Portfolio risk budget

Introduction to Portfolio Analysis in R

Kris Boudt

Professor, Free University Brussels & Amsterdam

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Introduction to Portfolio Analysis in R

Who did it?

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Introduction to Portfolio Analysis in R

Portfolio volatility in risk contribution

$$\displaystyle \text{Portfolio Volatility} = \sum_{i=1}^{N} RC_i$$

where: $RC_i = \dfrac{w_i(\Sigma w)_i}{ \sqrt{w'\Sigma w}}$

  • Risk contribution of asset $i$ depends on
    1. the complete matrix of weights $w$
    2. the full covariance matrix $\Sigma$
Introduction to Portfolio Analysis in R

Percent risk contribution

$$\%RC_i = \frac{RC_i}{\text{Portfolio volatility}}$$

  • where $\displaystyle \sum_{i=1}^{N} \% RC_i = 1$

Relatively less risky assets: $\%RC_i > w_i$

Relatively more risky assets: $\%RC_i < w_i$

Introduction to Portfolio Analysis in R

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Introduction to Portfolio Analysis in R

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