WEBVTT 00:00.610 --> 00:06.660 In this video we will create forward looking portfolios and the simplest case is actually the two asset 00:06.780 --> 00:11.300 to stark case and we are still imported the data from the last section. 00:11.300 --> 00:18.910 So for example uh the returns data frame with the the daily returns for our six stocks and the market 00:18.910 --> 00:19.980 portfolio. 00:20.110 --> 00:27.520 And in this video we will focus on the Amazon and the Boeing stock and we created a new data frame two 00:27.520 --> 00:35.510 assets and we can also calculate annualized the risk and return with the user defined function annualized 00:35.510 --> 00:39.200 risk and return and actually be safe. 00:39.200 --> 00:45.590 The summary data frame and the rabbi summary to and now in our next step we want to create a forward 00:45.590 --> 00:52.820 looking portfolio where we have a 60 percent invested in the Amazon stock and 40 percent in the Boeing 00:52.820 --> 00:54.230 stock. 00:54.230 --> 01:00.860 So we create two new variables here and we put also 60 percent and 40 percent and a number higher rate 01:00.870 --> 01:08.950 call it weights W S and now in a very first step we have to calculate the expected portfolio return 01:08.950 --> 01:15.170 of our portfolio consisting of 60 percent Amazon and 40 percent Boeing and therefore we have to predict. 01:15.250 --> 01:20.890 The expected return for Amazon and the we predict here 20 percent. 01:20.890 --> 01:26.980 And we have to predict to the Boeing return the future Boeing return 15 percent and we can also save 01:27.130 --> 01:36.910 those 2 in a panda series so here we are and actually calculating the expected return of our portfolios. 01:36.980 --> 01:37.820 Pretty simple. 01:38.180 --> 01:43.560 So we simply have to calculate uh the weighted average return and therefore we U.S.A. 01:43.580 --> 01:49.790 The weight of Amazon times uh the expected return of Amazon plus the weight of Boeing times. 01:49.860 --> 01:51.940 We expect that the return of Boeing. 01:52.730 --> 01:56.180 And that's exactly what what we are doing here actually. 01:56.330 --> 02:05.230 And uh we get actually the expected return of our portfolio and that is the 18 percent and actually 02:05.230 --> 02:10.200 using this formula is a bit uncomfortable and that's a shortcut. 02:10.270 --> 02:20.470 So we can simply use our a series the expected returns and we use the top method and pass our no higher 02:20.470 --> 02:28.580 rate with our two rates here so that's a matrix multiplication and by doing so we calculate the evaded 02:28.730 --> 02:30.520 average returns. 02:30.620 --> 02:37.820 So here we get to exactly the same result 18 percent and now coming to the more difficult part calculating 02:37.820 --> 02:38.750 the expected. 02:38.840 --> 02:45.860 Portfolio risk and therefore on a very first step we create the covariance matrix of our two assets 02:45.890 --> 02:53.750 and actually the annualized covariance matrix and we save the matrix and the rabbit covariance matrix 02:56.550 --> 02:59.580 so that's an 8 to acid case pretty simple here. 02:59.850 --> 03:02.840 So here we have the variance of the Amazon stock. 03:02.850 --> 03:05.670 Then here we have the variance off of the Boeing stock. 03:06.090 --> 03:13.260 And he and the diagonals we have actually the covariance between those two assets so we could actually 03:13.260 --> 03:17.330 save the variance off the Amazon stock in the variable variance. 03:17.460 --> 03:24.960 Amazon and it's here nine point six percent and the same we can do for the variance of the Boeing stock 03:25.890 --> 03:30.930 and we can also save the covariance between Amazon and Boeing returns. 03:30.930 --> 03:35.970 Also here in a new variable and it should be two point sixty one percent 03:40.780 --> 03:46.830 and now we can calculate the expected risk of our portfolio by simply following the formula here. 03:46.870 --> 03:50.920 So the expected risk of our portfolio is the square root. 03:50.920 --> 03:57.590 And then within the square root we have here the squared the weight of our Amazon stock times. 03:57.670 --> 04:06.100 The variance of the Amazon stock plus the squared weight of Boeing times the variance of uh Boeing stock 04:06.820 --> 04:10.880 and then plus uh two times uh the weight of Amazon times. 04:10.960 --> 04:18.760 The weight of Boeing times the covariance and let's have a look here and we get an expected risk in 04:18.760 --> 04:23.510 standard deviation terms of twenty three point six percent. 04:23.680 --> 04:26.560 And also here that's a pretty helpful shortcut. 