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INV4801 Assignment 2 2025 (165590) - Due 29 August 2025 | ANSWERS

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Investments: Portfolio Management - INV4801 Assignment 2 2025 (Unique Number: 65590) - Due 29 August 2025; 100 % TRUSTED workings, Expert Solved, Explanations and Solutions. For assistance call or W.h.a.t.s.a.p.p us on ...(.+.2.5.4.7.7.9.5.4.0.1.3.2)........... 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. (ii) Compute the conditional standard deviation for today. (iii) What will happen to the variance if the current return is in line with expectation? b) Multi manager strategy - University of Muchapatema (5) (2) (2) 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. c) Investec Investment Management - Market forecasting (6)

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INV4801
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

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