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)

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

The correlation between the returns of the two stocks is 0

Explanation / Answer

For The correlation between the returns of the two stocks is +1

Stock having higher return than another will have higher call premium

Portfolio would have 2nd rank

Stock having lower return would have lower rank

Since correlation is +1 and price will up and down in same direction

For The correlation between the returns of the two stocks is 0

Portfolio would have higher call premium

Stock having higher return would have 2nd rank

Stock having lower return would have lower rank

Since correlation is 0 and price can move in any direction portfolio would consist of 50% for each and if price of any stock falls or rise portfolio would be affected only by 50%

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