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# Finance Dictionary - S Terms

# Synthetic Option

Rubinstein and Leland (1981) suggest a strategy that replicates the returns on a call option by continuously adjusting a portfolio consisting of a stock and a risk-free asset (T-bill, cash). This is called a synthetic call-option strategy; it involves increasing the investment in stock by borrowing when the value of stocks is increasing, and selling stock and paying off borrowing or investing in the risk-free asset when market values are falling. The key variable in this strategy is the delta value, which measures the change in the price of a call option with respect to the change in the value of the portfolio of risky stocks. For deep-in-themoney options, the delta value will be close to one because a $1 change in the stock value will result in approximately a $1 change in the option value. Thus to replicate the option with cash and stock, almost one share must be purchased and the amount borrowed will be approximately equal to the exercise price. For deep out-of-the-money options, the value of the delta will be close to zero, and the replicating portfolio will contain very few shares and little or no borrowing. Hence in its simplest form the delta value largely depends on the relationship between the exercise price and the stock price. As the market moves to new levels, the value of the delta will change; hence the synthetic option portfolio must be rebalanced periodically to maintain the proper mix between equity and borrowing or cash. In a similar manner, a portfolio manager can createreplicated put options through a combination of selling short the asset and lending. The amount of stock sold short is equal to the delta value minus one. As the market decreases in value, more of the equity is sold (the short position increases), with the proceeds invested at the risk-free rate. If the market increases in value, money is borrowed to buy the stock and reduce the short position.