Portfolio A consists of 150 shares of a stock and 300 calls on that stock. Portfolio B consists of 575 shares of the stock. The call delta is 0.7. Which portfolio has a higher dollar exposure to a change in stock prices?

Question

BlackTom AI · Accepted Answer

Restating the scenario: Portfolio A has 150 shares of the stock and 300 call options on that stock, with the call delta given as 0.7. Portfolio B holds 575 shares of the stock. We are asked which portfolio has a higher dollar exposure to a change in stock prices.

Option a. Portfolio B
- To compare dollar exposure to stock price moves, sum the equity-like delta of each position. For shares, the delta is 1 per share, so 150 shares contribute 150 to A’s delta from the stock portion. The 300 calls have a total delta of 300 × 0.7 = 210. Therefore, Portfolio A’s total delta is 150 + 210 = 360.
- Portfolio B has 575 shares, so its delta is 575.
- Since 575 > 360, Portfolio B has the higher bilateral exposure to small price changes in the stock.

Option b. Portfolio A
- This would be true only if Portfolio A’s delta exceeded Portfolio B’s, which it does not as shown above (360 vs 575).

Option c. The two portfolios have the same exposure.
- Not correct because the computed deltas are different (360 for A vs 575 for B).

Option d. A if the stock price increases and B if it decreases.
- This misstates exposure symmetry. Delta measures exposure to price moves in either direction, and the magnitude is what matters; both portfolios move with the stock price, and B has the larger magnitude of exposure.

Option e. A if the stock price decreases and B if it increases.
- Similar to option d, this introduces an incorrect directional rule; delta provides the same directional sensitivity for both portfolios, not a conditional switch that changes with price direction.

In summary, evaluating the deltas reveals Portfolio B’s larger delta (575) compared with Portfolio A’s delta (360). Therefore, Portfolio B exhibits the higher dollar exposure to changes in stock prices.

Portfolio A consists of 150 shares of a stock and 300 calls on that stock. Portfolio B consists of 575 shares of the stock. The call delta is 0.7. Which portfolio has a higher dollar exposure to a change in stock prices?单项选择题

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