Two stocks (Stock J and Stock K) have the same current stock price, and the same
ID: 2767543 • Letter: T
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
Answer
Answer 1
Rank the three options based upon the size of the call premium (from highest call premium to lowest), If the correlation between the returns of the two stocks is +1
Explanation: Correlation between the returns of the two stocks is +1, then portfolio risk will be higher than risk of individual stocks. In that case Call premium will be higher for portfolio compared to individual stocks.
Rank 1 : call option on a portfolio of 50 shares of J and 50 shares of K
Rank 2 : call option on 100 shares of Stock J & call option on 100 shares of Stock K
Answer 2
Rank the three options based upon the size of the call premium (from highest call premium to lowest), if The correlation between the returns of the two stocks is 0
Explanation: Correlation between the returns of the two stocks is 0, then portfolio risk will be lower than risk of individual stocks. In that case Call premium will be lower for portfolio compared to individual stocks.
Rank 1 : call option on 100 shares of Stock J & call option on 100 shares of Stock K
Rank 2 : call option on a portfolio of 50 shares of J and 50 shares of K
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