# Please explain MV, resampled MV, Black-Litterman, and MCS to me

Like I’m 9 years old. I can probably somehow memorize the advantages and disadvantages but I just do not get how these things are set up. I have a mental block on this topic.

bump…

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.

nice explanation Dwight!

Thanks Dwight

“Starts with the market portfolio and backs out the expected returns, risk premiums, covariances, etc implied by market prices, assuming market equilibrium” Can someone please explain how the “expected returns” are backed out?

^^ i think that might be beyond the scope of the curriculum…just make you sure you state what’s written above…that should be enough…

Bond Supply Wrote: ------------------------------------------------------- > “Starts with the market portfolio and backs out > the expected returns, risk premiums, covariances, > etc implied by market prices, assuming market > equilibrium” > > Can someone please explain how the “expected > returns” are backed out? Yeah it’s not in the curriculum. In my head I remember it by thinking of the Black Scholes Model that “backed out” the option’s price given the relevant data. This is kind of the opposite, where you have a model in which you input market data and it generates expected returns and standard deviations based on the pricing mechanisms. Just remember that the returns are forward looking and based on the global market portfolio and you should be fine.

Bond Supply Wrote: ------------------------------------------------------- > “Starts with the market portfolio and backs out > the expected returns, risk premiums, covariances, > etc implied by market prices, assuming market > equilibrium” > > Can someone please explain how the “expected > returns” are backed out? Expected returns are backed out assuming that market weights are the optimal weights (optimize risk-adjusted return of the portfolio of assets in the benchmark). B - covariance matrix, w - vector of asset weights in the global benchmark (capitalization weights typically), lambda - normalization vector. Expected returns = lambda*B*w More in the first item in the search: http://www.google.com/search?hl=en&q=black-litterman+model+step+by+step does that help?