WEBVTT 00:00.700 --> 00:07.240 And the last videos we have seen that investing in the S&P 500 index can be a pretty risky investment 00:07.510 --> 00:11.910 where timing and market environment is actually key to success. 00:11.980 --> 00:16.280 And we've also seen that there's kind of a time diversification effect. 00:16.420 --> 00:23.260 So the longer the investment period the less volatile the overall performance as periods was poor returns 00:23.440 --> 00:27.670 can be recovered by strong periods with positive returns. 00:27.700 --> 00:34.240 And in this video we will create the ultimate visualization for this and the so-called return triangle. 00:34.930 --> 00:41.500 And in this video we are actually starting with the final output the return triangle for the S&P 500 00:41.500 --> 00:42.410 index. 00:42.460 --> 00:51.000 And afterwards I will show you how to get the return triangle with some pretty simple python code. 00:51.060 --> 00:54.840 Here we have the return triangle for the S&P 500 index. 00:55.020 --> 00:57.720 And let's go first of all to the x axis. 00:58.500 --> 01:07.980 So here we can see on the x axis the investment periods starting from one year and uh 30 years and we 01:07.980 --> 01:13.690 can see here on the y axis the final year of investment are to say the year of divestment. 01:14.010 --> 01:16.620 So for example let's have a look here at this. 01:16.650 --> 01:22.920 Here we are a investment period the following year and the final year is 2000 and 18. 01:22.980 --> 01:29.900 So actually the total investment period this year simply two thousand and eighteen and the salary is 01:29.940 --> 01:35.730 for example the total year of 2017 to 16 and so on. 01:36.000 --> 01:39.660 Then let's go here to an investment period of two years. 01:39.840 --> 01:47.280 So here and this uh the final year is 2018 and therefore the total investment period covers the years 01:47.280 --> 01:54.280 2017 and 2018 so let's randomly select this cell here. 01:54.290 --> 01:56.520 Eleven point three percent. 01:56.540 --> 02:03.750 And here we have an investment period of four years and the final year of investment is 2016. 02:03.860 --> 02:10.580 And we can also find easily the initial year of investment if we go up here the diagonal. 02:10.580 --> 02:13.570 So let's go the Sierra up and we can find us. 02:13.610 --> 02:16.840 The very first year the year 2000 and 13. 02:17.120 --> 02:25.300 So we actually started to invest here in uh January 2000 and 13 and the total investment period covers 02:25.370 --> 02:30.180 the year 2013 14 15 and 16. 02:30.410 --> 02:35.120 And actually on our return triangle we are working with a yearly lock returns. 02:35.150 --> 02:39.670 That means that for each year from a nineteen hundred eighty nine. 02:39.710 --> 02:48.170 So our triangle starts and the uh nineteen hundred eighty nine to 2018 we calculate the yearly lock 02:48.200 --> 02:55.370 returns and for periods longer than one year we actually calculate the mean or the average sum of the 02:55.370 --> 02:57.190 yearly lock returns. 02:57.230 --> 02:59.180 So let's have an example here. 02:59.180 --> 03:03.650 So here we have an investment period of two years and let's go into this year. 03:03.650 --> 03:12.500 So here we have 5.2 percent and this is simply the average of the yearly lucky returns of 2000 and 18 03:12.530 --> 03:13.880 and 17. 03:13.880 --> 03:20.140 So this is actually the average of seventeen point seven and the minus seven point three percent. 03:20.510 --> 03:26.660 And as a short recap the advantage of working with lock returns and the mean or the average of lock 03:26.660 --> 03:32.020 returns is that it gives you the right indication whether you made gains or losses. 03:32.060 --> 03:33.690 For the complete period. 03:33.770 --> 03:39.830 So whenever the average lock return is negative and I sell we made losses over the whole period and 03:39.950 --> 03:42.100 vice versa. 03:42.110 --> 03:48.320 So with simple returns and the average of simple returns we actually cannot draw these conclusions with 03:48.470 --> 03:56.540 100 percent certainty and we can also see here that the shorter the investment period the more riskier 03:56.570 --> 03:58.250 is the investment. 03:58.250 --> 04:01.710 For example if we only have a investment period of one year. 04:01.820 --> 04:03.590 So this is quite versatile. 04:03.620 --> 04:09.740 So for example here we have one year with a negative return of forty eight point six percent. 04:09.920 --> 04:16.350 And in contrast we have also yes with the plus 20 plus 27 percent and so on. 04:16.340 --> 04:23.540 And as we increase the investment period and as we go here more to the left hand side then we can see 04:23.540 --> 04:30.440 here that the overall performance of the average yearly return gets less volatile. 04:30.800 --> 04:34.310 So for example here we have an investment period of 20 years. 04:34.460 --> 04:42.190 Then our overall our average performance is somewhere between three point five percent per year and 04:42.200 --> 04:44.500 the seven point five percent. 04:44.630 --> 04:51.350 And actually one of the most interesting question is So what is the longest time period in the history 04:51.650 --> 04:55.300 where we still suffered losses and we can't see here. 04:55.310 --> 05:04.070 We have an investment period of 13 years and here we have uh a negative return of uh minus 0 point 2 05:04.070 --> 05:08.330 percent and starting with the investment period of 14 years. 05:08.330 --> 05:11.580 We do not have any negative returns here. 05:11.720 --> 05:16.160 So this is actually the worst example and we can go here and want to detail. 05:16.190 --> 05:24.230 So if we go here the diagonal up there and we are ending here at the starting point in 2000. 05:24.290 --> 05:32.120 So we invested here at the beginning of the year 2000 and we actually suffered the huge losses in the 05:32.150 --> 05:40.460 early years and the year 2000 saw minus 10 percent and 2000 minus 14 percent in 2001 and so on and we 05:40.460 --> 05:45.370 also participated here in the very poor year 2000 and 8. 05:45.470 --> 05:52.100 And actually as a side note I have to say that yeah the return triangle is based on price returns only. 05:52.100 --> 05:59.600 So without any dividends and if you include dividends then the returns will be higher a year and also 05:59.600 --> 06:03.650 the maximum period where we still suffer losses might be shorter. 06:03.680 --> 06:10.190 So for example it may be twelve or eleven years and you will have the opportunity to elaborate on this 06:10.250 --> 06:12.050 in the exercises. 06:12.050 --> 06:16.400 So this is the final output and now I will show you how to get this. 06:16.400 --> 06:19.010 With only a few lines of Python code.