Question

You have $9,000 to invest. You've done some security analysis and generated the following data for three stocks and Treasury bills, including weights in the optimal risky portfolio (ORP) from doing Markowitz portfolio optimization:

Security	Stock A	Stock B	Stock C	T-bills
Expected return (%)	12	8	5	4
Variance	0.04	0.03	0.02	0
Beta	1.2	1.5	0.8	0
Weight in ORP (%)	44	18	38	0

Part 1

What is the expected return of the optimal risky portfolio (ORP)?

Part 2

How much money should you invest in the ORP to achieve an expected return of 8% for the complete portfolio (in $)?

Part 3

If you want to achieve an expected return of 8% for the complete portfolio, how much money should you invest in stock A (in $)?

Answer 1

(A)      
Expected return of A = ℅   12  
Expected return of B= %   8  
Expected return of C = %   5  
weight of A in ORP= 44% or   0.44  
weight of B in ORP = 18% or   0.18  
weight of C in ORP = 38% or   0.38  

Expected return of risky portfolio with optimal weights= (return of A * Weight A) + ( Return of B* weight B)+(Return of C*Weight C)      
so Risky portfolio return =   (12*0.44)+(8*0.18)+(5*0.38)  
=8.62%
So, expected return of optimal risky portfolio is 8.62%      

(B) Expected return of ORP = 8.62   

Risk free rate % = 4  
Complete Portfolio Return % = 8  

Assume Risky Portfolio weight = x and Riskfree weight = (1-x)      

Expected return of complete Portfolio= (return of Risky P* Weight of Risky P) + ( Return of Risk free* weight of Risk free)      
8 = (8.62 * x) +( 4 * (1-x))      
8 = 8.62 x + 4 -4 x      
8-4 = 8.62 x - 4x      
4=   4.62x  
x =   4/4.62=   0.8658
So investment in Risky Portfolio = 9000*0.8658=       7,792.21

$7792.21 to be invested in optimal risky portfolio to achieve 8% complete portfolio return.
      
(C)      
Stock A weight in optimal risky Portfolio is 44%      
So, Investment amount = 9000*0.44= $3,960.00
      
So Amount to be invested in stock A is $3960