Question

Need to see this on worked out, thanks

You are considering investing $1,000 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 5% and a risky portfolio, P, constructed with two risky securities, X and Y. The optimal weights of X and Y in P are 60% and 40%, respectively. X has an expected rate of return of 14%, and Y has an expected rate of return of 10%. The dollar values of your positions in X, Y, and Treasury bills would be ________, ________, and ________, respectively, if you decide to hold a complete portfolio that has an expected return of 8%.

$595; $162; $243

$162; $595; $243

$595; $243; $162

$243; $162; $595

Answer 1

Expected return of x =   14%  
Expected return of y=   10%  
weight of x = 60% or   0.6  
weight of y = 40% or   0.4  
Expected return of risky with optimal weights= (return of X * Weight X) + ( Return of Y * weight Y)      
so Risky portfolio return = (14%*0.6)+(10%*0.4)      
12.40%      
Risk free rate =   5%  
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% = (12.4% * x) +( 5% * (1-x))      
8% = 12.4% x + 5% - 5%x      
8%-5% = 12.4% x - 5%x      
3%=   7.4%x  
x =   3%/7.4%=   40.54%
So investment in Risky Portfolio =        40.54%
Investment in risk free = 1-40.54%=       59.46%
      
In Stock x, weight of optimal Portfolio 60% = 40.54%*60%=       24.32%
Investment amount = 1000*24.32%=       $243.24

In Stock Y, 40% = 40.54%*40% =       16.22%
Investment amount = 1000*16.22%=       $162.16

Investment in risk free = 1-40.54%=       59.46%
investment amount = 1000*59.46%=       $594.60

So Answer is D 243, 162, 595