In this section we will deal with forward looking portfolios and we will find out that this is not as
easy as one might think.
And so far we analyzed the past and we created and optimize the random portfolios based on past performance
and by doing so we were able to get an intuition on modern portfolio theory and asset pricing.
However for some of you it might be even more interesting to forecast the future actually and to find
the best portfolios for the future.
So the question might be what are the optimal weights for my stock portfolio for the future and this
is also called asset allocation.
However there is one pitfall slaw I never you tried to forecast the future.
You have to make assumptions or predictions and forecasting the futures in particular challenging in
the finance and investment industry.
So let's have a look at the typical approach when forecasting portfolios.
So we need to make some predictions and the first of all we need.
The risk in variance standard deviation terms of the assets and the typical assumption is that the past
variances or the past the risk of assets that persist in the future so the variances are the Senate
deviations of assets are actually the total risk and uh to calculate the risk diversification effect
in our portfolio.
We need the core variances are the correlations between the assets and also here it's the typical approach
to use the past covariance and correlations.
Also for the future.
And finally the most important prediction or assumptions regarding future returns of the assets and
these have to be predicted.
So typically you don't assume that the past returns also persist in the future.
And uh they actually many approaches how to predict future returns and there's actually no optimal solution
if not to say it's impossible to predict the future returns.
But that's another story.
So let's have a look at the two asset example.
We have two stocks A and B and we want to calculate the expected risk and return for a portfolio consisting
of A and B and the first of all we have the return.
So here we have the expected return of the portfolio.
And this is simply the weighted average of the expected returns of the constituents.
So here we have the expected return of a stock A and this is the expected return of stock P.
And if we have the target weights in our portfolio.
So we fear the wait for the stock A and to wait for stock P and the 7 examples.
So let's assume that we predict that the expected return for stock a is 20 percent and the expected
return for stock P is 10 percent.
And.
We take a 50 50 approach.
So we have a portfolio consisting of 50 percent a and 50 percent stock P then our expected return of
the portfolio is simply the weighted average of the expected returns of the constituents and in this
case that's 15 percent.
So the formula for the return is pretty simple.
And the for the expected risk it's a bit more complicated
so the expected risk of our portfolio and standard deviation terms is um actually the square root of.
And then here we have uh these squared weight of stock a times uh the variance of stock a.
So this is year the seek my sign and the stance typically for standard deviation and the squared standard
deviation is that the variance that we have here the squared weight of a Times that the variance of
a and then plus uh this crowd rate of P times the variance of stock B plus two times the weight of a
times so the weight of b times the core variance of uh the stocks a and b and actually the variances
and the covariance this year are based on the returns.
And this actually annualized the standard deviation of returns and the annualized the covariance of
returns so that was the theory and in the next video we will coat this in Python and Panda.
So hope to see there by.