Question

We know the following expected returns for stock A and the market portfolio, given different states of the economy:

State (s) | Probability | E(r_{A,s}) |
E(r_{M,s}) |

Recession | 0.2 | -0.02 | 0.02 |

Normal | 0.5 | 0.13 | 0.05 |

Expansion | 0.3 | 0.21 | 0.09 |

The risk-free rate is 0.02.

Assuming the CAPM holds, what is the beta for stock A?

Answer #1

Expcted return on stock A | ||||

State | Probability | E(rA) | Expected return | |

a | b | c | d=b*c | |

Recession | 0.2 | -0.02 | -0.004 | |

Normal | 0.5 | 0.13 | 0.065 | |

Expansion | 0.3 | 0.21 | 0.063 | |

Total | 1 | 0.124 | ||

State | Probability | E(rM,s) | Expected return | |

a | b | c | d=b*c | |

Recession | 0.2 | 0.02 | 0.004 | |

Normal | 0.5 | 0.05 | 0.025 | |

Expansion | 0.3 | 0.09 | 0.027 | |

Total | 1 | 0.056 | ||

Calculation of beta | ||||

R = Rf+ B(Rm-Rf) | ||||

Where, | ||||

Rf = Risk Free Return | ||||

B= Beta | ||||

Rm = Market rate of return | ||||

Rm-Rf= Risk Premium | ||||

0.124=0.02+Beta*(0.056-0.02) | ||||

0.124=0.02+Beta*(0.036) | ||||

Beta = 2.89 |

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