WEBVTT 00:01.010 --> 00:06.080 We have already learned that there are three major weighting methods when constructing an index. 00:06.230 --> 00:11.990 And in this and the next video we will focus on price weighting and we will learn how to create a price 00:11.990 --> 00:18.620 weighted index with Python and pandas and also the pros and cons of a price weighted index. 00:18.710 --> 00:25.790 So when selecting the price weighting method that constituents are weighted by their stock prices and 00:25.940 --> 00:33.800 let's assume we create an index with only two stocks and stock a has a price of two and Stock B has 00:33.800 --> 00:38.790 a price of eight then actually the rating of stock in the index is 20 percent. 00:38.810 --> 00:46.850 So 2 divided by 10 and the weighting of stock P is 80 percent and that's actually a pretty easy intuition 00:46.850 --> 00:50.770 behind the creating price weighted indexes. 00:50.780 --> 00:58.610 It's like purchasing an equal amount of shares of each constituent and the most easy example is one 00:58.610 --> 00:59.930 share. 00:59.930 --> 01:07.970 So if our index consists of two constituents then we can simply create the index by purchasing one share 01:07.970 --> 01:09.110 per constituent. 01:09.110 --> 01:13.430 So that's the easy intuition behind the price weighted index. 01:13.430 --> 01:17.870 And let's have a look at an easy example with some numbers. 01:17.870 --> 01:25.230 So let's assume we have here a stock A and Stock B and we have two timestamps so we have timestamp 0 01:25.250 --> 01:25.850 and 1. 01:25.850 --> 01:33.440 This could be a yesterday and today and yesterday we had stock prices of five for stock eight and ten 01:33.440 --> 01:34.370 for stock P. 01:34.910 --> 01:39.020 And today the stock prices moved to 8 for both stocks. 01:39.020 --> 01:45.980 Then as we learned before to create a price weighted index we simply have to buy one share for each 01:45.980 --> 01:46.480 stock. 01:47.060 --> 01:55.700 And by doing so at timestamp 0 our index our portfolio with the two shares is worth fifteen. 01:55.970 --> 02:03.440 And consequently the value of our index at timestamp one is 60 and so we simply summed up the stock 02:03.440 --> 02:11.780 prices of the constituents and the we defined that a timestamp 0 our index should have a base value 02:11.780 --> 02:13.010 of 100. 02:13.220 --> 02:18.980 And now the task would be to calculate the value of our index that timestamp 1. 02:19.130 --> 02:23.660 And we can simply do this by having you 100 times. 02:23.690 --> 02:25.850 Sixteen divided by 15. 02:26.030 --> 02:32.440 And this gives us the index value at time stamp one of for one hundred six point six seven. 02:32.480 --> 02:35.120 So this is uh the easy example. 02:35.120 --> 02:41.270 And so to say the shortcut and the shortcut works pretty well here for the price weighted index. 02:41.300 --> 02:49.100 However there is a more general approach which we will use for the evaluated index also for the equal 02:49.100 --> 02:54.040 weighted index and the more general approach actually always works. 02:54.080 --> 03:00.210 And in most cases I prefer the more general approach because they work in each and every case. 03:00.210 --> 03:01.610 So let's have a look here. 03:01.640 --> 03:07.760 So again here we have our prices and having the prices here we can also calculate the weights of the 03:07.760 --> 03:10.580 constituents in a price weighted index. 03:10.580 --> 03:19.520 So we have one share per constituent and in total we have a timestamp zero a value of 15 and therefore 03:19.550 --> 03:21.670 the weight of stock a is here. 03:21.710 --> 03:29.210 O point three three four or five divided by 15 and consequently the weight of stock P in our indexes 03:29.270 --> 03:31.090 0 points 6 7. 03:31.400 --> 03:36.160 And then as a next step we calculate the returns of our constituents. 03:36.650 --> 03:41.380 So this is here actually the returns table and the time 0. 03:41.390 --> 03:45.980 We do not have any returns because of this year no timestamp minus 1. 03:46.040 --> 03:50.130 So the weighted average does also not exist here. 03:50.150 --> 03:55.180 And we also do find that the initial index value are the base value should be 100. 03:55.200 --> 04:01.870 Now we can actually calculate simple returns for the period from timestamp 0 to 1 and to the first stock 04:01.900 --> 04:03.500 A it's 60 percent. 04:03.500 --> 04:06.770 So this is simply 8 divided by 5 minus 1. 04:06.920 --> 04:15.360 And consequently the return for stock B is 8 divided by 10 minus one is minus 20 percent. 