WEBVTT 00:00.690 --> 00:06.330 In the last video we created this great aggregation and visualization of the past performance of the 00:06.330 --> 00:13.440 S&P 500 index and we actually calculated the average lucky returns over the respective periods. 00:13.440 --> 00:19.980 However it might be more common that people ask let's assume I invested one hundred dollars in the S&P 00:19.980 --> 00:24.190 500 index at the beginning of the year 2005. 00:24.210 --> 00:27.060 What would be the value of this investment today. 00:27.330 --> 00:33.590 So that's a maybe a bit more intuitive and we can change our returns triangle into a dollar triangle 00:33.900 --> 00:37.200 by changing only one coding cell. 00:37.230 --> 00:44.850 So here we are creating the dollar triangle and the steps are actually identical to the steps when creating 00:44.850 --> 00:46.340 the true return triangle. 00:46.770 --> 00:49.710 So I am just running the cells here 01:01.260 --> 01:04.720 so until here the code is actually identical. 01:05.230 --> 01:12.360 And then we are coming to the step where we are creating the 30 columns and that's the code for our 01:12.360 --> 01:13.800 return triangle. 01:13.800 --> 01:15.560 So we calculate it. 01:15.630 --> 01:18.370 The rolling average lock return. 01:18.370 --> 01:25.010 And this is here our new code and we've already learned this and the lecture on lock returns. 01:25.350 --> 01:31.110 So we take you to the power off and then here and parenting is this that we have the amount of years. 01:31.230 --> 01:35.920 My reply to buy the average lock returns for that period. 01:35.970 --> 01:40.590 So let's have an example here and let's assume we are considering a four year period. 01:40.590 --> 01:47.990 Then we have fear year to the power off and parenting is this four times the rolling average lock return. 01:48.240 --> 01:54.100 And then finally we multiply this with the initial investment of 100. 01:54.210 --> 02:02.560 So let's run near the sell and by doing so we are creating additional 30 columns for our annual data 02:02.560 --> 02:03.430 frame. 02:03.700 --> 02:10.850 And then again we create the triangle data frame by dropping the columns close and return. 02:11.020 --> 02:16.030 So this year the triangle data frame with the dollar amounts. 02:16.300 --> 02:19.420 And then finally we can make our plot. 02:19.430 --> 02:20.800 So let's simply run here. 02:24.820 --> 02:26.490 So that's the plot. 02:26.740 --> 02:33.720 And also here it's a bit trickier to the time and we mean we max and center to get a meaningful result 02:34.140 --> 02:35.140 and uh. 02:35.160 --> 02:38.710 So a center of a 100 definitely makes sense. 02:38.710 --> 02:44.160 So investing one hundred and getting my back 100 means uh 0 percent return. 02:44.170 --> 02:46.230 So you don't win or lose anything. 02:46.330 --> 02:48.420 And a final result of 60. 02:48.430 --> 02:51.050 So you lost the 40 dollars. 02:51.160 --> 02:52.910 That's a deep red. 02:53.060 --> 02:57.970 And everything above 140 is the deep green here actually. 02:58.390 --> 03:05.900 So let's have a look and the worst case here is actually investing at the beginning of the year 2000. 03:06.020 --> 03:13.100 And finally at the end of the year 2002 we end up with an investment value of 60. 03:13.130 --> 03:15.420 So we lost 40 dollars here. 03:15.650 --> 03:22.010 But also here we can see that when we extend to the investment period it's uh getting more unlikely 03:22.040 --> 03:23.920 that we lose money. 03:24.570 --> 03:35.360 That's the that's the 13 year period from uh the beginning of 2008 and 2012 where we have fear and negative 03:35.360 --> 03:36.460 returns. 03:36.470 --> 03:40.060 So in that period we lost the three dollars. 03:40.130 --> 03:43.060 So that's actually kind of the worst case. 03:43.220 --> 03:53.230 But if we also consider here a 20 year period then historically we end up with 200 to 300 or even 400 03:53.230 --> 03:55.400 tell us after 20 years. 03:55.520 --> 04:01.350 And finally we can also see here that a one year period is quite risky and volatile. 04:01.410 --> 04:03.780 So everything is possible here. 04:03.950 --> 04:05.780 And with this we are finished. 04:05.780 --> 04:08.180 And I hope to see also in the next video by.