_c1 - βcg = cov cg m/σ 2 m = 180/121 = 1.49 You can apply...

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Ch7.C1. (Beta and required return) The riskless return is currently 6%, and Chicago Gear has estimated the contingent returns given here. a. Calculate the expected returns on the stock market and on Chicago Gear stock. b. What is Chicago Gear’s beta? c. What is Chicago Gear’s required return according to the CAPM? Realized Return State of the Market Probability that State Occurs Stock Market Chicago Gear Stagnant 0.20 (10%) (15%) Slow growth 0.35 10 15 Average growth 0.30 15 25 Rapid growth 0.15 25 35 Solution: a. Calculate the expected returns on the stock market and on Chicago Gear stock. Expected Returns on the market = ∑Probability * Realized return of market = - 0.20*10 + 0.35*10 + 0.30*15 + 0.15*25 = -2+3.5+4.5+3.75 = 9.75% Expected Returns on the Chicago Gear Stock = ∑Probability * Realized return of stock = -0.20*15 + 0.35*15 + 0.30*25 + 0.15*35 = -3.0 + 5.25 + 7.5 + 5.25 = 15.00% b. What is Chicago Gear’s beta?
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Unformatted text preview: βcg = cov cg, m /σ 2 m = 180/121 = 1.49 You can apply the formula ∑Probability * (Expected Returns on the market - Realized return of market)*( Expected Returns on the Chicago Gear Stock- Realized return of stock) to calculate covariance between stock market and Chicago gear cov cg, m. which turns out to be 180. cov cg, m. = ∑Probability * (Expected Returns on the market - Realized return of market)*( Expected Returns on the Chicago Gear Stock- Realized return of stock) = 118.5 + 0.00 + 15.75 + 45.75 = 180.00 Variance of stock market can be calculated using ∑Probability * (Expected Returns on the market - Realized return of market) 2 which turns out to be 121 σ 2 m = ∑Probability * (Expected Returns on the market - Realized return of market) 2 = 78.01 + 0.02 + 8.27 + 34.88 = 121.19 c. What is Chicago Gear’s required return according to the CAPM? Chicago Gear’s required rate of return according to CAPM: Rcg = Rf + βcg(Rm-Rf) Required rate of return or Ks = r f + β (r m – r f) Rcg = .06 + 1.49 * (.0975-.06) = .1158 = 11.58%...
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