WEBVTT 00:01.130 --> 00:06.150 Welcome to the solution for coding exercise 15 and we import pen as an umpire. 00:06.180 --> 00:07.520 Matt plop plop. 00:08.000 --> 00:14.750 And then we import our six stocks and we should select to the appropriate price data to calculate total 00:14.750 --> 00:15.830 returns. 00:16.060 --> 00:25.850 And therefore we selected the adjusted close column because uh the adjusted clause includes dividends. 00:25.880 --> 00:31.970 And then we select the five year period from two 14 to 18 and be over right stocks 00:35.110 --> 00:42.280 so we we have a five year period for our six stocks and later we will need to calculate annualized risk 00:42.310 --> 00:45.430 and return and to make life easier. 00:45.460 --> 00:49.900 We can define you a user defined function annualized the risk and return. 00:50.050 --> 00:56.680 And we actually pass a data frame with daily returns uh to the user defined function and the function 00:56.680 --> 01:03.090 actually calculates uh the mean return and the standard deviation of returns and we can do this here 01:03.100 --> 01:08.410 with the ACT method and uh then the risk and return are getting annualized. 01:08.530 --> 01:12.030 So that's the user defined function. 01:12.850 --> 01:18.340 And first of all we have to create the returns data frame and we can simply do the service of the percentage 01:18.340 --> 01:23.030 change method on the prices on the stock prices. 01:23.110 --> 01:26.920 So that's the return data frame with daily returns. 01:26.920 --> 01:34.320 And then we can pass the return data frame to our user defined function and we create the summary data 01:34.330 --> 01:38.860 frame with annualized the risk and return for our six stocks. 01:38.860 --> 01:44.020 And then we can also visualize the risk and return in a total risk return framework. 01:44.020 --> 01:45.850 So we simply running the cell 01:48.370 --> 01:55.390 and we can see that the maximally the impact on McDonald's stock showed a quite good performance here 01:55.390 --> 01:56.740 on the upper left corner. 01:57.190 --> 02:00.310 And in contrast American Express is pretty weak. 02:00.310 --> 02:05.760 And actually Facebook showed high risk but also high return. 02:05.820 --> 02:11.820 Now the next step we want to create 10000 random portfolios with random weights of the constituents 02:12.540 --> 02:20.190 and uh therefore we define that the number of assets as six and the number of random portfolios 10000 02:22.390 --> 02:28.660 and then we create a number higher rate with 10000 roles and six columns and each element is a random 02:28.660 --> 02:35.860 float between 0 and 1 and we save the matrix and the variable matrix and actually we use the other random 02:35.860 --> 02:36.180 seed. 02:36.190 --> 02:37.410 1 2 3. 02:37.450 --> 02:43.230 And by doing so you should get the very same results as I do here in the solution. 02:43.270 --> 02:50.770 So we you see an umpire dot random dot random and create the 60000 the random floats between 0 and 1 02:51.460 --> 02:56.590 and we reshape those and 2 10000 rows and 6 columns 03:00.490 --> 03:08.020 and then for each row for each random portfolio we can create the weights that sum up to 1 and we can 03:08.020 --> 03:15.940 simply do this by dividing each and every element in a row by the sum of the row and here we have the 03:15.940 --> 03:24.150 weights array and we can also double check if the weights in each row sum up to 1 and this is obviously 03:24.150 --> 03:29.100 the case here so now we have far 10000 random portfolios. 03:29.110 --> 03:32.350 Ten thousand sets of random weights. 03:32.640 --> 03:40.460 And uh we can calculate actually the daily returns of uh these random portfolios by using here the top 03:40.460 --> 03:45.730 method on the returns data frame and pass the transpose the weights matrix. 03:46.040 --> 03:48.970 So this is a matrix multiplication and. 03:48.980 --> 03:52.820 We save the resulting data frame and the rabbit portfolio returns. 03:54.440 --> 03:58.800 So here we have for 10000 random portfolios of the daily returns. 03:58.940 --> 04:03.630 And then we can also annualize the risk and return for the 10000 portfolios. 04:03.710 --> 04:07.690 And we actually save for the resulting data frame and the value portfolio summary. 04:07.700 --> 04:13.020 So we simply pass here the portfolio returns data frame to our user defined function. 04:13.610 --> 04:14.750 And let's have a look here. 04:14.750 --> 04:16.320 So this takes a while 04:19.320 --> 04:24.480 and here we have the last five portfolios with annualized the risk and return. 04:24.480 --> 04:30.920 And then we can also visualize the six constituents and the 10000 the random portfolios here with the 04:30.960 --> 04:35.480 plotting the risk on the x axis and the return on the y axis. 04:35.490 --> 04:37.680 And the same we can do for the constituents 04:40.860 --> 04:48.500 so that's the cloud of random portfolios and to really verify the performance of the random portfolios 04:48.500 --> 04:49.850 in terms of risk and return. 04:49.850 --> 04:57.530 We have to calculate Sharpe ratio and uh therefore we have to define the risk free return of the risk 04:57.530 --> 05:04.910 free asset and we use the five year US Treasury note that was issued at the end of 213 and the coupon 05:04.940 --> 05:07.430 rate was one point seven percent. 