You are considering the purchase of two stocks, A and B. The initial price of each stock is $100. The prices of the stocks at the end of the year depend on the state of the economy over the year as follows (neither stock pays a dividend):
Price in One Year
State of Economy Probability Stock A Stock B
Boom .40 110 126
Moderate Growth .40 106 112
Recession .20 96 83
What are the expected rates of return and standard deviations for A and B?
If the risk-free rate is 4%, what is the risk premium on stock A? What is the risk premium on stock B? Which stock has the better risk-reward tradeoff as measured by the Sharpe ratio?
A European put option on one underlying share of stock B with a strike price of $112 and time to expiration of 1 year has a premium of $10. Consider a portfolio where you buy one share of stock B and buy one put option. What is the one-year holding period rate of return on this portfolio for each state of the economy? What is the expected rate of return on the portfolio? What is the standard deviation? In what sense does buying the put option when you own the stock constitute a purchase of insurance in this case?