Optimal Portfolio: Mean-Variance OptimizationIf you are a portfolio manager who predicted that the tension in Ukraine might spiral into a global economic problem back in December 2021. She decided to construct a portfolio that, she think, would outperform in a war scenario, or in a heightened war risk scenario. Please use the following ETFs:IAU: iShares Gold Trust ETFVDE: Vanguard Energy ETFXLB: Materials Sector SPDR ETFDBC: Invesco DB Commodity Index Tracking FundCQQQ: China Technology Index ETFConstraints:i. Use all ETF products. (Weight of each ETF>= 2% )ii. No ETF is to have more than 40% weight in portfolioObjective: Maximize Expected Return, Minimize volatility, ie. MaximizeSharpe RatioStep 1: Collect historical price/return data for the ETFs over Jan-2018 to Dec-21 period.Step 2: Assume the Average Historical Return is the Expected Return for each asset (strong assumption) and Historical Volatility is the Expected Volatility (strong assumption).Step 3: Present the var-cov matrix of returns based historical data. Which assets are the least correlated? Which asset has the highest volatility?Step 4: Run an optimizer function to find the optimal weights to satisfy the conditions given above. Show the optimal weights with a pie chart.Step 5: How did the optimal portfolio perform relative to S&P 500 and TSX 60 since Jan-2022? Compare the returns as of Oct-2024.

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter5: Business And Economic Forecasting

Section: Chapter Questions

Problem 2E

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Optimal Portfolio: Mean-Variance Optimization
If you are a portfolio manager who predicted that the tension in Ukraine might spiral into a global economic problem back in December 2021. She decided to construct a portfolio that, she think, would outperform in a war scenario, or in a heightened war risk scenario. Please use the following ETFs:
IAU: iShares Gold Trust ETF
VDE: Vanguard Energy ETF
XLB: Materials Sector SPDR ETF
DBC: Invesco DB Commodity Index Tracking Fund
CQQQ: China Technology Index ETF
Constraints:
i. Use all ETF products. (Weight of each ETF>= 2% )
ii. No ETF is to have more than 40% weight in portfolio
Objective: Maximize Expected Return, Minimize volatility, ie. Maximize
Sharpe Ratio
Step 1: Collect historical price/return data for the ETFs over Jan-2018 to Dec-21 period.
Step 2: Assume the Average Historical Return is the Expected Return for each asset (strong assumption) and Historical Volatility is the Expected Volatility (strong assumption).
Step 3: Present the var-cov matrix of returns based historical data. Which assets are the least correlated? Which asset has the highest volatility?
Step 4: Run an optimizer function to find the optimal weights to satisfy the conditions given above. Show the optimal weights with a pie chart.
Step 5: How did the optimal portfolio perform relative to S&P 500 and TSX 60 since Jan-2022? Compare the returns as of Oct-2024.