04:26.560 --> 04:34.870 So again we take the square root and then we use the covariance matrix and uh we apply here a matrix 04:34.870 --> 04:43.000 multiplication with the top method and we pass uh the weights array and then we assign another matrix 04:43.000 --> 04:45.220 multiplication with the weights array. 04:45.580 --> 04:50.360 So let's uh running the shortcut and uh the results should actually be the same here. 04:50.410 --> 04:55.630 So we get a standard deviation the expected standard deviation of uh twenty three point six percent. 04:56.320 --> 05:02.560 And if you have some spare time you can also check and verify whether this is exactly the same as uh 05:02.590 --> 05:06.490 this here or whether this leads here to the same formula. 05:06.490 --> 05:08.400 So have fun to do so. 05:08.590 --> 05:09.700 And that's actually here now. 05:09.700 --> 05:14.170 The expected return and the expected risk of our forecast the portfolio. 05:14.500 --> 05:20.200 So we have a risk of twenty three percent and a expected return of 18 percent. 05:20.200 --> 05:28.060 So that's uh 1 Uh random or forward looking portfolio and we can also create many random portfolios 05:28.630 --> 05:35.580 and let's assume we want to create 10000 the random portfolios with 10000 random weights. 05:35.890 --> 05:41.830 Then we create here a matrix uh consisting of 10000 rows and two columns. 05:41.830 --> 05:43.330 So 10000 portfolios. 05:43.330 --> 05:48.600 And we have two weights and then we calculate the weights actually. 05:48.600 --> 05:50.730 So here we have our 10000 portfolios. 05:50.730 --> 05:57.120 So the first one for example consisting of seventy point eight percent Amazon and twenty nine point 05:57.270 --> 05:59.740 one percent Boeing. 05:59.760 --> 06:06.750 And then for all of these 10000 random portfolios we can calculate the expected return of these portfolios 06:07.350 --> 06:15.850 by simply using here our panel serious was the expected returns of the two assets and applying the top 06:15.850 --> 06:20.500 method and passing the transposed the weights matrix here. 06:21.070 --> 06:21.870 So let's have a look. 06:26.050 --> 06:34.350 So here we have the returns array consisting of 10000 expected returns for our 10000 random portfolios. 06:34.360 --> 06:41.200 So for example the expected return of the very first portfolio is eighteen point five four percent. 06:41.200 --> 06:47.650 And this is based on a portfolio consisting of seventy point eight percent Amazon stock and twenty nine 06:47.650 --> 06:48.810 point one percent. 06:48.820 --> 06:53.210 Boeing stock and the same we can do also for the risk. 06:53.260 --> 06:57.630 So we take the square root here and within the square root. 06:57.670 --> 06:59.440 This looks a little bit different. 06:59.470 --> 07:01.660 So we have our covariance matrix. 07:01.810 --> 07:09.460 Then we use the top method and pass the transposed weights matrix and then again we multiply with the 07:09.460 --> 07:13.460 weights matrix and then we sum up all rows. 07:13.460 --> 07:15.430 So let's run the cell. 07:15.730 --> 07:24.750 And by doing so we should get the standard deviation of all 10000 random portfolios and we can all say 07:24.850 --> 07:29.670 look here. 07:29.780 --> 07:38.510 So for example the very first portfolio has a standard deviation of twenty five point two 2% and finally 07:38.510 --> 07:43.390 we can also create a summary data frame with the first column. 07:43.430 --> 07:48.200 The returns of the 10000 portfolios and as the second column the risk 07:50.840 --> 07:55.790 so here we have a risk and return for our 10000 random portfolios 07:58.870 --> 08:01.270 and of course we can also visualize them. 08:01.270 --> 08:05.160 So we create a set up plot with on the x axis. 08:05.290 --> 08:10.170 The risk column here and on the y axis the return column. 08:10.360 --> 08:11.510 And we also plot. 08:11.570 --> 08:15.120 We expect that risk and return for our two stocks. 08:15.130 --> 08:16.850 So you see our summary. 08:16.930 --> 08:23.770 To a data frame and take the risk and the expected returns actually of our two constituents and let's 08:23.770 --> 08:24.400 have a look here 08:27.790 --> 08:33.880 and here we have the expected risk and return for Boeing for Amazon and in red we have all possible 08:33.880 --> 08:41.020 combinations of risk and return if we create the portfolios consisting of Amazon and Boeing. 08:41.920 --> 08:48.640 So that's the two asset case and in the next video we will consider the more asset or many asset case 08:49.240 --> 08:51.250 and hope to see there by.