WEBVTT 00:01.070 --> 00:07.470 In the last video we discovered that investing in the S&P 500 fund investment period of three years 00:07.770 --> 00:14.400 can be a really volatile and risky investment depending on when and at which market conditions you are 00:14.400 --> 00:15.600 investing. 00:15.600 --> 00:22.620 So in this video we want to calculate the rolling return of the S&P 500 for different investment periods 00:22.620 --> 00:24.950 from one year to 20 years. 00:24.960 --> 00:31.290 So in other words we will calculate the annualized average monthly returns with rolling windows from 00:31.290 --> 00:34.060 a twelve month to 240 month. 00:34.530 --> 00:41.200 So that's 20 years and we want to discover whether there is kind of a time diversification effect. 00:41.310 --> 00:47.070 People typically say that stocks are long term investment Bear and the good days you recover the losses 00:47.100 --> 00:53.280 made and the bad days and we try to prove and visualize this in the next minutes. 00:53.280 --> 00:58.230 So first of all we import us and we also import met plot lip. 00:59.020 --> 01:03.310 Then we are again working with the S&P 500 see a three fire. 01:03.960 --> 01:05.280 So let's have a look here. 01:05.790 --> 01:12.030 So we are working only here with the closing prices and we can also call you the info method. 01:12.060 --> 01:14.410 So this is actually nothing new. 01:14.570 --> 01:20.070 And we can also plot um the S&P 500 price from the 70s to today. 01:22.520 --> 01:31.320 So this was a pretty good investment if you invested in the S&P 500 in the 70s and again also in this 01:31.320 --> 01:38.050 video we are working with monthly returns and therefore we need to recycle but here the closing prices 01:38.060 --> 01:41.820 to monthly and we calculate the percentage change. 01:41.820 --> 01:43.580 So this is nothing new. 01:44.190 --> 01:51.600 And let's have a look at the last five monthly returns here in 2000 and 18 and to avoid any confusion 01:51.600 --> 01:54.850 we rename here the column Labor Forum. 01:54.900 --> 01:59.190 Close the two monthly returns based on closing prices. 01:59.190 --> 02:02.940 So this is actually also nothing new. 02:03.030 --> 02:04.860 So let's again have a look here. 02:04.860 --> 02:10.410 So now our monthly returns column has that label monthly returns. 02:10.410 --> 02:16.980 And actually in the last video we calculated the rolling average return and the rolling standard deviation 02:16.980 --> 02:20.120 of returns for the last to 36 months. 02:20.940 --> 02:24.930 So let's repeat this here for the rolling returns. 02:24.930 --> 02:29.900 So we you see the rolling method and we multiply our desired investment period. 02:29.910 --> 02:33.180 So here three years by twelve twelve months. 02:33.210 --> 02:35.250 So in total we have 36 months. 02:35.790 --> 02:44.040 And then we calculate the rolling mean and by multiplying this uh with 12 we get actually annualized. 02:44.130 --> 02:45.360 Rolling mean returns. 02:45.350 --> 02:47.700 So this is also nothing new. 02:47.760 --> 02:49.010 Let's do this here. 02:49.260 --> 02:52.890 And apparently in the first thirty five months we have any end value. 02:52.890 --> 03:00.370 So no surprise here and now we actually want to do the same for investment periods of one year five 03:00.370 --> 03:03.090 years 10 years and 20 years. 03:03.250 --> 03:08.790 And we use here a for loop so we iterate over the investment period. 03:08.800 --> 03:11.530 So four years in uh the lists here. 03:11.530 --> 03:18.460 So we have 1 3 5 10 and 20 year and for each of these five investment periods you want to add here to 03:18.460 --> 03:22.510 our monthly returns data frame a new column. 03:22.510 --> 03:27.760 So we want to add to your column for the one year rolling return for our three year rolling return 5 03:27.790 --> 03:29.770 10 and 20 year. 03:30.040 --> 03:35.770 And we can actually create the columns with this column labeled here with this code here and let's have 03:35.770 --> 03:36.820 a look at an example. 03:36.820 --> 03:39.270 So let's take year the one year period. 03:39.640 --> 03:46.720 So we are creating here the one year column with the column label one year and what we are doing actually 03:46.720 --> 03:49.540 we take here the column monthly returns. 03:49.540 --> 03:51.600 So these are the monthly returns. 03:51.700 --> 03:58.120 Then we apply the rolling method and for the rolling window we are actually calculating here a yes times 03:58.120 --> 03:59.090 twelve. 03:59.140 --> 04:02.390 So in the very first iteration yes that's equal to 1. 04:02.620 --> 04:11.140 So one time twelve gives us a twelve as a window that we are calculating the mean and we are analyzing 04:11.140 --> 04:15.660 it and thus we are doing here for all five periods. 04:15.730 --> 04:19.180 So one year three year five year 10 year and 20 year. 04:19.180 --> 04:21.680 And by doing so we're creating five columns. 04:21.700 --> 04:30.280 So let's do this year and let's have a look here at the last five rows of our data frame. 04:30.340 --> 04:37.180 So here we have added successfully the columns one year three year five year 10 year and 20 year and 04:37.180 --> 04:39.240 let's have a look at the very last row. 04:39.640 --> 04:42.970 So this is December to 18. 