WEBVTT 00:01.850 --> 00:05.880 In this video I will explain the portfolio diversification effect. 00:05.960 --> 00:08.750 So what is the portfolio diversification effect. 00:08.750 --> 00:15.560 In simple words let's assume you have two stocks and you can invest only in one of them or you can invest 00:15.560 --> 00:17.890 in both and form a portfolio. 00:18.050 --> 00:25.940 And to keep it simple let's assume we invest in both and we have fates of 50 50 so we have equal rights 00:26.240 --> 00:33.060 then the return of the portfolio is simple the mean are the average return of the single stocks however 00:33.060 --> 00:38.640 the risk of our portfolio is less than the mean or the average of the single stocks. 00:38.730 --> 00:41.790 And that's actually a pretty metric. 00:41.890 --> 00:44.490 So let's make an easy example from real world. 00:44.520 --> 00:50.880 Let's assume that you like pizza and ice cream and both give you 100 percent satisfaction when you eat 00:50.880 --> 00:51.540 them. 00:51.600 --> 00:58.980 But on the other hand side pizza and ice cream both have 500 calories and if you eat them separately 00:59.010 --> 01:05.670 for example in the morning ice cream and in the evening pizza you get to two times 100 percent satisfaction 01:05.970 --> 01:08.670 and then total 1000 calories. 01:08.670 --> 01:14.820 However if you eat both together at lunch you also get two times the food satisfaction but your total 01:14.820 --> 01:18.030 calories is only 600 or 700. 01:18.210 --> 01:23.700 And yeah this sounds completely strange and it is but that's how portfolios work. 01:25.540 --> 01:31.100 All right so now let's stop coding and we still have imparted our summary data frame. 01:31.240 --> 01:37.790 Here we have our six constituents and our maximum Sharpe Ratio portfolio or market portfolio. 01:38.080 --> 01:46.290 And we also have here the optimum weights for our stocks so these are the optimum weights to create 01:46.290 --> 01:48.960 the maximum Sharpe Ratio portfolio. 01:48.960 --> 01:50.360 So this is nothing new. 01:53.200 --> 02:00.190 So here now a summary data frame we have the annualized the return and risk and the if we would calculate 02:00.370 --> 02:05.730 the evaded average return of the constituents of uh the M P portfolio. 02:05.860 --> 02:12.730 Then we would probably end up at the return of the MP portfolio so twenty five point five eight percent. 02:13.300 --> 02:15.490 However if we do the same for the risk. 02:15.610 --> 02:20.740 So we calculate the weighted average risk of our constituents. 02:20.740 --> 02:28.660 Then we probably wouldn't end up at the risk of our portfolio here and we can prove this by simply calculating 02:28.660 --> 02:34.060 the weighted average return and weighted average risk uh for our constituents. 02:34.060 --> 02:41.650 So we select our six constituents until the Microsoft stock including and uh we only select the return 02:41.650 --> 02:49.480 and risk and then we are calculating the weighted average with the top method and pass here the optimal 02:49.490 --> 02:54.250 weights and uh we save for the result and the variable weighted average. 02:54.280 --> 02:55.290 So let's do this here. 02:59.120 --> 03:04.880 So this is actually the weighted average return and evaded ever its risks for our constituents of our 03:04.880 --> 03:06.670 best portfolio. 03:06.670 --> 03:13.430 And we can see that the evaded ever its return is the same so twenty five point five eight percent. 03:13.430 --> 03:19.400 However the risk of our weighted average is higher than the risk of our portfolio and that's pretty 03:19.400 --> 03:25.610 significant so here we have twenty five point two five percent. 03:25.610 --> 03:32.530 And actually our portfolio only has about 20 percent risk and we can also create a plot here. 03:32.530 --> 03:41.800 So we are plotting our 100000 portfolios then we are plotting our market portfolio and also we are plotting 03:41.830 --> 03:44.140 our weighted average portfolio. 03:44.140 --> 03:45.160 So let's have a look. 03:52.890 --> 03:54.810 So this is actually nothing new. 03:54.810 --> 03:57.000 Here we can see our market portfolio. 03:57.510 --> 04:05.470 And here in pepper this uh would be uh the hypothetically uh weighted average portfolio. 04:05.610 --> 04:09.040 And we can also offer a more detailed look. 04:09.080 --> 04:11.290 So this is simply the weighted average. 04:11.300 --> 04:15.770 And this is the actual risk of our market portfolio. 