As inputs, we need a covariance matrix and a vector of expected returns,my friend says that using historical mean return here as expected returns is not a good idea...Any better ways?Thanks a lot!

You should think about why using the historical return isn't the best idea. You are trying to figure out the best tangency portfolio going forward some amount of time. You want to have predictions for return, variance, and correlation for that future.Chances are very good that the mean return isn't very representative for the upcoming future. Furthermore, the historical volatility is probably even more off.The problem here is that you need to somehow "figure out the future". You can use models for correlation/volatility and some sort of fundamental analysis for the companies.

My friends have the same double on the epxected returns/volatilities from historical data. But what models for correlation/volatility do not depends on the historical data? Do we have statistics on the improvement of using fundamental analysis over simple exponential moving average of the historical returns?My friend also said the normal distribution of the asset returns is also one of the big drawback of Mean Variance Analysis. However, I could not figure out where this assumption is applied in the process of establishing efficient frontier. Do you guys happens to know?

most models do use historical data and more recent data in a certain weighted way. look at Garch for example

QuoteOriginally posted by: phubabaYou should think about why using the historical return isn't the best idea. You are trying to figure out the best tangency portfolio going forward some amount of time. You want to have predictions for return, variance, and correlation for that future.Chances are very good that the mean return isn't very representative for the upcoming future. Furthermore, the historical volatility is probably even more off.The problem here is that you need to somehow "figure out the future". You can use models for correlation/volatility and some sort of fundamental analysis for the companies.Okay, so we need "future" returns and "future" covariance matrix!Where and how do we obtain them?Any pointers on literature and readings?

Take a look at Best and Grauer 1990 - can be downloaded from Grauer's page http://www.sfubusiness.ca/homes/grauer/It provides all the math. Take a look at Grauer 2009 "Extreme Mean-Variance Solutions: Estimation Error versus Modeling Error" In section IV he provides details of four estimation methods he uses. There are other estimation methods, but this is one way to do it. The asset management industry may use more sophisticated models. YOur friend is correct: to the extent that the mean return is not representative of returns in your horizon of interest, you may want to use a different estimator of the mean.You may want to look at http://www.northinfo.com/ They have their own optimizer and have lots of documents about their methods. This reflects a more industry approach.Otherwise, you can also look at the Black-Litterman literature that has often been mentioned at Wilmott

solutions are extremely sensitive to covariance matrix. so if your estimated covariance matrix is noisy, your portfolio weights are 10X more noisy. the multiplier is actually greater than 10.

QuoteOriginally posted by: obeelde The asset management industry may use more sophisticated models. They do, but I have not seen one quantitative asset manager who has been successfull over the long haul. Maybe they exist at hedge funds...but on the classic buy side: nada.The art of portfolio construction, bet sizing, trade selection, etc is learned with experience (and by doing a lot of painful mistakes in the beginning). The market is not a measurable system, here is where you need someone with street smarts. This is something the "computer boys" will never learn.

QuoteOriginally posted by: Gmike2000 The market is not a measurable system, here is where you need someone with street smarts. This is something the "computer boys" will never learn. this is because computer boys can only provide textbook solutions. however, beating the market requires being consistently above average. textbook systems can only do average.

I just posted a link to a (likely) relevant paper on the technical forum where you asked the same question.

It does not matter so much how you estimate the input parameters in the mean-variance problem, because you are ALWAYS incurring in estimation error (although you are a fortune teller). In finance, this estimation error is usually very large, and moreover the mean-variance problem is very sensitive to that error. Hence, a recent trend is to generalize the mean-variance problem in order to hedge against this estimation error. Some recent and promising approaches are proposed in the following references:How hedge against a worst-case scenario (for instance minimize the maximum portfolio loss): "Robust portfolio selection problems". Math. Oper.Res. 28(1) 1–38, 2003.How hedge against model error (for instance when we assume a normal distribution for the returns): "Portfolio Selection with Robust Estimation''. Operations Research, 57(3), pp. 560-577, 2009. How hedge against estimation error (for instance the vector of means and the covariance matrix): "A Generalized Approach to Portfolio Optimization: Improving Performance By Constraining Portfolio Norms''. Management Science, 55(5), pp. 798-812, 2009. An excellent overview about the role of estimation error in the mean-variance problem, and how simple strategies can beat more sophisticated ones, is the following: “Optimal versus naïve diversification: How inefficient is the 1/N portfolio strategy? Rev. Financial Stud. 22 1915–1953, 2009.