A portfolio consists of 225 shares of stock and 300 calls on that stock. If the hedge ratio for the call is 0.4, what would be the dollar change in the value of the portfolio in response to a $1 decline in the stock price?
A) −$345
B) +$500
C) −$580
D) −$520

Question

Quizplus · Accepted Answer

The dollar change in the portfolio due to a $1 decline in the stock price can be calculated by considering the impact on both the shares and the calls. The 225 shares would lose $225 in value (225 shares * -$1 per share). The 300 calls, with a hedge ratio (delta) of 0.4, would gain in value because they are calls on the stock, and their value moves inversely to the stock price. The gain from the calls would be 300 calls * 0.4 * $1 = $120. Therefore, the net change in the portfolio value would be -$225 (from the shares) + $120 (from the calls) = -$105. However, since this option is not available, the calculation must be revisited. The correct calculation is: The loss from the shares is straightforward, -$225. For the calls, the hedge ratio indicates how much the value of the calls would change for a $1 change in the stock price. Since the calls are on the stock, a decline in the stock price would actually decrease the value of the calls, not increase it as previously stated. Therefore, the correct calculation for the calls' part is actually a loss: 300 calls * 0.4 * -$1 = -$120. Adding this to the loss from the shares gives a total change of -$225 (from the shares) - $120 (from the calls) = -$345.

A Portfolio Consists of 225 Shares of Stock and 300