WEBVTT 00:00.910 --> 00:05.770 Welcome back to part two and we have still imparted the cap data frame. 00:05.770 --> 00:06.580 So let's have a look. 00:07.180 --> 00:13.840 So these are the market capitalizations for our constituents over time and then evaluated index each 00:13.840 --> 00:19.450 constituent has a way to corresponding to its proportional market capitalization. 00:19.450 --> 00:23.580 So therefore we have to calculate for each single timestamp. 00:23.590 --> 00:31.030 The total market capitalization for the constituents or to say the sum so we can do this with the sum 00:31.030 --> 00:31.570 method. 00:31.600 --> 00:33.310 So nothing new here. 00:33.310 --> 00:38.350 So this is uh on each timestamp the sum of market caps. 00:38.390 --> 00:44.800 Now we can actually calculate the weights of the constituents for each single timestamp and we can do 00:44.800 --> 00:52.540 this by dividing our M cap data frame by the total sum here. 00:52.570 --> 00:59.340 So actually for each single timestamp we actually calculate the proportion for each of the constituents. 00:59.470 --> 01:08.250 And uh we pass the index to the access parameter so here we have for each and every timestamp. 01:08.310 --> 01:09.610 The rates. 01:09.640 --> 01:13.530 So the proportional weights as per our market capitalization. 01:13.840 --> 01:20.640 And we can also save uh the weights data frame and the variable weights evaluated index. 01:20.860 --> 01:26.080 And let's again have a look at the last five rows here and 2000 and 18. 01:26.110 --> 01:32.770 And also here it makes sense to visualize the evolution of weights over time and we can do this here 01:32.800 --> 01:41.600 with the plot method on our weights evaluated index data frame so these is the evolution of weights 01:42.230 --> 01:48.290 and we can see here that uh the weight of the Microsoft the stock in our value weighted index is quite 01:48.290 --> 01:49.790 stable over time. 01:49.910 --> 01:59.420 So from 27 percent to about 35 percent and we have a significantly increasing weight of the Amazon stock 01:59.420 --> 02:03.030 starting from uh below 20 percent total. 02:03.050 --> 02:06.890 Also 34 thought 35 percent. 02:06.890 --> 02:11.250 So these are the weights of the constituents and our value weighted index. 02:11.460 --> 02:17.360 And uh yeah we can see that our value weighted index is kind of concentrated in two positions. 02:17.360 --> 02:21.280 So in the Amazon stock and in the Microsoft stock. 02:21.380 --> 02:27.070 So we are pretty far away from having a very diversified index portfolio. 02:27.290 --> 02:33.660 And now when the next step let's calculate the daily returns of our stock prices and we can do this 02:33.700 --> 02:35.630 with the percentage change method. 02:35.630 --> 02:37.400 So nothing new here. 02:37.400 --> 02:40.150 So these are the daily returns. 02:40.310 --> 02:43.950 And in addition to the daily returns we have also the daily rates. 02:43.970 --> 02:46.470 So that's again have a look here. 02:51.050 --> 02:54.380 And that's actually one pitfall that we have to keep in mind. 02:54.500 --> 03:01.310 So we can see here in the returns data frame the very first return we have on the second of January 03:01.310 --> 03:03.230 2014. 03:03.230 --> 03:11.300 So the immediately preceding price we had on the thirty first of December 2000 and uh 13 then the first 03:11.300 --> 03:13.450 of January was a bank holiday. 03:13.910 --> 03:21.500 And then on the 2nd of January we have um uh these daily returns here and these daily returns are based 03:21.500 --> 03:24.760 on the last price on the thirty first of December. 03:24.890 --> 03:30.950 And therefore if you want to calculate the weighted average return on the 2nd of January we have to 03:30.950 --> 03:38.110 do this with the rates of the thirty first of December so the next step we want to calculate for each 03:38.110 --> 03:46.660 single time stamp the weighted average return of our value weighted index by multiplying here the returns 03:46.660 --> 03:49.890 of our six constituents by the way. 03:50.230 --> 03:55.600 And we have to keep in mind that we have to shift our weights by one day. 03:56.080 --> 04:02.440 So we have to multiply the weights at the end of the thirty first of December with the return on the 04:02.440 --> 04:03.660 second. 04:03.700 --> 04:12.280 And uh we can do this here with the shift asset so let's do this here. 04:12.370 --> 04:15.800 So here we have shifted forward all rates by one day. 04:16.150 --> 04:20.980 So now we have the weights that we have to use the calculated the weighted average return on the 2nd 04:20.980 --> 04:24.610 of January here at the 2nd of January. 04:24.700 --> 04:28.180 And finally we should also drop here the very first row 04:32.460 --> 04:38.310 and calculating the weighted average returns for each single timestamp is actually now what we do. 04:38.310 --> 04:45.460 So we take our returns data frame and multiply it here with our shifted weights data frame. 04:45.540 --> 04:46.460 So let's have a look. 04:51.930 --> 04:57.460 So these are the daily returns of our six constituents made it by their respective rates. 04:57.540 --> 05:01.770 And finally we have to sum it up to get the weighted average return. 05:01.790 --> 05:02.700 So let's sort this 05:05.500 --> 05:10.300 so these are now the daily returns of our value weighted index. 05:10.300 --> 05:14.810 And um now we are only one step away from our value weighted index. 05:14.810 --> 05:23.640 So first of all we create the column in our norm data frame value weighted index and we assign 100 to 05:23.650 --> 05:30.370 each and every timestamp so here we are on the right hand side of our value weighted index. 05:30.370 --> 05:33.740 And same as with the equal weighted index. 05:33.850 --> 05:40.250 Now we can calculate for each and every a timestamp the cumulative investment might. 05:40.600 --> 05:44.920 And we can do this by adding one to each and every uh daily return. 05:44.920 --> 05:48.200 Then we are calculating the cumulative product. 05:48.310 --> 05:54.520 And this actually gives us uh then the cumulative investment multiple for each timestamp. 05:54.520 --> 06:02.820 And finally we multiply each uh multiple with 100 because uh we are starting here with a base value 06:02.820 --> 06:04.810 on normalized value of 100. 06:05.410 --> 06:06.630 So let's do this here. 06:07.810 --> 06:15.160 And here we have actually a beginning from the second of January our values for our value weighted index. 06:15.160 --> 06:21.050 So at the very first day it's 100 then you add the second day it's ninety nine point three two. 06:21.070 --> 06:26.580 And so on and therefore now we can over variety beginning from the second element. 06:26.590 --> 06:32.860 We can over variety of the values in our column value weighted index and exactly with the values that 06:32.860 --> 06:33.910 we calculated here. 06:33.940 --> 06:43.120 So let's do this and let's have a final look here so here we have our fine uh normalized data frame 06:43.630 --> 06:47.620 with the normalized prices of our six constituents. 06:47.680 --> 06:54.040 And in addition we FBA the three indexes the price weighted index so the equal weighted index and the 06:54.040 --> 06:55.750 value weighted index. 06:55.960 --> 07:04.470 And we can also visualize our new evaluated and next year with the six constituents. 07:04.590 --> 07:07.130 And here we can see in dark blue. 07:07.140 --> 07:14.870 So this this year our evaluated index so we are finished now with this video and in the next video we 07:14.870 --> 07:17.390 will compare our three indexes. 07:17.390 --> 07:19.580 So hope to see you also there by.