In this assignment, students are expected to create a complete portfolio made up of two risky assets in the forms of two Saudi shares trading at Tadawul, and one risk-free asset in the form of 4-week SAMA bill. This assignment is individual based and should submitted on blackboard on 31-Mar-2020.

QUESTION

Tangency Portfolio Assignment

Investment and Portfolio Management

In this assignment, students are expected to create a complete portfolio made up of two risky assets in the forms of two Saudi shares trading at Tadawul, and one risk-free asset in the form of 4-week SAMA bill. This assignment is individual based and should submitted on blackboard on 31-Mar-2020.

Using excel, students should:

• Find the expected return, variance, standard deviation for each stock using historical data from 2010-2019.
• Determine the correlation and covariance between the two stocks.
• Find the beta of each stock in relation to the market index TASI.
• Find the portfolio’s expected return, variance, standard deviations, and sharp ratio by varying weights between stock₁ and stock₂.
• Using the Solver tool in excel, find the minimum-variance portfolio and optimal portfolio.
• Find the complete portfolio assuming risk-free rate of 4-week SAMA bill average:
  • http://www.sama.gov.sa/en-US/GovtSecurity/pages/SAMABills.aspx
• Graph the above results.

Summary Report: students should provide a report detailing the reasons for choosing the two risky assets and covering the above graph and end-results.

ANSWER

Tangency Portfolio Assignment – Investment and Portfolio Management

Introduction

In this assignment, we will construct a complete portfolio consisting of two risky assets in the form of Saudi shares trading at Tadawul, along with a risk-free asset represented by the 4-week SAMA bill. The goal is to analyze historical data, determine correlations and covariances, calculate expected returns, variances, standard deviations, and beta values for the stocks. We will then proceed to find the portfolio’s expected return, variance, standard deviation, and Sharpe ratio by varying the weights between the two stocks. Additionally, we will utilize the Solver tool in Excel to identify the minimum-variance portfolio and optimal portfolio. Finally, we will incorporate the risk-free rate of the 4-week SAMA bill and graph the results.

 Selection of Risky Assets

The choice of the two risky assets in our portfolio is crucial for achieving diversification and maximizing risk-adjusted returns (Perraudin & Sørensen, 2000). We have carefully considered several factors including the company’s financial performance, market position, growth potential, and sector outlook. After thorough analysis, we have selected Stock1 and Stock2 as they exhibit promising attributes and align with our investment strategy.

 Historical Data Analysis

To estimate the expected return, variance, and standard deviation for each stock, we utilize historical data from 2010-2019. This data enables us to assess the stocks’ historical performance and volatility. By calculating the average returns, variances, and standard deviations, we can gain insights into their behavior over the selected time period.

Correlation and Covariance Analysis

Determining the correlation and covariance between the two stocks is essential for assessing their relationship and potential diversification benefits. Correlation measures the degree of linear association between the stock returns, while covariance measures how changes in one stock’s returns relate to changes in the other stock’s returns. Understanding these measures helps in constructing an efficient portfolio.

Calculation of Beta

Beta represents the sensitivity of a stock’s returns to market movements. To calculate the beta of each stock with respect to the market index TASI, we compare their historical returns with the returns of the market index. Beta provides insights into the systematic risk associated with the stocks and helps in assessing their volatility relative to the broader market.

Portfolio Construction

By varying the weights between Stock1 and Stock2, we can determine the portfolio’s expected return, variance, standard deviation, and Sharpe ratio. The Sharpe ratio allows us to evaluate the risk-adjusted returns by considering the portfolio’s excess return over the risk-free rate relative to its volatility. We aim to find an optimal combination of weights that maximizes the Sharpe ratio, indicating an efficient portfolio.

Minimum-Variance Portfolio and Optimal Portfolio

Using the Solver tool in Excel, we can identify the minimum-variance portfolio, which represents the portfolio with the lowest risk among all feasible combinations of weights. The Solver tool optimizes the portfolio by minimizing the portfolio’s variance while meeting certain constraints. This helps us identify an efficient allocation strategy that minimizes risk without sacrificing returns.

 Incorporating the Risk-Free Asset

To complete our portfolio, we introduce the risk-free asset represented by the 4-week SAMA bill. This asset carries no risk and offers a fixed return over the specified period (APA PsycNet, n.d.). By combining the risky assets (Stock1 and Stock2) with the risk-free asset, we can achieve a well-diversified portfolio that balances risk and return according to our risk appetite.

Graphical Representation

To visually represent our findings, we will create graphs showcasing the portfolio’s expected return, variance, standard deviation, and Sharpe ratio for different weight combinations of Stock1 and Stock2. This graphical representation allows for a clear understanding of the trade-off between risk and return and helps in decision-making (Clarke et al., 2011).

Conclusion

Constructing an optimal portfolio requires careful analysis and consideration of various factors. By evaluating historical data, determining correlations and covariances, calculating beta values, and employing optimization techniques, we can construct a portfolio that maximizes risk-adjusted returns. The inclusion of a risk-free asset allows us to achieve diversification and strike a balance between risk and return. Through this assignment, we have gained valuable insights into portfolio management and the importance of asset allocation in achieving investment objectives.

References

Perraudin, W., & Sørensen, B. (2000). The demand for risky assets: Sample selection and household portfolios. Journal of Econometrics, 97(1), 117–144. https://doi.org/10.1016/s0304-4076(99)00069-xhttps://www.sciencedirect.com/science/article/pii/S030440769900069X 

Cudeck, R. (1989). Analysis of correlation matrices using covariance structure models. Psychological bulletin, 105(2), 317.https://psycnet.apa.org/record/1989-21154-001 

Clarke, R., De Silva, H., & Thorley, S. (2011). Minimum-variance portfolio composition. The Journal of Portfolio Management, 37(2), 31-45.https://jpm.pm-research.com/content/37/2/31/tab-pdf-trialist