WEBVTT 00:01.280 --> 00:07.370 In the last video we examined the portfolio diversification effect and we learned that each stock contains 00:07.460 --> 00:14.450 and systematic risk that can be diversified when putting the stock into a portfolio and systematic risk 00:14.540 --> 00:16.850 that cannot be diversified. 00:16.910 --> 00:22.940 And in this video we will split the total risk of our constituents stocks into a systematic and and 00:22.940 --> 00:30.350 systematic risk and I must admit that we oversimplify things and the last video when we calculated the 00:30.350 --> 00:35.710 weighted average risk as we did this with the standard deviation of returns. 00:36.140 --> 00:43.730 However simple arithmetic operations like addition and multiplication with the standard deviation mathematically 00:43.730 --> 00:52.000 wrong and we have seen this when we convert a daily risk to annualized risk by multiplying the standard 00:52.000 --> 01:00.400 deviation of daily returns with the square root of 250 to s the standard deviation is the square root 01:00.400 --> 01:08.020 of the variance and when we have the risk and variance units it is the mathematically correct to perform 01:08.050 --> 01:08.850 arithmetic. 01:09.280 --> 01:16.090 And that's exactly the reason why in this video we will use the variance instead of the standard deviation. 01:16.090 --> 01:22.900 However the error we made in the last video was fairly low so we actually didn't change the big picture 01:22.930 --> 01:25.180 and the key findings. 01:25.240 --> 01:30.270 So let's move on here and we still have important. 01:30.340 --> 01:36.400 The summary data frame with the annualized the risk and return and the shop ratio. 01:36.400 --> 01:41.410 And as I said here we have the risk in standard deviation units. 01:41.410 --> 01:48.160 And so the standard deviation is simply the square root of the variance and we can convert the standard 01:48.160 --> 01:53.290 deviation to the variance by taking the standard deviation to the power of two. 01:53.740 --> 01:55.900 And this is exactly what we are doing here. 01:55.900 --> 02:03.270 So we're using the NUM pi function and people power we perceive the risk column and we are square actually 02:03.290 --> 02:09.010 the risk column and we created the new column total risk in the variance units 02:12.120 --> 02:14.130 so here we are on the right hand side. 02:14.130 --> 02:23.210 The variance of the standard deviation here and that's still the total risk of our constituents and 02:23.210 --> 02:27.020 we also still impart that the returns data frame. 02:27.020 --> 02:34.570 So these are the daily returns of the constituents and the M P portfolio and having the returns data 02:34.580 --> 02:36.090 frame we can create. 02:36.110 --> 02:42.360 The covariance matrix so we can do this with the method Cove. 02:42.620 --> 02:50.540 And by doing so we would get the daily code variances and also the same as the width of the variance 02:50.540 --> 02:53.540 and the standard deviation and also of the returns. 02:53.600 --> 02:59.820 You can annualize them the covariance matrix by multiplying with 252. 02:59.870 --> 03:06.330 So we have two hundred and fifty two trading days on average so let's have a look here. 03:06.690 --> 03:13.200 So here we have the new data frame Cove which is actually the covariance matrix with the annualized 03:13.200 --> 03:14.630 covariance us. 03:14.940 --> 03:22.200 And as a short recap of the covariance of the Amazon stock with the Amazon stock itself is a nine point 03:22.470 --> 03:23.580 six percent. 03:23.730 --> 03:29.410 And this is simply the variance so we can also verify this. 03:29.490 --> 03:37.720 And here we have the variance of the Amazon stock of nine point six percent and the same we have here 03:39.070 --> 03:47.260 and we also have still imparted the optimal way it's so these are the weights of uh the constituents 03:47.290 --> 03:49.580 and our MP portfolio. 03:50.110 --> 03:54.450 And we can actually see here on the right hand side the column MP portfolio. 03:54.490 --> 04:03.430 And here we have the CO variances of the MP portfolio with its constituents and actually we could simply 04:03.430 --> 04:08.610 calculate the weighted average covariance of the constituents. 