Essay About 4Z1 And Standart Deviation

Modern Portfolio Theory and Investment Analysis
Chapter 5 Problem: 5We 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 ratioSecuritiesExpected Return %Standart Deviation %Security 1105Security 2402         Standart deviation of this combinations is equal to standart deviation of equiton 2Qp = Q₂  = 2 When X₁ = Q₂ / Q₂ + Q₂X₁ = investment of Security 1X₂ = investment of Security 2Q ₁= Standart Deviation of Security 1Q₂ = Standart Deviation of Security 2X₁ = 2/5+2 = 2/7  X₂ = 1-X1 = 1-2/7 = 5/7P1= -1 and Qp =0The 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 / 29When 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 = %1,86Chapter 5 Problem 6We 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 2To solve this problem We must find out these equations : 11 – RF = 4Z1 + 10Z2 + 4Z3 14 – RF = 10Z1 + 36Z2 + 30Z3 17 − RF = 4Z1 + 30Z2 + 81Z3The optimum portfolio solutions using Lintner short sales and the given values for RF are:RF = % 6RF = % 8RF = % 10Z13.5100671.8523480.194631Z2−1.043624−0.526845−0.010070Z30.3489930.2147650.080537X10.7159500.7141000.682350X2−0.212870−0.203100−0.035290X30.7118000.0827900.282350Optimum Portfolio Mean Return %6.1056.41911.812Optimum Portfolio Standard Deviation %0.7370.8022.971