A bank is considering investing in a portfolio of stocks. The portfolio is expected to generate an annual return of 12%, with a standard deviation of 20%. The bank's risk management policy requires that the probability of losing money in any given year should not exceed 10%. To meet this requirement, the bank decides to purchase an option contract that will protect it from any losses beyond 10% in a year. The option contract costs $100,000 per year and has a strike price of 10% below the expected return. Is the option contract a good investment, and what is the expected value of the investment with and without the option contract?