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) b) Multi manager strategy - University of Muchapatema 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 multimanager 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. (6) c) Investec Investment Management - Market forecasting Chipo Gumbo is a market forecaster with Investec Investment Management. Gumbo is asked to review the current economic conditions and market outlook for South Africa (RSA) and to set longterm market return expectations for domestic equities. These expectations will form the basis of Investec’s future client asset allocations. Gumbo gathers RSA capital market data displayed below. Historical Data Equity compounded annual growth rate: 11.0% Equity risk premium: 4.3% Dividend yield: 7.0% Equity repurchase yield: -1.5% Real earnings growth rate: 4.5% Current and Forward-Looking Data Current equity price-to-earnings ratio: 12.2 Expected equities real earnings growth rate: 6.5% Expected long-term inflation rate: 3.1% This study source was downloaded by from CourseH on :19:30 GMT -05:00 INV4801/101 3 a) Use the Grinold-Kroner model to determine the following component sources of the historical nominal return for South African equities: (i) Income return (3) (ii) Earnings growth (3) (iii) Repricing return (4) d) Eagle Advisors case study Joseph Mhofu is a fixed income portfolio manager for Eagle Advisors. Mhofu is reviewing the portfolios of several pension clients that have been assigned to him to manage. Two of these portfolios are Woodlands Groove and LETS pension plan has the following characteristics: Woodlands Woodlands Groove LETS LETS Groove Spread Sector Allocation Allocation Duration Duration Singapore treasury 14.6% 10.1% 7.54 0.00 Singapore agencies 23.7% 14.5% 9.02 7.20 Singapore Corporates 13.8% 20.9% 4.52 5.80 Singapore mortgages 11.4% 33.7% 1.33 3.00 Singapore ABS 18.0% 8.20% 2.00 3.67 Non-Singapore governments 18.5% 12.6% 3.22 2.50 Bond index benchmark for LETS pension plan portfolio has an effective duration of 3.33. (i) Calculate the duration of LETS pension plan portfolio and asses the interest rate risk of the portfolio versus the benchmark. (2) (ii) Calculate the spread duration of Woodlands Groove bond portfolio and evaluate the credit risk of the portfolio versus the Singapore mortgages. (2) Tawananyasha Shava and Sharai Chitova are consultants to Eagle Advisors. Eagle manages funds for wealthy individuals and small institutions. Shava and Chitova have been asked by Eagle to develop a plan to evaluate investment manager performance and to create customized benchmarks, when necessary. As part of her service to Eagle Advisors, Shava creates a returns-based benchmark using monthly portfolio returns and the returns for large-cap value, large-cap growth, small-cap value, and smallcap growth indices over the past year. An algorithm is then used to determine the manager’s exposures to various styles. Shava uses this information to evaluate managers. She believes that this will help Eagle identify underperforming and outperforming managers. Regarding the identification of underperforming managers, the null hypothesis is that the manager adds no value. Shava states that Eagle should avoid a type I error, which, Shava continues, is failing to reject the null when it is false. Chitova adds that another danger for Eagle would be a This study source was downloaded by from CourseH on :19:30 GMT -05:00 4 type II error, where Eagle would reject the null hypothesis when it is true. In both cases, Shava and Chitova agree that the decisions reached would be faulty. Discussing returns-based style analysis further, Shava insists the model is purely statistical in nature, and one advantage to using this type of benchmark is that it is useful where the only information available is account returns. Chitova answers that a disadvantage to using this type of benchmark is that it is generally difficult to understand and not very intuitive. As part of Shava’s and Chitova’s task, Eagle asks them to perform micro performance attribution on one of its managers, Watson Munyanyi. Munyanyi invests primarily in large-cap value stocks. Munyanyi’s performance relative to the appropriate benchmark is shown in Exhibit 5. Exhibit 5 Portfolio Benchmark Portfolio Benchmark Sector Sector Sector Sector Weight Weight Return Return Agricultural 4.00% 6.00% –2.00% –1.00% Capital goods 8.00% 9.00% –4.00% –5.00% Consumer durables 32.00% 35.00% 2.00% 3.00% Energy 6.00% 6.00% 8.00% 2.00% Financial 20.00% 18.00% 6.40% 4.00% Technology 16.00% 16.00% 2.60% –2.00% Utilities 12.00% 10.00% 4.00% –2.00% Cash 2.00% 0.00% 0.20% Total 100.00% 100.00% Portfolio Plus cash return 2.90% 0.86% (iii) Justify why Shava’s use of the proposed benchmark is not appropriate. (3) (iv) From the data in exhibit 1.2, determine whether Munyanyi demonstrated an ability to wisely allocate funds within the durables and/or technology sectors? Show your calculations. (6) (v) Does Munyanyi demonstrate an ability to select stocks in the capital goods and/or financial sectors consumer? Show your calculations. (6) (vi) Does Munyanyi demonstrate an ability to generate a positive return from allocation/selection interaction effects in the agricultural and/or utilities sectors? Show your calculations. (6)