Question

Assume that you have an investment portfolio of $200,000. The investment consists of $100,000 in Amazon and $100,000 in Apple. You are thinking of rebalancing the portfolio by selling $30,000 worth of Alphabet and $30,000 worth of Apple. You plan to invest the realized proceeds of $60,000 in Facebook stock. Assume that betas of Amazon (1.63), Apple (0.99), and Facebook (1.18). A. What would be the beta of your new portfolio? B. Say you decide to sell off all the three stocks and invest 50% in treasury bonds and the remaining 50% in S&P 500 Index fund. What would be the new beta of your portfolio?

Answer 1

A.

Total Portfolio value = Value of Amazon + Value of Apple + Value of Facebook

=70000+70000+60000

=200000

Weight of Amazon = Value of Amazon/Total Portfolio Value

= 70000/200000

=0.35

Weight of Apple = Value of Apple/Total Portfolio Value

= 70000/200000

=0.35

Weight of Facebook = Value of Facebook/Total Portfolio Value

= 60000/200000

=0.3

Beta of Portfolio = Weight of Amazon*Beta of Amazon+Weight of Apple*Beta of Apple+Weight of Facebook*Beta of Facebook

Beta of Portfolio = 1.63*0.35+0.99*0.35+1.18*0.3

Beta of Portfolio = 1.271

B.

Total Portfolio value = Value of S&P + Value of T bond

=100000+100000

=200000

Weight of S&P = Value of S&P/Total Portfolio Value

= 100000/200000

=0.5

Weight of T bond = Value of T bond/Total Portfolio Value

= 100000/200000

=0.5

Beta of Portfolio = Weight of S&P*Beta of S&P+Weight of T bond*Beta of T bond

Beta of Portfolio = 1*0.5+0*0.5

Beta of Portfolio = 0.5