  Portfolio optimization is a challenging problem that has attracted
considerable attention and effort from researchers. The optimization of stock
portfolios is a particularly hard problem since the stock prices are volatile
and estimation of their future volatilities and values, in most cases, is very
difficult, if not impossible. This work uses three ratios, the Sharpe ratio,
the Sortino ratio, and the Calmar ratio, for designing the mean-variance
optimized portfolios for six important sectors listed in the National Stock
Exchange (NSE) of India. Three portfolios are designed for each sector
maximizing the ratios based on the historical prices of the ten most important
stocks of each sector from Jan 1, 2017, to Dec 31, 2020. The evaluation of the
portfolios is done based on their cumulative returns over the test period from
Jan 1, 2021, to Dec 31, 2021. The ratio that yields the maximum cumulative
returns for both the training and the test periods for the majority of the
sectors is identified. The sectors that exhibit the maximum cumulative returns
for the same ratio are also identified. The results provide useful insights for
investors in the stock market in making their investment decisions based on the
current return and risks associated with the six sectors and their stocks.
