INV4801 Assignment 2
(COMPLETE ANSWERS)
2025 (165590) - DUE 29
August 2025
For assistance contact
Email:
, a) Volatility Dynamics in South African Equity Markets
(i) Compute the conditional variance for today. Using the provided parameters and the
GARCH-like model formula, the conditional variance for today is calculated as follows:
σ_t2=alpha+gamma(textunexpectedreturn)2+betasigma_t−12
σ_t2=0.07+0.000015(0.045)2+0.91(0.0012) σ_t2=0.07+0.000000030375+0.001092
σ_t2=0.07109203 The conditional variance for today is 0.07109203.
(ii) Compute the conditional standard deviation for today. The conditional standard
deviation is the square root of the conditional variance. σ_t=sqrt0.07109203=0.2666 The
conditional standard deviation for today is 26.66%.
(iii) What will happen to the variance if the current return is in line with expectation? If
the current return is in line with the expectation, the unexpected return (the error term) is
zero. In this case, the second term in the conditional variance formula, which includes the
unexpected return, will become zero. σ_t2=alpha+betasigma_t−12
σ_t2=0.07+0.91(0.0012)=0.07+0.001092=0.071092 The variance would decrease from
0.07109203 to 0.07109200, as the volatility shock from the unexpected return no longer
contributes to the conditional variance.
b) Multi-manager strategy - University of Muchapatema
(i) Which optimization approach would better address the CIO's concern? Justify your
response with three reasons. The Mean-Conditional VaR (Mean-CVaR) optimization
approach would better address the CIO's concern regarding the return distribution. This is
because, unlike mean-variance optimization, Mean-CVaR does not assume that returns are
normally distributed and provides a more robust measure of risk.
Three reasons to justify this choice are:
1. Handles Non-Normal Returns: Mean-CVaR directly addresses the CIO's concern
about the non-normal distribution of returns. It is a more suitable model for portfolios
with skewed and fat-tailed returns, as it focuses on the tail risk, whereas Mean-
Variance Optimization (MVO) relies on the variance, which is an inadequate
measure of risk for non-normal distributions.
2. Focus on Extreme Losses: CVaR measures the expected loss beyond a certain
threshold (e.g., the worst 5% of outcomes), making it a more comprehensive and
intuitive measure of tail risk compared to MVO, which uses standard deviation and
may not fully capture the risk of large losses in the tails of the distribution.
3. Coherent Risk Measure: CVaR is a coherent risk measure, meaning it satisfies
properties like subadditivity. This ensures that the risk of a portfolio is no more than
the sum of the risks of its individual components, which encourages diversification
and aligns better with the objectives of a diversified global portfolio.
(COMPLETE ANSWERS)
2025 (165590) - DUE 29
August 2025
For assistance contact
Email:
, a) Volatility Dynamics in South African Equity Markets
(i) Compute the conditional variance for today. Using the provided parameters and the
GARCH-like model formula, the conditional variance for today is calculated as follows:
σ_t2=alpha+gamma(textunexpectedreturn)2+betasigma_t−12
σ_t2=0.07+0.000015(0.045)2+0.91(0.0012) σ_t2=0.07+0.000000030375+0.001092
σ_t2=0.07109203 The conditional variance for today is 0.07109203.
(ii) Compute the conditional standard deviation for today. The conditional standard
deviation is the square root of the conditional variance. σ_t=sqrt0.07109203=0.2666 The
conditional standard deviation for today is 26.66%.
(iii) What will happen to the variance if the current return is in line with expectation? If
the current return is in line with the expectation, the unexpected return (the error term) is
zero. In this case, the second term in the conditional variance formula, which includes the
unexpected return, will become zero. σ_t2=alpha+betasigma_t−12
σ_t2=0.07+0.91(0.0012)=0.07+0.001092=0.071092 The variance would decrease from
0.07109203 to 0.07109200, as the volatility shock from the unexpected return no longer
contributes to the conditional variance.
b) Multi-manager strategy - University of Muchapatema
(i) Which optimization approach would better address the CIO's concern? Justify your
response with three reasons. The Mean-Conditional VaR (Mean-CVaR) optimization
approach would better address the CIO's concern regarding the return distribution. This is
because, unlike mean-variance optimization, Mean-CVaR does not assume that returns are
normally distributed and provides a more robust measure of risk.
Three reasons to justify this choice are:
1. Handles Non-Normal Returns: Mean-CVaR directly addresses the CIO's concern
about the non-normal distribution of returns. It is a more suitable model for portfolios
with skewed and fat-tailed returns, as it focuses on the tail risk, whereas Mean-
Variance Optimization (MVO) relies on the variance, which is an inadequate
measure of risk for non-normal distributions.
2. Focus on Extreme Losses: CVaR measures the expected loss beyond a certain
threshold (e.g., the worst 5% of outcomes), making it a more comprehensive and
intuitive measure of tail risk compared to MVO, which uses standard deviation and
may not fully capture the risk of large losses in the tails of the distribution.
3. Coherent Risk Measure: CVaR is a coherent risk measure, meaning it satisfies
properties like subadditivity. This ensures that the risk of a portfolio is no more than
the sum of the risks of its individual components, which encourages diversification
and aligns better with the objectives of a diversified global portfolio.
