WEBVTT 00:01.280 --> 00:01.890 All right. 00:01.890 --> 00:03.720 And the last video we created. 00:03.770 --> 00:06.200 The equal weighted portfolio. 00:06.360 --> 00:11.860 And in this video we are going to create many random portfolios consisting of our six stocks. 00:11.910 --> 00:20.250 So we want to have kind of a cloud here with random portfolios and random means so that we have randomly 00:20.250 --> 00:21.220 generated. 00:21.240 --> 00:28.320 The weights of the constituents and the only constraint or assumption is that each single way is between 00:28.320 --> 00:29.710 0 and 1. 00:29.760 --> 00:37.230 So there are no short positions and of course the weights of all six stocks have to sum up to one. 00:37.230 --> 00:44.730 So let's start here and we still have defined our user defined function annualized the risk and return 00:45.180 --> 00:53.410 where we can transform a return data frame into a summary data frame with the annualized risk and return. 00:53.490 --> 00:55.310 And so let's start here. 00:55.320 --> 01:03.820 We import panda's name pi and met plop lip and also seaborne and again we are importing and working 01:03.820 --> 01:08.390 with our stocks the portfolio stocks data frame. 01:08.590 --> 01:11.340 So this is nothing new here. 01:11.710 --> 01:17.110 And then in the next step we create actually the returns data frame with the percentage change method 01:19.590 --> 01:25.890 so here we have our returns data frame Staley returns and bypassing our returns data frame to our user 01:25.890 --> 01:28.500 defined function annualized risk and return. 01:28.650 --> 01:35.840 We can simply create our summary data frame so let's have a look so here we have the annualized return 01:35.870 --> 01:41.850 and risk for a six stocks and now we want to create random portfolios. 01:42.030 --> 01:45.780 And first of all we have to define the number of constituents. 01:46.230 --> 01:53.020 So here in our example these six stocks and we save six to the variable number of assets so we have 01:53.120 --> 01:53.960 six. 01:54.390 --> 01:59.710 And then we define that in our first simulation we want to simulate 10 portfolios. 01:59.820 --> 02:10.030 So a number of portfolios of random portfolios is 10 so we have in total 10 random portfolios and in 02:10.030 --> 02:13.090 each portfolios we have our six stocks. 02:13.090 --> 02:20.980 So in total we have 60 a random weights and we can actually create random numbers with the name pi dot 02:21.100 --> 02:22.420 random module. 02:23.140 --> 02:29.820 So if we apply here the random module and the free selected the method random. 02:29.860 --> 02:30.820 So let's have a look here. 02:31.810 --> 02:40.540 So the random method returns a Random float in the half open interval between 0 and 1 and 2 we find 02:40.540 --> 02:43.980 that we want to have a 60 a random numbers. 02:44.080 --> 02:45.040 So let's have a look here 02:47.920 --> 02:52.070 so here we have 60 random floats between 0 and 1. 02:52.300 --> 03:01.750 And as we have 10 portfolios with each uh six stocks we can also then reshape here or a nun pie array 03:02.020 --> 03:09.250 to 10 rows which are the portfolios and 6 columns and we can do this with the reshape method. 03:10.900 --> 03:12.970 So here we have an array with 10 rows. 03:12.990 --> 03:20.510 So one two three and 10 I was 10 rows and in each row we have uh six elements. 03:20.530 --> 03:21.660 So we have six columns. 03:21.680 --> 03:25.960 So the first second third fourth fifth and sixth. 03:25.960 --> 03:27.740 So these are our random numbers. 03:27.760 --> 03:35.420 And the fear Rita run here the cell and recreate our random numbers then we should get different numbers. 03:35.440 --> 03:42.030 So here the very first numbers 0 point 5 2 and if you rerun here the cell we get 0 point 7 3. 