Portfolio optimization is a mathematical approach to making investment decisions across a collection of financial instruments or assets. The goal of portfolio optimization is to find the mix of investments that achieve a desired risk versus return tradeoff. The conventional method for portfolio optimization is mean-variance portfolio optimization, which is based on the assumption that returns are normally distributed.

On the other hand, conditional value-at-risk (CVaR) is the extended risk measure of value-at-risk that quantifies the average loss over a specified time period of scenarios beyond the confidence level. For example, a one-day 99% CVaR of $12 million means the expected loss of the worst 1% scenarios over a one-day period is $12 million. Moreover, CVaR is also known as expected shortfall.

With CVaR portfolio optmization, you do not need to assume normally distributed returns. In this example, you will learn:

1. How to use copula to generate correlated asset scenarios that try to mimic the pattern of historical returns
2. How to apply CVaR portfolio optimization based on simulated asset scenarios
3. How to compare the efficient frontiers between CVaR portfolio optimization and mean-variance portfolio optimization