No. When doing a tick-by-tick analysis (i.e. using high frequency data), all security prices follow jump processes rather than Wiener processes. And for jump processes volatility and correlation are not the appropriate measures. I suggest to use shortfall measures.

Can u suggest any paper which supports your claim ..ie on which proper statistical analysis has been done...i am about to fetch data of 1/5 min interval....would it be a worthy investment as i am also doing my phd on portfolio optimization

High frequency data for your portfolio analysis means that you will look at a time scale from nanoseconds to at most a few seconds (depending on the liquidity of the stock). Whereas there might be a lot going on in the electronic orderbook of the stock exchange, the midprice of the stock itself is very likely to remain unchanged for most of the time with a few jumps up and/or down (depending on the liquidity). So on the microscopic scale you won't have a Wiener process / Brownian motion. When on these time scales you want to estimate variances and covariances you are most likely lacking enough observations to obtain a meaningful and robust estimate. Keep in mind that for a random variable X we have var(X)=E(X^2)-E(X)^2 and the law of large numbers is applied to obtain estimates for E(X^2) and E(X), i.e E(X^2) = (X_1+...+X_n)/n with n very large and likewise for E(X).

A possible way of handling theoretically the portfolio optimisation problem for jump processes (without the not applicable framework of Markovitz) was proposed by Runggaldier et al. in 2006 using a concave utility function for the investor (see attached pdf document). Here, however you need to "count" the jumps of the stockprices empirically to get the intensities for the jump processes. Final remark: consider the difference of bid- and ask-prices and the fact that the difference between them (called the spread) might change on your time interval of observation. This will also have a major impact on your estimation quality.

Thanks Markus