QUESTIONS AND PROBLEMS 1. Assume that the following two-index model describes returns: R=a+b+b212 +e; Assume that the following three portfolios are observed. Portfolio ABC Expected Return 12.0 13.4 12.0 bil b₁₂ 0.5 1 0.2 3 -0.5 3 Find the equation of the plane that must describe equilibrium returns. 111 illustrate the arbitrage opportunities that

Draw the profit diagram of the portfolio just drawn (and clearly state any assumptions you make). The profit is equal to the difference between the payoff of the portfolio at expiry (maturity) date and the cost of the portfolio. Is the cost of the portfolio positive?

Suppose you have an investment portfolio with fraction x invested in a market portfolio and (1-x) in a risk- free asset. Increasing fraction x invested in the market portfolio and consequently decreasing (1-x) invested in the risk-free asset shall (select any correct answer, if there are multiple correct answers) Select one or more: O decrease the Sharpe ratio of the resulting portfolio O decrease the expected return of the resulting portfolio increase the Sharpe ratio of the resulting portfolio increase the expected return of the resulting portfolio Dincrease the risk of the resulting portfolio

Consider the following single factor specification: R₁ = a¡ + ßi, Rµ + €i. Where R; is the return on security i, RM is the return on index M (a broad market index) and e, is a zero- mean white noise random variable not correlated with anything. Assume that the single factor specification above correctly describes the return generating processes of all securities. Furthermore, you have the following descriptive statistics for returns of well-diversified Portfolios X, Y, and index M. Portfolio X Portfolio Y Index M Risk-Free Expected return 14% 17% ?? ?? B₁ 1.2 1.6 1 0 a. Assume that the corresponding single factor APT correctly prices Portfolios X and Y. In other words, the expected returns of Portfolios X and Y shown above - 14% and 17% respectively - are equal to their APT-predicted expected returns. Calculate the expected return of Index M and risk-free rate. b. Another well-diversified portfolio Z has a beta, ßz, of 0.8 while its expected return is 10%. Form a portfolio consisting…

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Portfolio theory with two assets E(R1)=0.15 E(01)= 0.10 W1=0.5 E(R2)=0.20 E(02) = 0.20 W2=0.5 Calculate the expected return and the standard deviation of the two portfolios if r1,2 = 0.4 and -0.60 respectively.

Vijay

Return on a portfolio of two risky assets which are perfectly negatively correlated is equivalent to a. Risk-free rate b. Return on market portfolio c. Zero return d. -1%

Consider following information on a risky portfolio, risk-free asset and the market index. What is the Sharpe ratio of the market index?   Risky portfolio Risk-free asset Market index Average return 8.2% 2% 6% Std. Dev. 26%   20% Residual std. dev. 10%     Alpha 1.4%     Beta 1.2

The portfolio with the highest Sharpe Ratio is I. The minimum-variance point on the efficient frontier II. The tangency point of the capital market line and the efficient frontier III. The maximum-return point on the efficient frontier  IV. The line with the steepest slope that connects the risk-free rate to the efficient frontier Select one: a. II and IV only b. I and IV only c. III and IV only d. Only IV e. I and II only