resampled efficient frontier; black-litterman approach, and monte carlo simulation

Can any one provide a summary on the difference (advantages and disadvantages ) on this method and in which situation we should use or not use?

Thanks in advance!

Courtesy of Dwight

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.

I know it’s implied when you say to rerun the MVO but it’s in this crucial step the manager applies his own judgment of asset returns by tweaking the implied returns. He also changes the vol behind the return to reflect his level of confidence.


Nice post genericuser. To add to that, one key advantage of the BL approach is the ability to incorporate an investor’s capital market expectations.

I think this is the key overriding factor for BL which offsets the “base on historical estimates” biase.

look at Colleen Finnegan case in 2011 AM . Excellent to the point analysis , hits every point

Mark it