03:42.760 --> 03:49.960 And if you work with random numbers that might be desirable to have some kind of reproducibility and 03:50.080 --> 03:53.410 we can do this by setting a random seed. 03:53.530 --> 04:00.310 So we are using here the seed method and we pass an integer as well for example 1 2 3 and then in the 04:00.310 --> 04:02.740 next step when we are creating random numbers. 04:02.830 --> 04:09.610 So whenever we have a set of the same seed then we get the identical random numbers. 04:09.610 --> 04:12.280 So to say upside or random numbers. 04:12.280 --> 04:16.240 So first of all we set CAC to off one two three. 04:16.810 --> 04:24.830 And then again we're creating here a num pi matrix with 10 rows and six columns. 04:24.880 --> 04:29.830 So we are using the random method and we pass an always on number of assets. 04:29.830 --> 04:31.600 Times number of portfolios. 04:31.610 --> 04:33.570 So this is six times ten. 04:33.790 --> 04:41.920 And then we reshape to 10 rows and six columns and then we actually saving the NUM pi array and the 04:41.920 --> 04:42.850 rabble matrix. 04:42.850 --> 04:46.820 So let's do this and let's have a look. 04:46.840 --> 04:49.250 So this our 60 random floats. 04:49.390 --> 04:55.720 And if you rerun the code here we should exactly get the same random numbers as we set a seed. 04:55.720 --> 04:57.570 So let's try this out. 04:57.580 --> 05:05.580 So here the very first numbers 0 point 6 9 and yet still 0 point 6 9. 05:05.580 --> 05:11.430 So here we have our 10 portfolios with uh each six weights. 05:11.650 --> 05:17.130 And we can easily see here that debates that do not sum up to a one. 05:17.130 --> 05:19.420 So here we have the first portfolio. 05:19.710 --> 05:23.530 And here we have 69 percent 71 percent. 05:23.580 --> 05:29.680 So we are far away from a sum of weights of one. 05:29.700 --> 05:38.100 However we can simply normalize the weights here and get the weights that sum up to 1 and the first 05:38.100 --> 05:45.450 of all that's created the sum of weights for each portfolio and we can do this by applying the sum method 05:45.480 --> 05:48.510 and pass one to the axis pair meter. 05:48.600 --> 05:56.280 So we want to have the sums for all rows and we actually pass true to the keep them parameter to have 05:56.280 --> 05:57.550 an umpire array. 05:57.570 --> 06:03.350 Still with 10 rows and one column so let's have a look. 06:03.400 --> 06:06.910 So this the sums for the rose so far the first row. 06:06.910 --> 06:12.910 We have a sum of two point nine and get actually rates that sum up to one. 06:12.910 --> 06:20.760 We simply have to divide each element here in one portfolio on one row by the sum of the row. 06:20.770 --> 06:24.670 So for example the sum of the first row is two point nine. 06:24.670 --> 06:30.640 And we have to divide each single element in our first row by two point nine. 06:30.670 --> 06:37.430 And by doing so we are normalizing here our values and the values that then should sum up to 1. 06:37.450 --> 06:38.780 So let's do this year. 06:38.800 --> 06:46.870 So we're dividing our matrix by the sum of the rows of the matrix and then we are saving actually the 06:46.870 --> 06:52.440 resulting matrix with weights and all rows that sum up to 1 in the variable rates. 06:52.450 --> 07:00.020 So let's do this and let's have a look so here we have again our first portfolio. 07:00.020 --> 07:03.610 And here we have a point two three 0 point too far. 07:03.620 --> 07:06.950 So this pretty looks good actually. 07:06.950 --> 07:13.010 And we can also prove that in each portfolio the weights sum up to 1. 07:13.460 --> 07:23.250 So again we use here the sum method and we can see here that needs a single row for each single portfolio. 07:23.250 --> 07:26.330 We have a total sum up a weight of 11. 07:26.340 --> 07:33.570 So this is exactly what we need and now we can calculate the re weighted average daily return for each 07:33.580 --> 07:38.920 random portfolio and for each time stamp with the top method. 07:38.920 --> 07:45.820 So we use our returns data frame and we pass Yeah our transposed weights num pi array to the top method. 