WEBVTT 00:00.660 --> 00:06.150 In this section we will deal with forward looking portfolios and we will find out that this is not as 00:06.180 --> 00:08.260 easy as one might think. 00:08.340 --> 00:17.100 And so far we analyzed the past and we created and optimize the random portfolios based on past performance 00:17.460 --> 00:23.850 and by doing so we were able to get an intuition on modern portfolio theory and asset pricing. 00:23.850 --> 00:32.370 However for some of you it might be even more interesting to forecast the future actually and to find 00:32.460 --> 00:34.840 the best portfolios for the future. 00:34.860 --> 00:41.700 So the question might be what are the optimal weights for my stock portfolio for the future and this 00:41.700 --> 00:44.220 is also called asset allocation. 00:44.220 --> 00:49.320 However there is one pitfall slaw I never you tried to forecast the future. 00:49.320 --> 00:55.330 You have to make assumptions or predictions and forecasting the futures in particular challenging in 00:55.330 --> 00:58.000 the finance and investment industry. 00:58.050 --> 01:03.330 So let's have a look at the typical approach when forecasting portfolios. 01:03.330 --> 01:08.210 So we need to make some predictions and the first of all we need. 01:08.280 --> 01:15.270 The risk in variance standard deviation terms of the assets and the typical assumption is that the past 01:15.270 --> 01:23.120 variances or the past the risk of assets that persist in the future so the variances are the Senate 01:23.120 --> 01:30.560 deviations of assets are actually the total risk and uh to calculate the risk diversification effect 01:30.560 --> 01:31.520 in our portfolio. 01:31.520 --> 01:38.840 We need the core variances are the correlations between the assets and also here it's the typical approach 01:38.930 --> 01:42.140 to use the past covariance and correlations. 01:42.140 --> 01:43.930 Also for the future. 01:44.120 --> 01:51.170 And finally the most important prediction or assumptions regarding future returns of the assets and 01:51.380 --> 01:53.120 these have to be predicted. 01:53.300 --> 01:58.310 So typically you don't assume that the past returns also persist in the future. 01:58.310 --> 02:05.390 And uh they actually many approaches how to predict future returns and there's actually no optimal solution 02:05.420 --> 02:10.510 if not to say it's impossible to predict the future returns. 02:10.730 --> 02:12.750 But that's another story. 02:12.950 --> 02:15.320 So let's have a look at the two asset example. 02:15.320 --> 02:24.590 We have two stocks A and B and we want to calculate the expected risk and return for a portfolio consisting 02:24.590 --> 02:29.800 of A and B and the first of all we have the return. 02:29.810 --> 02:33.980 So here we have the expected return of the portfolio. 02:34.340 --> 02:40.220 And this is simply the weighted average of the expected returns of the constituents. 02:40.610 --> 02:47.400 So here we have the expected return of a stock A and this is the expected return of stock P. 02:47.510 --> 02:50.410 And if we have the target weights in our portfolio. 02:50.420 --> 02:55.880 So we fear the wait for the stock A and to wait for stock P and the 7 examples. 02:55.880 --> 03:02.270 So let's assume that we predict that the expected return for stock a is 20 percent and the expected 03:02.270 --> 03:05.160 return for stock P is 10 percent. 03:05.180 --> 03:06.030 And. 03:06.050 --> 03:08.150 We take a 50 50 approach. 03:08.150 --> 03:15.740 So we have a portfolio consisting of 50 percent a and 50 percent stock P then our expected return of 03:15.740 --> 03:21.680 the portfolio is simply the weighted average of the expected returns of the constituents and in this 03:21.680 --> 03:24.430 case that's 15 percent. 03:24.470 --> 03:26.960 So the formula for the return is pretty simple. 03:26.990 --> 03:31.220 And the for the expected risk it's a bit more complicated 03:33.930 --> 03:41.880 so the expected risk of our portfolio and standard deviation terms is um actually the square root of. 03:41.940 --> 03:48.500 And then here we have uh these squared weight of stock a times uh the variance of stock a. 03:48.690 --> 03:55.740 So this is year the seek my sign and the stance typically for standard deviation and the squared standard 03:55.740 --> 04:00.540 deviation is that the variance that we have here the squared weight of a Times that the variance of 04:00.570 --> 04:09.510 a and then plus uh this crowd rate of P times the variance of stock B plus two times the weight of a 04:09.780 --> 04:17.910 times so the weight of b times the core variance of uh the stocks a and b and actually the variances 04:17.930 --> 04:21.710 and the covariance this year are based on the returns. 04:21.920 --> 04:28.940 And this actually annualized the standard deviation of returns and the annualized the covariance of 04:28.940 --> 04:36.600 returns so that was the theory and in the next video we will coat this in Python and Panda. 04:36.620 --> 04:38.180 So hope to see there by.