WEBVTT 00:00.970 --> 00:06.580 In this video we will learn some more application soft rolling statistics and finance in the last video 00:06.580 --> 00:12.220 we have learned how to calculate simple moving averages for stock prices and in this video we will have 00:12.220 --> 00:18.840 a look at the rolling performance of stocks and financial securities and we've already learned that 00:18.840 --> 00:24.500 the risk and return are the most important performance metrics for financial securities like stocks 00:25.040 --> 00:28.170 and in the finance and investment funds industry. 00:28.370 --> 00:34.340 It's quite standard to report risk and return of financial securities for the last three years based 00:34.340 --> 00:35.630 on monthly data. 00:35.990 --> 00:43.180 So that means that the return is reported as the annualized average monthly return over the last the 00:43.220 --> 00:50.990 thirty six month period and the risk is typically reported as the annualized standard deviation of monthly 00:50.990 --> 00:52.580 returns over that period. 00:53.480 --> 00:59.930 So in the next minutes he will calculate rolling risk and return for the S&P 500 and we will find out 01:00.230 --> 01:04.280 if and to what extent risk and to try and change over time. 01:04.280 --> 01:04.700 All right. 01:04.700 --> 01:05.380 So let's start. 01:05.390 --> 01:10.930 And first of all we import pandas an umpire and also met plot lip as always. 01:11.240 --> 01:19.130 Then we are working with the S&P 500 see a sweet fire and of course we want to pass um the date column 01:19.430 --> 01:23.230 to a date time index and we only want to use them. 01:23.230 --> 01:30.020 The column stayed and the closing prices and uh actually we save for the data frame and the variable 01:30.050 --> 01:31.800 S&P 500. 01:32.510 --> 01:33.800 So let's have a look here. 01:34.130 --> 01:40.960 So these are the first five rows starting at the very last day of the year nineteen hundred and seventy. 01:41.630 --> 01:48.740 And as I said before it's quite standard in uh the finance and investment industry to report monthly 01:48.740 --> 01:49.890 returns. 01:49.910 --> 01:57.050 So as we have here daily data or daily timestamps with daily price information first of all we need 01:57.050 --> 02:04.240 to read sample our data frame to monthly and we can do the same with other release sample method and 02:04.250 --> 02:10.270 we too see a monthly and actually you want to have the very last trading price of each month. 02:10.370 --> 02:13.800 And finally we also past the period to the kind parameter. 02:13.800 --> 02:17.020 So let's run through the sell and let's have a look. 02:17.030 --> 02:19.700 So here we have monthly price data. 02:20.120 --> 02:25.720 And on the left hand side we have now a period index as we pass superior to the kind parameter. 02:25.790 --> 02:28.400 So we have a December nineteen hundred seventy. 02:28.400 --> 02:33.590 January nineteen hundred seventy one and two we have our column close. 02:33.590 --> 02:37.330 And here we have for the very last trading price of each month. 02:37.340 --> 02:41.910 So now we have monthly data and we want to calculate monthly returns. 02:41.930 --> 02:46.280 And we can do this here with the percentage change method. 02:46.490 --> 02:49.260 So we change here the read sample method. 02:49.490 --> 02:52.430 The last method and the percentage change method. 02:52.880 --> 02:57.260 And finally we want to drop them all rows with an A values. 02:57.260 --> 03:04.640 So if you calculate the percentage change then in the very first row we will have a uh and a value. 03:04.640 --> 03:07.910 So therefore we you see also the drop in a method. 03:08.060 --> 03:11.310 So we are calculating your monthly returns and we save. 03:11.360 --> 03:14.840 The resulting data frame and the variable monthly returns. 03:14.840 --> 03:18.470 So let's do this here and let's have a look 03:21.270 --> 03:23.610 so here we have the monthly returns. 03:23.610 --> 03:29.040 So for example the return in January in nineteen hundred seventy one was 4 percent. 03:29.040 --> 03:35.430 So this is exactly the change from ninety two point one five to ninety five point eighty seven. 