04:08.650 --> 04:16.420 And we can do this by selecting the column here and then we are using the top method and we pass the 04:16.450 --> 04:17.590 optimal weights. 04:17.650 --> 04:26.720 So let's do this and we get the weighted average covariance off the constituents of MP with MP and this 04:26.720 --> 04:28.610 is three point nine percent. 04:29.210 --> 04:31.730 And uh this looks pretty familiar. 04:31.730 --> 04:38.530 So the total risk or the variance of the MP portfolio is also three point nine percent. 04:38.570 --> 04:43.960 So we can also explicitly select the variance of the MP portfolio here. 04:44.390 --> 04:48.410 So this is what we are doing and uh. 04:48.420 --> 04:55.270 So here we have two times exactly the same result and as a summary we could say that the total risk 04:55.270 --> 05:05.050 of the portfolio consists of the evaded average covariance us of the constituents of the portfolio and 05:05.050 --> 05:12.310 therefore the covariance of the constituents of the portfolio are actually the systematic risk of the 05:12.310 --> 05:20.140 constituents and therefore we can include to our summary data frame the columns systematic risk. 05:20.380 --> 05:24.390 And we simply copy here the CO variances. 05:24.400 --> 05:28.660 So this column here into our summary data frame 05:32.800 --> 05:39.790 so here we f on the right hand side the columns systematic risk and variance terms and actually these 05:39.790 --> 05:45.460 values are their core variances of the constituents with the market portfolio. 05:45.850 --> 05:52.330 So we have here the total risk then we have here the systematic risk and actually the difference between 05:52.330 --> 06:00.040 the total risk and the systematic risk is the and systematic risk that can be diversified and therefore 06:00.070 --> 06:05.070 we can create also the column and systematic risk where we have abstract. 06:05.120 --> 06:09.040 The systematic risk from the total risk and let's do this 06:13.680 --> 06:17.910 so here we have for all stocks and also for the market portfolio. 06:18.030 --> 06:21.820 The total risk the systematic risk and and systematic risk. 06:21.900 --> 06:28.410 So let's have a look here for example at the Amazon stock the total risk and variance unit is nine point 06:28.410 --> 06:34.590 six percent and actually almost 50 percent of the total risk is and systematic risk. 06:34.650 --> 06:39.020 That can be diversified and that's also if you look at the market portfolio. 06:39.030 --> 06:47.640 So the total risk is uh about 4 percent and uh the systematic risk is also 4 percent and that's actually 06:47.640 --> 06:50.020 0 and systematic risk costs. 06:50.060 --> 06:57.510 This is already the market portfolio where we diversify it away the and systematic risk of the constituents 06:58.110 --> 07:04.830 and the market portfolio by definition only consists of systematic risk or market risk. 07:04.830 --> 07:09.660 And we can also visualise this for our constituents and the market portfolio. 07:09.660 --> 07:15.940 So we're creating here a buyer plot and we actually selected the Amazon stock. 07:16.020 --> 07:23.580 The Boeing stock and the Microsoft stock in our portfolio and we we're actually visualizing in a stacked 07:23.580 --> 07:24.520 bar plot. 07:24.600 --> 07:28.040 The systematic risk and the and systematic risk. 07:28.110 --> 07:32.330 So the last uh two columns here and let's have a look 07:36.270 --> 07:45.630 so here we have on the x axis our stocks and the portfolio and on the y axis the risk and variance units 07:46.050 --> 07:52.890 and in blue we can see here the systematic risk and in green the UN's systematic risk and actually the 07:52.890 --> 08:00.000 systematic risk of our market portfolio here is simply the weighted average of the systematic risk of 08:00.140 --> 08:08.840 the three constituents and by forming a portfolio we get rid of the and systematic risks offer the constituents 08:09.290 --> 08:13.230 so the green parts here completely diminish in our portfolio. 