WEBVTT 00:00.950 --> 00:07.270 In the last video we included the sharp rise so to our portfolio analysis and to our graph here is a 00:07.280 --> 00:09.320 couple of the portfolios. 00:09.320 --> 00:15.740 And in this video we will identify the best portfolio with the highest chop ratio the so-called maximum 00:15.740 --> 00:17.690 sharp ratio portfolio. 00:17.690 --> 00:21.330 And this should be somewhere here in this region. 00:21.440 --> 00:23.390 So we have still important. 00:23.480 --> 00:31.130 The portfolio summary data frame with our 100 thousand portfolios and the annualized the return risk 00:31.160 --> 00:33.080 and the ratio. 00:33.080 --> 00:40.910 And we again can also call the scribe method here and we can see that the best portfolio has a sharp 00:40.910 --> 00:47.780 ratio of one point eighteen and in the next step we want to find exactly this portfolio. 00:48.140 --> 00:56.500 But first of all we have also here the weights matrix with the weights of the 100000 portfolios and 00:56.570 --> 01:03.740 we want to find the max sharp racial portfolio and we can do this by selecting the shop column of our 01:03.740 --> 01:10.970 portfolio summary data frame and then we use the idea X Max method and by doing so append us actually 01:10.970 --> 01:19.310 returns as the index labor of uh the portfolio with the highest chop ratio and we can also look at inside 01:19.310 --> 01:20.690 the idea X Max method. 01:20.690 --> 01:22.050 So let's have a look here. 01:22.070 --> 01:30.440 So the idea X Max method returns the roll label of the maximum value in this case in the shop column 01:31.010 --> 01:36.180 and then we actually save for the row label and the variable maximum Sharpe Ratio portfolio. 01:36.650 --> 01:39.310 So let's do this here and let's have a look. 01:39.320 --> 01:43.040 So we have 100000 portfolios and. 01:43.190 --> 01:50.930 The portfolio with the indexed label seventy six thousand eight hundred seventy nine has the highest 01:50.930 --> 01:57.650 chop ratio of one point eighty in and now we can also select the row with the maximum Sharpe ratio in 01:57.650 --> 02:04.400 our portfolio summary data frame and of course we can do this with the ILO operator and we pass here 02:04.490 --> 02:05.720 the ROE label. 02:06.710 --> 02:07.510 Let's have a look here. 02:08.820 --> 02:15.570 So here the very best portfolio gives us a an annualized return of 25 percent. 02:15.570 --> 02:19.400 We have a risk in terms of standard deviation of 19 percent. 02:19.560 --> 02:26.490 And of course we uh the shop ratio the max job ratio of one point eighteen and that's actually the portfolio 02:26.490 --> 02:30.480 with the number seventy six thousand eight hundred seventy nine. 02:30.630 --> 02:38.660 And we can also get the weights of this portfolio by passing the ROE label of the best portfolio which 02:38.670 --> 02:44.750 is also the index positions so we have a uh Range Index starting from zero. 02:44.760 --> 02:51.360 So we pass here the index position to the weights matrix and then we get the weights of uh this best 02:51.360 --> 03:00.220 portfolio and we save the weights and the variable maximum sharp racial portfolio weights so here we 03:00.220 --> 03:07.390 have uh the six weights and to have a better overview we can also create a panda series with the stock 03:07.390 --> 03:09.580 ticker as the index. 03:09.580 --> 03:10.900 And are our weights. 03:10.900 --> 03:13.710 So let's do this and let's have a look. 03:14.190 --> 03:21.960 So here in our best portfolio we have for the Amazon stock a rate of 27 percent for the Boeing column 03:21.960 --> 03:23.730 of 39 percent. 03:23.730 --> 03:25.760 Then we have only one point seven percent. 03:25.770 --> 03:36.240 This may then almost 0 percent IBM 5 percent Coca-Cola and the 25 percent Microsoft in our portfolio. 03:36.250 --> 03:43.560 And this is actually the best portfolio of our 100000 random portfolios but it's actually not the absolutely 03:43.560 --> 03:45.090 best portfolio. 03:45.180 --> 03:54.320 So we can also optimize for the very best portfolio by using some advanced optimization algorithms. 03:54.540 --> 03:57.640 But this is clearly beyond the scope of this course. 03:57.750 --> 04:04.650 And I have done this in the background and I could solve for the weights of the very best portfolio. 04:04.740 --> 04:09.840 So we say for the weights and the variable optimal weights and let's have a look here. 04:09.990 --> 04:15.190 So by using some optimization algorithms we get here the very best portfolio. 04:15.330 --> 04:23.040 And here we can see that we have zero weight for Disney IBM and Coca-Cola and the 25 percent for Amazon 04:23.040 --> 04:28.020 35 percent for Boeing and 39 percent for Microsoft. 04:28.020 --> 04:32.220 So this is our very best portfolio are the weights of our very best portfolio. 04:32.670 --> 04:36.720 And then we can also create the evaded average daily returns. 04:36.840 --> 04:44.130 For this portfolio and we create a new column for our returns data frame and we will see the top method 04:44.160 --> 04:46.200 and pass the optimal weights. 04:46.210 --> 04:48.840 So let's do this and let's have a look. 04:48.840 --> 04:50.790 So here we have our six constituents. 04:50.790 --> 04:58.570 And on the right hand side that daily returns of the maximum Sharpe Ratio portfolio MP and we can also 04:58.570 --> 05:04.900 create these summary data frame by passing the returns that are frame to our user defined function annualized 05:04.900 --> 05:06.250 the risk and return. 05:06.250 --> 05:07.930 So let's do this. 05:07.930 --> 05:14.710 And we also add the column shop with the top ratio which is the portfolio return minus the return of 05:14.710 --> 05:18.070 the risk free rate divided by the risk of the portfolio. 05:18.070 --> 05:21.690 So let's do this and let's have a look. 05:21.700 --> 05:28.630 So here we have in the very last row of our maximum sharp racial portfolio with some return of 25 percent 05:28.630 --> 05:35.790 a risk of 20 percent and the maximum Sharpe ratio of one point nineteen six. 05:35.800 --> 05:39.670 And finally of course we can also visualize our results here. 05:39.670 --> 05:45.300 So we create a scatter blood again with all of our 100000 portfolios. 05:45.400 --> 05:53.410 And on the x axis we have the risk and on the y axis the return and the color is determined by the sharp 05:53.410 --> 05:54.400 ratio. 05:54.520 --> 06:02.030 And we also create a point or a star with the the maximum Sharpe Ratio portfolio. 06:02.050 --> 06:03.880 So it's a black star here. 06:03.880 --> 06:05.410 And uh let's have a look. 06:08.850 --> 06:12.500 So here we have our 100000 portfolios. 06:12.600 --> 06:20.910 And here is the Black Star we can see the maximum sharp ratio portfolio that we derive to with our optimization 06:20.910 --> 06:22.290 algorithm. 06:22.320 --> 06:27.330 So that's the very best portfolio that we could have created five years ago. 06:27.330 --> 06:35.010 So for the period of the last five years and actually you might ask yourself why exactly this portfolio 06:35.010 --> 06:40.980 is here the maximum Sharpe Ratio portfolio so it could also be another portfolio here on the efficient 06:40.980 --> 06:41.610 frontier. 06:41.610 --> 06:48.980 So for example this one and exactly this question I have a hand and answer in the next video. 06:48.990 --> 06:50.490 So I hope to see you there by.