in a porfolio optimization problem is it better to use daily or monthly returns?the trade-off is as follow:- monthly returns held better properties (less leptokurtosis etc.);- daily returns increase the number of observations for the same time period;For the latter reason I use daily returns. I clean data from autocorrelation using residuals and then I compute the covariance matrix.At this point I don't know how I can trasform this matrix to apply a monthly optimization approach.for instance for volatility in a general case people applythis relationship sigma(yearly)=sigma(daily)*sqrt(250).What about correlation and covariance?any idea? please, could you help me to clarify.As you can see I'm a bit confused.

Assuming multivariate normal distributions,sigma annual = sigma daily * sqrt(250)variance annual = variance daily * 250covarience annual = covariance daily * 250as correlation = covariance / (sigma_i * sigma_j)then it should be clear thatcorrelation annual = correlation daily.

thanks gjlipman,but are you really sure that annual correlation is equal to daily correlation?I would like to ask you if you know a good "practical" book for portfolio mgmt?

Use weekly. Daily may run you into the problem of data holes, where e.g. one market is on holiday and the other is not. Also there is too much noise. Monthly is too coarse. Use weekly, then do the scaling glpglman suggested.

It depends on your application. Usually, you optimize your portfolio for one period. Then the correlation should be estimated on a history of values with this period length. All other approaches (explicitely or implicitely) assume some (mathematical) model, e.g. Brownian motion. Use different estimators to get an idea of the reliability of your estimates.

QuoteOriginally posted by: misithanks gjlipman,but are you really sure that annual correlation is equal to daily correlation?I would like to ask you if you know a good "practical" book for portfolio mgmt?MisiModern Investment Management, Litterman has a whole chapter on covariance matrix estimation, and in general is an excellent intro to portfolio management. In addition if you ever go for an interview with GS it'll stand you in great stead - (they wrote it).