solution

In the following questions, express your answer with no decimals (i.e. 20 for a profit of 20USD or -20 for a loss of 20USD), or answer in decimal form with one decimal (i.e. 20.33% is 0.2):

1. A put option on a stock with a strike price of 50USD was bought for a price of 5USD. What is the profit or loss if the underlying stock is trading at 40USD at maturity?
2. A call option on a stock with a strike price of 50USD was bought for a price of 3USD. What is the profit or loss if the underlying stock is trading at 49USD at maturity?
3. Let’s say a long-term bond issued by the French government has an expected return of 0.02 and a volatility of 0.10, and the CAC 40 index of French stocks has an expected return of 0.05 and a volatility of 0.2. Their covariance is 0.002 and the risk-free rate is 0.04. What is your optimal allocation to CAC 40 index if you maximize your tradeoff between portfolio expected return and variance, your risk aversion is 3, and you do not face any financial constraints?
4. In your portfolio, you allocated 40% to the Chinese stock market, 80% to the British stock market, -40% to the U.S. stock market, and 20% to the risk-free asset (i.e. you borrowed money). What is your net leverage (using only risky assets)?