05:08.090 --> 05:13.540 And by definition the risk free risk of the risk free asset is a zero. 05:13.550 --> 05:21.370 So we say if risk free return and risk free risk here in a list and we are still our summary data frame 05:21.380 --> 05:27.710 with our constituents and then we can calculate the sharp ratio of our six constituents by adding an 05:27.770 --> 05:33.830 additional column sharp and we can actually calculate the sharp racial bias of selecting the risk we 05:33.830 --> 05:42.570 return from the return of the constituents divided by the risk and let's have a look here. 05:42.600 --> 05:46.160 The question here is which stocks showed the highest chop ratio. 05:46.620 --> 05:54.340 And obviously at this McDonald's and the same we can also do for our Random portfolios so we calculated 05:54.370 --> 06:04.110 the SAP ratio and we add another column sharp to our portfolio summary data frame A.B. f the last five 06:04.110 --> 06:11.310 random portfolios and the sharp ratio and the question is also what is the maximum Sharpe ratio and 06:11.460 --> 06:19.320 we can determine this with the described method and we can see that the maximum value in the column 06:19.320 --> 06:20.790 Sharp is the one. 06:20.790 --> 06:27.750 So this is the highest Sharpe Ratio and again we can plot our visualize the random portfolios and the 06:27.750 --> 06:34.050 constituents and we can actually create a third I mentioned the sharp Ray Shaw and the color will indicate 06:34.080 --> 06:38.130 whether the portfolio has a high or low Sharpe ratio. 06:38.130 --> 06:44.070 And it is always a bit tricky to select the appropriate values for women and we mix. 06:44.130 --> 06:48.650 But you can see here in the shop ratio column the highest Sharpe Ratio is 1. 06:48.780 --> 06:55.350 So we could pass the one to We Max and the minimum value here is so point 3 4. 06:55.350 --> 07:02.670 So we could use here maybe 0 point 5 for movement but this they are actually a trial and error process 07:02.700 --> 07:05.220 to get the most meaningful plot. 07:05.280 --> 07:07.100 So let's try this out here. 07:11.360 --> 07:18.020 And here we can see that here we have the portfolios with the highest chop ratios and being a dark red 07:18.050 --> 07:26.430 actually here the next question we have to get the ROE label off the max Sharpe Ratio portfolio and 07:26.580 --> 07:33.300 we can do this year with the idea X Max method on the shop column and by doing so we're getting the 07:33.360 --> 07:39.500 ROE label of the max operational portfolio and this is four thousand five hundred fifty five. 07:39.720 --> 07:46.330 And then we can also select that particular portfolio by passing five thousand five hundred fifty five 07:46.620 --> 07:49.090 to the local operator here. 07:49.680 --> 07:56.850 And here we have the return of 16 percent and the risk of 14 percent and the sharp ratio of 1 and then 07:56.850 --> 08:03.930 we can also get the rates of the constituents and the max Sharpe Ratio portfolio by passing here their 08:03.930 --> 08:06.890 own label which is also here the ROE index position. 08:06.990 --> 08:16.360 To the weights matrix are weights array and these are actually the weights and to make this more explicit. 08:16.410 --> 08:22.150 We can also add uh the stock takers and created a panel series. 08:22.440 --> 08:29.680 So we are 5 percent for American Express 16 for Facebook and for example 45 for McDonald's. 08:29.700 --> 08:34.890 And the question is Where do you think that the Sox American Express Procter and Gamble and Wal-Mart 08:35.010 --> 08:38.060 have any weights or weights higher than zero. 08:38.070 --> 08:45.030 And the real Max sharp Rachel portfolio and either we can you see uh optimization algorithms or we can 08:45.030 --> 08:51.480 simply increase the number of random portfolios and uh let's do this here. 08:51.690 --> 09:05.580 So we could increase to 50000 thousand and rerun the says here. 09:06.070 --> 09:10.380 So here we increase the number of portfolios to 50000 09:15.510 --> 09:22.920 so I free run our coding SATs and our max Sharpe Ratio portfolio has now a return of 18 percent and 09:22.920 --> 09:30.190 a risk of 15 percent and a sharp ratio of 4 one point 0 4 and let's have a look at the weights. 09:30.300 --> 09:36.930 So obviously we have zero weight for American Express for Procter and Gamble and from Walmart and we 09:36.930 --> 09:43.400 have kind of an concentrated position in the McDonald's stock and that's also if I look at the weights 09:43.400 --> 09:49.300 of the max Sharpe ratio that can be derived with optimization algorithms. 09:49.320 --> 09:55.170 So here are the weights and let's create a panel series and let's compare here. 09:55.230 --> 10:03.180 So indeed we have zero weight in those uh three stocks and we have even a higher concentration in McDonald's. 10:03.210 --> 10:05.550 So 62 percent. 10:05.550 --> 10:12.870 And even if this was the very best portfolio in the past it's uh not really optimal because it's pretty 10:12.870 --> 10:19.860 much concentrated in the McDonald's stock so nobody would invest in this portfolio here in a forward 10:19.890 --> 10:25.890 looking case and for the time being we are not finished yet with exercise 15 and I hope to see you also 10:25.890 --> 10:27.120 in the next exercise by.