A stock is trading at $80.You hold a delta-hedged portfolio in which you are short a call and long $\Delta$ units of the stock.The delta of the call is 0.65 and the gamma of the call is 0.06.If the stock registers an unexpected price decrease of $4,the value of your delta-hedged portfolio will

Question

Quizplus · Accepted Answer

The value of a delta-hedged portfolio changes primarily due to gamma when the stock price moves. The change in portfolio value due to a price move can be approximated by $0.5 \times \gamma \times (\Delta S)^2$, where $\Delta S$ is the change in stock price. Here, $\gamma = 0.06$ and $\Delta S = -4$, so the change in value is approximately $0.5 \times 0.06 \times (-4)^2 = 0.5 \times 0.06 \times 16 = 0.48$. Since the portfolio is short a call, a decrease in stock price (which benefits the short call position) leads to a decrease in the portfolio's value, making the correct answer a decrease by approximately $0.48.

A Stock Is Trading at $80 Δ\DeltaΔ Units of the Stock

A Stock Is Trading at $80 $\Delta$ Units of the Stock