04:15.680 --> 04:23.870 And then we can calculate the evaded average return and we actually await the returns with the the weights 04:23.890 --> 04:25.560 at timestamp 0. 04:25.790 --> 04:33.170 So that's the important part here that we created the 60 percent return of stock a and b minus 20 percent 04:33.260 --> 04:41.350 return of stock P with the weights that we had at timestamp 0 so point 3 3 and 0 point 6 7. 04:41.660 --> 04:48.500 And therefore we can calculate the weighted average return by evading the return of stock a 0 point 04:48.500 --> 04:50.420 6 with 0 point. 04:50.470 --> 04:51.470 3 3. 04:51.470 --> 04:58.550 And by weighting the return of stock B minus 20 percent with 0 points 6 7 and this gives us a weighted 04:58.550 --> 05:02.310 average return of 6 points 7 percent. 05:02.330 --> 05:07.400 And now finally we know that our index value at timestamp 0 is 100. 05:07.580 --> 05:15.290 Then we have an index return of six point seven percent and therefore we can calculate the index value 05:15.290 --> 05:17.220 at timestamp 1. 05:17.420 --> 05:22.790 And this is simply one hundred times one plus a six point seven percent. 05:22.850 --> 05:27.640 And also here we get the indexed value of one hundred six point six seven. 05:27.710 --> 05:34.370 So this is the more general approach which is a bit more complicated but this should work actually and 05:34.400 --> 05:42.300 each and every case all right so now let's go to the pros and cons of the price weighted index and the 05:42.330 --> 05:43.530 one advantages. 05:43.650 --> 05:50.330 We have seen that that it's quite easy to compute and we actually only need a very few data. 05:50.340 --> 05:57.220 So we only need the prices three of our constituents then next to the intuition behind a price weighted 05:57.220 --> 05:58.840 index is pretty easy. 05:59.200 --> 06:06.410 So it's like having a portfolio where we have one share on equal amount of shares per constituent. 06:06.610 --> 06:10.870 And finally a price weighted index is the self rebalancing. 06:10.870 --> 06:17.050 So that means that we do not have to rebalance the weights of the constituents as the time goes on. 06:17.050 --> 06:21.410 And this minimizes actually transaction costs and also Texas. 06:21.640 --> 06:28.510 And we will see later in the equal weighted index that an index does not automatically get set off rebalanced. 06:28.510 --> 06:28.990 All right. 06:28.990 --> 06:32.770 And let's go also to the disadvantages of a price weighted index. 06:32.770 --> 06:38.920 So first of all a price weighted index might have concentrated positions and stocks with the highest 06:38.920 --> 06:40.390 prices. 06:40.390 --> 06:47.050 So if you have stock a bit the price of two and stock B with the price of eight then we have a concentrated 06:47.050 --> 06:54.850 position in stock B and having high prices does not necessarily mean that the stock has a higher value 06:55.030 --> 06:57.430 or has economic importance. 06:57.490 --> 07:03.910 So the market capitalization actually better reflects a company's economic importance and the market 07:03.910 --> 07:09.260 capitalization is actually the product of price and the number of shares. 07:09.280 --> 07:11.650 So let's assume we have a stock with a very high price. 07:11.650 --> 07:13.430 So for example 1000. 07:13.570 --> 07:19.980 So if they are in total only 10 stocks in the market then the company has only a little economic importance. 07:20.020 --> 07:26.860 But it has a quite high price and a high rate in a price weighted index. 07:26.860 --> 07:33.560 And moreover a price weighted index does not necessarily reflect a typical portfolio construction. 07:33.580 --> 07:38.190 So actually investors and funds that rarely buy an equal number of shares. 07:38.500 --> 07:44.140 And finally stock splits can complicate the construction of a price weighted index. 07:44.140 --> 07:46.860 So stock splits lobby under the scope of this cost. 07:46.870 --> 07:50.470 But let's assume BFA stock with a price of 1000. 07:50.530 --> 07:56.480 Then the company could decide to split the stock and distribute for each stock to stocks. 07:56.500 --> 08:01.040 And then the stock price automatically declines to 500. 08:01.150 --> 08:05.080 And this has to be considered and reflected in a price weighted index. 08:05.500 --> 08:13.060 But for us this is actually no problem as to the historical prices that we get from Yahoo Finance already 08:13.060 --> 08:19.700 include the impact of stock splits and the furthest we are finishing with this video and I hope to see 08:19.730 --> 08:20.140 also. 08:20.140 --> 08:21.400 And then next one by.