Page 47 - FINAL CFA I SLIDES JUNE 2019 DAY 3
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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?
