, INV4801 Assignment 2 (COMPLETE ANSWERS) 2025 – DUE 29
August 2025; ;100% trusted ,comprehensive and complete reliable
solution with clear explanation
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)
Answers (using the standard GARCH/ARCH update)
We'll use the usual variance update rule
σt2 = α + γεt2 + βσt−12\sigma_t^2 \;=\; \alpha \;+\; \gamma
\varepsilon_{t}^2 \;+\; \beta \sigma_{t-1}^2σt2=α+γεt2+βσt−12
with the values you gave:
α=0.07, γ=0.000015, β=0.91, σt−12=0.0012,\alpha=0.07,\
\gamma=0.000015,\ \beta=0.91,\ \sigma_{t-
August 2025; ;100% trusted ,comprehensive and complete reliable
solution with clear explanation
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)
Answers (using the standard GARCH/ARCH update)
We'll use the usual variance update rule
σt2 = α + γεt2 + βσt−12\sigma_t^2 \;=\; \alpha \;+\; \gamma
\varepsilon_{t}^2 \;+\; \beta \sigma_{t-1}^2σt2=α+γεt2+βσt−12
with the values you gave:
α=0.07, γ=0.000015, β=0.91, σt−12=0.0012,\alpha=0.07,\
\gamma=0.000015,\ \beta=0.91,\ \sigma_{t-
