Assignment2_433_533_Winter2024_c5bb3a02f9faf5a5a050e73536332126

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Concordia University *

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Finance

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Apr 3, 2024

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ECON433/533: Financial Economics Winter 2024 Assignment 2 Upload your scanned or typed solutions as a pdf to Moodle by April 10, 1:00 PM. 1 Arbitrage Pricing Theory (20 points) (1) Contrast the CAPM and the APT main assumptions. (2) Consider the Fama-French three-factor model: ˜ r i = E r i ) + β i,m r m E r m )) + β i,s ( ˜ SMB E ( ˜ SMB )) + β i,h ( ˜ HML E ( ˜ HML )) + ˜ ε i where ˜ r m is the random return on the market portfolio, ˜ SMB is the random return on the “small-minus- big” portfolio (size factor), and ˜ HML is the random return on the “high-minus-low” book-to-market value portfolio (book-to-market value factor). Assume that for a specific well-diversified portfolio, portfolio 1, β w,m = 0 . 9 , β w,s = 0 . 3 , β w,h = 0 . 2. The market beta is the same for the CAPM and the three-factor model. Let the market, the size, and the book-to-market risk premiums be 12%, 6%, and 5%, respectively. The risk-free interest rate is 3%. a) If you believe the CAPM to be valid, what should be the expected return on portfolio 1? b) Assume you believe the the three-factor model to be more accurate. i. What should the expected return be on portfolio 1? ii. Suppose there is another well-diversified portfolio, portfolio 2, with betas half the size of those of portfolio 1, but with the same expected return. Would an arbitrage opportunity exist? If so, what would be the arbitrage strategy? 2 Efficient Market Hypothesis (20 points) (1) Define the weak, semi-strong and strong forms of the Efficient Market Hypothesis. Explain how they differ. (2) Suppose that your security analysis has discovered that stock prices tend to rise significantly during the month of January. Does this finding provide evidence against the semi-strong form of the Efficient Market Hypothesis? (3) If individual stock prices follow a random walk process (they are as likely to go up as to go down on any given day) why do investors earn positive returns from the market on average over time? 3 Bond Pricing (10 points) Consider a bond with a face value of $ 1,000, a coupon rate of 5% paid annually, and a remaining maturity of 5 years. The current market interest rate is 6% per annum. a) Determine the present value of the bond’s future cash flows, assuming the market interest rate is used as the discount rate. How the bond’s price would change if the market interest rate increases to 7% per annum. b) Discuss the relationship between the coupon rate, market interest rate, and bond price in relation to the bond’s yield to maturity. 1
4 Equity Pricing (10 points) ZZZ stock is expected to pay a dividend of $ 1 next year and $ 1.25 the year after. What should be the price of ZZZ if we expect the dividends to grow at a constant rate? The appropriate discount rate is 7%. 5 Pricing of Derivatives (40 points) 1) Explain the concepts of hedging, speculation, and arbitrage. Provide an example of each strategy using derivatives. 2) Consider the following information for a forward contract on a nondividend-paying stock. Stock spot price $ 80 Forward price 83 $ Time until delivery date 1 year The continuously compounded risk-free rate per annum 5% Is there an arbitrage opportunity? If there is, provide a strategy to exploit it. 3) Consider the following information on a stock whose price is expected to increase by 6% or decrease by 5% in each of the following two quarters. European put option time to maturity 6 months European put strike price $ 51 Stock price $ 50 The continuously compounded risk-free rate per annum 5% a) Assuming the stock pays no dividends, apply the risk-neutral valuation method to price the option. Round all calculations to three decimal places. b) Are investors’ risk preferences important in option pricing? 4) Consider the following information on a stock whose price is expected to increase to $ 60 or decrease to $ 40 in one month. European call option time to maturity 1 month European call strike price $ 55 Stock price $ 50 The monthly continuously compounded risk-free rate 1% a) Assuming the stock pays no dividends, apply the replicating portfolio method to price the option. Round all calculations to three decimal places. b) Assuming the stock pays no dividends, apply the hedging portfolio method to price the option. Round all calculations to three decimal places. 2
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