A certain stock returns 20% annually if the economy is in a strong growth regime 5% annually if the economy is growing midly and drops 10% anually recession periods.Your company applied its proprietary economy forecasting model to the upcoming year and obtained the probabilities for the ecnomy to be in strong growth, mild growth and recession states as 30% 50% and 20% respectively.Calculate the expected annual return of the stock in question under such an economic forecast

Calculate the ecpected annual standard deviation in % of the stock?

A colleague discussed with you the stock from the previous question and is interested in the valuation of put options on that stock around 1 year expiration. Would you recommend your colleague to use 20% as a risk- neutral probability of the underlying stock going down for the derivative pricing purposes ? Please briefly justify your answer.