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This assignment guide explains how to download stock price data from Yahoo Finance, construct an optimal complete portfolio using two risky assets and a risk-free asset, and analyze their systematic risks. The steps include selecting stocks from the Australian Stock Exchange (ASX), downloading historical monthly prices for specific periods, calculating returns, variances, covariances, and then determining optimal asset weights. Additionally, it involves assessing the systematic risk (beta) of each stock during different periods—namely during the Global Financial Crisis (GFC) and the post-GFC era—using market index data from ASX. The analysis aims to understand how stock risk profiles and market sensitivities change across varying market conditions.

Paper For Above instruction

The process of constructing an optimal complete portfolio, which combines risky assets with a risk-free asset, is a fundamental task in modern portfolio theory (MPT). This approach enables investors to maximize expected utility based on their risk preferences, represented through risk aversion coefficients. The initial step involves selecting two stocks from the Australian Stock Exchange (ASX), downloading their historical price data, and then calculating their return series. The data should span from July 2008 to December 2016, with a focus on monthly observations to simplify analysis and avoid complications arising from non-trading days and holidays.

Once the stock prices are obtained, the next step is to convert the price data into return series using the formula:

rt = (Pt - Pt-1) / Pt-1

Here, Pt and Pt-1 refer to stock prices at times t and t-1, respectively. This calculation provides the monthly returns necessary for further statistical analysis. It is crucial to ensure the data are ordered chronologically from oldest to newest to maintain accurate calculations. Variance, covariance, and standard deviation of returns are computed to understand the risk and correlation between the stocks.

Using the mean return and risk measures, the optimal weights of the two risky assets are calculated based on Markowitz's portfolio optimization models. The formula for determining these weights incorporates expected returns, variances, covariances, and the investor's risk aversion coefficient. For this assignment, the subjective risk aversion coefficient A is chosen as either 3, 4, or 5, reflecting low, moderate, or high risk tolerance, respectively. The objective is to maximize the utility function, which balances expected return against risk, for different levels of risk aversion.

In addition to the portfolio construction, the assignment requires analyzing portfolio risk across different market periods. The GFC period (July 2008 - December 2011) and the post-GFC period (January 2012 - December 2016) are segmented to observe how the risk profile and asset correlations shift under varying macroeconomic conditions. This is achieved by recalculating the portfolio weights and risk measures for each sub-period, providing insights into how market crises influence asset performance and investor strategies.

The second crucial aspect of the analysis involves calculating the systematic risk or beta of each stock. Beta measures the sensitivity of a stock's returns relative to the overall market, represented here by the ASX All Ordinary index (^AORD). To compute beta, the covariance between a stock's returns and the market returns is divided by the variance of the market index returns. Consistent with the previous steps, this calculation is conducted separately for the GFC and post-GFC periods to compare how market risk exposure varies over time. A higher beta during the GFC might indicate greater market sensitivity and risk, whereas a lower beta in the post-GFC period could suggest increased resilience or diversification benefits.

The calculation framework involves downloading the market index data, converting prices into returns, and then statistically analyzing these returns. The covariance and variance calculations are performed using Excel or similar tools, following the formulas:

β = Cov(rstock, rmarket) / Var(rmarket)

where Cov represents the covariance, and Var indicates the variance. Interpreting the beta estimates allows investors to assess the systemic exposure of stocks and tailor their portfolios accordingly, especially in times of economic turmoil or stability. Comparing beta across different periods provides a dynamic view of risk that informs both strategic asset allocation and risk management practices.

Overall, this process emphasizes data acquisition from Yahoo Finance, statistical calculation of returns and risk measures, and strategic portfolio optimization grounded in theoretical principles. The insights gained from analyzing the shifts in systematic risk and portfolio risk profiles help investors better understand market behavior and make informed investment decisions aligned with their risk preferences.

References

  • Markowitz, H. (1952). Portfolio Selection. The Journal of Finance, 7(1), 77–91.
  • Sharpe, W. F. (1964). Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk. The Journal of Finance, 19(3), 425–442.
  • Lynch, A. W. (2020). Practical Portfolio Optimization and Risk Management. Journal of Investment Management, 18(2), 1-25.
  • Elton, E. J., & Gruber, M. J. (1995). Modern Portfolio Theory and Investment Analysis. Wiley.
  • Ross, S. A. (1976). The Arbitrage Theory of Capital Asset Pricing. Journal of Economic Theory, 13(3), 341–360.
  • Australian Securities Exchange. (2023). ASX Listing Rules and Market Data. Retrieved from https://www.asx.com.au
  • Reserve Bank of Australia. (2023). Monthly Interest Rates. Retrieved from https://www.rba.gov.au/statistics/tables/interest-rates.html
  • Yahoo Finance. (2023). Stock Data and Historical Prices. Retrieved from https://finance.yahoo.com
  • Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1), 3-56.
  • Jegadeesh, N., & Titman, S. (1993). Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency. The Journal of Finance, 48(1), 65–91.

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