Assignment 3

Assignment 3, which is worth 15 percent of your total grade for the course, is made up of 14 questions worth a total of 85 marks. Review the “Course Assignments” page in the Welcome and Orientation section of this course website for important information regarding requirements for submitting your answers to problem-solving questions. Include your student ID number and contact information on the top page of your assignment. If you have any questions about Assignment 3, contact the Student Support Centre.

1.

Given a risk free rate of 5%, a market return of 15%, and the information for stocks A and B in the following table, determine if stock A and stock B are undervalued or overvalued if they are valued by the security market line.

Stock

Beta

Estimated Return

A

1.3

17%

B

0.9

15%

(6 marks)

2.

A stock has an expected ROE of 14% per year, expected earnings per share of $3, and retention ratio of 40%. Its market capitalization rate is 11% per year. What are its expected growth rate, its price, and its P/E ratio?

(6 marks)

3.

To estimate the value of a stock, an analyst may use the dividend discount model, multiply the forecast of the stock’s next period earnings per share by the P/E ratio, or estimate the present value of expected future free cash flows. How are the three methods related? Discuss their strengths and weaknesses.

(5 marks)

4.

The textbook expresses ROE two different ways: (A) and (B) Why is ROE written two different ways? What implicit assumptions are required for these two formats to make sense?

(6 marks)

5.

Collect data on the S&P/TSX Composite index for two months on a daily basis. Calculate the five-day moving average for each day, then discuss the trend of the index.

(7 marks)

6.

Is an at-the-money call option on a stock more expensive than an at-

(5 marks)

the-money put option on the same stock with the same maturity and same strike price? Prove your answer.

7.

A three-month European call on a non-dividend-paying stock is currently selling for $1. The strike price of the option is $85. The underlying stock trades for $85. The risk-free interest rate is 6%. Does an arbitrage opportunity exist? If you answered “yes,” explain what type of transaction you should execute to make an arbitrage profit, and show how this profit comes about.

(9 marks)

8.

A small, highly leveraged firm has debt with a face value of D that will be expired in six months. If, by then, the firm’s value is higher than D, the firm will pay the debt’s face value to debt holders. If the firm’s value is lower than D, the firm will be in bankruptcy and will be taken over by debt holders.

a. How do you express the firm’s equity position as an option?

(2 marks)

b. How do you express the debt holders’ position as an option?

(2 marks)

c. What can a firm do to increase its value?

(2 marks)

9.

Suppose that the risk free rate is 4% per six months, the exercise price for a call option on stock A is $80, and the option will be expired in six months. The current stock price for A is $80. If the stock price can either move up or down by 5% each six month period, what will the call price be if valued by the binomial option pricing method?

(5 marks)

10.

Suppose you are a financial advisor to an investor whose portfolio consists of 400 shares of Delta Cruise Inc. stock and 10 put options on the same stock. The risk free rate is 6%, time to maturity is six months, exercise price and stock price are both at $82, and the market observed put price is $4.56. The stock does not pay out any dividend. After your analysis of the Delta Cruise Inc. stock prices, you find out that the standard deviation is at 30%. Is the investor position well hedged? What is your advice to the investor?

(5 marks)

11.

As a canola producer in Alberta, you expect to harvest 80 tonnes of canola in October. The current price of canola is $380 per tonne. You are considering using November Canola futures to hedge. The price of the futures contract is $390 per tonne. Each contract is for 20 tonnes. What is the original basis? How many futures contracts are needed? Should you take a long or short position in canola futures? If you decide to close your futures position at the end of October when the basis is 7, what will the hedge profit be?

(6 marks)

12.

Suppose you manage an equity portfolio of $40 million with a beta of 1.2. You are afraid of a downturn in the market and decide to hedge your portfolio using the three month S&P/TSX 60 index futures. The index is currently selling at $645, the three month index futures price is at $635, and the futures contract’s multiplier is $200. How many futures contracts would be needed to hedge your portfolio? If, at the end of one month, the index futures price and the index cash prices are

(6 marks)

$630 and $640 respectively, then what would your gain or loss be?

13.

Given the data in the table below for a sample period, calculate the Sharpe, Jensen, Treynor, and M2 measures for the portfolio P and the market. The risk free rate is at 5%. Did the portfolio P outperform the market? By which measure?

Portfolio P

Market M

Average return

0.34

0.27

Beta

1.10

1.00

Standard deviation

0.40

0.30

(8 marks)

14.

Suppose the current value of an index is S0 and the risk free rate is rf. How much would you pay for perfect forecast of the index value in six months?

(5 marks)

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