Question

Assume that you hold a well-diversified portfolio that has an expected return of 11.0% and a beta of 1.20. You are in the process of buying 1,000 shares of Alpha Corp at $10 a share and adding it to your portfolio. Alpha has an expected return of 22.5% and a beta of 1.20. The total value of your current portfolio is $90,000. What will the expected return and beta on the portfolio be after the purchase of the Alpha stock? Do not round your intermediate calculations. 13.97%:0.97 12.15%; 1.20 11.54%: 1.26 15.07%: 1.33 11.42%: 104

Answer 1

Solution:

Calculation of Expected Return of a portfolio:

The formula for calculation of Expected Return of a portfolio is

E(R_P) = ( R_A * W_A ) + ( R_B * W_B )

Where

E(R_P) = Expected return on a portfolio after the purchase of Alpha stock

R_A = Return of Portfolio before purchase of stock    W_A = Weight of Investment in portfolio before purchase of stock    

R_B = Return of Alpha Corp.   W_B = Weight of Investment in Alpha Corp.

As per the information given in the question we have

Investment in portfolio before purchase of stock = $ 90,000

No. of shares Invested in Alpha corp. = 1,000 shares

Price per share invested in Alpha Corp. = $ 10

Thus total amount of Investment in Alpha corp. = 1000 * $ 10 = $ 10,000

R_A = 11 %   ; R_B = 22.5 % ;

W_A = ( Investment in portfolio before purchase of stock ) / (Investment in portfolio before purchase of stock + Investment in Alpha Corp. )

= $ 90,000 / ( $ 90,000 + $ 10,000 ) = $ 90,000 / $ 100,000 = 0.90    ;   

W_B = ( Investment in Alpha Corp. ) / (Investment in portfolio before purchase of stock + Investment in Alpha Corp. )

= $ 10,000 / ( $ 90,000 + $ 10,000 ) = $ 10,000 / $ 100,000 = 0.10   ;

Applying the values in the formula we have

= ( 11 % * 0.9 ) + ( 22.5 % * 0.1 )

= 9.9 % + 2.25 % = 12.15 %

Thus the expected return of the Portfolio after purchase of Alpha stock = 12.15 %

Calculation of Beta of a portfolio :

The formula for calculation of Beta of a portfolio is

β_P = ( β_A * W_A )+ ( β_B * W_B )

Where

β_P = Beta of the portfolio after the purchase of Alpha stock

β_A = Beta of Portfolio before purchase of stock    W_A = Weight of Investment in portfolio before purchase of stock    

β_B = Beta of Alpha Corp.   W_B = Weight of Investment in Alpha Corp.

As per the information given in the question we have

β_A = 1.20   ; β_B = 1.20

Investment in portfolio before purchase of stock = $ 90,000

No. of shares Invested in Alpha corp. = 1,000 shares

Price per share invested in Alpha Corp. = $ 10

Thus total amount of Investment in Alpha corp. = 1000 * $ 10 = $ 10,000

W_A = ( Investment in portfolio before purchase of stock ) / (Investment in portfolio before purchase of stock + Investment in Alpha Corp. )

= $ 90,000 / ( $ 90,000 + $ 10,000 ) = $ 90,000 / $ 100,000 = 0.90    ;

W_B = ( Investment in Alpha Corp. ) / (Investment in portfolio before purchase of stock + Investment in Alpha Corp. )

= $ 10,000 / ( $ 90,000 + $ 10,000 ) = $ 10,000 / $ 100,000 = 0.10   ;

Applying the values in the formula we have

= ( 1.20 * 0.9 ) + ( 1.20 * 0.1 )

= 1.08 + 0.12 = 1.20

Thus the Beta of the Portfolio after purchase of Alpha stock = 1.20

The solution is Option 2 = 12.15 % ; 1.20