07:46.390 --> 07:54.040 And by doing so we're creating a data frame with portfolio returns for our 10 portfolios. 07:54.040 --> 07:58.540 And actually we save the portfolio returns on the variable part red. 07:58.660 --> 08:05.760 So let's do this and let's have a look so here he CFS columns our 10 random portfolios starting from 08:05.760 --> 08:09.800 0 to 9 and still we have each timestamp. 08:10.020 --> 08:18.660 And here we have actually the daily returns for all of our random portfolios and now in the next step 08:18.660 --> 08:24.980 we can also create the summary data frame of our random portfolios by passing here. 08:24.990 --> 08:30.650 The portfolio returns to the annualized the risk return user defined function. 08:30.660 --> 08:39.280 So let's do this and let's have a look so here we have now on the left hand side as the index our random 08:39.280 --> 08:47.530 portfolios from 0 to 9 and we have actually the annualized the returns and the annualized the risk for 08:47.530 --> 08:51.100 each and every random portfolio here. 08:51.190 --> 08:55.820 And finally we can also plot our random portfolios and create a set up plot. 08:56.390 --> 09:03.400 So first of all we create a scatter plot for our Random portfolios with actually the risk on the x axis 09:03.400 --> 09:06.010 and the return on the y axis. 09:06.220 --> 09:13.240 And we also plotted our six stocks with the risk on the x axis and the return on the y axis. 09:13.480 --> 09:16.680 And actually our random portfolios have a size of 20. 09:16.690 --> 09:27.230 And a red color and our stocks have a higher size of 50 year black colour and a marker of the year. 09:27.250 --> 09:30.070 So Diamond so let's have a look here 09:36.280 --> 09:41.620 so here you have now 10 random portfolios and this looks quite nice. 09:41.650 --> 09:48.970 However if you want to perform a deeper analysis we need a lot of more random portfolios and we can 09:48.970 --> 09:52.690 do so by simply increasing the number of portfolios. 09:52.720 --> 09:54.280 Let's go up again here 09:58.180 --> 10:01.450 so here we have the numbers of portfolios. 10:01.450 --> 10:04.810 And for example we could simulate and set of 10. 10:04.810 --> 10:08.640 We could simulate 100 a thousand random portfolios. 10:08.650 --> 10:09.790 So let's throw this here. 10:13.750 --> 10:17.560 And what we simply have to do now we have to rerun our code. 10:17.560 --> 10:21.020 So starting with this line here. 10:21.070 --> 10:27.280 So we are creating 100000 portfolios each consisting of our six stocks with random weights 10:31.630 --> 10:41.000 so let's again normalize the weights to have a sum of 1 and let's check it here so for each portfolio 10:41.030 --> 10:47.710 we FBA some of weights of 1 and let's create the daily returns for each and every random portfolio 10:50.120 --> 10:59.390 so here we have our random portfolios starting with the very first one and ending at portfolio one hundred 10:59.570 --> 11:07.730 thousand and then we also create the annualized risk and return for each and every portfolio by passing 11:07.730 --> 11:12.090 year the portfolio return to our user defined function. 11:12.110 --> 11:20.770 So this is the most time consuming operation here and it could take a while so let's simply wait here 11:25.130 --> 11:31.340 so we are finished and here we have the annualized risk and return for all 100000 portfolios 11:34.210 --> 11:35.930 so let's have a look down here. 11:36.070 --> 11:45.700 So it's here until we have fear of 100000 portfolios and the then we can create here our cloud of portfolios. 11:45.700 --> 11:46.570 So let's say this 11:49.860 --> 11:57.500 and if we can see and read our 100000 portfolios in black here we have the risk return profile of our 11:57.500 --> 12:00.110 six constituent stocks. 12:00.170 --> 12:01.540 So this looks pretty cool. 12:01.550 --> 12:08.810 And in the next video we are going to analyze our 100000 portfolios so hope to see there by.