WEBVTT 00:00.620 --> 00:06.650 In the last part we found out that our customized healthcare sector index showed that the second highest 00:06.650 --> 00:10.460 chop ratio and we presented this to our client Mary. 00:10.760 --> 00:16.910 However the results of Part 5 supported Mary's belief that the health care sector is the one and only 00:16.910 --> 00:19.270 sector to be invested in. 00:19.350 --> 00:26.780 And she says even if the consumer services sector showed a better Sharpe ratio and a higher return than 00:26.780 --> 00:33.380 the healthcare sector the risk is simply too high and that there's no benefit to add other sectors with 00:33.560 --> 00:36.240 lower Sharpe ratio than the healthcare sector. 00:36.350 --> 00:42.980 Because this will not improve the shop ratio of the overall portfolio and therefore I will stick to 00:42.980 --> 00:44.940 my current stock portfolio. 00:45.050 --> 00:48.230 So that's the marriage statement here and our argument. 00:48.230 --> 00:56.390 Past performance is no guarantee or no indicator of future results did not impress her much and I mean 00:56.390 --> 01:02.270 Mary's arguments are reasonable for a person who is not an expert in finance and investments but they 01:02.270 --> 01:08.390 are nevertheless wrong because they do not take into account the portfolio diversification effect and 01:08.390 --> 01:13.790 that means that by creating a portfolio with many sectors we can reduce the sector specific risk not 01:13.790 --> 01:18.350 only for the healthcare sector but also for the other sectors. 01:18.440 --> 01:24.770 And that's why there still a good chance to find portfolios that so a better Sharpe ratio with the same 01:24.770 --> 01:30.140 or lower risk than the health care sector on a standalone basis. 01:30.140 --> 01:36.680 And our client Mary might not be an easy person but she is definitely open to a reasonable and well-founded 01:36.710 --> 01:45.410 arguments and therefore we will create 50000 random portfolios and show her that she could have done 01:45.440 --> 01:49.940 even better with a higher degree of diversification in her portfolio. 01:49.940 --> 01:53.720 All right let's stop coding here and we have still important here. 01:53.720 --> 02:03.000 Our returns state frame with the daily returns of the sectors here and in total we have 11 sectors or 02:03.000 --> 02:11.210 eleven assets and we tried to simulate 50000 random portfolios number of portfolios. 02:11.210 --> 02:17.120 And then on the next step we create the fifty thousand times eleven the random numbers between 0 and 02:17.120 --> 02:24.290 1 and we reshape them in two or fifty thousand rows and eleven columns and we save them in the variable 02:24.290 --> 02:28.200 matrix and we set to the random C 2 1 1 1. 02:28.310 --> 02:37.400 So this shows actually a reproducibility here and let's do this and then we transform our random numbers 02:37.400 --> 02:45.410 into weights where for each and every of the 50000 portfolios the weights of the constituent sum up 02:45.410 --> 02:46.390 to 1. 02:46.970 --> 02:55.330 And we save the weights matrix and the variable weights so here we have fifty thousand portfolios with 02:55.390 --> 03:01.720 eleven constituents and we can also have a look here at the very first portfolios. 03:01.750 --> 03:10.840 So here is one portfolio with a 13 percent for the very first asset and so on and having the daily returns 03:10.840 --> 03:18.760 of the eleven constituents and the random weights we can actually create the daily returns of our fifty 03:18.760 --> 03:26.500 thousand random portfolios by using here the top method and actually we are performing a matrix multiplication 03:27.490 --> 03:34.900 and uh we save um the daily returns of the fifty thousand portfolios and the variable part read and 03:34.930 --> 03:36.330 let's have a look here. 03:36.340 --> 03:43.590 So here we have fifty thousand columns and fifty thousand portfolios then in the next set we can calculate 03:43.590 --> 03:50.940 the annualized the risk and return for those portfolios by simply passing our data frame portfolio returns 03:51.420 --> 03:57.130 to our user defined function annualized the risk and return and be safe. 03:57.180 --> 04:00.480 The summary here and the variable portfolio summary. 04:00.480 --> 04:03.810 So this is the most time consuming step here 04:07.930 --> 04:15.430 and let's have a look at the portfolio summary data frame so here we have uh the annualized the return 04:15.430 --> 04:20.530 and the annualized risk for fifty thousand random portfolios. 04:20.530 --> 04:26.890 And then the next step we can visualize the fifty thousand portfolios in a total risk return framework 04:28.270 --> 04:35.350 and again we are creating the scatter plot twists on the x axis the risk column and on the y axis the 04:35.350 --> 04:36.650 return column. 04:36.850 --> 04:39.560 And we also plot our 11 indexes. 04:39.610 --> 04:40.860 So let's have a look here. 04:45.900 --> 04:49.260 And that's actually our cloud of potential portfolios. 04:49.260 --> 04:51.680 And here we have the efficient frontier. 04:51.930 --> 04:59.510 And this is near our healthcare index and at a first glance we can see that there are indeed portfolios 05:00.080 --> 05:02.140 that have actually the same risk. 05:02.140 --> 05:06.890 Yes our healthcare index on a standalone basis but deliver more return. 05:06.890 --> 05:14.960 So here and are even portfolios that have less risk and at least the same return as our health care 05:14.960 --> 05:15.380 index. 05:15.380 --> 05:23.660 So here for example and finally we can also calculate the SAP ratio for our 50000 portfolios. 05:23.800 --> 05:31.400 So we are creating the additional column sharp and that's our portfolio summary data frame with the 05:31.400 --> 05:41.050 addition column sharp and we can also call the scribe method here and here we can see that the maximum 05:41.050 --> 05:48.520 Sharpe ratio is one point fourteen one and then we can also get the index label of the max swap rates 05:48.520 --> 05:52.180 for portfolio with the idea X Max method 05:55.120 --> 06:03.100 and the index label of the max Sharpe ratio is the forty six thousand nine hundred fifty seven and we 06:03.100 --> 06:10.300 can also select a complete row with our Max Sharpe Ratio portfolio and here we have a return of 17 percent 06:10.330 --> 06:17.620 and they risk off thirteen point seven percent resulting in a sharp ratio of one point fourteen and 06:17.680 --> 06:28.930 let's compare this also to our health care index and here we had a return of about 14 percent and a 06:28.930 --> 06:31.740 risk of fourteen point three percent. 06:31.870 --> 06:37.240 So the max Sharpe Ratio portfolio delivered actually a lower risk and higher return. 06:37.240 --> 06:40.410 And of course then also a higher Sharpe ratio. 06:40.480 --> 06:48.040 And last but not least we can also get the rates of the constituents and the max Sharpe Ratio portfolio. 06:48.040 --> 06:57.660 So let's also create a pen a serious and we can see that we have in the MAX Sharpe Ratio portfolio high 06:57.660 --> 06:59.550 rates of the health care index. 06:59.550 --> 07:01.560 So that's no surprise. 07:01.560 --> 07:09.330 And also of the Consumer Services Index and actually finally we presented our results to marry and showed 07:09.330 --> 07:12.740 her the portfolio diversification effect. 07:12.870 --> 07:20.960 And uh finally we could manage to convince Mary to diversify her stock portfolio so for the future she 07:20.960 --> 07:25.450 will also add some more sectors to her health care portfolio. 07:25.760 --> 07:29.130 And we will do this in the very last step Step 7. 07:29.210 --> 07:31.190 And I hope to see you there by.