Question

You are given the following information

                                    Stock 1            Stock 2              

Expected Return         30%                 15%

Standard Deviation     20%                 12%

Assume that the correlation coefficient between stock 1 and stock 2 returns is 10%. Compute the portfolio expected return and standard deviation if you invest 10% of your wealth in stock 1.

Answer 1

Solution:

Calculation of Portfolio Expected Return :

The formula for calculation of Portfolio Expected Return is

E(RP) = ( R1 * W1 )+ ( R2 * W2 )

Where

E(RP) = Portfolio Expected return

R1 = Expected Return of Stock 1 ;   W1 = Weight of Stock 1 ;

R2 = Expected Return of Stock 2 ;   W2 = Weight of Stock 2 ;

As per the information given in the question we have

R1 = 30 %   ; W1 = 10 % = 0.10    ;    R2 = 15 %   ;    W2 = ( 100 % - 10 % ) = 90 % = 0.90 ;

Applying the values in the formula we have

= ( 30 % * 0.10 ) + ( 15 % * 0.90 )

= 3 % + 13.50 % = 16.50 %

Thus the Portfolio expected return = 16.50 %

Calculation of Standard Deviation of a portfolio :

The formula for calculation of Standard Deviation of a portfolio is

σP = [ ( σ1 2 * W1 2  ) + ( σ2 2 * W2 2 ) + ( 2 * (σ1   * W1 * σ2   * W2   * ρ 12 ) ) ] ( 1 / 2 )

Where

σ1 = Standard Deviation of Stock 1     ;     W1 = Weight of Stock 1

σ2 = Standard Deviation of Stock 2    ;     W2 = Weight of Stock 2

ρ 12 = Correlation coefficient between two stocks i.e., Stock 1 and Stock 2

As per the Information given we have:

σ1    = 20 % = 0.20    ;    W1   = 10 % = 0.10    ;     σ2 = 12 % = 0.12 ;       W2 = 90 % = 0.90 ;     ρ 12 = 10 % = 0.10 ;

Applying the above values in the formula we have:

= [ (( 0.20 )2 * ( 0.10 )2 ) + (( 0.12 )2 * (0.90)2 ) + ( 2 * 0.20 * 0.10 * 0.12 * 0.90 * 0.1 ) ] (1 / 2 )

= [ ( 0.04 * 0.01 ) + ( 0.0144 * 0.81 ) + 0.000432 ) ] (1 / 2 )

= [ 0.0004 + 0.0117 + 0.000432 ] (1 / 2 )

= ( 0.012496 ) (1 / 2 )

= ( 0.012496 ) 0.5

= 0.111786

= 11.1786 %

= 11.18 % ( When rounded off to two decimal places )

Thus the Standard Deviation of the portfolio is = 11.18 %

Note : The value of ( 0.012496) 0.5   has been calculated using the excel function =POWER(Number,Power). Thus =POWER(1.012496,0.5) = 0.111786