Question

Suppose Johnson​ & Johnson and the Walgreen Company have the expected returns and volatilities shown​ below, with a correlation of 21.8%.

	Upper E left bracket Upper R right bracketE [R]	SD left bracket Upper R right bracketSD [R]
Johnson​ & Johnson	7.2%	15.6%
Walgreen Company	10.3%	19.4%

For a portfolio that is equally invested in Johnson​ & Johnson's and​ Walgreen's stock,​ calculate:

a. The expected return.

b. The volatility​ (standard deviation).

Answer 1

Solution:

a. Calculation of Expected Return of a portfolio:

The formula for calculation of Expected Return of a portfolio is

ER = ( RA * WA )+ ( RB * WB )

Where

E(RP) = Expected return on a portfolio

RA = Return of Johnson & Johnson    ;    WA = Weight of Investment in Johnson & Johnson

RB = Return of Walgreen Company    ;    WB = Weight of Walgreen Company

As per the information given in the question we have

RA = 7.2 %   ; WA = 50 % = 0.50    ;    RB = 10.3 %    ;    WB = 50 % = 0.50

Applying the values in the formula we have

= ( 7.2 % * 0.5 ) + ( 10.3 % * 0.5 )

= 3.60 % + 5.15 % = 8.75 %

Thus the expected return of the Portfolio = 8.75 % ( when rounded off to one decimal place )

b. Calculation of Volatility (Standard Deviation ) of a portfolio:

The formula for calculation of Volatility (Standard Deviation) of a portfolio is

σP = [ ( σA 2 * WA 2 ) + ( σB 2 * WB 2 ) + ( 2 * (σA   * WA * σB   * WB   * ρ AB ) ) ] ( 1 / 2 )

Where

σA = Volatility (Standard Deviation) of Johnson & Johnson    ;     WA = Weight of Johnson & Johnson

σB   = Volatility (Standard Deviation) of Walgreen company    ;     WB = Weight of Walgreen company

ρ AB = correlation between two stocks i.e., Johnson and Johnson and Walgreen company

As per the Information given we have:

σA   = 15.6 % = 0.156   ;    WA   = 50 % = 0.50         ;     σB = 19.4 % =0.194 ;      

WB = 50 % = 0.50 ;     ρ AB = 21.8 % = 0.218

Applying the above values in the formula we have:

= [ (( 0.156 )2 * ( 0.50 )2 ) + (( 0.194 )2 * ( 0.50 )2 ) + ( 2 * 0.156 * 0.50 * 0.194 * 0.50 * 0.218 ) ] (1 / 2 )

= [ 0.006084 + 0.009409 + 0.003299 ] (1 / 2 )

= ( 0.018792 ) (1 / 2 )

= ( 0.018792 ) 0.5

= 0.137083

= 13.7083 %

Thus the Volatility (Standard Deviation) of the portfolio is = 13.71 %

= 13.71 % ( when rounded off to two decimal places )

Note: ( 0.018792) ( 0.5 )   is calculated using the excel formula =POWER(Number,Power)

=POWER( 0.018792,0.5) = 0.137083