Classical Portfolio Construction 239
From the parameters the investor has input, we can calculate theco-
variancebetween any two securities as:
COVa, b=Ra, b∗Sa∗Sb (7.01)where: COVa,b=The covariance between the ath security and the
bth one.
Ra, b=The linear correlation coefficient between a and b.
Sa=The standard deviation of the ath security.
Sb=The standard deviation of the bth security.The standard deviations, Saand Sb, are obtained by taking the square root
of the variances in expected returns for securities a and b.
Returning to our example, we can determine the covariance between
Toxico (T) and Incubeast (I) as:
COVT, I=√
−. 15 ∗. (^10) *
√
. 25
=−. 15 ∗. 316227766 ∗. 5
=−. 02371708245
Thus, given a covariance and the comprising standard deviations, we can
calculate the linear correlation coefficient as:
Ra, b=COVa, b/(Sa∗Sb) (7.02)where: COVa, b=The covariance between the ath security and the
bth one.
Ra, b=The linear correlation coefficient between a and b.
Sa=The standard deviation of the ath security.
Sb=The standard deviation of the bth security.Notice that the covariance of a security to itself is the variance, since
the linear correlation coefficient of a security to itself is 1:
COVx, x= 1 ∗Sx∗Sx
= 1 ∗S^2 x
=S^2 x
=Vx(7.03)
where: COVx, x=The covariance of a security to itself.
Sx=The standard deviation of a security.
Vx=The variance of a security.