WEBVTT 00:00.690 --> 00:06.960 In this video we are going to create an equal weighted stock index containing our six stocks our constituents 00:07.740 --> 00:14.010 and creating an equal weighted index means that at each single point in time we have invested the same 00:14.010 --> 00:17.020 dollar amount into all constituents. 00:17.040 --> 00:24.990 In our example with six stocks one sixth of our investment is invested in each stock and therefore the 00:24.990 --> 00:32.430 performance or the return of our index for each period should be the equal weighted the return of the 00:32.430 --> 00:34.230 six constituents. 00:34.260 --> 00:40.830 So we still have imparted the stocks data frame and the normalized data frame and now in a very next 00:40.830 --> 00:46.190 step we are calculating the simple returns for stocks by using here. 00:46.200 --> 00:53.180 The percentage change method and we are actually saving the returns data frame and the variable rate. 00:53.310 --> 00:54.600 So let's do this. 00:54.630 --> 00:55.230 Let's have a look. 00:55.980 --> 01:00.380 So these are actually the daily simple returns for our stocks. 01:00.420 --> 01:08.630 And as I said to the Simple Return of the equal weighted index is uh simply the equal weighted average 01:09.030 --> 01:11.910 of the returns of the constituents here. 01:11.910 --> 01:15.800 And therefore we can create a new column called mean return. 01:16.050 --> 01:23.220 And uh here for each timestamp of each row we are actually calculating the mean of the returns of the 01:23.220 --> 01:24.710 constituents. 01:24.900 --> 01:31.380 And of course we can do the service of the mean method and passing one to the access parameter and say 01:31.530 --> 01:34.050 OK so here's on the right hand side. 01:34.070 --> 01:34.540 Um. 01:34.590 --> 01:36.120 The mean returns. 01:36.120 --> 01:42.040 And by convention we already know that our equal weighted index should have the value one hundred at 01:42.090 --> 01:50.880 the very first day here at the thirty first of December 2000 and 13 and therefore we can already create 01:50.910 --> 01:58.790 a column for our normal data frame called Equal Weighted Index and in a first step we assign 100 to 01:58.800 --> 02:00.520 each timestamp so let's do this. 02:01.800 --> 02:09.450 So here we are from the right hand side our equal weighted index with uh 100 at the beginning and we 02:09.450 --> 02:11.640 already have everything in place to calculate. 02:11.640 --> 02:13.770 Also the following prices. 02:13.790 --> 02:20.920 So we have for the starting price of 100 and we have the simple returns of our equal weighted index. 02:20.970 --> 02:28.220 And if you want to calculate uh the index price um on the second timestamp here on the second of January 02:28.890 --> 02:36.600 then we simply have to multiply 100 with the investment multiple which is here in this case the one 02:36.600 --> 02:38.530 plus the return. 02:38.580 --> 02:45.360 So the next step is actually to convert all the returns here into the investment multiply by adding 02:45.360 --> 02:45.810 1. 02:46.740 --> 02:49.090 Let's do this here. 02:49.110 --> 02:51.040 So these are the multiple births. 02:51.240 --> 02:56.400 And if you want to calculate the price here at the second timestamp we simply have to multiply one hundred 02:56.430 --> 02:59.020 and O point nine nine four. 02:59.070 --> 03:01.710 So this would be the price on the second timestamp. 03:02.160 --> 03:10.230 And for all of the other timestamps we actually have to multiply the initial value of 100 with the accumulated 03:10.460 --> 03:11.750 investment multiple. 03:12.270 --> 03:18.360 And we can actually calculate the cumulative investment multiple by actually multiplying the single 03:18.420 --> 03:19.440 investment multiple. 03:19.440 --> 03:27.840 So for example on the third timestamp the cumulative investment multiple is uh 0 point 9 9 4 times 0 03:27.840 --> 03:36.880 point 9 9 9 so that would be the cumulative investment multiple for the third timestamp and uh for the 03:36.880 --> 03:42.800 fourth timestamp consequently we would have to multiply the first three investment multiples. 03:42.880 --> 03:44.330 Cumulatively. 03:44.380 --> 03:45.660 And so on. 03:46.600 --> 03:53.140 And we can actually calculate all cumulative investment my words with the come proud method. 