08:13.230 --> 08:15.020 So there's no Green Party here. 08:15.950 --> 08:19.140 And at this point I have to make one important note. 08:19.250 --> 08:25.940 So this particular split into a systematic and unsourced somatic risk is well it only for our specific 08:25.940 --> 08:27.110 case. 08:27.110 --> 08:34.940 So our portfolio consists of only those three stocks and a three stock portfolio is actually not a very 08:34.940 --> 08:42.650 perfectly diversified portfolio and in a sense um the market portfolio here still contains and systematic 08:42.650 --> 08:48.110 risk of each constituents as the weight of each constituent is still high. 08:48.170 --> 08:54.890 And if we had a portfolio with 100 stocks then the answers the medic risk portion of our three stocks 08:54.890 --> 08:57.060 here would even be higher. 08:57.080 --> 09:01.670 So this split only applies here for this specific case. 09:02.330 --> 09:04.250 All right now let's move on and. 09:04.280 --> 09:11.210 Throughout the costs we implicitly agreed on the fact that there is a relationship between risk and 09:11.210 --> 09:12.290 return. 09:12.290 --> 09:16.760 So the higher the risk of a stock the higher should be the return. 09:17.030 --> 09:20.820 And the question is which relationship do we have here. 09:20.840 --> 09:26.480 And of course we would always prefer a linear relationship so that would be great. 09:26.570 --> 09:35.150 And uh we can try to visualize this or try to get a linear relationship by plotting the risk on the 09:35.150 --> 09:38.200 x axis and the return on the y axis. 09:38.210 --> 09:40.950 So this is actually nothing new. 09:41.050 --> 09:46.040 And the first try we use of the total risk and variance unit. 09:46.070 --> 09:52.450 So we have on the x axis the total risk and on the y axis the return. 09:52.580 --> 09:57.640 And we do this for our six stocks and for our market portfolio here. 09:57.650 --> 09:58.720 So let's have a look. 10:03.640 --> 10:09.570 So here we have also the risk free asset then our constituents and the market portfolio. 10:09.670 --> 10:17.930 And on the x axis as I said we feel the total risk and the return here on the y axis and by drawing 10:17.930 --> 10:24.770 a line here from the risk free asset to the market portfolio then we can see here that there is no linear 10:24.770 --> 10:33.350 relationship between total risk and return and therefore instead of using the total risk we should also 10:33.350 --> 10:36.400 try to use the systematic risk. 10:36.440 --> 10:43.730 So maybe there's a significant linear relationship between the systematic risk and the return and uh 10:43.970 --> 10:51.800 therefore we created again a set up plot and uh we choose from our summary data frame the columns the 10:51.830 --> 10:58.760 systematic risk and variance units and the returns column and that's simply running the set and let's 10:58.760 --> 10:59.240 have a look 11:03.010 --> 11:07.860 so here we plotted systematic risk of our stocks versus the return. 11:08.080 --> 11:09.940 And we can see that. 11:10.030 --> 11:15.730 When we are creating a line from the risk free asset to the market portfolio which is here. 11:15.790 --> 11:20.560 So this is the Microsoft stock and this is the market portfolio. 11:20.560 --> 11:26.840 So when we draw here a line from the risk free asset to the market portfolio then our constituent stocks. 11:26.950 --> 11:33.550 So the Boeing stock the Microsoft stock and also the Amazon stock they are on this line here. 11:33.790 --> 11:40.840 So the market portfolio consists of uh these three stocks and of course the market portfolio was designed 11:40.840 --> 11:48.910 in a way that it's actually the optimal portfolio when taking here the six constituents and we can also 11:48.910 --> 11:55.220 see here that the stocks Coca-Cola Disney and IBM are not on our line here. 11:55.330 --> 12:02.890 And the reason for this is that they did not deliver the return that they should deliver based on the 12:02.890 --> 12:07.570 systematic risk that they had with the market portfolio. 12:07.660 --> 12:13.600 So they actually underperformed in terms of systematic risk and return and therefore they have zero 12:13.600 --> 12:20.460 weight in our optimal portfolio and with this we are finished with this video and I hope to see you 12:20.470 --> 12:22.120 also in the next one by.