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quidni
Topic Author
Posts: 27
Joined: November 5th, 2008, 7:32 pm

### Markowitz: input mean returns

Hi all,

excuse me for tha naive question, but I'm implementing in MATLAB the Markowitz (mean-variance) model, for Asset Allocation Optimization, by using the portfolio object and related functions available in MATLAB.

In MATLAB it seems possible to define the input mean returns in an arbitrary way, but... sticking to the Markowitz model, should they be only as "historical returns" (the same I use to built the covariance matrix indeed)? Maybe it's only with a model like the Black-Litterman one that I can introduce some views about the (expected) returns, right?

Thanks a lot!

Alan
Posts: 10617
Joined: December 19th, 2001, 4:01 am
Location: California
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### Re: Markowitz: input mean returns

It's a model about the tradeoff between expected returns and expected volatility: use anything you like.

quidni
Topic Author
Posts: 27
Joined: November 5th, 2008, 7:32 pm

### Re: Markowitz: input mean returns

Ok thanks! But... if I don't use historical returns as input, but some expected ones get in some way, I should then use also expected volatilities at the same time? I mean, couldn't I use in Markowitz expected returns, and historical volatilities for the correlation matrix at the same time?

bearish
Posts: 6451
Joined: February 3rd, 2011, 2:19 pm

### Re: Markowitz: input mean returns

It’s probably best to think of the model as Alan said. How you come up with the mean vector and covariance matrix is a separate question from how to use them to create an optimal portfolio. You could, for example, use a historical correlation matrix along with implied single stock option volatilities to create the covariance matrix, and combine that with expected returns generated from historically estimated CAPM betas scaled by some reasonable guess at a market risk premium and added to the current risk free rate.