WEBVTT 00:01.070 --> 00:06.950 In this video we are going to create the equal weighted portfolio consisting of our six portfolio stocks 00:07.520 --> 00:12.770 and equal weighted means that at each timestamp the weight of each single stock in the portfolio is 00:12.770 --> 00:14.770 one divided by six. 00:14.810 --> 00:20.330 So let's first of all import pen us and we also import an umpire and met plot lip and also seaborne 00:20.840 --> 00:22.540 and we define that float object. 00:22.560 --> 00:24.390 So to have uh two decimals. 00:24.410 --> 00:30.190 So let's do this and then we import our portfolio stocks from the portfolio of stocks. 00:30.210 --> 00:37.130 Yes we file and we create a day time index and we save uh the data frame and the value of stocks. 00:37.130 --> 00:38.380 So let's have a look. 00:38.390 --> 00:45.140 So these are the adjusted to close prices over time and actually calculating the return of an equal 00:45.140 --> 00:47.930 weighted portfolio is pretty simple. 00:47.930 --> 00:54.050 So we simply have to calculate the mean return of our six stocks on each timestamp and therefore first 00:54.050 --> 01:01.400 of all we create the returns data frame with the percentage change method and we save the returns data 01:01.400 --> 01:08.110 frame and the variable red so this is the returns data frame as the daily returns. 01:08.110 --> 01:13.770 And as I said to get the daily returns for our equal weighted portfolio we simply have to calculate 01:13.780 --> 01:21.850 here the average are the mean return of the six stocks on each timestamp so to say we have to calculate 01:21.850 --> 01:29.440 the row vice mean and we can do this with the mean method and pass on to the access parameter to get 01:29.530 --> 01:37.960 the mean values per Roe so these are the mean values are the mean returns pair Roe up her timestamp 01:38.890 --> 01:41.030 and with this we are finished here. 01:41.100 --> 01:46.900 That's uh that daily returns of the equal weighted portfolio but as the next step we also want to create 01:46.900 --> 01:53.500 portfolios that are not equal weighted and therefore we have to derive a more general way to get to 01:53.500 --> 01:56.850 the weighted average return on each timestamp. 01:56.950 --> 01:58.840 And uh let's have a look here. 01:58.840 --> 02:05.530 So first of all we need to define the amount of assets or the amount of stocks that should be in our 02:05.530 --> 02:06.460 portfolio. 02:06.700 --> 02:13.990 So in this case we are working with six stocks and we actually can determine the length of our columns 02:14.020 --> 02:15.160 index. 02:15.160 --> 02:22.860 So no surprise we have six and the next step we create a list with the weights of our 6 stocks. 02:22.870 --> 02:30.170 So with the equal weighted portfolio we have six times the weight of fund divided by six. 02:30.190 --> 02:33.550 So we are creating the list weights. 02:33.610 --> 02:36.690 And this is a list comprehension. 02:36.730 --> 02:42.300 So for you and range six or six times we create 1 divided by 6. 02:42.310 --> 02:43.060 So let's have a look. 02:44.780 --> 02:48.790 So you have six times the rate one divided by six. 02:48.860 --> 02:55.040 And now we want to calculate the evaded average return for all time stems and therefore on the first 02:55.040 --> 02:58.730 step we have to multiply the return of each stock. 02:59.180 --> 03:06.800 So here these are the daily returns and we have to multiply them by the respective weights here and 03:06.860 --> 03:09.080 uh we have to do this for each timestamp. 03:09.470 --> 03:16.940 And finally we have to sum up then the weighted daily returns to get uh the weighted average return 03:16.940 --> 03:18.540 for the six stocks. 03:18.860 --> 03:26.030 And uh we can do this year and two steps are first of all we have our returns data frame and we multiply 03:26.030 --> 03:33.770 the returns data frame with the weights list and we pass columns to the access parameter because we 03:33.770 --> 03:38.400 want to apply here the respective weights on our columns. 03:38.510 --> 03:44.150 So here the first weight should always be applied on the Amazon stock for example. 03:44.630 --> 03:46.770 So let's do this here. 03:49.090 --> 03:54.030 So these are the evaded daily returns and to get the weighted average. 