Suppose you are an investor considering buying shares in a company with a current stock price of $100. You have identified that there is a 60% chance that the company will have a good year, in which case the stock price will increase by 30%. On the other hand, there is a 40% chance that the company will have a bad year, in which case the stock price will decrease by 20%. In addition, you believe that your own optimism bias makes you more likely to overestimate the probability of a good year by 10%.

a) What is the expected return of the stock, taking into account your optimism bias?

b) What is the standard deviation of the stock return, taking into account your optimism bias?

c) Should you invest in the stock, given your optimism bias?