My option portfolio's
Δ
is positive $5,000. I am happy to see the underlying stock price go up.

Question

My option portfolio's 
Δ
 is positive $5,000. I am happy to see the underlying stock price go up.

BlackTom AI · Accepted Answer

The question describes a portfolio where the delta (Δ) is positive $5,000 and the holder is happy when the underlying stock price rises. 
Option 1: 'Make sense' — This makes sense because a positive delta indicates that the portfolio value tends to increase when the underlying stock price goes up. A delta of +$5,000 means for a small upward move in the stock, the portfolio gains are expected to be in the positive direction, aligning with the investor’s happiness about higher stock prices. 
Option 2: 'Make no sense' — This would be incorrect given standard delta interpretation. A positive delta means exposure to upside; therefore, being happy when the stock goes up is the expected outcome. The statement 'Make no sense' would reflect a misunderstanding of delta, as it would imply the portfolio benefits from a price decline or is indifferent to movements, which contradicts a positive delta. 
In summary, the reasoning rests on the core idea that delta measures the sensitivity of the portfolio value to small moves in the underlying price, and a positive delta corresponds to gains when the stock price rises, while a negative delta would correspond to gains when the stock price falls.

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My option portfolio's Δ is positive $5,000. I am happy to see the underlying stock price go up.

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