Derivatives have emerged as the key financial instruments to hedge financial risk. The volatility and uncertainty in the global market has forced investors to use derivatives to hedge their positions. The speculator, being a risky player in the market, needs sound strategies for speculation, otherwise he may end up in making huge losses. This study aims at constructing an optimal portfolio of options for speculators and compares its performance with that of an optimal stocks portfolio. A mathematical programming model similar to Sharpe’s optimization model is used to construct these optimal portfolios. An attempt has been made to compare and analyze both the portfolios to show how the options portfolio gives better returns on average than the stocks portfolio.