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. Is the following statement true or false (you must explain why!)? If the correlation between Stock J and K is +0.3, the call premium for the option on the two stock portfolio will be higher than either of the individual stock option call premiums due to the benefits of diversification.

Explanation / Answer

Lets say volatility, spot price and strike price is same for both stocks

Lets say call premium on J is X for 1 stocks and also X for 1 stocks on K..

Call premium on portfolio of 1 stock of J and 1 stock of K is Y..total premium=50*Y

Volatility of portfilio will be less than individual stock volatility

As volatility is less, call premium will be less for the portfolio

False

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