ASSIGNMENT 2 2025
UNIQUE NO. 165590
DUE DATE: 29 AUGUST 2025
, Investments: Portfolio Management
Question (a): Volatility Dynamics in South African Equity Markets
We are given:
ARCH/GARCH model parameters: 𝛼 = 0.07, 𝛾 = 0.000015, 𝛽 = 0.91.
Daily standard deviation = 1% → variance = (0.01)2 = 0.0001.
Previous period variance = 0.0012.
Current return = 4.5% above expected value → 𝜖𝑡 = 0.045.
ARCH/GARCH variance model:
2 2
𝜎𝑡2 = 𝛾 + 𝛼𝜖𝑡−1 + 𝛽𝜎𝑡−1
(i) Compute the conditional variance for today
𝜎𝑡2 = 0.000015 + (0.07 × 0.0452 ) + (0.91 × 0.0012)
= 0.000015 + (0.07 × 0.002025) + 0.001092
= 0.000015 + 0.00014175 + 0.001092
= 0.00124875
Conditional variance = 0.00125 (approx.)
(ii) Compute the conditional standard deviation for today
𝜎𝑡 = ξ 0.00124875 ≈ 0.03534
Conditional standard deviation = 3.53%
(iii) Variance if current return is in line with expectation
If 𝜖𝑡 = 0, then the shock term vanishes:
𝜎𝑡2 = 0.000015 + (0.07 × 0) + (0.91 × 0.0012)
= 0.000015 + 0 + 0.001092 = 0.001107