Composites: Inclusion and Exclusion of ...
The GIPS standards for constructing composites mandate the timely and consistent inclusion of... Read More
Risk budgeting involves distributing the total portfolio risk efficiently among its components. It's a crucial element of a robust risk management process, which consists of these four steps:
Absolute risk in a portfolio arises from its variance, which is only relative to the portfolio itself, not compared to a benchmark. To calculate the contribution of a specific asset (i) to the portfolio's variance, we use this equation:
$$ Cv_i = \sum(W_iW_jC_{ij}) = w_iC_{ip} $$
Where:
This formula is multiplicative, meaning that each variable's increase leads to a higher contribution to portfolio variance. So, if an asset has a higher weight in the portfolio or tends to move closely with the portfolio, it contributes more to the portfolio's variance.
The contribution of asset i to portfolio active variance can be determined using the following equation:
$$ CAV_i = (W_{pi} -W_{bi}) rC_{ip} $$
Where:
The sum of individual CAVs provides the portfoli's active return variance.
When customizing portfolios for clients, financial professionals should consider the following factors to align risk with individual needs:
For those curious about the mathematical aspect of the last point, this formula illustrates the connection between geometric and arithmetic returns. When leverage is increased, both \(R_a\) and \(\sigma\) go up. However, the negative relationship between standard deviation and the exponent means that continually escalating leverage will eventually outweigh the augmented returns.
$$ R_g = R_a – \left(\frac {\sigma^2}{2} \right) $$
Where:
\(R_g\) = Geometric compound returns. \(R_a\) = Arithmetic return. \(\sigma^2\) = Portfolio standard deviation.
Question
Based on the table below, what is asset b's relative contribution to portfolio variance?
$$ \begin{array}{c|c}
\textbf{Asset} & {\textbf{Absolute Contribution} \\ \textbf{to Portfolio Variance}} \\ \hline
A & 0.0434 \\ \hline
B & 0.0019 \\ \hline
C & 0.0355
\end{array} $$
- 0.0808.
- 0.0019.
- 0.0235.
Solution
The correct answer is C.
Step 1: Calculate the overall portfolio variance by summing the absolute contributions:
$$ 0.0434 + 0.0019 + 0.0355 = 0.0808 $$
Step 2: Calculate the relative contribution from asset B:
$$ \frac {0.0019}{0.0808} = 0.0235 $$
The relative contribution from asset B is relatively low because its absolute contribution to portfolio variance is low.
A and B are incorrect. From the calculation the correct value is 0.0235
Reading 26: Active Equity Investing: Portfolio Construction
Los 26 (d) Discuss the application of risk budgeting concepts in portfolio construction