Question

**An investor can design a risky portfolio based on two
stocks, 1 and 2. Stock 1 has an expected return of 15% and a
standard deviation of return of 25%. Stock 2 has an expected return
of 12% and a standard deviation of return of 20%. The correlation
coefficient between the returns of 1 and 2 is 0.2. The risk-free
rate of return is 1.5%.**

**Approximately what is the proportion of the optimal
risky portfolio that should be invested in Stock 2?**

Answer #1

**WEIGHT OF STOCK 2 = 0.55**

EXPECTED RETURN A | 15% |

EXPECTED RETURN B | 12% |

SD OF STOCK A | 25% |

SD OF STOCK B | 20% |

CORELATION | 0.2 |

VARIANCE OF STOCK A (SDa^2) | 0.06 |

VARIANCE OF STOCK B (SDb^2) | 0.04 |

COVARIANCE A&B (COVab) | -0.050 |

OPTIMAL RISKY PORTFOLIO | ((SDb^2)-COV(ab))/((SDa^2)+(SDb^2)-2xCOV(ab)) |

PORTFOLIO INVESTED IN A (Wa) | 0.45 |

PORTFOLIO INVESTED IN B (Wb) | 0.55 |

NOTE -COVARIANCE A&B IS NEGATIVE TO AN OPPOSITE EFFECT TO STANDARD DEVIATION

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