Fall 2007

FINANCIAL MARKETS Master International and Corporate Finance (ISC Paris) and Risk Management in Finance and Insurance (University of Cergy-Pontoise) Prof. Duc K. Nguyen 25a, ISC2, ISC Paris School of Management [email protected] http://khuongnguyen.free.fr/

LIST OF APPLICATIONS Risk and Rates of Return STUDY QUESTIONS 1. Explain the effect of inflation on rates of return. An investment offers a 25-percent rate of return in two years, what would be the real rate of return today if the inflation rate equals 5% in year 1 and 7% in year 2. 2. What does the investor’s required rate of return stand for? Where do you get it? 3. How do we measure the beta of a portfolio? 4. In his paper entitled "A Critique of the Asset's Pricing Theory's Tests: Part I", Journal of Financial Economics 4, 129-176, Roll (1997) stresses that the theory of CAPM is not testable because the market portfolio is unobservable. Why is the CAPM still used in practice?

STUDY PROBLEMS Problem 1 How would you construct a portfolio with a beta of 0.25? What is the expected return to this strategy? Assume Treasury bills yield 6 percent and the market risk premium is 9 percent. Problem 2 Suppose you invest $400,000 in Treasury bills and $600,000 in the market portfolio. What is the return on your portfolio if Treasury bills yield 6 percent and the expected return on the market is 15 percent? What does the return on this portfolio imply for the expected return on individual stocks with betas of 0.6? Problem 3 Suppose you buy a bond for $1,020 with a 10-year maturity paying an annual coupon of $80. A year later interest rates have dropped and the bond’s price has increased to $1,080. What are your nominal and real rates of return? Assume the inflation rate is 6 percent. Problem 4 Consider the following random game with different possible outcomes of the revenues and their probabilities of occurrence. The cost of participation is €100 and the benefits resulting from the game is equal to the difference between revenues and participation cost. Probabilities Revenues Benefits 0.10 €500 €400 0.50 €100 €0 0.40 €0 -€100 a) Determine the expected revenue and expected rate of return b) Calculate the variance and standard deviation of the rate of return Problem 5 The following table provides the nominal rates of stock market return and the inflation rate in Mexico. 1|Page

Year Nominal rates of return 1995 16.5% 1996 21.9% 1997 53.4% 1998 -20.8% 1999 84.3% a) What is the standard deviation of stock market return? b) Calculate the average rate of return in real terms

Inflation rate 52.0% 27.7% 15.7% 18.6% 12.3%

Problem 6 Data on the financial performance (annual rates of return) of a Mutual Fund from 1996 to 2000 are provided in the following table. 1996 1997 1998 Mutual Fund 16.1% 28.4% 25.1% S&P’s 500 index 23.1% 33.4% 28.6%

and the S&P’s 500 index for the period 1999 14.3% 21.0%

2000 -6.0% -9.1%

A portfolio manager said that the Mutual Fund has realized higher performance than the S&P’s 500 index over the period under consideration. Is this affirmation correct? Problem 7 Based on historical performance of Alcatel and LVMH stocks, we have the following information: Alcatel LVMH Beta 2.79 1.63 Standard deviation 87.9% 48.7% Assume that the standard deviation of the market’s return is 25% and the correlation coefficient between Alcatel and LVMH stocks is 0.65. a) What is the standard deviation of the portfolio combining these two assets if we invest 50% in Alcatel stock and 50% in LVMH stock? b) What is the standard deviation of the portfolio of Alcatel, LVMH and Treasury bills? The respective weights are 1/3, 1/3 and 1/3. Problem 8 The rate of return on Treasury bills is 4% and the expected return on market portfolio is 12%. On the basis of CAPM: a) Trace the security market line b) What is the market risk premium? c) What is the investor’s required rate of return if the beta of the investment is 1.5? d) If an investment’s beta equals 0.8 and the resulting expected return is 9.8%, is the VAN positive? e) If the expected return on the stock X is 11.2%, what is its beta? Problem 9 The following table provides realized rates of returns of two stocks, A and B, for a 5-year period: Year 1 2 3 4 5 Stock A 0.30 0.10 0.04 0.19 0.13 Stock B 0.50 0.25 0.15 0.32 0.20 Suppose that the CAPM is valid for pricing these securities, establish the pricing equations for A and B assets given that βA = 1.65 and the rate of return on the risk-free asset is 2%. 2|Page