(Beta and required return) The riskless return is currently6%, and Chicago Gear
ID: 2661782 • Letter: #
Question
(Beta and required return) The riskless return is currently6%, and Chicago Gear has estimated the contingent returns givenhere.
a. Calculate the expectedreturns on the stock market and on Chicago Gear stock
b. What is Chicago Gear’sbeta?
c. What is ChicagoGear’s required return according to the CAPM?
Realized Return
State of the Market Probability that State OccursStock Market Chicago Gear
Stagnant
0.2
-10%
-15%
Slow Growth
0.35
10
15
Average growth
0.3
15
25
Rapid growth
0.15
25
35
Realized Return
State of the Market Probability that State OccursStock Market Chicago Gear
Stagnant
0.2
-10%
-15%
Slow Growth
0.35
10
15
Average growth
0.3
15
25
Rapid growth
0.15
25
35
Explanation / Answer
(a) Calculating Expected Returns onthe Stock Market and on Chicago GearStock: Expected Return on StockMarket E(Rstock market) = [(0.20 * -0.10) + (0.35 *0.10) + (0.30 * 0.15) + (0.15 * 0.25) Expected Return on StockMarket E(Rstock market) = [-0.02 + 0.035 + 0.045 +0.0375] Expected Return on StockMarket E(Rstock market) = 0.0975 (or)9.75% Expected Return on StockMarket E(Rstock market) = 9.75% Expected Return onChicago Gear E(Rchicago gear) = [(0.20 *-0.15) + (0.35 * 0.15) + (0.30 * 0.25) + (0.15 * 0.35)] Expected Return onChicago Gear E(Rchicago gear) = [-0.03 +0.0525 + 0.075 + 0.0525] Expected Return onChicago Gear E(Rchicago gear) = 0.15 (or)15% Expected Returnon Chicago Gear E(Rchicago gear) =15% (b) Calculating ChicagoGear's Beta(ß): Average Realized Returnon Chicago Gear = [-0.15 + 0.15 + 0.25 + 0.35] / 4 Average Realized Returnon Chicago Gear = 0.15 (or) 15% Expected Return onChicago Gear E(Rchicagogear) = 15% Risk-free Return(Rf) = 6% 0.15 = 0.06 + Beta (ß) * (0.15- 0.06) 0.15 = 0.06 + ß *0.09 0.15 - 0.06 = ß *0.09 0.09 = ß * 0.09 ß * 0.09 = 0.09 ß = 0.09 /0.09 Beta Value (ß) =1 ( c) Calculating Chicago Gear's Required Return accordingto the CAPM: According to CAPM, theRequired Return (RE) = Rf + ß(RM - Rf) Required Return ofChicago Gear's Required Return (Rchicago gear's) =0.06 + 1 (0.15 - 0.06) Required Return ofChicago Gear's Required Return (Rchicago gear's) =0.06 + 1 (0.09) Required Return ofChicago Gear's Required Return (Rchicago gear's) =0.06 + 0.09 Required Returnof Chicago Gear's Required Return (Rchicagogear's) = 0.15 (or) 15% (a) Calculating Expected Returns onthe Stock Market and on Chicago GearStock: Expected Return on StockMarket E(Rstock market) = [(0.20 * -0.10) + (0.35 *0.10) + (0.30 * 0.15) + (0.15 * 0.25) Expected Return on StockMarket E(Rstock market) = [-0.02 + 0.035 + 0.045 +0.0375] Expected Return on StockMarket E(Rstock market) = 0.0975 (or)9.75% Expected Return on StockMarket E(Rstock market) = 9.75% Expected Return onChicago Gear E(Rchicago gear) = [(0.20 *-0.15) + (0.35 * 0.15) + (0.30 * 0.25) + (0.15 * 0.35)] Expected Return onChicago Gear E(Rchicago gear) = [-0.03 +0.0525 + 0.075 + 0.0525] Expected Return onChicago Gear E(Rchicago gear) = 0.15 (or)15% Expected Returnon Chicago Gear E(Rchicago gear) =15% (b) Calculating ChicagoGear's Beta(ß): Average Realized Returnon Chicago Gear = [-0.15 + 0.15 + 0.25 + 0.35] / 4 Average Realized Returnon Chicago Gear = 0.15 (or) 15% Expected Return onChicago Gear E(Rchicagogear) = 15% Risk-free Return(Rf) = 6% 0.15 = 0.06 + Beta (ß) * (0.15- 0.06) 0.15 = 0.06 + ß *0.09 0.15 - 0.06 = ß *0.09 0.09 = ß * 0.09 ß * 0.09 = 0.09 ß = 0.09 /0.09 Beta Value (ß) =1 ( c) Calculating Chicago Gear's Required Return accordingto the CAPM: According to CAPM, theRequired Return (RE) = Rf + ß(RM - Rf) Required Return ofChicago Gear's Required Return (Rchicago gear's) =0.06 + 1 (0.15 - 0.06) Required Return ofChicago Gear's Required Return (Rchicago gear's) =0.06 + 1 (0.09) Required Return ofChicago Gear's Required Return (Rchicago gear's) =0.06 + 0.09 Required Returnof Chicago Gear's Required Return (Rchicagogear's) = 0.15 (or) 15%Related Questions
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