# Modern Portfolio Theory and Investment Analysis

Autor: infinity • December 2, 2018 • Case Study • 432 Words (2 Pages) • 105 Views

**Page 1 of 2**

Chapter 5 Problem: 5

We assume There is no short selling and the point where p= 1, security 2 is the least risky combination of security . It is required that X1 = 0 and X2 = 1 , X means that investment weight ratio

Securities | Expected Return % | Standart Deviation % |

Security 1 | 10 | 5 |

Security 2 | 40 | 2 |

Standart deviation of this combinations is equal to standart deviation of equiton 2

Qp = Q₂ = 2 When X₁ = Q₂ / Q₂ + Q₂

X₁ = investment of Security 1

X₂ = investment of Security 2

Q ₁= Standart Deviation of Security 1

Q₂ = Standart Deviation of Security 2

X₁ = 2/5+2 = 2/7

X₂ = 1-X1 = 1-2/7 = 5/7

P1= -1 and Qp =0

The minimum risk of combination of two assets can be calculated :

X₁ = Q₂2 / Q ₁2 * Q₂2 = 4/4+25 = 4/29

X2 = 1-X1 = 1-4/29 = 25 / 29

When p = 0 , standart deviation of two portfolios :

Qp = √ X22* Q ₁2 + (1- X1)2* Q₂2

Qp = √(4/29)2*25+(25/29)2 *4 = √2900/841 = %1,86

Chapter 5 Problem 6

We assume that the riskless rate of %10 , so the risk and return both risky assets are affected by risk free assets , because at zero risk, they offer higher return than both the asssets.We should think that invester’s choice is from higher to lower return so optimal investment is risk – free assets.

Chapter 6 Problem 2

To solve this problem We must find out these equations :

11 – RF = 4Z1 + 10Z2 + 4Z3

14 – RF = 10Z1 + 36Z2 + 30Z3

17 − RF = 4Z1 + 30Z2 + 81Z3

The optimum portfolio solutions using Lintner short sales and the given values for RF are:

RF = % 6 | RF = % 8 | RF = % 10 | |

Z1 | 3.510067 | 1.852348 | 0.194631 |

Z2 | −1.043624 | −0.526845 | −0.010070 |

Z3 | 0.348993 | 0.214765 | 0.080537 |

X1 | 0.715950 | 0.714100 | 0.682350 |

X2 | −0.212870 | −0.203100 | −0.035290 |

X3 | 0.711800 | 0.082790 | 0.282350 |

Optimum Portfolio Mean Return % | 6.105 | 6.419 | 11.812 |

Optimum Portfolio Standard Deviation % | 0.737 | 0.802 | 2.971 |

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