Portfolio optimization: Max Sharpe

In this exercise, you're going to calculate the portfolio that gives the Maximum Sharpe ratio. Often, this is the portfolio the investor wants to invest in, as it provides the highest possible return to risk ratio.PyPortfolioOpt makes it very easy to calculate this portfolio from a set of historical price data.

Available for you are the mean historic return for a small portfolio of stocks under mu and a covariance matrix belonging to our portfolio under Sigma. You'll need these as inputs to calculate the Efficient Frontier and Maximum Sharpe portfolio. Let's try it!

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Introduction to Portfolio Analysis in Python

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# Define the efficient frontier
ef = ____(____, ____)

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Diese Übung ist Teil des Kurses

Introduction to Portfolio Analysis in Python

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In the first chapter, you’ll learn how a portfolio is build up out of individual assets and corresponding weights. The chapter also covers how to calculate the main characteristics of a portfolio: returns and risk.

Exercise 1: Welcome to Portfolio Analysis!Exercise 2: Why invest in portfolios Exercise 3: The effect of diversification Exercise 4: Portfolio returns Exercise 5: Portfolio losses and gaining it back Exercise 6: Calculate mean returns Exercise 7: Portfolio cumulative returns Exercise 8: Measuring risk of a portfolio Exercise 9: Portfolio variance Exercise 10: Standard deviation versus variance

Chapter 2 goes deeper into how to measure returns and risk accurately. The two most important measures of return, annualized returns, and risk-adjusted returns, are covered in the first part of the chapter. In the second part, you’ll learn how to look at risk from different perspectives. This part focuses on skewness and kurtosis of a distribution, as well as downside risk.

Exercise 1: Annualized returns Exercise 2: Annualizing portfolio returns Exercise 3: Comparing annualized rates of return Exercise 4: Risk adjusted returns Exercise 5: Interpreting the Sharpe ratio Exercise 6: S&P500 Sharpe ratio Exercise 7: Portfolio Sharpe ratio Exercise 8: Non-normal distribution of returns Exercise 9: Skewness of the S&P500 Exercise 10: Calculating skewness and kurtosis Exercise 11: Comparing distributions of stock returns Exercise 12: Alternative measures of risk Exercise 13: Sortino ratio Exercise 14: Maximum draw-down portfolio

In chapter 3, you’ll learn about investment factors and how they play a role in driving risk and return. You’ll learn about the Fama French factor model, and use that to break down portfolio returns into explainable, common factors. This chapter also covers how to use Pyfolio, a public portfolio analysis tool.

Exercise 1: Comparing against a benchmark Exercise 2: Active return Exercise 3: Industry attribution Exercise 4: Risk factors Exercise 5: Size factor Exercise 6: Momentum factor Exercise 7: Value factor Exercise 8: Factor models Exercise 9: Fama French factor correlations Exercise 10: Linear regression model Exercise 11: Fama French Factor model Exercise 12: Portfolio analysis tools Exercise 13: Performance tear sheet Exercise 14: Industry exposures with Pyfolio

In this last chapter, you learn how to create optimal portfolio weights, using Markowitz’ portfolio optimization framework. You’ll learn how to find the optimal weights for the desired level of risk or return. Lastly, you’ll learn alternative ways to calculate expected risk and return, using the most recent data only.

Exercise 1: Modern portfolio theory Exercise 2: Understanding the efficient frontier Exercise 3: Calculating expected risk and returns Exercise 4: PyPortfolioOpt risk functions Exercise 5: Optimal portfolio performance Exercise 6: Maximum Sharpe vs. minimum volatility Exercise 7: Portfolio optimization: Max Sharpe

Aktuelle Übung

Exercise 8: Minimum volatility optimization Exercise 9: Comparing max Sharpe to min vol Exercise 10: Alternative portfolio optimization Exercise 11: Exponentially weighted returns and risk Exercise 12: Comparing approaches Exercise 13: Changing the span Exercise 14: Recap