04:43.000 --> 04:45.240 And if we have a look here at the column one year. 04:45.260 --> 04:53.170 So we have a minus 6 percent and this is actually the annualized the mean return over the last 12 months 04:53.860 --> 04:59.380 and consequently here in the column 3 year we have a seven point one percent. 04:59.380 --> 05:05.570 And this is actually the annualized the mean return for the preceding thirty six month period form to 05:05.570 --> 05:07.810 a sixteen to to 18. 05:08.230 --> 05:12.000 And that's also if I look at the 20 year column. 05:12.250 --> 05:20.260 So here we have an annualized monthly return of 4.5 percent and this is actually the mean return over 05:20.260 --> 05:23.310 the last 240 months. 05:23.620 --> 05:25.260 And we can also create a plot. 05:25.290 --> 05:28.110 Um this this uh five columns. 05:28.300 --> 05:31.240 So we are selecting the last five columns. 05:31.240 --> 05:40.540 And uh let's see what we got here so uh here we can see on the x axis the respective date and on the 05:40.540 --> 05:41.620 y axis. 05:41.710 --> 05:43.300 The annualized return. 05:43.870 --> 05:50.140 And here we have actually five lines uh which are actually are rolling statistics are rolling returns. 05:50.140 --> 05:56.500 So the blue line here is the the rolling return on the investment period of one year. 05:56.620 --> 06:00.200 And this is actually quite volatile as you can see here. 06:00.220 --> 06:07.780 So if you have invested in 2 8 and divested and 2 9 then in this case you've got a negative annualized 06:07.780 --> 06:11.100 return of uh let's say minus 50 percent. 06:11.230 --> 06:15.300 And in contrast the few invested and 2 9 2 to 10. 06:15.330 --> 06:21.700 Then you analyze them mean return would be around 40 percent and you can also see here that the longer 06:21.700 --> 06:26.670 the investment period the less volatile our graph is here. 06:26.680 --> 06:30.100 So we have here the green graph within the investment period of three years. 06:30.790 --> 06:38.680 And the yellow curve which is not volatile at all actually was on the rolling investment period of 20 06:38.680 --> 06:39.530 years. 06:39.730 --> 06:46.480 And we can also create subplots to have a better view here and we can do a service of the subplots perimeter 06:46.510 --> 06:47.650 and pass see a true 06:54.320 --> 06:57.710 so for each investment period we have here now a subplot. 06:57.710 --> 07:04.060 And we can also increase here the figure size to let's say 50 and uh 40 07:10.200 --> 07:16.920 so we are starting here with a one year investment period and the rolling return and uh the rolling 07:17.160 --> 07:21.970 return this year between minus 50 percent and plus 40 percent. 07:21.990 --> 07:25.520 Then we have a look here at the three year rolling return. 07:25.740 --> 07:32.250 And this is already here between a minus let's say 15 percent and plus the 25 percent. 07:32.250 --> 07:36.810 Then we have the five year rolling return and the 10 year rolling return. 07:36.870 --> 07:39.970 And then finally the 20 year rolling return. 07:40.110 --> 07:45.600 And as we can see here on the left hand side the scale is different than for the other graphs subplots. 07:45.630 --> 07:52.920 So the 20 year annualized rolling return is between a plus 5 percent and 14 percent. 07:52.920 --> 08:00.270 So in the history of the S&P 500 index there's actually no 20 year period where we actually made the 08:00.270 --> 08:00.740 losses. 08:00.740 --> 08:08.460 So after 20 years we are always positive actually so we gained or we increased our investment. 08:08.460 --> 08:16.170 And uh this is uh different to uh let's say the 10 year or the five year or even the the one year investment 08:16.170 --> 08:16.620 period. 08:16.650 --> 08:22.300 So here it's quite likely that over one year we make losses also. 08:22.710 --> 08:28.220 And we can even better see this effect by passing true to the share by parameter 08:32.020 --> 08:39.450 and by doing so for each subplot we I have actually the uh y axis of uh the one year period. 08:39.520 --> 08:46.450 So here we have the returns between minus 40 and the 40 percent and we can see here. 08:46.470 --> 08:54.860 So one year is quite volatile and the SBA increases the investment period the volatility decreases. 08:54.970 --> 08:58.210 So this is quite obvious here. 08:58.210 --> 09:06.520 So finally with 20 years period there's hardly any volatility here so as a summary we can agree that 09:06.580 --> 09:09.810 that's kind of a time diversification effect. 09:10.090 --> 09:16.690 And uh the longer the investment period the less likely it is that you will suffer losses. 09:16.750 --> 09:23.590 So actually stocks a risky investment and it's quite likely that over a period of 1 to 5 for 10 years 09:23.620 --> 09:28.100 you made some losses but were periods of 15 or 20 years. 09:28.220 --> 09:34.420 It's uh at least if you have a look at historical data it's quite unlikely that you'll lose money over 09:34.420 --> 09:40.590 that long time periods and uh with this we are finished with this video and I hope to see you also and 09:40.590 --> 09:41.620 the next one by.