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Modern Portfolio Theory and Investment Analysis

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

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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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