WEBVTT 00:01.310 --> 00:08.840 In this video we are going to analyze our 100000 portfolios with these sharp Ray saw and we have still 00:08.840 --> 00:16.160 here our summary data frame with our six stocks and the annualized risk and return and the same we have 00:16.160 --> 00:20.580 for our 100000 portfolios. 00:20.630 --> 00:27.500 So here we have the data frame portfolio summary and actually for both data frames we can add to the 00:27.500 --> 00:36.230 column shop where we calculate actually the shop ratio which is simply the return minus the return of 00:36.410 --> 00:43.910 the risk free asset which is here one point seven percent and this is also called the risk premium. 00:43.910 --> 00:48.800 And then we divide the risk premium by the portfolio risk. 00:48.980 --> 00:57.570 So we are doing this for the summary data frame as well as for the portfolio summary data frame so let's 00:57.570 --> 01:00.720 have a look first at the summary data frame. 01:00.720 --> 01:01.910 So we on the right hand side. 01:01.920 --> 01:09.180 We have now the sharp ratio and actually the higher the sharp ratio the better the risk adjusted return 01:09.180 --> 01:10.200 or performance. 01:10.980 --> 01:16.430 So the best performance has had the Microsoft stock within Sharpe ratio of one. 01:16.590 --> 01:23.110 Then we have here Emmerson and we have IBM with a negative Sharpe ratio. 01:23.220 --> 01:29.080 So the return of the IBM stock itself was already negative minus 4 percent. 01:29.300 --> 01:37.290 And if you subtract one point seven percent from minus 4 percent then in the end it's no surprise that 01:37.290 --> 01:40.620 we get a negative Sharpe ratio. 01:40.920 --> 01:48.910 And now let's also create here the sharp column for our 100000 portfolios and let's have a look at the 01:48.910 --> 01:51.130 first five portfolios. 01:51.130 --> 01:58.710 So here we have portfolios with sharp ratios from 0 point 5 7 to 1 point 0 3. 01:59.230 --> 02:08.090 And let's also call here the informal method so we have 100000 portfolios and three columns. 02:08.090 --> 02:15.770 And let's also call here the described method and here we can see that the mean are the ever at Sharpe 02:15.770 --> 02:24.760 ratio is 0 point 8 5 and the portfolio with the lowest Sharpe ratio has a sharp ratio of minus 0 point 02:24.790 --> 02:34.350 0 1 and we have also a highest Sharpe Ratio of one point eighteen and in the next step we can also visualize 02:34.500 --> 02:43.680 this OP ratio and we actually created a scatter plot again with our 100000 portfolios and our stocks 02:43.680 --> 02:44.940 like here. 02:44.940 --> 02:52.360 So we create the same graph but we will create kind of a three dimensional graph. 02:52.500 --> 03:01.560 So the third dimension will be the sharp ratio and therefore we to see for each and every point a color 03:01.590 --> 03:05.290 that reflects the top ratio of the point. 03:05.340 --> 03:06.720 So let's do this here 03:10.570 --> 03:18.400 so we are again plotting our portfolio summary data frame with the risk on the x axis and the return 03:18.400 --> 03:23.320 on the y axis and the size of each dot or point is 20. 03:23.860 --> 03:31.090 And then we also define the color of each point or dot and the color is determined by the column sharp 03:32.210 --> 03:40.160 and we also define a color map which is a cool warm so high Sharpe Ratios will have a red color and 03:40.270 --> 03:47.060 a low Sharpe Ratios will have a blue color and we can also scale our color maps so we can say that all 03:47.060 --> 03:57.140 portfolios with a sharp ratio of four point seventy six and lower deep blue and all portfolios with 03:57.140 --> 04:00.460 a sharp ratio of one point one eight or higher. 04:00.470 --> 04:01.760 Deep Red. 04:01.760 --> 04:09.290 So setting here the optimal values for women and we mix this kind of a trial and error process and by 04:09.290 --> 04:13.040 doing so we can actually optimize our graph and optimize. 04:13.160 --> 04:17.960 The message of our graph and then we also created a color bar. 04:18.470 --> 04:25.210 And in addition we also create the points that dots for our six stocks here. 04:25.220 --> 04:29.050 So this is nothing new with a size or 50. 04:29.060 --> 04:32.950 And the black color and let's simply run here. 04:32.990 --> 04:33.410 So 04:40.700 --> 04:48.260 so here we have our shop race so and still on the x axis that we have the annualized risk in terms of 04:48.260 --> 04:53.670 standard deviation and the annualized return here on the y axis. 04:53.720 --> 05:02.720 And here we have all of our portfolios and our stocks and the color of the dots here give us the information 05:02.720 --> 05:11.270 about the shop ratio so high shop ratios are here in the dark red color and the low shop ratios are 05:11.270 --> 05:20.180 here in dark blue color and we can see here that portfolios with the highest chop ratio are in this 05:20.180 --> 05:28.320 area here so from a risk and return perspective these are the best portfolios and you will see in later 05:28.320 --> 05:35.630 videos why this is the case and we get a graphical intuition on this here but for the time being we 05:35.630 --> 05:43.460 can also include our stocks here and to the color bar and give the color corresponding to their Sharpe 05:43.480 --> 05:44.230 ratio. 05:44.930 --> 05:47.930 So this is actually quite similar in addition. 05:47.930 --> 05:56.810 So here we are defining the dots are the points for our stocks and also here we include the color perimeter 05:57.320 --> 06:00.340 and we include our stocks into the color bar. 06:00.350 --> 06:01.750 So let's have a look again here 06:08.320 --> 06:14.830 and if you can see that investing in single stocks might not reside in the best chop ratios. 06:14.830 --> 06:18.810 So here we offer the Amazon stock and some other stocks here. 06:18.820 --> 06:26.020 And I think two stocks are somewhere here and we can also see here that there might be a curve here 06:26.410 --> 06:35.320 which marks actually the optimal portfolios for a given amount of risk so having a given amount of risks 06:35.320 --> 06:42.790 for example 0.01 5 that's a portfolio that actually gives us the highest possible return. 06:42.820 --> 06:45.940 So here and having a given level of return. 06:45.940 --> 06:48.030 So for example 20 percent. 06:48.280 --> 06:55.810 That's actually one portfolio that actually realizes this return with the lowest possible risk. 06:55.840 --> 07:04.730 So this portfolio here and actually all portfolios on this curve here actually form the efficient frontier. 07:05.030 --> 07:08.310 And we can also plot here the efficient frontier. 07:08.390 --> 07:13.010 So in the background I have created the efficient frontier. 07:13.340 --> 07:21.620 So this is clearly beyond the scope of this cost because uh we use some kind of optimization algorithms 07:22.120 --> 07:24.440 but uh to show you the efficient frontier. 07:24.440 --> 07:26.480 So let's simply plot it here 07:32.100 --> 07:38.890 and here in black we can see the efficient frontier and actually at one particular portfolio on this 07:38.890 --> 07:45.120 efficient frontier is actually the portfolio with the highest Sharpe Ratio man in the next video. 07:45.120 --> 07:48.650 We will identify the maximum shop raised for portfolio. 07:49.080 --> 07:50.970 So I hope to see you there by.