I am getting very frustrated with this one problem I have about the pearson correlation coefficient. I have a program that outputs stock values for two tickers for each day for a specified period of time and I also draw a graph of those values. You can choose between USD, EUR and SEK for output. However, my pearson correlation coefficient seems to be different depending on what currency I choose? I can't figure out if that is correct or if there's an error somewhere? The actual function that does the calculation seems to be OK, so I don't understand...
Should the coefficient be different or should it be the same depending on currency? EUR and SEK currency values for the stocks are calculated by multiplying the USD value of the stock with the close value for either EUR or SEK for that same day.
This method caculates the coefficient:
public double CorrelationCalc(ArrayList<Integer> list1, ArrayList<Integer> list2) {
double sumX= 0.0, sumY = 0.0, sumXX = 0.0, sumYY = 0.0, sumXY = 0.0;
int length = list1.size();
for (int i=0; i<length; i++) {
int x = list1.get(i);
int y = list2.get(i);
sumX+=x;
sumY+=y;
sumXX+=x*x;
sumYY+=y*y;
sumXY+=x*y;
}
double cov = sumXY / length - sumX*sumY / length / length;
double sigmaX = Math.sqrt(sumXX / length - sumX*sumX / length / length);
double sigmaY = Math.sqrt(sumYY / length - sumY*sumY / length / length);
return cov/sigmaX/sigmaY;
}
The stock close values are fetched from yahoo finance through .csv files and these loops get the values and add them to an arraylist.
//This one is for when USD is selected. (Close value for each date located
//at index 4 on each line in the csv file)
while ((line = buf.readLine())!=null && (line2 = buf2.readLine())!= null) {
if(n != 0) { //First row contains text only
close1 = (Math.round(100 * Double.parseDouble(line.split(",")[4]))/100.0);
close2 = Math.round(100 * Double.parseDouble(line2.split(",")[4]))/100.0;
ticker1List.add((int) Math.round(close1));
ticker2List.add((int) Math.round(close2));
}
n++;
}
And. buf3 is a stringbuffer reading the currency rates csv
//This one is for non USD (SEK or EUR). multiplies the values with the currency rate
while ((line = buf.readLine())!=null && (line2 = buf2.readLine())!= null && (line3 = buf3.readLine())!= null) {
if(n != 0) {//First row contains text only
while (!line.split(",")[0].equals(line3.split(",")[0])) { //Makes sure that dates match
line3 = buf3.readLine();
}
close1 = (Math.round(100 * Double.parseDouble(line.split(",")[4])*Double.parseDouble(line3.split(",")[4]))/100.0);
close2 = Math.round(100 * Double.parseDouble(line2.split(",")[4])*Double.parseDouble(line3.split(",")[4]))/100.0;
ticker1List.add((int) Math.round(close1));
ticker2List.add((int) Math.round(close2));
}
n++;
}
ticker1List and ticker2List are later the lists sent to the above method for calculation.
OUTPUT samples:
USD
ticker1List = {542, 535, 539, 547, 559, 563, 575, 579, 578, 581, 573, 574, 560, 556, 561, 553, 562, 558, 566, 564, 565, 565, 578, 567, 564, 558, 561, 555, 549, 541, 544, 545, 549, 548, 549, 549, 540, 541, 544, 533, 545, 543, 549, 557, 574, 566, 564, 561, 549, 551, 553, 543, 535, 542, 549, 546, 539, 539, 549, 546, 547, 549, 553, 557, 555, 547, 554, 554, 545, 549, 554, 555, 552, 550, 543, 542, 553, 550, 547, 543, 545, 547, 556, 558, 560, 563, 559, 558, 553, 541, 540, 543, 547, 546, 550, 542, 545, 556, 572, 584, 584, 602, 700, 693, 695, 695, 675, 655, 658, 660, 661} ticker2List = {44, 44, 44, 44, 44, 44, 44, 43, 43, 43, 42, 43, 42, 42, 41, 41, 42, 42, 43, 42, 43, 43, 43, 41, 41, 41, 41, 41, 41, 40, 42, 42, 41, 41, 42, 42, 42, 42, 42, 42, 43, 43, 43, 43, 48, 48, 49, 49, 49, 49, 48, 48, 46, 47, 48, 47, 47, 48, 49, 48, 48, 48, 48, 47, 47, 47, 48, 47, 47, 47, 47, 47, 46, 46, 46, 46, 47, 46, 46, 45, 46, 46, 47, 46, 46, 46, 46, 46, 45, 44, 44, 44, 44, 44, 44, 44, 45, 45, 46, 46, 46, 47, 47, 47, 47, 46, 46, 46, 45, 45, 46 }
