INV4801
ASSIGNMENT 2 2026
DUE: 19 AUGUST 2026
SEMESTER 1 2026
, INV4801 Assessment 2 2026
Due: 19 August
Question 1
a) GARCH (1,1) Case Study
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.
a) GARCH (1,1) Case Study
(i) Calculate the conditional variance for today using the re-parameterized GARCH(1,1) model.
α = -0.08
γ = 0.00010
β = 0.35
Daily standard deviation = 1%
Previous period estimated variance = 0.0144
Comparable company estimated standard deviation = 0.012
Current period return is 7.77% above the expected value
Determine the variance parameters
The GARCH(1,1) model specification is:
σt2 = γ + ασt−1
2
+ βηt2
γ = 0.00010 (the constant term)
α = -0.08 (coefficient on lagged variance)
β = 0.35 (coefficient on the squared innovation)
2
σt−1 = 0.0144 (previous period variance)
ηt = current period return above expectations = 7.77% = 0.0777
ASSIGNMENT 2 2026
DUE: 19 AUGUST 2026
SEMESTER 1 2026
, INV4801 Assessment 2 2026
Due: 19 August
Question 1
a) GARCH (1,1) Case Study
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.
a) GARCH (1,1) Case Study
(i) Calculate the conditional variance for today using the re-parameterized GARCH(1,1) model.
α = -0.08
γ = 0.00010
β = 0.35
Daily standard deviation = 1%
Previous period estimated variance = 0.0144
Comparable company estimated standard deviation = 0.012
Current period return is 7.77% above the expected value
Determine the variance parameters
The GARCH(1,1) model specification is:
σt2 = γ + ασt−1
2
+ βηt2
γ = 0.00010 (the constant term)
α = -0.08 (coefficient on lagged variance)
β = 0.35 (coefficient on the squared innovation)
2
σt−1 = 0.0144 (previous period variance)
ηt = current period return above expectations = 7.77% = 0.0777
