Assignment 1: Average Covariance, Correlation, Standard Devi ✓ Solved

Assignment 1average Covariance Correlation Standard Deviation

Analyze and compute statistical measures related to asset returns, such as covariance, correlation, and standard deviation, using provided financial data. Calculate excess returns, covariances, and correlations between assets. Develop feasible portfolios combining specified assets, identify portfolios with minimum variance and maximum utility, and determine optimal asset allocations. Use Excel functions and Solver to optimize portfolios according to the Markowitz model, considering constraints like positive weights and target returns. Plot Capital Allocation Lines (CAL) and identify optimal portfolios on the efficient frontier based on specified risk and return parameters.

Sample Paper For Above instruction

The analysis of asset return data through covariance, correlation, and standard deviation measures provides critical insights into portfolio risk management. In this study, we evaluate these financial metrics systematically using the data available for the ETFs IVV and IYR, along with other global assets, to demonstrate the process of optimal asset allocation and portfolio optimization. The objective is to derive an efficient frontier, identify the minimum variance portfolio, and construct the tangency portfolio that maximizes the Sharpe ratio, ultimately enabling investors to make informed decisions based on risk-return trade-offs.

The initial step involves calculating excess returns for the assets, which is achieved by subtracting the risk-free rate from the observed asset returns. Excess returns provide a more accurate measure of the assets’ performance relative to the risk-free investment, enabling comparability across assets with different risk profiles. Using Excel functions such as AVERAGE and STDEV.P, the mean and standard deviation of excess returns are computed for both IVV and IYR. These statistical measures serve as inputs for further portfolio analysis.

Next, covariance and correlation between IVV and IYR are evaluated. Covariance measures how two assets move together, while correlation standardizes this measure to a value between -1 and 1, indicating the strength and direction of their relationship. Using Excel functions COVARIANCE.P and CORREL, these are obtained, facilitating the understanding of diversification benefits when combining assets in a portfolio.

Subsequently, a set of feasible portfolios is generated by varying asset weights in specified intervals. Expected returns and standard deviations are calculated for each portfolio, enabling the plotting of the risk-return space. The utility of each portfolio, defined by a mean-variance utility function considering the investor’s risk aversion, is also computed. Portfolios are then ranked based on their utility, with the minimum variance portfolio highlighted in yellow and the highest utility portfolio highlighted in orange, aiding investors in selecting portfolios aligned with their risk appetite.

Further optimization involves calculating the weights of the tangency portfolio, which maximizes the Sharpe ratio, i.e., the excess return per unit of risk. Excel formulas and Solver are employed to determine the optimal asset weights that maximize this ratio under investment constraints. The expected return and standard deviation of this portfolio are then derived, forming the basis of the Capital Allocation Line (CAL). The CAL depicts the risk-return trade-off achievable by combining the risk-free asset with the tangency portfolio, guiding investors in constructing portfolios that align with their return objectives and risk tolerances.

Finally, solving the Markowitz mean-variance optimization problem requires applying Excel’s Solver tool to identify the portfolio with a specified target return, subject to constraints such as non-negative weights. This procedure is performed twice: once allowing short sales and once restricting the portfolio to long positions only. The solutions then inform the formulation of efficient portfolios, enabling investors to select the optimal combination of assets that satisfy their risk and return preferences.

References

  • Brealey, R. A., Myers, S. C., & Allen, F. (2020). Principles of Corporate Finance (13th ed.). McGraw-Hill Education.
  • Lhabitant, F.-S. (2004). Hedge Funds: Myths and Limitations. Financial Analysts Journal, 60(6), 80-89.)
  • Sharpe, W. F. (1964). Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. The Journal of Finance, 19(3), 425-442.)
  • Markowitz, H. (1952). Portfolio Selection. The Journal of Finance, 7(1), 77-91.)
  • Graham, J., & Harvey, C. (2001). The Theory and Practice of Corporate Finance: Evidence from the Field. Journal of Financial Economics, 60(2–3), 187–243.)
  • Ross, S. A. (1976). The Arbitrage Theory of Capital Asset Pricing. Journal of Economic Theory, 13(3), 341–360.)
  • Fabozzi, F. J., Gupta, F., & Markowitz, H. M. (2002). The Legacy of Modern Portfolio Theory. The Journal of Investing, 11(3), 7-22.)

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