INV4801 Assignment 2 (COMPLETE ANSWERS) 2025 (165590) - DUE 29 August 2025

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INV4801
Assignment 2
(COMPLETE
ANSWERS) 2025
(165590) - DUE 29
August 2025
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,INV4801 Assignment 2 (COMPLETE
ANSWERS) 2025 (165590) - DUE 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)
Thought for 19s
Here we’ll use a GARCH(1,1)-type structure:

𝜎𝑡2

𝛾+𝛼 𝜀𝑡−12+𝛽 𝜎𝑡−12σt2
=γ+αε t−1 2
+βσ t−1 2

, with 𝛼

0.07 , 𝛾

0.000015 , 𝛽

0.91 α=0.07, γ=0.000015, β=0.91, previous variance 𝜎 𝑡 − 1 2

0.0012 σ t−1 2

=0.0012, and shock 𝜀 𝑡 − 1
0.045 ε t−1
=0.045 (i.e., 4.5%).
(i) Conditional variance today 𝛼 𝜀 𝑡 − 1 2

= 0.07 × ( 0.045 ) 2

0.07 × 0.002025
0.00014175
𝛽 𝜎𝑡−12

= 0.91 × 0.0012
0.001092
𝜎𝑡2
=𝛾+𝛼𝜀𝑡−12+𝛽𝜎𝑡−12

= 0.000015 + 0.00014175 + 0.001092
0.00124875 αε t−1 2
βσ t−1 2
σt2