03:54.060 --> 04:01.230 We have to take the sum so we use the same method and pass one to the access parameter to uh some of 04:01.270 --> 04:04.060 the data frame upper row wise or per row. 04:05.950 --> 04:10.850 And again here we have for the daily returns for our equal weighted portfolio. 04:11.020 --> 04:13.890 And as you can see here we change here two methods. 04:13.990 --> 04:21.970 So the model method and the sum method and we can actually combine these two steps into one step by 04:21.970 --> 04:30.130 using the dot product on a matrix multiplication and we can do this with the top method. 04:30.580 --> 04:38.300 So we take our returns data frame and we apply a matrix multiplication with the top method and we pass 04:38.450 --> 04:40.710 our weights the list. 04:40.720 --> 04:43.120 So this gives us actually the same result. 04:43.990 --> 04:48.520 So here we have the daily returns of the equal weighted portfolio. 04:48.640 --> 04:55.450 And finally we create a new column equal weighted portfolio for our returns data frame by using exactly 04:55.720 --> 04:59.190 the code so let's do this and let's have a look. 05:00.350 --> 05:07.280 So here we have the six constituents of our portfolio and the equal weighted portfolio and for all of 05:07.280 --> 05:10.430 them we feel that daily returns on each timestamp. 05:10.660 --> 05:14.990 And now as a next step we want to aggregate here the daily returns. 05:14.990 --> 05:22.520 And we want to calculate the annualized mean return and the annualized standard deviation of returns. 05:22.520 --> 05:26.390 And therefore we create here the summary data frame. 05:26.450 --> 05:33.560 So first of all we calculate the mean return of our daily returns and the standard deviation of daily 05:33.560 --> 05:34.800 returns. 05:35.000 --> 05:36.710 And we use here the ACT method. 05:36.740 --> 05:39.860 So let's do this and let's have a look. 05:39.860 --> 05:47.510 So we actually transposed the data frame in order to FESA the index our stocks and our portfolio and 05:47.510 --> 05:48.560 as columns. 05:48.710 --> 05:53.010 The mean return and the standard deviation of returns. 05:53.420 --> 06:02.740 And then it's definitely a good idea to rename the column labels to return and risk and still we have 06:02.750 --> 06:06.030 yeah the mean and the standard deviation of daily returns. 06:06.320 --> 06:15.850 And uh it's more intuitive to analyze them so we multiply the mean return with 252. 06:15.860 --> 06:19.020 So that's the average amount of trading days. 06:19.250 --> 06:24.320 And we multiply the risk by the square root of 252. 06:24.350 --> 06:25.810 So this is nothing new. 06:26.970 --> 06:34.860 And finally we feel our summary data frame with the annualized return and the annualized risk. 06:34.860 --> 06:37.700 And finally we can also create a scatter plot. 06:37.860 --> 06:46.050 So we use the plot method on our summary data frame and on the x axis we have the risk column and on 06:46.050 --> 06:48.420 the y axis the return column. 06:49.050 --> 06:54.460 So we actually should get the seven dots seven points here and our scatter plot. 06:54.570 --> 06:58.770 And we also annotate the label for each point for each dot here. 06:58.770 --> 07:02.760 So that's the take us and the equal weighted portfolio. 07:03.330 --> 07:04.520 And let's have a look here. 07:06.890 --> 07:13.600 So here we have the total risk return profile for our six stocks and for our equal weighted portfolio. 07:14.300 --> 07:16.370 So this is also nothing new here. 07:16.370 --> 07:21.880 So here we have our equal weighted portfolio and these are our six constituents. 07:22.160 --> 07:29.840 And finally to save some time and some code in our next videos we define a function annualized the risk 07:29.870 --> 07:33.950 and return where we pass a return data frame. 07:33.950 --> 07:43.630 So for example here this is our returns data frame and we pass the return data frame to the function 07:44.590 --> 07:51.520 and actually the function calculates the mean and the standard deviation and it renames the columns 07:51.550 --> 07:54.190 and annualize this risk and return. 07:54.190 --> 07:59.140 And then finally returns the final summary data frame. 07:59.410 --> 08:04.340 So we are defining the function here for the next videos to save some code and some time. 08:04.580 --> 08:10.750 And uh with uh this we are finishing with this video and I hope to see you also in the next one by.