Question

You are holding call options on a stock. The stock’s beta is 0.76, and you are concerned that the stock market is about to fall. The stock is currently selling for $16 and you hold 1 million options on the stock (i.e., you hold 10,000 contracts for 100 shares each). The option delta is 0.80. How much of the market-index portfolio must you buy or sell to hedge your market exposure?

Answer 1

1) You have to sell some amount of the market index portfolio, to be on the profiting and secured side.

2) The amount of market index

portfolio to sell is $9,728,000

Explanation:

Since the stock market is about to fall. That means the market index will increase.

Let's assume the stock market index will increase by 1%. That means the 1million share option of the stock will increase by;

Beta% × Delta × price unit of stock × Share option on stock.

Therefore;

0.76% × 0.8 × $16 × 1,000,000 = $97,280

Since each option has 100 shares. Therefore the amount of market index portfolio to sell will be;

$97,280 × 100 = $97,280 × 100 = $9,728,009.

For the shareholder to hedge it's market exposure, $9,728,000 of the market index portfolio must be sold. Since 1% change in the index would cause the portfolio value to change by $97,280