03:35.430 --> 03:38.220 So this is a monthly return of 4 percent. 03:38.400 --> 03:42.750 And actually here now a new data for a monthly return we have actually the monthly returns starting 03:42.750 --> 03:49.760 from January nineteen hundred seventy one and to December 2000 and 18. 03:49.770 --> 03:52.170 Now we want to calculate rolling statistics. 03:52.590 --> 04:00.660 So we want to calculate the mean are the average return of the immediately preceding 36 months. 04:00.870 --> 04:06.960 And we want to do this for timestamps here and therefore we use here the rolling method and the window 04:06.960 --> 04:08.810 is a thirty six. 04:08.820 --> 04:16.410 So on each timestamp we actually group uh the last the 36 month and then we change the mean method to 04:16.410 --> 04:19.410 calculate the mean return. 04:19.500 --> 04:21.810 The mean rolling return. 04:21.810 --> 04:26.400 And by doing so we would end up with average monthly returns. 04:26.400 --> 04:31.570 And it's also quite standard in the finance industry to annualized returns. 04:31.680 --> 04:39.030 So to have kind of a feeling how the return would look like over a complete year and therefore we multiply 04:39.030 --> 04:42.480 the monthly rolling returns by twelve. 04:42.510 --> 04:44.540 So let's do this here. 04:44.580 --> 04:52.530 Consequently we get here now the annualized average monthly returns over the last uh thirty six periods 04:53.010 --> 04:55.890 and in kind of a rolling statistics manner. 04:55.890 --> 05:02.160 So we have for each timestamp actually the annualized mean return for the last three years. 05:02.550 --> 05:07.760 And finally we create in the new column return so let's do this here. 05:07.770 --> 05:14.770 So now we have added the rolling return of the S&P 500 index and now we want to add also the year risk 05:14.880 --> 05:22.560 and um the risk is typically calculated as a standard deviation of monthly returns and we can actually 05:22.560 --> 05:27.840 simply calculate the rolling standard deviation of monthly returns by a take here. 05:27.840 --> 05:34.620 The monthly returns based on the close price then we change the rolling method and of course also here 05:34.620 --> 05:41.850 we pass um thirty six to the window parameter and then we calculate a standard deviation. 05:41.850 --> 05:46.830 So this would uh then reside in the standard deviation of monthly returns. 05:47.190 --> 05:50.170 So to say the monthly standard deviation. 05:50.340 --> 05:56.970 And finally we can also annualize a monthly standard to creation by multiplying with the square root 05:57.030 --> 05:58.040 of twelve. 05:58.050 --> 05:59.140 So let's do this here. 06:00.240 --> 06:11.030 So here we have the rolling standard deviation and finally we can also create a new column risk. 06:11.030 --> 06:17.270 So now we have two new columns the return and risk for our monthly return data frame and then we could 06:17.270 --> 06:18.620 also drop and a rose. 06:18.620 --> 06:24.920 So the first the thirty five rows should contain and a values in both new columns. 06:24.920 --> 06:30.820 So let's do this here and now let's finally inspect our monthly return data frame. 06:30.860 --> 06:35.580 So here we have the monthly returns of the closing prices. 06:35.720 --> 06:38.450 Then we have uh the rolling return. 06:38.750 --> 06:43.540 So this is uh the return of the last uh 36 months. 06:43.550 --> 06:46.160 And we have here the rolling risk. 06:46.160 --> 06:53.310 And apparently he had the first rolling such as Six we have on December nineteen hundred seventy three. 06:53.720 --> 07:00.620 And we could say that um the annualized average monthly return for the preceding three years is actually 07:00.620 --> 07:02.120 two point six percent. 07:02.600 --> 07:05.130 And the risk is twelve percent. 07:05.150 --> 07:12.020 So let's also have a look at the last five rows here and we could say that the annualized average monthly 07:12.020 --> 07:20.990 return from January to 16 to December to eighteen is seven point one percent and the annualized standard 07:20.990 --> 07:25.670 deviation of monthly returns in this period is 11 percent. 