Pair-trading portfolio strategies gainfully exploit the fluctuations of the prices in a pair of stocks over a short-term period. However, in the long term, the pair exhibit a strong relationship in their prices. When the prices deviate significantly, the stock having increased price is usually sold to gain profit (also referred to as a short strategy), while the one with a falling price is purchased and retained (also referred to as a long strategy). This work demonstrates a pair-trading portfolio design approach based on the cointegration of prices of stocks chosen from five sectors listed on the National Stock Exchange (NSE) of India. The historical prices for three years (from January 1, 2018 - December 31, 2020) are used for identifying the cointegrated stocks from each sector for designing the pair portfolios. The pair portfolios are tested based on returns over the year 2021. The results provide some significant insights into the profitability of several pairs of stocks.