Evaluating the Risk and Return of an Initially Delta-Hedged Portfolio

As assumed in the Black Scholes Option Pricing Model, a hedged portfolio consisting of longing delta number of shares of stock and shorting one call option is riskless because the price changes in these two positions offset one another. Such portfolio is a hedged portfolio whose return should be the riskless rate. However, this is true only if the hedged portfolio is continuously rebalanced or adjusted according to price changes. In the real world, such dynamic hedging is rarely implemented because the transaction cost of continuous rebalancing would exceed the benefit of keeping the portfolio riskless. This paper examines the risk and return of such portfolio when it is hedged initially according to delta but is not rebalanced afterward. The result shows that such portfolio, though not riskless, achieves a superior reward to risk ratio than pure stock investment.