Question

Suppose the expected returns and standard deviations of Stocks A
and B are E( |

a-1. |
Calculate the expected return of a portfolio that is composed of
43 percent Stock A and 57 percent Stock B when the correlation
between the returns on A and B is .58. |

a-2. |
Calculate the standard deviation of a portfolio that is composed
of 43 percent Stock A and 57 percent Stock B when the correlation
between the returns on A and B is .58. |

b. |
Calculate the standard deviation of a portfolio with the same
portfolio weights as in part (a) when the correlation coefficient
between the returns on Stocks A and B is −.58. |

Answer #1

Formulae used are:

**E(p) = E(rA) * W(A) + E(rB) * W(B)**

**SD(p) = sqrt(W(A)^2 * SD(A)^2 + W(B)^2 * SD(B)^2 + 2*
W(A) * SD(A) * W(B) * SD(B) * corr(A,B))**

a1 and a2

E(rA) | 9.80% |

E(rB) | 15.80% |

SD(A) | 36.80% |

SD(B) | 62.80% |

Corr | 0.58 |

W(A) | W(B) | E(p) |
Var(p) | SD(p) |

0.43 | 0.57 | 13.22% |
21.89% | 46.78% |

b.

E(rA) | 9.80% |

E(rB) | 15.80% |

SD(A) | 36.80% |

SD(B) | 62.80% |

Corr | -0.58 |

W(A) | W(B) | E(p) |
Var(p) | SD(p) |

0.43 | 0.57 | 13.22% |
8.75% | 29.58% |

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