04:16.250 --> 04:22.640 And the differential Yes actually the risk uh that we can diversify when we create a portfolio. 04:23.360 --> 04:30.890 And therefore this is also called the and systematic or diversified risk of uh the single stocks. 04:30.950 --> 04:33.410 And as an example let's take the Boeing stock. 04:33.420 --> 04:41.390 So Boeing had recently some technical issues with uh the uh new airplane 7 3 7 Max. 04:41.510 --> 04:45.490 And this would be a so-called and systematic or Boeing specific risk. 04:45.950 --> 04:52.760 And if you form a portfolio with the Boeing stocks and many other stocks you can actually fully diversify 04:52.790 --> 04:58.040 the risk of the technical issues um of uh the new airplane. 04:58.040 --> 05:02.240 So we have our six stocks and we created the best possible portfolio. 05:02.540 --> 05:04.400 However still we have some risks. 05:04.410 --> 05:13.070 So we have a stellar 20 percent and this is actually the systematic risk of so-called market risk and 05:13.160 --> 05:16.040 the market risk cannot be diversified away. 05:16.490 --> 05:21.660 And the best example for the market risk is actually the state of the economy. 05:21.680 --> 05:27.370 So if the whole economy is weak then also the performance of the single stocks this week. 05:27.470 --> 05:33.740 So people buy less on Amazon and also the airlines buy less aircraft from Boeing. 05:33.800 --> 05:41.390 So this is a risk that affects all stocks and therefore by forming a portfolio of stocks this risk cannot 05:41.390 --> 05:42.840 be diversified away. 05:43.010 --> 05:47.710 And therefore it's a systematic non diverse viable risk. 05:47.720 --> 05:52.880 All right now let's go back to our Jupiter notebook and then the following I would like to present a 05:52.880 --> 05:57.920 pretty easy attitude for example of uh risk diversification. 05:58.070 --> 06:06.590 So let's assume we have three stocks A B and C and we actually have uh the returns of a b and c for 06:06.620 --> 06:08.270 10 periods. 06:08.270 --> 06:12.170 So this could be for example a month or years. 06:12.230 --> 06:13.540 So here we have 10 periods. 06:13.550 --> 06:20.900 And uh the return data for the three stocks and that's simply getting graphical intuition how the stocks 06:20.990 --> 06:22.720 A and B perform 06:25.470 --> 06:30.890 so here we have the return of a and b a we have here in blue and B and green. 06:31.110 --> 06:35.160 And actually the average return is about 5 percent. 06:35.640 --> 06:43.560 And whenever a is higher than 5 percent p s lower than 5 percent and whenever a is lower than 5 percent 06:43.590 --> 06:46.020 B is higher than 5 percent. 06:46.020 --> 06:50.010 So A and B are actually negatively correlated. 06:50.010 --> 06:55.200 So whenever a is high P as low and vice versa. 06:55.200 --> 06:58.940 And that's also compared the performance of A and C 07:02.000 --> 07:06.050 and here we can see that both stocks pretty much move together. 07:06.590 --> 07:12.440 So when the return of A is higher than the return of C is also high and vice versa. 07:12.440 --> 07:15.960 And if you have a look at the data at the raw data. 07:16.250 --> 07:21.160 So the return of C is always two times the return of a. 07:21.170 --> 07:30.560 So here we are five and 10 10 and 20 minus two and the minus 4 so the stocks ANC pretty much move together 07:30.590 --> 07:34.720 and in contrast A and B move in the opposite directions. 07:34.820 --> 07:40.810 And if you have look at the single periods so the average of A and B is always 5 percent so you have 07:40.820 --> 07:48.410 5 percent on average and year 10 plus several gifts 5 percent minus two and twelve gifts a 5 percent 07:48.410 --> 07:49.070 on average. 07:49.520 --> 07:57.620 So you could say that poor periods for stock H with low returns are offset by high returns for stock 07:57.620 --> 07:59.580 P and vice versa. 08:02.250 --> 08:10.690 And we can also calculate the correlation between the stocks so the correlation factor and it's no surprise 08:11.140 --> 08:21.090 that a and b are perfectly and negative correlated and the stocks ANC are perfectly positive correlated. 08:21.550 --> 08:26.810 And now let's create portfolios of the stocks A and B and ANC. 08:26.950 --> 08:35.470 And for simplicity reasons we assume equal weights low 50 50 and therefore we can at year two new columns 08:35.470 --> 08:37.990 to our three stocks data frame. 