WEBVTT 00:01.030 --> 00:04.050 In this video we will learn how to calculate a stock's Alpha. 00:04.090 --> 00:10.230 And we will also discover an alternative and more graphical explanation of a stocks paid factor. 00:10.450 --> 00:16.160 And in the last video we have learned that there is a strong positive relationship between a stocks 00:16.170 --> 00:19.030 the beta and the return. 00:19.300 --> 00:25.870 And with the cap M formula we can calculate the required return of a stock given its systematic risk 00:25.870 --> 00:33.400 in terms of the beta factor and in the optimal case that the stock is located here on the security market 00:33.400 --> 00:37.990 line and returns exactly the cap m return. 00:37.990 --> 00:42.460 However if you have a look at historical data then stocks can also be a buffer. 00:42.460 --> 00:49.900 These security market line showing an over performance or below the security market line and showing 00:49.900 --> 00:57.220 an underperformance and this over performance or underperformance is also the stocks alpha. 00:58.000 --> 01:05.380 So for example here for our this nice stock the distance from the distance a stock to the security market 01:05.380 --> 01:11.110 line is actually the stocks Alpha and in this example it's a negative. 01:11.110 --> 01:18.580 So far these three stocks here we have a negative outlook for us and for the other stocks we have zero 01:18.580 --> 01:25.570 alpha here because they are exactly located on the security market line and we actually have no stock 01:25.570 --> 01:27.320 with positive alpha. 01:27.520 --> 01:34.840 As we construct it the market portfolio in a way that this is the optimal portfolio based on the historical 01:34.840 --> 01:42.090 data of these six stocks here and in the next video we will consider a more real world scenario where 01:42.100 --> 01:46.600 we will also have positive and negative of stocks. 01:46.600 --> 01:54.060 But for the time being we can go on here and we can simply calculate the alpha of each stock and we 01:54.060 --> 01:55.060 are still imparted. 01:55.060 --> 02:02.210 Our summary data frame and we've already learned that actually the alpha is the difference between the 02:02.270 --> 02:06.200 actual return and the year required return. 02:06.410 --> 02:08.240 According to the cap and model. 02:08.540 --> 02:16.940 So we simply deduct our cap em return column from the uh return column and uh by doing so we're creating 02:17.000 --> 02:22.360 a new column out of FA so let's do this and let's have a look here again. 02:22.400 --> 02:25.530 Here we are on the right hand side we have now the alpha. 02:25.790 --> 02:30.040 And we can see that for our three constituents of our market portfolio. 02:30.040 --> 02:38.380 So the Amazon stock uh the Boeing stock and the Microsoft stock we have an outflow of uh 0 and uh 4. 02:38.390 --> 02:43.150 The other three stocks uh where we have 0 8 in our market portfolio. 02:43.280 --> 02:51.650 We have a negative 5 5 uh 3 percent 18 percent and still for the Coca-Cola stock minus 1 percent. 02:52.340 --> 02:56.890 And by definition the alpha of the market portfolio is zero. 02:57.770 --> 03:03.170 And last but not least we can also get an alternative more graphical intuition of these stocks beta 03:03.210 --> 03:09.950 factor and we are still impart that the returns data frame with the daily returns of the stocks and 03:09.950 --> 03:17.730 the market portfolio and we can actually get a stock sped up by having a linear regression between the 03:17.730 --> 03:25.880 stocks returns and the returns of the market portfolio and we can do this graphically with a seaborne 03:25.890 --> 03:27.060 joint plot. 03:27.180 --> 03:30.860 So we are using other returns data frame and on the x axis. 03:30.930 --> 03:36.840 We will have for the daily returns of the market portfolio and on the y axis we have the daily returns 03:36.840 --> 03:38.480 of the Amazon stock. 03:39.120 --> 03:40.080 So let's have a look 03:44.480 --> 03:52.430 and we can clearly see that there is a strong positive relationship between returns of the market portfolio 03:52.460 --> 03:54.730 and the Amazon returns. 03:54.740 --> 04:01.940 So whenever the returns of the market portfolios are higher then also the return of the Amazon stock 04:01.940 --> 04:04.040 is high and vice versa. 04:04.040 --> 04:11.570 So here we have a linear regression and this is the regression line and we can actually describe a linear 04:11.570 --> 04:14.210 regression with the two coefficients. 04:14.210 --> 04:21.950 So we have the beta coefficient which is actually the slope of the regression line here and we have 04:21.950 --> 04:28.520 actually the intercept and the beta factor that we calculated before is actually nothing else. 04:28.550 --> 04:35.960 Then here the slope of the regression line so we can also calculate the slope of our regression line 04:35.960 --> 04:43.700 here by performing the linear regression with an umpire and we can do this with the NPR dot poly fit 04:43.700 --> 04:44.350 function. 04:44.360 --> 04:45.170 Let's have a look here. 04:46.740 --> 04:54.080 And here we have to pass um x values slowly he and our example the daily returns of the market portfolio 04:54.110 --> 04:55.740 and y values. 04:55.740 --> 04:58.250 So the daily returns of the Amazon stock. 04:58.430 --> 05:02.330 And finally we have to determine a degree for the regression. 05:02.690 --> 05:09.860 So here we have a linear regression with a degree of one so a quadratic regression would have a degree 05:09.860 --> 05:11.780 of 2 and so on. 05:11.930 --> 05:19.070 And uh that's running at the center and actually the NPD are poorly fed function returns. 05:19.100 --> 05:24.850 Uh the coefficients of the regression and here at the index position zero. 05:24.850 --> 05:27.970 So this is an umpire Ray at an exposition 0. 05:27.970 --> 05:36.100 We have uh the beta of the regression to say the slope of the regression line and at the next position 05:36.100 --> 05:38.380 1 we have the intercept. 05:38.410 --> 05:46.290 Now we can also select the pater at index positions that are and save it and the available Amazon beta. 05:46.840 --> 05:54.850 And this is exactly one point two to nine and we can also recall he our summary data frame where we 05:54.850 --> 06:02.500 have also calculated the beta factor as being the normalized the systematic risk and also here we have 06:02.530 --> 06:04.800 a value of 1 point 2 2 9. 06:04.810 --> 06:10.130 So this is C around it but we have actually exactly the same value. 06:10.330 --> 06:14.020 So this is a graphical intuition behind the beta effect to us. 06:14.050 --> 06:21.420 So it's simply the regression slope between the particular stock and the market portfolio. 06:21.580 --> 06:23.770 And with this we are finished here. 06:24.040 --> 06:30.350 So we created here our summary data frame with lots of information of our six stocks. 06:30.370 --> 06:37.720 So first of all we created the market portfolio which is actually the optimal portfolio for our six 06:37.720 --> 06:41.610 stocks for the respective historical time period. 06:41.620 --> 06:44.490 Then we calculated annualized risk and return. 06:44.500 --> 06:51.160 And the sharp ratio then we divided the total risk into a systematic risk and and systematic risk. 06:51.310 --> 06:59.350 And based on the systematic risk we calculated the normalized systematic risk which is the data then 06:59.380 --> 07:06.580 we calculated the required return according to the cap and model which uh takes into consideration the 07:06.640 --> 07:08.260 beta factor. 07:08.260 --> 07:17.600 And finally we were able to calculate over our underperformance with the alpha and with this we are 07:17.600 --> 07:21.050 finished here and I hope to see you also in the next video by.