Why does a stock index option sell at a lower price than the cost of a portfolio

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Why does a stock index option sell at a lower price than the cost of a portfolio of options on the constituent stocks? (Assume that the index call option and the portfolio of call options control the same dollar value of stocks.)
Portfolio
A portfolio is a grouping of financial assets such as stocks, bonds, commodities, currencies and cash equivalents, as well as their fund counterparts, including mutual, exchange-traded and closed funds. A portfolio can also consist of non-publicly...
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Fundamentals of Investments

ISBN: 978-0132926171

3rd edition

Authors: Gordon J. Alexander, William F. Sharpe, Jeffery V. Bailey

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