Question

Your portfolio has 40% of its funds invested in IBM and 60% invested in GM. IBM stock has a standard deviation of 30% and GM stock has a standard deviation of 50%. The correlation between IBM and GM stock returns is 0.7. What is the standard deviation of your portfolio return

Answer 1

Solution:

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 IBM     ;     W1 = Weight of Stock IBM

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

ρ 12 = Correlation coefficient between two stocks i.e., IBM and GM

As per the Information given we have:

σ1    = 30 %    ;    W1   = 40 % = 0.40    ;     σ2 = 50 %   ;       W2 = 60 % = 0.60 ;     ρ 12 = 0.7

Applying the above values in the formula we have:

= [ (( 30 )2 * ( 0.40 )2 ) + (( 50 )2 * (0.60)2 ) + ( 2 * 30 * 0.40 * 50 * 0.60 * 0.7 ) ] (1 / 2 )

= [ ( 900 * 0.16 ) + ( 2500 * 0.36 ) + 504 ) ] (1 / 2 )

= [ 144 + 900 + 504 ] (1 / 2 )

= ( 1548 ) (1 / 2 )

= ( 1548 ) 0.5

= 39.3446 %

= 39.34 % ( when rounded off to two decimal places )

Thus the Standard Deviation of the portfolio is = 39.34 %

Note: The value of ( 1548 ) 0.5   is calculated using the Excel formula =POWER(Number,Power)

=POWER(1548,0.5) = 39.3446