CFL01-S01-C05 – Quantitative Methods – Portfolio Mathematics

This course provides a rigorous approach to understanding and applying statistical techniques used in portfolio construction and risk assessment. Learners will delve into calculations of expected return, variance, standard deviation, covariance, and correlation of portfolio returns—including using joint probability functions. The course also introduces shortfall risk and Roy’s safety-first criterion, offering practical tools for identifying optimal portfolios under specific risk constraints. Through a mix of theory, practical exercises, and case studies, participants will gain the analytical tools necessary to assess portfolio performance and make data-driven investment decisions.

Course Objective:

This course is designed to equip participants with foundational and applied skills in portfolio mathematics, specifically within the context of quantitative investment analysis. The course emphasizes core statistical concepts and their application in measuring and interpreting portfolio risk and return characteristics. A key focus is placed on understanding relationships between asset returns and making informed portfolio decisions using mathematical tools such as expected value, variance, covariance, and Roy’s safety-first criterion.

Expected Learning Outcomes:

By the end of this course, learners will be able to:
✔ Calculate and interpret the expected value, variance, and standard deviation of portfolio returns
✔ Determine covariances and correlations using both standard and joint probability functions
✔ Define and apply shortfall risk as a downside risk measure
✔ Calculate the safety-first ratio
✔ Identify an optimal portfolio using Roy’s Safety-First Criterion