Question

A portfolio has an expected return of 12.3 percent. This portfolio contains two stocks and one risk-free security. The expected return on stock X is 9.7 percent and on stock Y it is 17.7 percent. The risk-free rate is 3.8 percent. The portfolio value is $78,000 of which $18,000 is the risk-free security. How much is invested in stock X

Answer 1

Answer:

Investment in stock X is worth $21,387.60

Explanation:

Expected Return of the protfolio is calculated:

$Stock.X.return*invest.x + Stock.Y.return*invest.Y + Risk.free*invest.RF$

Where:

• Stock X return = 9.7%
• Stock Y Return = 17.7%
• Risk free = 3.8% (investment in Risk free = 18,000/78,000 = 23.08%)
• Investment in X+Y = 1 - Invetment in RF = 1 - 0.2308 = 0.7692

So, replacing the numbers

$0.097*x + 0.177*Y + 0.038*0.2308 = 0.123$

Where X+Y = 0.7692, so X = 0.7692-Y

$0.097*(0.7692-Y) + 0.177*Y = 0.123 - 0.0088$

Then

$0.0746 - 0.097*Y + 0.177*Y = 0.1142$

$0.08*Y = 0.0396$

So Y = 0.0396/0.08 = 0.495 = 49.5%

X = 0.7692 - 0.495 = 0.2742 = 27.42%

27.42% * 78000 =