Pearson: 0.1439484634863799
SEK
Currency rate = {8.55523, 8.509, 8.5914, 8.564, 8.5947, 8.5379, 8.6162, 8.6554, 8.54502, 8.5075, 8.5015, 8.4947, 8.4503, 8.4634, 8.46479, 8.51185, 8.4701, 8.51984, 8.38558, 8.2967, 8.23152, 8.4052, 8.24647, 8.23443, 8.253, 8.13911, 8.11373, 8.12167, 8.09872, 8.17692, 8.1593, 8.20512, 8.2148, 8.26875, 8.28135, 8.29895, 8.3914, 8.2918, 8.31362, 8.4409, 8.58413, 8.548, 8.4556, 8.51005, 8.4676, 8.4153, 8.33381, 8.3411, 8.3424, 8.22841, 8.19809, 8.24101, 8.23992, 8.3265, 8.30831, 8.25121, 8.2754, 8.2294, 8.3507, 8.36978, 8.40981, 8.3328, 8.34131, 8.5058, 8.60651, 8.6354, 8.6344, 8.72934, 8.6574, 8.69648, 8.63365, 8.58971, 8.714, 8.7647, 8.81522, 8.81353, 8.75727, 8.6755, 8.6743, 8.5591, 8.52942, 8.65399, 8.6243, 8.5889, 8.586, 8.58851, 8.493, 8.51087, 8.50157, 8.61801, 8.6706, 8.6013, 8.68419, 8.6546, 8.7287, 8.5913, 8.62343, 8.55167, 8.4879, 8.4632, 8.33779, 8.32539, 8.2671, 8.3381, 8.36064, 8.3922, 8.28541, 8.40471, 8.4139, 8.3832, 8.42055 }
gives
ticker1List = {4562, 4485, 4532, 4600, 4634, 4722, 4808, 4826, 4781, 4841, 4777, 4859, 4752, 4752, 4839, 4751, 4902, 4826, 4917, 4848, 4898, 4872, 4910, 4826, 4787, 4789, 4818, 4764, 4739, 4684, 4640, 4664, 4761, 4754, 4804, 4835, 4758, 4742, 4736, 4576, 4701, 4721, 4754, 4866, 4953, 4889, 4857, 4775, 4577, 4593, 4649, 4545, 4468, 4461, 4543, 4503, 4476, 4492, 4525, 4504, 4482, 4520, 4609, 4644, 4621, 4605, 4693, 4716, 4611, 4695, 4755, 4687, 4587, 4557, 4561, 4499, 4576, 4548, 4497, 4455, 4446, 4470, 4504, 4528, 4541, 4585, 4610, 4594, 4561, 4549, 4445, 4508, 4590, 4649, 4659, 4611, 4610, 4707, 4831, 4962, 4965, 5120, 5978, 5997, 5991, 5935, 5799, 5607, 5655, 5613, 5659}
ticker2List = {369, 370, 371, 370, 365, 368, 367, 361, 356, 359, 353, 363, 357, 359, 354, 356, 363, 361, 369, 364, 372, 369, 365, 353, 350, 352, 352, 349, 351, 349, 354, 355, 359, 360, 365, 368, 367, 370, 367, 358, 370, 371, 372, 378, 413, 415, 423, 417, 406, 405, 406, 398, 386, 384, 395, 391, 393, 397, 401, 398, 394, 392, 397, 396, 391, 392, 403, 404, 396, 404, 403, 395, 385, 383, 384, 379, 386, 384, 378, 373, 374, 376, 378, 374, 375, 374, 377, 376, 373, 373, 363, 369, 372, 378, 375, 377, 377, 378, 385, 388, 389, 397, 398, 406, 407, 389, 396, 393, 390, 386, 396}
Pearson: 0.20617640237659246
Your implementation works only if both stocks are quoted in the same currency, as they are both being converted via the same FX rate time series (buf3 in your code). The correlation when they are both in their native currency can differ from when they are both converted to another currency because the FX rate is not constant. For example, if both stocks are in EUR, and you calculated their correlation in USD, you are calculating the correlation that a USD-based investor would experience after converting dollars to euros, then purchasing the stocks. Part of the fluctuation in the time series is due to the movement in the EURUSD exchange rate, not just the stock price. By comparison, the EUR-based investor in both assets would only experience the correlation of the stock prices, and would have no exposure to the FX rate.
It really depends on what you are trying to accomplish here. Your code won't handle stocks which are quoted natively in different currencies, for example. If that were the case, the correlation between the asset prices after conversion to a common currency would be the same, regardless of the currency in which you calculate the correlation, as long as the FX rates are consistent and assuming perfect precision. If asset1 is quoted in EUR and asset2 is quoted in USD, you would get the same correlation in the following cases:
Even when comparing assets in different currencies, there are reasonable applications of computing their correlations without FX rates at all, i.e. asset1 in EUR vs asset2 in USD. That would result in a different correlation from those above.