WEBVTT 00:01.040 --> 00:05.310 In the last couple of videos we extensively worked with rolling statistics. 00:05.330 --> 00:11.660 For instance we calculated the simple moving average of stock prices and also the rolling mean return 00:11.990 --> 00:17.260 and the rolling standard deviation of returns and actually all examples. 00:17.260 --> 00:22.520 For one thing in common they're rolling statistics I calculated on one time series. 00:22.520 --> 00:28.850 So for example on the Apple stock price and in this video we will learn how to calculate rolling statistics 00:28.850 --> 00:34.490 like correlation or the covariance where we need to operate on two time series. 00:34.490 --> 00:41.960 So for example we could to calculate the rolling correlation of Apple monthly returns with the Boeing 00:41.960 --> 00:43.740 monthly returns. 00:43.760 --> 00:51.770 So now let's start here and as always import pandas and met plot lip and we use the Seabourn style and 00:51.770 --> 00:58.460 then we import our six stocks that we have in our stock so yes we fire and we create a daytime index 00:58.490 --> 01:01.850 and we only select here the close column. 01:02.150 --> 01:04.380 So let's do this and let's have a look here. 01:04.400 --> 01:05.950 So these are our stocks. 01:06.080 --> 01:10.600 Apple Boeing Disney IBM Coca-Cola and Microsoft. 01:10.700 --> 01:15.680 And now in the following minutes we want to calculate the rolling correlation between the Apple stock 01:16.130 --> 01:17.270 and the Boeing stock. 01:17.270 --> 01:26.010 And therefore we only select the apple and Boeing and from our time period from end of 2009 and the 01:26.090 --> 01:32.760 end of 2000 and 18 and we actually created a new data frame and called the data frame. 01:32.810 --> 01:34.350 Apple Boeing. 01:34.550 --> 01:37.120 So let's do this and let's have a look. 01:37.130 --> 01:41.630 So here we have the two columns Apple and Boeing with the stock prices. 01:41.630 --> 01:48.020 And I want a first step we calculate the monthly returns and therefore first of all we have to re sample 01:48.020 --> 01:54.950 the data frame to a monthly and we pass a period to the kind parameter and we take actually the very 01:54.950 --> 02:01.570 last the trading price of each month and then with the percentage change method we actually calculate 02:01.570 --> 02:05.600 the simple returns and we are actually saving. 02:05.630 --> 02:10.080 The new returns data frame and the variable monthly returns. 02:10.210 --> 02:11.010 So let's have a look. 02:13.060 --> 02:21.730 So here we have the monthly returns for Apple and Boeing starting in January 2010 and December 2000 02:21.790 --> 02:23.350 and 18. 02:23.650 --> 02:26.480 And that's also the a look here with the info method. 02:26.530 --> 02:33.830 So we have a total one hundred eight monthly returns for nine years times twelve months gives us one 02:33.830 --> 02:40.540 hundred eight monthly returns and then we could simply calculate the correlation between the apple return 02:40.900 --> 02:44.860 and the Boeing return for the whole nine year period. 02:44.860 --> 02:53.340 So by using here the com method let's do this year and no surprise there that we have a perfect positive 02:53.340 --> 02:58.020 correlation between the Apple stock and the Apple stock and the Boeing stock and the Boeing stock. 02:58.470 --> 03:03.730 But here we can see uh the correlation of the last nine years. 03:03.750 --> 03:07.440 The monthly returns between Apple and Boeing. 03:07.500 --> 03:10.870 And this is the kind of positive so point to two. 03:11.190 --> 03:18.240 And I wouldn't say that this is a strong positive correlation but still it's a significant uh positive 03:18.240 --> 03:19.620 correlation. 03:19.620 --> 03:24.410 So that's the significant trend that whenever the apple return is positive. 03:24.420 --> 03:29.390 Then also the Boeing return is positive and vice versa. 