03:53.140 --> 03:54.700 So cumulative product 04:01.180 --> 04:04.100 so these are here the cumulative products. 04:04.270 --> 04:12.610 And for example if you want to calculate uh the price of our index at the 9th of January 2014 we have 04:12.760 --> 04:20.470 to multiply the cumulative product so point nine eight nine by the initial price of one hundred and 04:20.470 --> 04:21.980 so on. 04:22.040 --> 04:28.760 This is now our very last step so we calculate and multiply the cumulative investment manager built 04:28.790 --> 04:34.610 by the initial value of one hundred or the initial price. 04:34.610 --> 04:38.260 And now we have actually the prices of our equal weighted index. 04:38.450 --> 04:48.530 So starting at the second time with ninety nine point four 0 0 right and now what we have to do we have 04:48.530 --> 04:55.580 to simply replace here the value starting from the second of January by these values here. 04:55.580 --> 04:57.110 So let's do this. 04:57.110 --> 05:00.740 So this is nothing nothing new here. 05:00.860 --> 05:05.320 And finally now we have you on the right hand side of our neon data frame. 05:05.570 --> 05:13.170 Our equally weighted index and now we can also plotted the constituents here and our equal weighted 05:13.170 --> 05:22.200 index so let's do this here and let's have a look so here we can see in dark blue our equal weighted 05:22.200 --> 05:23.550 index. 05:23.550 --> 05:25.890 And we can also only plot. 05:25.920 --> 05:28.980 The Equal Weighted Index with the Amazon stock 05:33.890 --> 05:40.280 and we can already see here that the equal weighted index is less correlated to the Amazon stock. 05:40.310 --> 05:46.670 Then the price weighted index because the weight of the Amazon stock here in the equal weighted index 05:46.680 --> 05:48.730 is much smaller. 05:49.430 --> 05:56.170 And for comparison purposes we can also plot to the equal weighted index and the price weighted index 05:57.780 --> 06:03.190 so here we have in blue the price weighted index and in green the equal weighted index. 06:03.330 --> 06:10.620 And it seems like that over the whole period the price weighted index showed a higher return. 06:10.620 --> 06:14.500 And this is simply the case because the Amazon stock soars. 06:14.580 --> 06:20.490 For all the constituents the highest return and the weight of Amazon and the price weighted indexes 06:20.700 --> 06:23.850 are actually much higher than in the equal weighted index. 06:24.000 --> 06:30.990 And for the sake of completeness we can also create a data frame with the rates over time so we create 06:31.020 --> 06:38.100 a copy of our stocks data frame and call it the way it's equally weighted index and then for each and 06:38.100 --> 06:42.350 every value we assign actually the value of one sixth. 06:42.420 --> 06:43.290 So let's have a look. 06:43.290 --> 06:47.730 So this is actually no surprise and it's more or less a no brainer. 06:47.730 --> 06:52.310 And we can also plot and visualize the rates over time. 06:52.750 --> 06:59.750 So here we have add to the value of 1 6 actually all the stocks that our constituents. 06:59.860 --> 07:02.430 And the weights actually totally stable over time. 07:02.450 --> 07:05.030 At 1 6. 07:05.130 --> 07:11.760 So this is the equal weighted index and one advantage is that it shows the best possible diversification 07:11.760 --> 07:17.730 and there's actually no concentration of a single stock on the other inside smaller stocks in terms 07:17.730 --> 07:25.110 of market cap favored and have higher rates than they should have according to the market cap and a 07:25.110 --> 07:25.970 smaller stocks. 07:26.040 --> 07:33.390 In many cases they're riskier than larger stocks an equal weighted index has typically higher risk. 07:33.390 --> 07:35.840 And finally as another disadvantage. 07:35.850 --> 07:43.410 So at each point in time you would have to rebalance the stocks to equal weight by selling winners and 07:43.440 --> 07:44.830 buying losers. 07:44.940 --> 07:49.110 And that would create a substantial transaction costs. 07:49.170 --> 07:56.130 So also here we have uh disadvantages and advantages and in the next video we will create a value weighted 07:56.130 --> 07:56.580 index. 07:56.580 --> 07:58.470 So I hope to see you there by.