WEBVTT 00:00.930 --> 00:06.210 And the last video we have seen that there is or there should be a linear relationship between systematic 00:06.210 --> 00:07.770 risk and return. 00:07.890 --> 00:14.070 And we are actually only one step away from the Capital Asset Pricing Model at least from the cap and 00:14.070 --> 00:14.930 formula. 00:15.300 --> 00:21.360 And again we are not deriving the Capital Asset Pricing Model here and we do not take any assumptions. 00:21.360 --> 00:27.410 We are just looking at historical data and try to identify some parents in our historical data. 00:28.150 --> 00:36.190 So this is actually the graph that we derived in the last video and we have here on the x axis that 00:36.200 --> 00:43.290 is systematic risk and covariance units and actually covariance is maybe not the most comfortable way 00:43.290 --> 00:50.520 to display systematic risk and therefore we could also normalize our core variances by dividing each 00:50.520 --> 00:58.350 covariance by the variance of the market portfolio and by doing so we are actually normalizing the systematic 00:58.350 --> 01:04.140 risk in a way that we have a systematic risk of one for the market portfolio. 01:04.200 --> 01:07.550 So let's have a look here and we are still important. 01:07.590 --> 01:16.770 The summary data frame and here we have the columns systematic risk and variance are covariance terms 01:18.040 --> 01:24.130 and what we want to do now we want to normalize each and every element here and divide each element 01:24.610 --> 01:28.400 by the variance of the market portfolio. 01:28.420 --> 01:35.420 So this is exactly what we are doing here and let's have a look. 01:35.510 --> 01:43.100 Here we have the normalized systematic risk and we are fair value of 1 for the market portfolio then 01:43.100 --> 01:50.390 for Amazon we have a higher systematic risk of one point to 2 and for example for Coca-Cola we have 01:50.420 --> 01:58.510 quite a low systematic risk of 0 point to 5 and actually this normalized a systematic risk metric is 01:58.520 --> 02:07.390 actually the popular and very famous beta effect or and we can also create a new column here and our 02:07.400 --> 02:13.700 summary data frame called beta and we exactly are using these values here. 02:13.700 --> 02:14.630 So let's do this 02:18.290 --> 02:26.360 so here we have the new column beta and now we can again plot the systematic risk versus the return 02:26.960 --> 02:33.640 by using here the beta on the x axis and the return on the y axis. 02:33.710 --> 02:34.960 So let's do this here 02:37.790 --> 02:40.240 and let's have a look. 02:40.320 --> 02:48.810 Here we have the beta on the x axis and the market portfolio as a paid off one here and we have further 02:48.810 --> 02:56.040 return on the y axis and still of course we can see here the linear relationship between systematic 02:56.040 --> 02:58.150 risk and return. 02:58.230 --> 03:06.840 So the constituents of the optimal portfolio Boeing Microsoft and Amazon and the optimal portfolio our 03:06.840 --> 03:08.440 market portfolio itself. 03:08.490 --> 03:16.230 So they are all here on the one line and this line actually links the risk free asset and the market 03:16.230 --> 03:17.710 portfolio. 03:17.760 --> 03:24.690 And again we can also see here that the Coca-Cola stock that Disney's stock and the IBM stock they are 03:24.690 --> 03:31.860 below the line here because they're actually underperforming and actually in the Capital Asset Pricing 03:31.860 --> 03:32.430 Model. 03:32.430 --> 03:39.840 This line is called the security market line and in the optimal world actually each security should 03:39.840 --> 03:47.610 lie on this line here and in other words each security should actually deliver the return corresponding 03:47.610 --> 03:49.670 to its systematic risk. 03:50.130 --> 03:51.660 So we feel a line. 03:51.810 --> 03:59.550 And if we recall some high school math then we can also derive the equation for that line here. 03:59.700 --> 04:04.190 And in general the equation for a line looks as follows. 04:04.200 --> 04:12.870 So y equals to the intercept plus the slope times X and transferring this to our case here. 04:13.290 --> 04:22.080 So our Y is actually the return of our security is then the intercept with the y axis is actually the 04:22.080 --> 04:25.700 risk free asset at one point seven percent. 04:25.920 --> 04:35.070 Then we have here the slope and the slope is actually that y divided by that X and Y is actually the 04:35.090 --> 04:44.970 mark at portfolio return minus the risk free rate and that X is actually 1 minus 0 is 1. 04:45.000 --> 04:53.610 So the slope of the security line is simply the market portfolio return minus the risk free return which 04:53.610 --> 04:57.850 is also called the market excess return. 04:57.870 --> 05:01.140 And finally our x axis is actually the beta. 05:01.830 --> 05:09.910 So this is actually the formula to calculate the return of a security given the security is better. 05:10.500 --> 05:14.120 And this is exactly the Capital Asset Pricing Model formula. 05:14.670 --> 05:19.380 And we can also cross-check this for example for the Amazon stock. 05:19.530 --> 05:27.000 So we want to calculate here the Amazon stock return based on its beta and therefore we take you the 05:27.060 --> 05:29.130 risk free return. 05:29.370 --> 05:35.000 Then we are calculating here the market portfolio return minus the risk free return. 05:35.730 --> 05:40.100 And then we finally multiply here with the Amazon beta factor. 05:40.320 --> 05:41.300 So let's have a look. 05:42.620 --> 05:50.330 And we get to thirty point one percent and let's have a look at our summary data frame. 05:50.420 --> 05:56.840 So this is exactly the return that we have here and our historical data thirty one point five percent 05:58.370 --> 06:05.420 and we can also calculate for each and every stock and also for the market portfolio the return based 06:05.450 --> 06:07.170 on our formula here. 06:07.200 --> 06:09.220 So the cap m return. 06:09.380 --> 06:11.540 So let's do this. 06:11.540 --> 06:17.060 And by doing so we're actually creating a new column for our summary data frame. 06:17.060 --> 06:22.670 So the cap m return column A.B. F on the right hand side. 06:22.690 --> 06:30.820 The new column and we can actually compare the cap and return column with the actual return. 06:30.820 --> 06:36.180 And actually for our constituents of the market portfolio these are actually equal. 06:36.180 --> 06:38.800 So for Amazon we have uh 31 percent. 06:38.810 --> 06:45.190 Also here then for Boeing we have the same values then for the Microsoft stock. 06:45.190 --> 06:52.870 We have almost the same values then for the market portfolio of course we have also the same values 06:54.150 --> 07:02.580 and we can see for the three stocks that have zero weight and our optimal portfolio that the cap M returns 07:02.580 --> 07:05.370 are higher than the actual returns. 07:05.370 --> 07:12.330 So for the at this nice talk the cap m return is twelve point eight percent and the actual return is 07:12.330 --> 07:13.250 10. 07:13.500 --> 07:21.360 And we could say here that the Disney stock should have returned twelve point eight but it underperformed 07:21.390 --> 07:24.390 and only showed a 10 percent. 07:24.390 --> 07:29.250 And that's exactly the reason why there's zero weight in our optimal portfolio. 07:29.850 --> 07:32.730 And also here for the IBM stock. 07:32.730 --> 07:41.070 So the actual historical return is far below the cap m return and for Coca-Cola it's actually pretty 07:41.070 --> 07:42.080 close. 07:42.420 --> 07:47.400 And with this we are finished with our video and I hope to see also in the next one by.