); % use regression function 
hedgeRatio = results.Coefficients{2, "Estimate"}; 
spread=cl1{:,"Adj Close"}-hedgeRatio*cl2{:,"Adj Close"}; % spread = GLD - hedgeRatio*GDX
plot(spread(trainset));
figure;
plot(spread(testset));
figure;
spreadMean = mean(spread(trainset)); % mean  of spread on trainset
spreadStd = std(spread(trainset)); % standard deviation of spread on trainset
zscore = (spread - spreadMean)./spreadStd; % z-score of spread
longs=zscore <= -2; % buy spread when its value drops below 2 standard deviations.
shorts = zscore >= 2; % short spread when its value rises above 2 standard deviations.
exits = abs(zscore)<=1; % exit any spread position when its value is within 1 standard deviation of its mean.
positions = NaN(length(tday), 2); % initialize positions array
positions(shorts, :)=repmat([-1 1], [length(find(shorts)) 1]); % long entries
positions(longs,  :)=repmat([1 -1], [length(find(longs)) 1]); % short entries
positions(exits,  :)=zeros(length(find(exits)), 2); % exit positions
positions=fillmissing(positions, "previous"); % ensure existing positions are carried forward unless there is an exit signal
% combine the 2 price series
ccl1 = table2array(cl1); 
ccl2 = table2array(cl2);
ccl = [ccl1, ccl2];
dailyret=(ccl - lag1(ccl))./lag1(ccl);
pnl=sum(lag1(positions).*dailyret, 2);
sharpeTrainset=sqrt(252)*mean(pnl(trainset(2:end)))./std(pnl(trainset(2:end))); % the Sharpe ratio on the training set should be about 2.3
sharpeTestset=sqrt(252)*mean(pnl(testset))./std(pnl(testset)); % the Sharpe ratio on the test set should be about 1.5
plot(cumsum(pnl(testset)));

Answer 1

[wayne w]

I answered this using Latex but this editor wants me to do half latex and half retyping everything which is annoying. See pdf attachment.