# Question 1 _25 marks_ by keara

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BEFM015

UNIVERSITY OF EXETER

May 2007

PORTFOLIO MANAGEMENT AND ASSET ALLOCATION Module Convenor: Zhenxu Tong

Duration: Two hours. Answer THREE questions out of SIX: TWO questions from Part A and ONE question from Part B. All questions carry 25 marks. Only silent non-programmable calculators are permitted. This is a closed-book exam.

BEFM015 PM&AA June 2007

Part A Question 1 (25 Marks) 1.1 Suppose an investor has the following information: • The risk-free rate is 7 percent. • The standard deviation of market returns is 35 percent. • The market risk premium is 7 percent. • Stock A has a beta of 1.30. • Stock A is estimated to generate a 15.5 percent return. • The covariance of Stock B with the market is 0.18. • The standard deviation of Stock B’s returns is 41 percent. a) Calculate the beta of Stock B. (3 Marks) b) Explain whether or not the investor should buy Stock A. (6 Marks) 1.2 The beta between a fund and the EAFE index is 1.2. The standard deviation of the fund is 0.41. The standard deviation of the EAFE index is 0.25. What is the correlation between the fund and the EAFE index? (5 Marks) 1.3 Discuss the impact of transaction costs on the Security Market Line (SML) of the CAPM. (4 Marks) 1.4 a) What are the objectives when we select the factors in the APT model? b) Outline the macroeconomic and microeconomic factors which have been suggested for the APT model. (7 Marks) Question 2 (25 Marks) 2.1 Suppose an investor has the following information: Spot Rates EUR/USD GBP/USD Bid 1.0000 2.0000 Ask 1.0015 2.0100

The investor is interested in pursuing profitable arbitrage opportunities. Using the appropriate bid or ask rates for the EUR/USD and GBP/USD, and assuming the EUR/GBP rate is 0.4000 EUR/GBP, what will be the profits from triangular arbitrage, starting with 1,000 USD ? (9 Marks)
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2.2 A U.S. investor purchased a U.K. bond one year ago. The exchange rate at the time was 1.5 to 1 (dollars to pounds) and the beginning-of-period ratio of the price levels of the consumption baskets was 2 (US to UK). During the year, inflation in the U.S. was 5 percent and in the U.K. was 10 percent. Today the exchange rate is 1.6. What is the end-of-period real exchange rate? (4 Marks) 2.3 Assume there is a Eurozone investor who is restricted to investing only in two currencies: the Euro and the US dollar. The US risk-free rate is 3 percent and the Eurozone risk-free rate is 4 percent. The expected appreciation of the US dollar is 2 percent. The world portfolio risk premium is 8 percent. The currency exposures based on Euro returns and world betas for three portfolios are as follows: A 1.2 1.5 B 1.4 0.8 C 0.8 2.0 (3 Marks)

World beta Currency exposure

a) What is the foreign currency risk premium?

b) What is the expected return of each portfolio to the Eurozone investor? (5 Marks) 2.4 What assumptions are needed in order to extend the domestic CAPM to an international setting? (4 Marks)

Question 3 (25 Marks) 3.1 Suppose S is the spot exchange rate (DC/FC) at time 0. DC is the domestic currency. FC is the foreign currency. RD is the domestic interest rate for both borrowing and lending in the DC. RF is the foreign interest rate for both borrowing and lending in the FC. By using the above notation: a) Construct a synthetic forward purchase by listing the relevant transactions at time 0 and time 1. (4 Marks) b) Derive the implied or synthetic forward rate. Explain under what condition an investor can make a speculative profit through a synthetic forward purchase. (3 Marks) c) How can this investor remove the risk by using a forward contract? List the relevant transactions at time 0 and time 1. (5 Marks) Turn over/…
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3.2 Suppose S0 and S1 are the spot rates for USD/EUR at the beginning and the end of the period, and IUSD and IEUR are USD and EUR inflation rates over the period. Write the equation for relative Purchasing Power Parity. (4 Marks)

3.3 The exchange rate between the U.S. and Canada was 1.5 to 1 (\$/Can\$) one year ago. At that time, the ratio of the price levels of the U.S. consumption basket to the Canadian consumption basket was also 1.5. During the year, U.S. inflation was 4 percent and Canadian inflation was 2 percent. What must the end-of-period nominal exchange rate be in order for the end-of-period real exchange rate to be the same as the beginning of period real exchange rate? (5 Marks) 3.4 In the money demand model, what is the relationship between an appreciation in the domestic currency and the level of the domestic equity markets? (4 Marks) Question 4 (25 Marks) 4.1 What are the five elements in the Black-Scholes formula for a European call option on a non-dividend paying stock? (5 Marks) 4.2 An investor has the following information on currency quotes. USD/EUR (\$/€) USD/GBP (\$/£) Spot rate \$1.2139 \$1.7730 6-month forward rate \$1.2067 \$1.7894 For each of them, calculate the annualized forward premium or discount and explain which currency is relatively strong. (6 Marks) 4.3 Explain the major differences between forward and futures contracts. (5 Marks) 4.4 Consider a fixed-for-fixed 1-year \$100,000 semi-annual-pay currency swap with rates of 5.2 percent in USD and 4.8 percent in CHF, originated when the exchange rate is \$0.34. 90 days later, the exchange rate is \$0.35 and the term structure is: LIBOR Swiss 90 days 5.2% 4.8% 270 days 5.6% 5.4% (9 Marks) 4

What is the value of the swap to the USD payer?
BEFM015 PM&AA June 2007

BEFM015 PM&AA June 2007

Question 6 (25 Marks)

Answer all parts: Write short explanatory notes on: a. i. ii. iii. The concept of a Trust? The concept of a Fiduciary Investor? The concept of a Trustee? 5 marks total

b.

Both the investment and legal professions had come to find the Old Prudent Man Rule too restrictive for guiding the investment of trust assets in the modern world. As a result this law was restated in the form of the New Prudent Investor Rule. With reference to the sentence above explain the ways in which the Old Prudent Man Rule had become inappropriate for modern investment. 5 marks total

c.

Describe the management and investment requirements that the Uniform Prudent Investor Act sets out for each of the aspects listed below. i. ii. iii. iv. v. vi. vii. viii. Risk and Reward Strategy Diversification Review Loyalty Impartiality Costs Delegation 15 marks total

*** End of Exam ***

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