INV4801
ASSIGNMENT 2 2025
UNIQUE NO. 165590
DUE DATE: 29 AUGUST 2025
, a) Volatility Dynamics in South African Equity Markets
A portfolio manager at a Johannesburg-based investment firm is tasked with managing a fund
heavily exposed to the South African Top 40 Index. Following a period of heightened market
uncertainty due to geopolitical tensions and fluctuating commodity prices, the firm decides to
model daily equity return volatility more accurately using a Time-Varying Volatility-ARCH Models.
The portfolio manager gathered the following daily information: α = 0.07, γ = 0.000015, and β =
0.91. Given these parameters, the daily standard deviation is 1%. Suppose the previous period
estimated variance was 0.0012 and the current period return is 4.5% above the expected value.
(i) Compute the conditional variance for today. (5)
(ii) Compute the conditional standard deviation for today. (2)
(iii) What will happen to the variance if the current return is in line with expectation? (2)
b) Multi manager strategy - University of Muchapatema
Tawana, was recently hired by the University of Muchapatema which has a USD 50 million global
diversified portfolio. In a meeting with the University’s CIO, the CIO asks Abigail which multi-
manager strategy, Fund-of-Fund and Multi-strategy Fund, provides better liquidity and more
normally distributed returns. To address the CIO's concern regarding the return distribution,
Tawana evaluates two optimization approaches to overall portfolio construction:
• mean-variance optimization using a maximum asset class weight constraint (constrained
MVO)
• mean-conditional VaR optimization (mean-CVaR).
(i) Which optimization approach would better address the CIO's concern? Justify your
response with three reasons. (6)
c) Investec Investment Management - Market forecasting
Chipo Gumbo is a market forecaster with Investec Investment Management. Gumbo is asked to
review the current economic conditions and market outlook for South Africa (RSA) and to set long-
term market return expectations for domestic equities. These expectations will form the basis of
Investec’s future client asset allocations. Gumbo gathers RSA capital market data displayed
below.
Historical Data
Equity compounded annual growth rate: 11.0%
Equity risk premium: 4.3%
Dividend yield: 7.0%
Equity repurchase yield: -1.5%
Real earnings growth rate: 4.5%
Current and Forward-Looking Data
Current equity price-to-earnings ratio: 12.2
Expected equities real earnings growth rate: 6.5%
Expected long-term inflation rate: 3.1%
2
ASSIGNMENT 2 2025
UNIQUE NO. 165590
DUE DATE: 29 AUGUST 2025
, a) Volatility Dynamics in South African Equity Markets
A portfolio manager at a Johannesburg-based investment firm is tasked with managing a fund
heavily exposed to the South African Top 40 Index. Following a period of heightened market
uncertainty due to geopolitical tensions and fluctuating commodity prices, the firm decides to
model daily equity return volatility more accurately using a Time-Varying Volatility-ARCH Models.
The portfolio manager gathered the following daily information: α = 0.07, γ = 0.000015, and β =
0.91. Given these parameters, the daily standard deviation is 1%. Suppose the previous period
estimated variance was 0.0012 and the current period return is 4.5% above the expected value.
(i) Compute the conditional variance for today. (5)
(ii) Compute the conditional standard deviation for today. (2)
(iii) What will happen to the variance if the current return is in line with expectation? (2)
b) Multi manager strategy - University of Muchapatema
Tawana, was recently hired by the University of Muchapatema which has a USD 50 million global
diversified portfolio. In a meeting with the University’s CIO, the CIO asks Abigail which multi-
manager strategy, Fund-of-Fund and Multi-strategy Fund, provides better liquidity and more
normally distributed returns. To address the CIO's concern regarding the return distribution,
Tawana evaluates two optimization approaches to overall portfolio construction:
• mean-variance optimization using a maximum asset class weight constraint (constrained
MVO)
• mean-conditional VaR optimization (mean-CVaR).
(i) Which optimization approach would better address the CIO's concern? Justify your
response with three reasons. (6)
c) Investec Investment Management - Market forecasting
Chipo Gumbo is a market forecaster with Investec Investment Management. Gumbo is asked to
review the current economic conditions and market outlook for South Africa (RSA) and to set long-
term market return expectations for domestic equities. These expectations will form the basis of
Investec’s future client asset allocations. Gumbo gathers RSA capital market data displayed
below.
Historical Data
Equity compounded annual growth rate: 11.0%
Equity risk premium: 4.3%
Dividend yield: 7.0%
Equity repurchase yield: -1.5%
Real earnings growth rate: 4.5%
Current and Forward-Looking Data
Current equity price-to-earnings ratio: 12.2
Expected equities real earnings growth rate: 6.5%
Expected long-term inflation rate: 3.1%
2