03:29.430 --> 03:36.990 So this is the correlation for the complete one hundred eight month period and the same with the returns 03:37.020 --> 03:38.730 and standard deviations. 03:38.730 --> 03:43.040 Let's assume that you want to calculate the rolling correlation. 03:43.290 --> 03:45.250 And also here we can define that. 03:45.300 --> 03:49.050 We want to have a window of 36 months. 03:49.170 --> 03:56.670 So it's quite common in the finance industry to calculate return and standard deviation outlaw correlation 03:56.820 --> 04:04.200 based on monthly returns of uh the last uh 36 six months and coding wise we can actually start to do 04:04.200 --> 04:07.200 so by selecting here the apple return. 04:07.620 --> 04:15.750 Then we apply the rolling method and we pass the thirty six uh to the windows parameter and we already 04:15.750 --> 04:16.390 know that. 04:16.440 --> 04:21.260 Now we can for example calculate the rolling mean return by chaining here. 04:21.270 --> 04:22.230 The mean method. 04:24.930 --> 04:26.580 So this is nothing new. 04:26.610 --> 04:32.580 So this is the three years uh rolling mean return for the Apple stock. 04:32.580 --> 04:39.990 And we also have calculated the rolling standard deviation of returns by chaining here the standard 04:39.990 --> 04:41.220 deviation method. 04:41.220 --> 04:44.370 So this is actually nothing new. 04:44.520 --> 04:50.190 And now we want to calculate that the rolling correlation and it's actually no surprise that we have 04:50.190 --> 04:56.680 to change the car method and inside the parenting is this. 04:56.730 --> 05:03.390 Now we have to decide for which time seriously want to have the role in correlation to the Apple return. 05:03.390 --> 05:08.490 And if we can simply pass the panda series with the Boeing returns. 05:08.490 --> 05:17.530 So it's here monthly return the data frame and then we select uh the Boeing returns. 05:17.790 --> 05:25.010 And now let's run here the cell and it's actually no surprise that here for the first the thirty five 05:25.050 --> 05:27.060 data points we have any end values. 05:27.480 --> 05:34.320 But then here in the very end we have actually the thirty six month rolling correlation between the 05:34.410 --> 05:37.860 Apple stock return and the Boeing stock return. 05:38.250 --> 05:42.830 And as in most cases the graphs are more intuitive than a lot of numbers. 05:42.870 --> 05:48.580 So therefore we can also plot here and visualize a reading role rolling correlation. 05:48.630 --> 05:52.410 So we use here the plot method and let's have a look. 05:56.310 --> 06:00.940 So this is of the year all in correlation between APA returns and Boeing returns. 06:01.230 --> 06:10.240 And we have seen before that the average over the nine year period is 0 point 2 to so the average C 06:10.240 --> 06:11.940 is somewhere here. 06:11.940 --> 06:15.780 But we can also see here that the correlation is quite volatile. 06:16.290 --> 06:21.300 So we have fear at the end of the year 2000 and 13. 06:21.600 --> 06:24.040 Even a negative correlation. 06:24.220 --> 06:31.680 And here into a 16 and 17 we have a correlation of 0 point 5 and actually currently we are quite close 06:31.890 --> 06:34.250 to the mean of 0 point to 2. 06:34.250 --> 06:40.380 So here we are currently somewhere at 0 point 1 8 0.01 7. 06:41.070 --> 06:42.960 And actually the key message is here. 06:42.960 --> 06:49.080 Same with return and risk that also the correlation heavily depends on the market environment and on 06:49.080 --> 06:50.410 the timing. 06:50.430 --> 06:53.690 So these metrics are actually quite volatile over time. 06:54.090 --> 07:00.320 And having only a look at one single timestamp might not give us the complete information. 07:00.570 --> 07:08.340 So it's also quite it to have a look at the rolling statistics and with this we are finished here and 07:08.340 --> 07:10.890 I hope to see you also in the next video by.