5. (Risk and return of option; Sharpe ratio) James would like to speculate on a possible rise in the stock price of QQQ (an exchange traded fund launched and managed by PowerShares Capital Management LLC). The current stock price of QQQ is $82. James expects that in one year the stock price of QQQ will be either $110 (up move; 60% chance) or $60 (down move; 40% chance). The exercise price of one-year European call option of QQQ=$80 and risk-free rate r=3% per annum. James would like to construct a portfolio with the stock (n shares) and cash from borrowing ($B) to replicate the payoff of 500 units of European call options of QQQ.

(a) Calculate the options leverage ratio [nS/(nS+B)] (up to 4 decimal places).

(b) Calculate the expected return for the call option.

(c) Calculate the standard deviation of returns for the European call option.

(d) Calculate the Sharpe ratio for the European call option.