Resampled Efficient Frontier

Why is the resampled efficient frontier more stable than traditional Mean variance optimization? I guess the first step is to understand how both are constructed…

Isn’t MVO constructed by finding the portfolios with the best return for a given risk and including it in the portfolio. Since the expected return is based on historical data, why is this input less accurate than the resampled version?

ANy help here would be great thanks.

Mean Variance: Optimizes a portfolio based on inputs of historical/expected returns and standard deviations. ie, given expected returns/deviations for 4 asset classes the Mean Variance method will calculate the optimal portfolio combination of the 4 assets to yield the best risk/return trade-off.

Benefits - easy/cheap to implement and understand, only 1 output given. Negatives - requires a large amount of estimated input data, static approach (one iteration), can result in concentrations due to the way the optimization works.

______________________________________________________________

Resampled Mean Variance: basically runs a bunch of Mean Variance optimizations based on different assumptions and averages the results to get an optimizes portfolio.

Benefits - more optimizations result in better diversification and a more stable efficient frontier. Negatives - no mathematical rationale behind doing this method, still a static approach, relies on estimates.

______________________________________________________________

Black-Litterman: Starts with the market portfolio and backs out the expected returns, risk premiums, covariances, etc implied by market prices, assuming market equilibrium. From there a Mean-Variance optimization is run using those inputs to generate an efficient frontier.

Benefits - high level of diversification, overcomes weakness of MV which is the variability of estimated returns. Negatives - static approach, difficult to estimate returns.

______________________________________________________________

Monte Carlo Simulation: Computer generated iterative process that incorporates different input variables (contributions/withdrawals, taxes, capital market factors, etc) to generate a range of possible outcomes.

Benefits - multiple output = not a static approach, incorporates compounding and other relevant information, generates a distribution of returns instead of a single prediction. Negatives - complex and expensive to generate, still relies on the accuracy of input data.