WEBVTT 00:01.010 --> 00:06.710 In the last videos we derived various performance metrics five or six stocks and we also created the 00:06.710 --> 00:13.760 optimal portfolio of these stocks based on historical returns and the fact that our three constituents 00:13.790 --> 00:21.790 of the optimal portfolio exactly lie on the security market line with Zero Alpha was kind of a self-fulfilling 00:21.800 --> 00:29.660 prophecy as we used to the optimal portfolio for our considerations and we called it the market portfolio. 00:29.660 --> 00:37.130 However the market portfolio should be the portfolio that the market or the average investor hold and 00:37.130 --> 00:42.890 in an ex post scenario where we want to figure out whether our stocks performed well in the past or 00:42.890 --> 00:43.580 not. 00:43.580 --> 00:50.480 We should therefore use a market cap or weighted portfolio and for our six stocks we already did this 00:50.510 --> 00:53.150 in the section on financial indexes. 00:53.720 --> 01:01.040 So instead of using the optimal portfolio we will now use the evaluated Performance Index of our six 01:01.040 --> 01:02.210 stocks. 01:02.210 --> 01:10.760 So we still have imparted our returns data frame and still we have the optimal portfolio here and we 01:10.760 --> 01:15.440 want to drop or delete the optimal portfolio. 01:15.530 --> 01:22.840 So now we only have our six constituents and then we are importing from the CSP file market cap waits 01:23.130 --> 01:27.020 the rates that would actually apply in a value weighted index. 01:27.760 --> 01:35.570 So I have already prepared these and we just import the weights here so let's have a look and this is 01:35.570 --> 01:40.520 actually nothing new compared to our section on financial indexes. 01:40.520 --> 01:48.620 So we have the highest rates for the Amazon stock and the Microsoft stock and uh they increase over 01:48.620 --> 01:49.520 time. 01:49.520 --> 02:00.000 So at the end of 2018 we have a market cap wait for Amazon of 33 percent and for Microsoft of 35 percent. 02:00.080 --> 02:08.100 So having the rates and the daily returns then we can also calculate the daily returns of uh the way 02:08.150 --> 02:15.140 you rate the performance index and we are actually saving the daily returns in the new column market 02:15.140 --> 02:16.540 cap portfolio. 02:16.910 --> 02:26.740 So this is actually nothing new and let's have a look here at our returns data frame. 02:26.800 --> 02:29.740 So here we are on the right hand side. 02:29.830 --> 02:34.360 Our new evaluated the performance portfolio our index 02:36.930 --> 02:41.160 and now with our user defined function annualized the risk and return. 02:41.290 --> 02:44.240 Uh we pass our returns data frame into. 02:44.270 --> 02:53.800 We create the summary data frame so here we have the annualized the risk and return for our six constituents 02:53.830 --> 02:56.170 and the evaluated portfolio. 02:56.710 --> 03:05.170 So the risk is here in standard deviation units and we can also create the covariance matrix of uh these 03:05.200 --> 03:13.870 uh seven securities and we can do this with the Koth method and then we can also annualize the covariance 03:13.870 --> 03:17.230 by multiplying with two hundred fifty two. 03:17.230 --> 03:19.180 So let's do this. 03:19.180 --> 03:26.220 So here we have the covariance terms and as a short recap here on the right hand side we have the core 03:26.220 --> 03:31.540 variances of our constituents with our market portfolio. 03:31.540 --> 03:38.680 And here in the end that's the variance of the market portfolio and the covariance length of the market 03:38.680 --> 03:42.970 portfolio is the systematic risk of a stock here. 03:42.970 --> 03:49.750 And therefore we can also create here for our summary data from the new column systematic risk and variance 03:49.750 --> 03:58.630 units by taking uh the column on the right hand side and then we can also calculate the Beda effect 03:58.630 --> 04:06.910 or by normalizing the systematic risk by the variance of the market portfolio and let's have a look 04:06.910 --> 04:07.270 here. 04:08.230 --> 04:13.330 So here we have the systematic risk and variance units and the beta factor. 04:13.510 --> 04:20.500 And of course it's no surprise that our market portfolio has the bad effect of 1 then our Amazon stock 04:20.500 --> 04:28.930 has a quiet high paid off factor of one point for two and the Coca-Cola stock has a quite a low paid 04:28.930 --> 04:36.860 off factor and now finally we can visualize the relationship between the data and the return. 04:37.610 --> 04:44.810 And we can actually trade these security market line from their risk free asset to the market portfolio 04:45.080 --> 04:50.380 and then we can see which of our stocks are located above the security market line. 04:50.380 --> 04:56.590 And so overall performance and which are located below the security market line. 04:56.750 --> 05:06.810 So let's create here the graph and uh this is uh the security market line from the risk free asset to 05:06.840 --> 05:14.550 our market portfolio and we can see here that the stocks Boeing Microsoft and Amazon are above the security 05:14.550 --> 05:15.870 market line. 05:15.870 --> 05:21.990 So the positive distance between the stocks and the securities market line is actually the positive 05:22.050 --> 05:30.210 alpha of the stocks and we can also see that the stocks Coca-Cola Disney and IBM are still below the 05:30.210 --> 05:39.150 security market line and therefore show an underperformance and an underperformance means also a negative 05:39.180 --> 05:44.130 Alpha and we can also get another intuition on this finding here. 05:44.160 --> 05:51.810 So we learned that when we created the optimal portfolio then we have quite high rates of these three 05:51.810 --> 05:52.470 stocks here. 05:52.510 --> 06:00.200 Our optimal portfolio and we have zero weight in these three stocks and when considering our market 06:00.200 --> 06:07.430 cap portfolio there we have positive rates for our underperforming stocks and this means actually that 06:07.430 --> 06:15.380 our three stocks here are compared to their performance overweighted in the market portfolio and a similar 06:15.380 --> 06:19.570 conclusion we can also draw here for our over performing stocks. 06:19.580 --> 06:27.320 So compared to the optimal portfolio our overall performing stocks here are unabated in the market cap 06:27.320 --> 06:33.980 portfolio and it's important to say here that this holds true for the past period that we considered 06:34.310 --> 06:36.770 and not necessarily for the future. 06:37.280 --> 06:44.930 So in this video we have seen a more realistic case by having a market cap portfolio and still in the 06:44.930 --> 06:52.100 complete the last two sections we actually assumed that these six stocks are actually the only stocks 06:52.460 --> 06:54.060 that we can consider. 06:54.140 --> 06:59.500 But of course we all know that there are hundreds or thousands of stocks in the market. 06:59.540 --> 07:01.580 So only in the US market. 07:01.850 --> 07:07.640 And if you really want to figure out whether our six stocks over performed or underperformed the market 07:08.030 --> 07:13.430 we would need to consider a broad stock market index the dozens or hundreds of constituents. 07:13.880 --> 07:22.590 So for example we could use the S&P 500 as the market portfolio containing the largest 500 U.S. stocks. 07:22.760 --> 07:25.300 So feel free to make your own examination here. 07:25.310 --> 07:31.610 But for the time being we reached the end of this section and I hope to see you also in the exercises 07:31.790 --> 07:32.150 by.