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CASE: PERFORMANCE LAWN EQUIPMENT The CFO at Performance Lawn Equipment, Brian Ferguson, wishes to design a minimum variance portfolio of index funds to invest some of the firm's cash reserves. The funds selected for consideration and their variance- covariance matrix and average returns are given in the table below. Bond: between 10% and 50% S&P 500: between 30% and 50% Small cap: no more than 20% Mid cap: no more than 20% Large cap: no more than 25% Emerging market: no more than 10% Commodity: no more than 20% 2. The firm would like to achieve a target return of 0.19%. What mix of investments would achieve this? To obtain better diversification, the CFO would like to restrict the percentage of investments in each fund as follows: How would the optimal portfolio and objective change? Summarize your findings in a short memo to Mr. Ferguson Bond S&P 500 Small Cap Mid Cap Emerging Large Cap Market Commodity Bond S&P 500 0.002% -0.001% -0.001% -0.001% -0.001% 0.000% 0.020% 0.027% 0.024% 0.019% 0.032% 0.047% 0.039% 0.027% 0.050% 0.033% 0.023% 0.043% 0.027% 0.041 % 0.085% Small cap Mid cap Large cap Emerging market Commodity Average weekly return 0.005% 0.000% 0.044% 0.000% 0.118% 0.005% 0.256% 0.009% 0.242% 0.015% 0.447% 0.054% 0.053% 0.226% CASE: PERFORMANCE LAWN EQUIPMENT The CFO at Performance Lawn Equipment, Brian Ferguson, wishes to design a minimum variance portfolio of index funds to invest some of the firm's cash reserves. The funds selected for consideration and their variance- covariance matrix and average returns are given in the table below. Bond: between 10% and 50% S&P 500: between 30% and 50% Small cap: no more than 20% Mid cap: no more than 20% Large cap: no more than 25% Emerging market: no more than 10% Commodity: no more than 20% 2. The firm would like to achieve a target return of 0.19%. What mix of investments would achieve this? To obtain better diversification, the CFO would like to restrict the percentage of investments in each fund as follows: How would the optimal portfolio and objective change? Summarize your findings in a short memo to Mr. Ferguson Bond S&P 500 Small Cap Mid Cap Emerging Large Cap Market Commodity Bond S&P 500 0.002% -0.001% -0.001% -0.001% -0.001% 0.000% 0.020% 0.027% 0.024% 0.019% 0.032% 0.047% 0.039% 0.027% 0.050% 0.033% 0.023% 0.043% 0.027% 0.041 % 0.085% Small cap Mid cap Large cap Emerging market Commodity Average weekly return 0.005% 0.000% 0.044% 0.000% 0.118% 0.005% 0.256% 0.009% 0.242% 0.015% 0.447% 0.054% 0.053% 0.226%