A portfolio consists of 100 shares of stock and 1500 calls on that stock. If the hedge ratio for the call is 0.7, what would be the dollar change in the value of the portfolio in response to a $1 decline in the stock price?
A) +$700
B) +$500
C) −$1,150
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 change in value of both the stocks and the calls. The 100 shares of stock would decrease by $100 (100 shares * -$1). The 1500 calls, with a hedge ratio of 0.7, would increase in value by $1,050 (1500 calls * 0.7 hedge ratio * -$1). The net change is -$100 (stocks) + $1,050 (calls) = +$950. However, since the question asks for the change in response to a decline in stock price, and considering the positive impact of the calls, the correct interpretation should lead to a decrease in portfolio value due to the direct loss on the stocks not being fully offset by the gain on the calls. The correct calculation should reflect the net effect of both positions, indicating a mistake in the initial explanation. The correct approach is to calculate the net exposure: 100 shares - (1500 calls * 0.7) = 100 - 1050 = -950 shares equivalent. Thus, a $1 decline would lead to a -$950 change in the portfolio, which is not listed as an option, indicating a mistake in the calculation or interpretation of the options provided. Correcting this, for a $1 decline, the direct loss on the stocks is -$100, and the gain on the calls, considering the correct interpretation of the hedge ratio, should actually result in a net loss when properly accounting for the direction of the stock price movement and the nature of the calls as part of the portfolio's overall exposure. The error in the explanation lies in the misinterpretation of the hedge ratio's impact on the portfolio's value change in response to the stock price decline. The correct calculation should directly address the combined effect of the stock and option positions in relation to the stock price movement.

A Portfolio Consists of 100 Shares of Stock and 1500