Consider a position in a single option on a stock. The position has a delta 12. The stock price is 10. What is an approximate relationship between the change in the portfolio value in one day, $\Delta P$ , and the return on the stock in one day, $\Delta x$ ? choose one)
A) $\Delta P = 12 \Delta x$
B) $\Delta P = 1.2 \Delta x$
C) $\Delta P = 120 \Delta x$
D) $\Delta P = 22 \Delta x$

Question

Quizplus · Accepted Answer

Delta represents the change in the option's price for a $1 change in the stock price. With a delta of 12, the change in the portfolio value is 12 times the change in the stock price. Since the stock price is $10, the return on the stock ($\Delta x$) is the change in stock price divided by 10, leading to $\Delta P = 120 \Delta x$.

Consider a Position in a Single Option on a Stock ΔP\Delta PΔP

Consider a Position in a Single Option on a Stock $\Delta P$