EC3330 Theories and International Finance Summer Examinations 2021/22

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EC3330

Summer Examinations 2021/22

Topics in Financial Economics: Theories and International Finance

Section A: Answer the ONE question

1. Are the following statements True, False, or Ambiguous? Provide a short justification for your answer. (You will be evaluated mostly on the basis of your justification).

(a) Suppose you hold an equally weighted portfolio of two stocks, each with a beta of 0.6. The beta of your portfolio equals 0.6. (10 marks)

(b) Suppose you hold an equally weighted portfolio of two stocks, each with a Sharpe ratio of 0.6. The Sharpe ratio of your portfolio equals 0.6. (10 marks)

(c) We consider American options on a stock that does not pay dividends. The put-call parity holds provided that the risk free rate is positive. (10 marks)

The following information is relevant for the next two statements. The current exchange rate is 1.19 Euro per one British pound. The one–year Euro and Pound interest rates are -1% and 1% respectively.

(d) An arbitrage exists if the one-year forward rate is 1.21 Euros per one British pound. (10 marks)

(e) Let C and P denote the prices of one year put and call options on the pound with a strike of 1.21 Euros respectively. An arbitrage exists if C = P. (10 marks)

Section B: Answer ONE question

2. In this question, we examine the conditions under which we would like to exercise early an American put option. We consider a binomial model in which the current share price equals 50 and the interest rate is 5%. Next year, the stock may appreciate by 20% or decrease by 15%.

(a) What is the risk-neutral probability? (10 marks)

(b) Using the binomial model for each of the following strike prices determine whether the early exercise of an American put option is optimal: (i) K = 40, (ii) K = 50, (iii) K = 60. Show your work. (30 marks)

(c) How would your answers change to part (b) if this was an American call option? (10 marks)

3. In this question, we examine the economic implication of a lock-up period that prevents a large shareholder from selling his shares in a given time period. We assume that the market expected return rm = 10% with a standard deviation of σm = 15%. The risk-free rate is rf = 2%. The correlation between Adora and the market is ρAdora,M = 0.5 with a standard deviation of σAdora = 30%. As one of the founders you hold all your wealth, £5M, in Adora shares. You have committed not to sell your Adora shares during the upcoming year.

(a) Based on CAPM, what is the expected wealth you will have one year from now and what is the standard deviation? (10 marks)

(b) Based on CAPM, what is the highest expected return you can achieve for the same risk level as your holdings? (10 marks)

(c) Based on parts (a) and (b) , what is the economic cost of the restriction of not selling your Adora shares? (10 marks)

Hint: The economic cost can be calculated based on the amount of money that if invested efficiently would generate the same outcome.

(d) Redo part (c), assuming that in addition to your Adora holdings you have £5M invested in the market portfolio. (10 marks)

(e) Provide an intuitive explanation for the finding in part (c) as compared to part (b). (10 marks)