Mean-Variance Portfolio Optimization
Lesson 1 of 1
  1. 1
    The fundamental goal of portfolio theory is to allocate your investments between multiple assets optimally. A Markowitz mean-variance optimization (MVO) is an approach to choosing how to allocate m…
  2. 2
    Typically, when we download stock data, the information is formatted as asset values at the end of a period (daily, monthly, quarterly). When we calculate the efficient frontiers, we need to struct…
  3. 3
    Estimating the expected return of an asset is at the core of all financial investments. People often invest based on their interest in a company’s product – maybe they make your favorite sneakers o…
  4. 4
    In the last exercise, you calculated the expected return of individual assets. But we’re interested in the return of a portfolio with multiple assets. To calculate the expected return of a portfoli…
  5. 5
    It would be nice if every asset made large, consistent positive returns every period. If that were the case, we could invest all of our money in the asset with the highest expected return. But, the…
  6. 6
    To make computations more manageable, we store variances and covariances of assets in a covariance matrix. A covariance matrix is symmetric, with the variance of each asset on the diagonal. For exa…
  7. 7
    Now we’re ready to visualize the mean-variance tradeoff for a collection of random portfolios. In this exercise, we provide you with a function, called return_portfolios() that accepts the expected…
  8. 8
    When we have a set of portfolios, we typically plot them on a two-dimensional scatter plot, with standard deviation on the x-axis and expected return on the y-axis. In the last exercise, we showed…
  9. 9
    At this point, we know how to visualize the range of possible portfolios. We still have not found the set of portfolios that optimize for both the expected return and risk of our assets. In this ex…
  10. 10
    In the last exercise, you found the efficient frontier of a portfolio with Delta, Jet Blue, Chevron, Exxon, Adobe, and Honeywell stocks. The red X marks in the figure to the right display the vol…
  11. 11
    In the last exercise, you added Nvidia to your portfolio. Nvidia is a high-risk, high-return asset. Despite Nvidia’s risk, it improved the efficient frontier by increasing the expected return at mo…
  12. 12
    In this lesson, you learned how to find the efficient frontier – a set of portfolios that minimizes risk and maximizes expected return. You also learned: - How to calculate the weight of each asset…

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