Question

The standard deviations of two data series is:

std dev series 1 = 20%

std dev series 2 = 15%

The correlation between these two data series = 0.2

The covariance between the two data series equals

A. 7%

B.60%

C.-7%

D. .6%

E. -.6%

Answer 1

Solution :

The formula for calculating the correlation between the two a set of two data series is

ρ _{1, 2}  = Cov _{1, 2} / ( σ₁ * σ₂ )

where

ρ _{1, 2} = Correlation between data series 1 and data series 2 ;

Cov _{1, 2} = Covariance between Data Series 1 and Data Series 2

σ₁ = Standard Deviation of Data Series 1 ; σ₂ = Standard Deviation of Data Series 2 ;

As per the information given in the question we have

ρ _{1, 2}  = 0.2   ; σ₁ = 20 % = 0.2 ;   σ₂ = 15 % = 0.15 ;

Applying the above values in the formula we have

0.2 = Cov _{1, 2} / ( 0.2 * 0.15 )

0.2 = Cov _{1, 2} / 0.03

0.2 * 0.03 = Cov _{1, 2}

Cov _{1, 2} = 0.2 * 0.03

Cov _{1, 2} = 0.006

Cov _{1, 2} = 0.6 % = .6%

The covariance between Data Series 1 and Data Series 2 equals .6 %

Thus the solution is option D. .6%