 # Modern Portfolio Theory and Investment Analysis

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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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