WEBVTT 00:01.300 --> 00:06.900 And this in the next video we will create forward looking portfolios with many constituents. 00:06.900 --> 00:13.120 So our six stocks and you will see in this and the next video that this is not that easy. 00:13.140 --> 00:14.880 So we are still important. 00:15.150 --> 00:23.160 The returns data frame with the daily returns of our six stocks and also the market the portfolio. 00:23.190 --> 00:31.430 And still we have imported the covariance matrix and uh here we are only interested in the covariance 00:31.430 --> 00:33.770 us of the six stocks. 00:33.890 --> 00:44.820 So we exclude here the market portfolio and we only select the covariance as of our six constituents. 00:45.020 --> 00:52.730 And also we have still imported the summary data frame with uh the annualized risk return systematic 00:52.730 --> 00:57.230 risk and better effect of our six constituents and the market portfolio. 00:57.320 --> 01:01.890 And also here we drop the market portfolio and the safe. 01:01.940 --> 01:07.040 The summary data frame with the constituents and the Arab summary constituents 01:09.990 --> 01:12.850 and also the many assets of many constituents. 01:12.960 --> 01:20.460 First of all we have to make predictions for the returns of the single assets and then calculate the 01:20.460 --> 01:27.960 expected return of the random portfolios and we create another column for our summary constituents data 01:27.960 --> 01:32.670 frame expected return 1 and the reset. 01:32.750 --> 01:38.820 The expected return of the Amazon stock to 25 percent then for Boeing 15 percent. 01:38.850 --> 01:40.420 Disney 8 percent. 01:40.650 --> 01:42.120 IBM 8 percent. 01:42.180 --> 01:46.710 Coca-Cola 10 and Microsoft 15 percent. 01:46.710 --> 01:53.690 So that's our expected return here and again we have uh six assets. 01:53.690 --> 01:56.210 So our six constituents. 01:56.210 --> 02:00.890 And in this video we want to create 1 million random portfolios 02:04.420 --> 02:08.380 and therefore first of all we said that the random C to a 1 2 3. 02:08.500 --> 02:18.490 And we create a matrix uh with 1 million times 6 random numbers between 0 and 1 and we reshape them 02:18.490 --> 02:21.950 into 1 million rows and 6 columns. 02:22.000 --> 02:24.310 So that's the matrix here. 02:24.700 --> 02:29.250 And then we normalize the elements in the matrix and create the weights. 02:29.260 --> 02:36.900 So this is actually nothing new so that's uh the weights of one million random portfolios. 02:36.900 --> 02:44.310 And then we can calculate the expected return of these 1 million random portfolios by having here our 02:44.310 --> 02:52.680 expected return 1 column and we apply the top method and pass the transpose the weights matrix here 02:55.900 --> 03:02.560 and here we get an umpire rate with 1 million elements and each element is actually a expected return 03:02.560 --> 03:09.370 of one random portfolio and the the same we can do for the risk so we can calculate the expected risk 03:09.370 --> 03:11.740 of our 1 million random portfolios. 03:12.250 --> 03:18.580 So we take the square root to calculate the standard deviation and then we use the dot method on the 03:18.580 --> 03:27.460 covariance matrix and pass the transpose the weights matrix then we transpose the result and multiply 03:27.460 --> 03:36.130 it again with the weights matrix and then we take the sum over all rows so let's have a look here. 03:38.320 --> 03:46.090 And we should actually get for one million random portfolios of 1000000 times the expected risk in terms 03:46.090 --> 03:48.000 of standard deviations. 03:48.010 --> 03:51.850 So here we have a number higher array also with the 1000000 elements. 03:51.940 --> 03:58.090 So we have in the risk an umpire race 1 million elements and in the returns an umpire Ray 1 million 03:58.090 --> 04:01.510 elements and now the next step. 04:01.520 --> 04:06.470 We also want to calculate the expected chop ratio of our 1 million portfolios. 04:06.740 --> 04:11.210 And therefore we need an approximation for the risk free return. 04:11.690 --> 04:15.430 And let's simply use here 2 percent. 04:15.820 --> 04:19.780 And then we can also calculate the SAP ratio. 04:19.780 --> 04:27.760 So we have the returns of our portfolios minus the risk free rate divided by the risk and finally we 04:27.760 --> 04:34.860 can create a summary data frame with the three columns so we have the returns of our 1 million portfolios. 04:34.870 --> 04:44.610 Then the expected risk and the expected chop ratio so that's the summary data frame with the one million 04:44.610 --> 04:54.000 portfolios and then we can also visualize our 1 million portfolios with the risk on the x axis and the 04:54.000 --> 04:55.680 return on the y axis 05:01.900 --> 05:04.840 so that's our cloud of portfolios. 05:04.870 --> 05:07.390 And this looks pretty amazing. 05:07.390 --> 05:14.980 So here we have the efficient frontier and now we can also search for the maximum Sharpe Ratio portfolio. 05:14.980 --> 05:24.030 So first before we use the described method on our summary data frame and we can see here that uh the 05:24.030 --> 05:32.460 max Sharpe Ratio portfolio has a sharp ratio of 0 point 8 8 3 4 and then with the idea smacks method 05:32.490 --> 05:40.050 we can also get uh the index label of the max operator or portfolio and this is the portfolio with the 05:40.050 --> 05:46.140 index label eight hundred seventy three thousand nine hundred fifteen and we can also filter for that 05:46.140 --> 05:47.080 portfolio. 05:47.100 --> 05:56.040 So let's have a look here and we have a return of sixteen point one three percent and a risk of 16 percent. 05:56.250 --> 06:02.820 And then finally we can also get to the rates of the max sharp racial portfolio bypassing the index 06:02.820 --> 06:11.930 label to the weights matrix and to have it more explicit we can also create a panel series with the 06:11.930 --> 06:17.330 index labels s index and the rates here as the column. 06:17.330 --> 06:25.160 So let's have a look here and here our max Sharpe Ratio portfolio we have 34 percent Amazon then 17 06:25.160 --> 06:34.190 percent Boeing almost 0 percent Disney and IBM and also Microsoft and the 45 percent Coca-Cola. 06:34.190 --> 06:41.090 And here we can see one pitfall of creating forward looking portfolios and optimizing them for the best 06:41.090 --> 06:41.930 portfolio. 06:42.230 --> 06:49.880 So this leads typically to concentrated positions and this portfolio is clearly not a perfectly diversified 06:49.880 --> 06:51.510 portfolio. 06:51.530 --> 06:56.470 That's one pitfall and in the next video we will discover some more problems and pitfalls. 06:56.470 --> 06:57.890 So I hope to see you there by.