Q&A: List 3 things that define the normal distribution for the return of a portfolio of 10 securities.

CppQuant Answer

10 means, 10 variances and 10*(10-1)/2=45 correlations of the component securities.

Bonus Points

  • The need to specify correlations is a distinguishing feature of the multivariate normal distribution in contrast to the univariate normal distribution.
    • A multivariate normal distribution is completely specified if one has the lists for the mean returns, variances, and correlations or covariances between the variables.
  • Portfolio return is a normally distributed if the individual security returns are (joint) normally distributed
    • Portfolio return is a weighted average (ie. a linear combination)of the returns on the component securities
  • When we have a group of assets, we can model the distribution of returns on each asset individually, or the distribution of returns on the assets as a group.

Category: Quantitative Analysis > Probability > Distribution

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