In the analysis of the stock market and its market indices, instead of estimating returns and their distributions at a given time interval, it is possible to extract optimal time to achieve a certain return. In this study, the distribution of investment horizons and optimal investment horizons through inverse gamma statistics method for the indices of automobile, sugar, pharmaceutical, financial and banks industries in Tehran Stock Exchange were extracted, analyzed and compared. The results of the research show that at the levels of access to +5 percent return, automotive, sugar , banking and financial indices have shorter horizons than the total index, while in terms of access to negative returns ,the only indicator of the drug group has a longer horizon than the total index.