Page 79 - FINAL CFA SLIDES DECEMBER 2018 DAY 3
P. 79
Session Unit 3:
10. Common Probability Distributions
LOS 10.j: Distinguish between a univariate and a multivariate distribution and explain
the role of correlation in the multivariate normal distribution, p.224
Univariate distributions have a single random variable. In practice, however, the relationships
between two or more (multivariate) random variables are often relevant. E.g. Absa share
price random variable against banking index or say FNB’s?
The Role of Correlation in the Multivariate Normal Distribution, p.224
Correlation distinguishes a multivariate distribution (MD) from a univariate normal distribution.
Formally stated, using asset returns as random variables (Remember 2 asset portfolio covariance?):
• n means of the n series of returns (μ1, μ2, …, μn).
• n variances of the n series of returns ( σ21 , σ22 , …, ) σ2n .
• 0.5n(n – 1) pair-wise correlations.
• E.G for 2 assets, n = 2, then 2 means, 2 variances, and 1 correlation [0.5(2)(2 – 1) = 1].
• If 4 assets, n = 4, then 4 means, 4 variances, and 6 correlations [0.5(4)(4 – 1) = 6].
When building a portfolio of assets, it is generally desirable to combine assets having low returns correlation
because this will result in a portfolio with a lower variance than one composed of assets with higher correlations.
Diversification?
