Two stocks (Stock J and Stock K) have the same current stock price, and the same

Question

Two stocks (Stock J and Stock K) have the same current stock price, and the same standard deviation. There exists a call option on 100 shares of Stock J, a call option on 100 shares of Stock K, and a call option on a portfolio of 50 shares of J and 50 shares of K. All three call options have the same expiration date, and all three options are trading “at the money.” Rank the three options based upon the size of the call premium (from highest call premium to lowest) in each of the following (independent) cases (explain briefly)

A) The correlation between the returns of the two stocks is +1

B) The correlation between the returns of the two stocks is 0

Explanation / Answer

A. The correlation between the returns of the two stocks is +1

Since the stock price and standard deviation are same, the price of the call option will also be the same. One can assume that the returns will also be same given that the stock prices are behaving in the same way. Thus, the returns will be equal or in direct proportion of each other. Thus, correlation will be +1.

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