Portfolio Mathematics
Refresher reading access
Introduction
Modern portfolio theory makes frequent use of the idea that investment opportunities can be evaluated using expected return as a measure of reward and variance of return as a measure of risk. In Lesson 1, we will develop an understanding of portfolio return and risk metrics. The forecast expected return and variance of return are functions of the returns on the individual portfolio holdings. To begin, the expected return on a portfolio is a weighted average of the expected returns on the securities in the portfolio. When we have estimated the expected returns on the individual securities, we immediately have portfolio expected return. Lesson 2 focuses on forecasting certain portfolio metrics, such as correlations and covariances by looking at the risk and return on the individual components of a portfolio. Lesson 3 introduces various portfolio risk metrics widely used in portfolio management.
Learning Outcomes
The candidate should be able to:
- calculate and interpret the expected value, variance, standard deviation, covariances, and correlations of portfolio returns
- calculate and interpret the covariance and correlation of portfolio returns using a joint probability function for returns
- define shortfall risk, calculate the safety-first ratio, and identify an optimal portfolio using Roy’s safety-first criterion
0.75 PL Credit
If you are a CFA Institute member don’t forget to record Professional Learning (PL) credit from reading this article.