08:37.990 --> 08:43.180 So the portfolio A B and the returns and the returns of a c. 08:43.210 --> 08:46.170 So let's do this let's have a look. 08:47.490 --> 08:54.430 So here we have uh the period returns for the portfolio a and b and a and c and. 08:54.450 --> 09:02.070 We can see here that the portfolio a and b we have in each and every period a stable return of 5 percent. 09:02.460 --> 09:09.450 And we can also see that the portfolio with the stocks a and c is there shows quite a high volatility 09:10.260 --> 09:11.660 and we can also plot this. 09:11.680 --> 09:15.640 So we are applauding the portfolios A B and A C. 09:15.960 --> 09:24.430 So the period returns and they are completely stable for the A B portfolio and they are still pretty 09:24.430 --> 09:26.830 volatile for the A C portfolio. 09:28.450 --> 09:34.830 And now we can also grade these summary data frame with the ever rates return and the standard deviation 09:34.830 --> 09:44.710 of returns and let's have a look so the mean return of the stock is 4.5 and uh the mean return of the 09:44.710 --> 09:46.410 B stock 5.5. 09:46.990 --> 09:52.540 And consequently the portfolio return of a and b is um the average. 09:52.630 --> 10:01.100 So 5 percent and we can also see that the standard deviation of returns all the risk is the five point 10:01.090 --> 10:01.930 four six. 10:01.950 --> 10:04.890 And also 5.5 6 percent for a and b. 10:05.430 --> 10:13.980 And if you create a portfolio with uh both stocks then the risk of uh the portfolio B is 0 because here 10:13.980 --> 10:17.470 we are in each and every period the return of 5 percent. 10:17.520 --> 10:20.200 So there's zero variability here. 10:20.430 --> 10:26.700 And we can also make this more explicitly so we can calculate uh the evaded ever its risk and return 10:26.700 --> 10:36.300 of a and b and this would be 5 percent return and five point for six percent risk. 10:36.770 --> 10:41.240 And let's also calculate the weighted average of the single stocks ANC. 10:41.310 --> 10:48.330 So the weighted average return and risk and the weighted average return of six point seven five and 10:48.330 --> 10:52.110 exactly the same return we have for the portfolio ANC. 10:52.380 --> 10:59.940 And uh we can also see here that the risk of the portfolio ANC is 8 percent and the same we have here 10:59.940 --> 11:01.530 for the weighted average. 11:02.430 --> 11:08.930 So to summarize we can see here for the portfolio a b a huge diversification effect. 11:08.970 --> 11:15.120 So even if the single stocks ANP are risky itself the portfolio has no risk at all. 11:15.450 --> 11:20.840 So by forming a portfolio we fully diversified the risk and the opposite. 11:20.850 --> 11:23.030 We can say for the portfolio a C. 11:23.310 --> 11:27.710 So here we have no portfolio diversification effect at all. 11:27.810 --> 11:29.670 And the reason for this is pretty simple. 11:29.700 --> 11:38.010 So the stocks ANP are perfectly negative correlated and in contrast the stocks ANC are perfectly positive 11:38.010 --> 11:39.060 correlated. 11:39.330 --> 11:45.350 And whenever two stocks are perfectly positive correlated so whenever they have a correlation factor 11:45.350 --> 11:50.640 of one then there is no portfolio diversification effect at all. 11:51.240 --> 11:58.230 Or to put it the other way around whenever the correlation between two stocks is less than one. 11:58.230 --> 12:05.160 So whenever they are not perfectly positive correlated then that is a portfolio diversification effect 12:05.770 --> 12:13.730 and uh therefore we could also have a look at the correlation factors of our six stocks and as we have 12:13.730 --> 12:16.860 here portfolio diversification effects. 12:16.950 --> 12:23.420 So I would assume that the correlation effect does between our six stocks less than one and this is 12:23.420 --> 12:25.110 C or exactly the case. 12:25.110 --> 12:31.480 So for example for our Amazon stock we have a correlation of 0 point 3 6 with Boeing. 12:31.530 --> 12:34.550 So this is clearly less than one. 12:34.590 --> 12:40.940 And also with the Microsoft stock here we have a correlation effect of 0 point 5 and so on but that's 12:41.000 --> 12:44.450 the reason why we a portfolio diversification effect. 12:44.490 --> 12:52.610 So our single stocks are not perfectly positive correlated and with this we are finished here and I 12:52.610 --> 12:54.990 hope to see you also in the next video by.