Winter 2024
RSM332 Sample Midterm Quiz
1. (20 marks) Using put options with the same expiration date, a trader constructs a strategy that buys two $50 put options and simultaneously sells one $60 put option. Draw the payoff diagram of the strategy and explain carefully why it is the right diagram.
2. A stock price is currently $85. Over each of the next two three-month periods it is expected to go up by 10% or down by 8%. The risk-free interest rate is 6% per annum with continuous compounding. Show your main steps clearly for both (a) and (b).
(a) (20 marks) Use the risk-neutral method to calculate the value of a six-month European put option with strike price of $85. Show the binomial tree with the stock price and option price/payoff at each node.
(b) (10 marks) Calculate the value of a six-month American put option with strike price of $85. Using the binomial tree, explain why the option premium of this American put may be larger than that of the European put in (a).
3. (20 marks) You need to calculate the stock price (per share) of RSM, a financial company. RSM has just paid $3 per share in dividends. You estimate that dividends will grow at 20% per year for the next three years, at 10% per year for the following two years (years 4 and 5), and then at 5% per year perpetually. The cost of equity is 9.5% per year.
What should be the stock price of RSM three years from now (right after the dividend at the time is paid)? What should be today’s stock price of RSM? Show your steps.
4. Consider two investment assets with the following characteristics:
The correlation coefficient between returns of assets 1 and 2 is of the value ρ12 = −0.5.
(a) (15 marks) Suppose that a portfolio P1 formed from assets 1 and 2 has an expected return of 16%. Calculate the portfolio weights of P1. What is the standard deviation of the return of P1? Show your steps.
(b) (15 marks) Let P2 be a portfolio of 50% in asset 1 and 50% in asset 2. Calculate the covariance and correlation coefficient between returns of P1 and P2. Show your steps.