To do so, we take the space between the minimum and maximum return and split it into a grid. With these two points on the curve we can then start building portfolios that lie between these two and run the optimizer to find the minimum possible variance portfolio for a certain level of return. We then take the asset with the highest return as we know there's no way to get a higher return without using leverage. Since we know there's no way to get a lower return, we know that is is on the curve. Now we have the covariance matrix, the weight vector, and now we're trying to determine the plot of the efficient frontier.įrom here, we want to take a portfolio that we already know lies on the efficient frontier, which is the asset with the lowest return. Mathematically, we can express the volatility of two asset combinations as follows: Specifically, the less correlated each asset with one another the less volatile the portfolio will be. On the risk side, however, the volatility of the portfolio depends on the correlation between assets. The return of this asset allocation is simply the weighted average of the components of the portfolio: To start, let's consider a simple example of the return and volatility of combining two assets: $A$ and $B$, with 50% of the portfolio in each. See our policy page for more information.

You can learn more about the MLQ app here or sign up for a free account here. The platform combines fundamentals, alternative data, and ML-based insights. If you're interested in learning more about machine learning for trading and investing, check out our AI investment research platform: the MLQ app. Fund Separation Theorem and the Capital Market Line.Using Quadratic Programming to Draw the Efficient Frontier.Markowitz Optimization and the Efficient Frontier.This article is based on Week 2 of this Investment Management with Python and Machine Learning Specialization and is organized as follows: In particular, we'll look at Markowitz portfolio optimization and the efficient frontier. In this article, we'll expand on these concepts and discuss how to use them for the purpose of portfolio optimization. In our previous article on portfolio construction we discussed several ways to measure the risk and return of investments.

What is portfolio optimization