1. Modern portfolio theory of Harry Markowitz
The final objective of this course is to teach you
2. Portfolio weights are optimal
the skill to determine the portfolio weights that are optimal in the sense that there is no other portfolio with a higher expected return for the same or lower level of volatility.
Optimizing the portfolio weights requires us to first specify exactly the objective to be optimized, and the constraints the optimal portfolio weights should satisfy.
There are many possible objective functions, such as maximizing the expected return, minimizing the variance, or maximizing the portfolio’s Sharpe ratio.
In terms of constraints, there are almost always constraints on the weights. Examples of weight constraints include imposing that the portfolio weights are positive and that all the weights sum to one, such that the portfolio is fully invested.
Another popular constraint is to impose that the portfolio expected return is equal to a target value. Of all possible combinations, we will focus on the objectives and constraints recommended
3. Harry Markowitz
by Nobel prize winner Harry Markowitz. In his modern portfolio theory, he recommends to find optimal portfolios by minimizing the portfolio variance, under the constraint of full investment and that the expected return should be equal to a pre-specified return target.
4. The H. Markowitz approach
The approach of minimizing the portfolio variance under a return target constraint leads to
5. The H. Markowitz approach
an optimized portfolio that is mean-variance efficient.
6. The H. Markowitz approach
This means that there is no
7. The H. Markowitz approach
other portfolio with a higher expected return
8. The H. Markowitz approach
at the same or lower level of portfolio volatility. This is equivalent to saying that there is no other portfolio with a lower volatility, at the same or higher expected return.
9. Let's practice!
Practice makes the master. Let’s find out how easy it is to find mean-variance efficient portfolios in R.