Finding the efficient frontier using Monte Carlo simulations
According to the Modern Portfolio Theory, the efficient frontier is a set of optimal portfolios in the risk-return spectrum. This means that the portfolios on the frontier:
- Offer the highest expected return for a given level of risk
- Offer the lowest level of risk for a given level of expected returns
All portfolios located under the efficient frontier curve are considered sub-optimal, so it is always better to choose the ones on the frontier instead.
In this recipe, we show how to find the efficient frontier using Monte Carlo simulations. Before showing more elegant approaches based on optimization, we employ a brute force approach in which we build thousands of portfolios using randomly assigned weights. Then, we can calculate the portfolios’ performance (expected returns/volatility) and use those values to determine the efficient frontier. For this exercise, we use the returns of four...
