Resampled Efficient Frontier

[doobsmeister]

HI Guys, I am having trouble trying to understand the resampled efficient frontier, but maybe its because I forgot how the normal efficient frontier is created!
From what I understand, the efficient frontier is created by finding assets with the higher returns for every given level of risk and plotting them, but they are just epected returns. Now, these expected returns and risk are based on historical data (averaged?).
With the resampled versian, it runs sensitivity analyses by changing the inputs. Why would you change the inputs if those inputs are averages themselves? For instance it says to average all the results once you get them, but arent the inputs already averages of historical inputs?
ANy help here would be great thanks!

 

[S2000magician]

Maybe a simple example will help.
Suppose that you have two assets with very similar risk and return, and a relatively high correlation of returns. In a mean-variance efficient frontier, whichever asset had the higher return will be included in the portfolios, while the other one will likely not be included, even if its return were only slightly lower.
Now, suppose that you run a Monte Carlo simulation in which, instead of just using the mean return for each asset, you create a (normal, say) probability distribution of returns for each asset (using the mean and variance from your historical data); in each iteration you randomly choose a return for each asset from its probability distribution, and use that return, with the historical risk, and create an efficient frontier. Sometimes one of these two assets will have the higher return and be included, other times the other asset will have a higher return and be included. Maybe it will be 55%/45%.
When you average the portfolios from your Monte Carlo simulation to create your resampled efficient frontier, the new portfolios will have both of these assets, with the first one weighted slightly higher.
That’s the advantage of the resampled efficient frontier: it gives more-diversified portfolios.