You have $300,000 to invest in a portfolio containing Stock X and Stock Y . Your
ID: 2710214 • Letter: Y
Question
You have $300,000 to invest in a portfolio containing Stock X and Stock Y. Your goal is to create a portfolio that has an expected return of 14.50 percent. Stock X has an expected return of 13.28 percent and a beta of 1.44, and Stock Y has an expected return of 9.08 percent and a beta of .84.
How much money will you invest in stock X? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places. (e.g., 32.16))
What is the beta of your portfolio? (Do not round intermediate calculations and round your answer to 3 decimal places. (e.g., 32.161))
You have $300,000 to invest in a portfolio containing Stock X and Stock Y. Your goal is to create a portfolio that has an expected return of 14.50 percent. Stock X has an expected return of 13.28 percent and a beta of 1.44, and Stock Y has an expected return of 9.08 percent and a beta of .84.
Explanation / Answer
Step 1.) Setup Variables
Weights
Wx : The amount of the portfolio composed of Stock X
Wy: The amount of the portfolio composed of stock Y
_______________________________
Expected Returns
E(p) : Expected portfolio return
E(x): Expected Return on stock X
E(y): Expected Return on stock Y
_________________________________
Beta Values
Pb: Portfolio Beta
Xb: Stock X Beta
Yb: Stock Y Beta
Step 2.) Setup Equations
The weights must follow this property
Wx + Wy = 1
The Expected Rate of Return for the Portfolio Equation
E(p) = Wx * E(x) + Wy * E(y)
The Portfolio Beta Equation
Pb = Wx * Xb + Wy * Yb
Step 3.) Solve for Unknowns using the above equations
We have these equations
Wx + Wy = 1
E(p) = Wx * E(x) + Wy * E(y)
Pb = Wx * Xb + Wy * Yb
We are given E(p) = 0.145 (14.5%) ; E(x) = 0.1328 (13.28%) ; E(y) = 0.0908 (9.08%)
Xb = 1.44; Yb = 0.84
Substitute into the Equations to get this system
Wx + Wy = 1
0.145 = Wx * 0.145 + Wy *0.0908
Pb = Wx * 1.44 + Wy * 0.84
Solving for Wy in the top equation we get
Wy = 1 - Wx
(Substitute this into the 2nd equation "the expected return equation" to get)
0.145 = 0.1328 Wx + (1 - Wx) * 0.0908
= 0.1328 Wx + 0.0908 - 0.0908 Wx
Wx = 1.290
substitute this into this equation (Wx + Wy = 1) to get
1.290 + Wy = 1
Wy = - 0.290 (the negative indicates that you are short selling stock Y)
Using our weight values, we can now calculate the portfolio beta
Pb = Wx * Xb + Wy * Yb
=(1.290) * (1.44) + (-0.290) * (0.84)
= 1.614
So the portfolio beta is 1.6
The amount invested in stock Y is
Investment in Stock Y = (-.290) * (300,000) = - $87,000
Investment is stock X = 387,000
Investment is stock Y = -87,000
Portfolia beta 1.6
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.