Questions-Risk and Return

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Presentation transcript:

Questions-Risk and Return

Q1 A portfolio has 85 shares of Stock A that sell for $45 per share and 115 shares of Stock B that sell for $17 per share. What is the portfolio weight of A? and B? (a)The portfolio weight of an asset is total investment in that asset divided by the total portfolio value. First, we will find the portfolio value, which is: Total value = 85($45) + 115($17) = $5,780 The portfolio weight for stock A is: WeightA = 85($45)/$5,780 = 0.6618 (b)The portfolio weight for stock B is: WeightB = 115($17)/$5,780 = 0.3382

Q2 You own a portfolio that has $1,800 invested in Stock A and $3,400 invested in Stock B. If the expected returns on these stocks are 9 percent and 14 percent, respectively, what is the expected return on the portfolio? The expected return of a portfolio is the sum of the weight of each asset times the expected return of each asset. The total value of the portfolio is: Total value = $1,800 + 3,400 = $5,200 So, the expected return of this portfolio is: E(Rp) = ($1,800/$5,200)(0.09) + ($3,400/$5,200)(0.14) = 0.1227 or 12.27%

Q4) Consider the following information: Calculate expected return State of Economy Probability Rate of return Recession 0.11 -0.03 Normal 0.65 0.12 Boom 0.24 0.31 E(R) = 0.11(-0.03) + 0.65(0.12) + 0.24(0.31) = 0.1491 or 14.91%

Q5 You own a stock portfolio invested 25 percent in Stock Q, 15 percent in Stock R, 10 percent in Stock S, and 50 percent in Stock T. The betas for these four stocks are 1.74, 0.81, 1.56, and 0.73, respectively. What is the portfolio beta? The beta of a portfolio is the sum of the weight of each asset times the beta of each asset. So, the beta of the portfolio is: βp = 0.25(1.74) + 0.15(0.81) + 0.1(1.56) + 0.5(0.73) = 1.08

Q6 A stock has a beta of 1.1, the expected return on the market is 9 percent, and the risk-free rate is 5.4 percent. What must the expected return on this stock be? CAPM states the relationship between the risk of an asset and its expected return. CAPM is: E(Ri) = Rf + [E(RM) – Rf] × βi Substituting the values we are given, we find: E(Ri) = 0.054 + (0.09 – 0.054)(1.1) = 0.0936 or 9.36%

Q7 A stock has an expected return of 10 percent, its beta is 0.9, and the risk-free rate is 4 percent. What must the expected return on the market be? Here we need to find the expected return of the market using the CAPM. Substituting the values given, and solving for the expected return of the market, we find: E(Ri) = 0.1 = 0.04 + [E(RM) – 0.04](0.9) E(RM) = 0.1067 or 10.67%