07:25.730 --> 07:32.660 Now we can also plot the rolling statistics so the column return and risk and we can do this year of 07:32.660 --> 07:40.280 course with the plot method and we take the last two columns of our data for a monthly returns. 07:40.280 --> 07:41.150 So let's have a look 07:44.750 --> 07:51.980 and here you can actually see that change of Risk and Return of the S&P 500 index over time. 07:51.980 --> 08:00.260 So we have uh the blue line or the blue curve which is the rolling return for the last three years. 08:00.440 --> 08:06.780 And the green line is actually the risk or the standard deviation of monthly returns for the preceding 08:06.800 --> 08:08.970 uh three years period. 08:09.230 --> 08:14.590 And we can also see here that depending on the market environment and depending on the time. 08:14.780 --> 08:18.460 So risk and the return are quite volatile here. 08:18.470 --> 08:26.560 So for example here in 2009 2010 we can see here a quite high risk and a very low return. 08:26.570 --> 08:30.500 So minus 10 percent annualized and the opposite. 08:30.500 --> 08:36.080 We can see for example here in the middle or the end of the 90s. 08:36.140 --> 08:37.950 So we have quite high returns. 08:37.940 --> 08:39.830 So what 20 percent. 08:39.830 --> 08:42.760 And we have quite a low risk here. 08:42.830 --> 08:51.170 So it seems like investing in the S&P 500 over a period of three years is quite volatile and uh really 08:51.170 --> 08:57.190 depends on the market environment and the time you are investing so it can be a good investment. 08:57.200 --> 09:00.980 But it can also be a very poor investment. 09:00.980 --> 09:07.340 And from the two lines see we can also see that the risk and return could be negatively correlated. 09:07.340 --> 09:09.350 So whenever the risk is quite high. 09:09.350 --> 09:15.570 So for example here or here then the returns are pretty low and vice versa actually. 09:15.620 --> 09:20.020 So here we have a higher return and a fairly low risk. 09:20.240 --> 09:24.290 And also here we have a high return and the risk is fairly low. 09:24.860 --> 09:30.560 So it might be worth it to also calculate the correlation between the rolling return and the rolling 09:30.560 --> 09:31.550 risk. 09:31.550 --> 09:34.290 And we can do this with the car method. 09:34.400 --> 09:38.760 So we take the two columns here of monthly returns. 09:38.760 --> 09:41.970 So the last two columns and the change the car method. 09:41.990 --> 09:50.060 So let's do this and we can see here that there is a significant negative correlation between risk and 09:50.060 --> 09:50.530 return. 09:50.540 --> 09:52.110 So minus 0 point. 09:52.190 --> 09:53.270 3 2. 09:53.900 --> 10:01.640 And we can also create a scatter plot with all parcels of risk and return for the last 40 years. 10:01.700 --> 10:05.030 So we plotted the columns the risk and return. 10:05.030 --> 10:12.080 And we use here a scatter plot and on the x axis we want to have the risk a standard deviation and on 10:12.080 --> 10:14.810 the y axis the return. 10:14.900 --> 10:16.040 So let's do this here 10:19.240 --> 10:24.580 so here we have the risk on the x axis and the return on the y axis. 10:24.580 --> 10:30.490 And actually each point is a combination of rolling risk and rolling return for a particular month from 10:30.490 --> 10:34.420 nineteen hundred seventy three until 2018. 10:34.420 --> 10:39.970 So for example we have quite good three year periods with a quiet low risk. 10:39.970 --> 10:44.710 So twelve percent and a high return over 20 percent. 10:44.710 --> 10:49.980 And we can also see periods with a quite poor performance of the S&P 500. 10:50.380 --> 10:54.140 So for example a fairly high standard deviation or risk. 10:54.190 --> 11:01.620 So what 20 percent and a mean return of less than minus 10 percent. 11:01.630 --> 11:10.090 So again we found out that investing in the S&P 500 over a period of three years is a quite risky and 11:10.420 --> 11:12.060 volatile investment. 11:12.190 --> 11:18.820 And in the next two videos we want to investigate how this picture changes if we increase our investment 11:18.820 --> 11:22.120 period also decrease our investment period. 11:22.180 --> 11:24.850 So I hope to see you also in the next videos by.