Financial Risk Manager Part 1

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Explanation:

To construct a riskless portfolio, the delta ( $\Delta$ ) of the position should perfectly hedge the short call option so that the portfolio's value remains constant regardless of the stock's price movements. The formula for option delta is: $\Delta = \frac{C_u - C_d}{S_u - S_d}$ Where: $C_u = 10$ , $C_d = 0$ $S_u = 125$ , $S_d = 85$ $\Delta = \frac{10 - 0}{125 - 85} = \frac{10}{40} = 0.25$

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Q.55 Simon Adams holds a portfolio consisting of a long position in $\Delta$ shares of the stock and a short position in one call option so that the portfolio is riskless. The current stock price is USD 100. After one year, if the value of the stock increases from USD 100 to USD 125, the option's value is USD 10. Also, if the current stock price decreases from USD 100 to USD 85, the option price is 0. What value of $\Delta$ makes the portfolio riskless?

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Last updated: June 22, 2026 at 14:11

0.25.

0.33.

0.5.

0.66.