Portfolio Performance Analysis and Optimization Utilizing Multiple Financial Models

by Pablo Javier López Esteras Espino

Index:

1. Introduction

2. Portfolio Models and Performance Metrics

2.1 Calculation of Portfolio Weights and Performance Metrics

2.2 Portfolio Models Table

2.3 Efficient Frontier Analysis

2.4 CAPM-based Performance Estimation

3. Performances

3.1 Performance Assessment of Our 15-Stock Portfolio vs Alternative Models

3.2 Evaluation of Portfolio Performance Using Daily Returns

4. Conclusion and Strategic Insights

1. Introduction

In the world of investment, constructing an optimal portfolio is a fundamental task for investors seeking to balance risk and return. The process of portfolio management involves selecting a mix of assets that align with an investor’s financial goals and risk tolerance. This project focuses on evaluating and optimizing a portfolio consisting of 15 carefully selected stocks. To start, we built an initial portfolio based on stock weights that we believed were appropriate, taking into consideration factors such as the company size, financial stability, and the level of risk we were willing to assume. We believed that a thoughtful combination of these elements would provide a well-balanced portfolio suited to our investment objectives.

Once we established our own portfolio, we expanded the analysis by comparing its performance with several established models, including the Tangency Portfolio, the equal-weighted portfolio, and other variations based on the Capital Asset Pricing Model (CAPM). These models offer different approaches to portfolio construction, each with its own assumptions and objectives, providing a range of potential strategies for managing risk and return. The Tangency Portfolio, for instance, seeks to identify the portfolio that maximizes the Sharpe Ratio, balancing risk against expected return, while CAPM models estimate the expected returns based on market risk exposure.

Through this comparative analysis, we aimed to explore how varying stock weightings and different model assumptions affect the performance of the portfolio over a defined period. We used key financial metrics such as Sharpe Ratio, alpha, and beta to evaluate each portfolio’s performance. The Sharpe Ratio helps assess the risk-adjusted return, alpha indicates the portfolio's ability to outperform its expected market return, and beta measures the portfolio's sensitivity to overall market movements.

The objective of this study is to demonstrate how portfolio optimization can be achieved by carefully selecting stock weights according to specific factors like company size and the desired risk profile. By comparing our constructed portfolio with the more established models, we seek to understand which strategies lead to better risk-adjusted returns and how different models perform in various market conditions. Ultimately, this analysis offers valuable insights into the role of model-driven strategies in enhancing portfolio returns while effectively managing risk.

2. Portfolio Models and Performance Metrics

The table below presents the weights assigned to each stock in our portfolio using various portfolio models. The models include our custom portfolio, an equal-weighted portfolio, the Tangency Portfolio (Historical), the Tangency Portfolio (CAPM), the Tangency Portfolio (CAPM-Adjusted), and the Tangency Portfolio with constrained weights (where stock weights are limited between -0.3 and 0.5). These models differ in their approach to portfolio optimization, with the Tangency portfolios aiming to maximize the Sharpe Ratio and the CAPM models incorporating market risk factors into the weighting process. The portfolio weights reflect our strategy and analysis, considering the risk and return profile of each stock in the context of different optimization methods.

In our custom portfolio, we based the stock weights on the size of the company and the level of risk we were willing to assume. We assigned higher weights to more established, less volatile companies, and lower weights to smaller companies with higher risk. This approach reflects our strategy to balance stability with growth potential, providing a diversified portfolio with a tailored risk-return profile.

2.1 Calculation of Portfolio Weights and Performance Metrics

All the calculations for the portfolio models are presented in the accompanying Excel file. The analysis utilizes matrices and various methods to optimize and assess the performance of each portfolio. Using matrix operations, the portfolio weights were determined based on different optimization techniques, including the Tangency Portfolio and CAPM models. The file also contains the calculation of key performance metrics such as the Sharpe Ratio, alpha, and beta, which are derived through methods like regression analysis and risk-return trade-offs. These calculations allow for a comprehensive comparison of the portfolios in terms of risk-adjusted returns, market sensitivity, and excess returns. The Excel file provides a detailed, step-by-step breakdown of the data used in the analysis, offering transparency and clarity for the results presented in this report.

https://docs.google.com/spreadsheets/d/1Piak_ngjPkaFOGxKIJKQlmvgBgIB05-Y/edit?usp=sharing&ouid=109840622104215188080&rtpof=true&sd=true 

2.2 Portfolio Models Table

The portfolio weights for each model are calculated and presented in an Excel file.

2.3 Efficient Frontier Analysis

The graph above illustrates the Efficient Frontier, which represents the optimal risk-return trade-offs for a portfolio. The blue dots on the chart correspond to various portfolios with different combinations of risk (standard deviation) and expected return. The purple line, known as the Efficient Frontier, shows the portfolios that offer the highest expected return for each level of risk. Portfolios located on this line are considered to be "efficient," as they provide the maximum return for the given risk level. The portfolio with the highest Sharpe Ratio, which optimizes risk-adjusted return, would lie on this line. This visualization allows us to see how different portfolios compare in terms of risk and return, helping investors make informed decisions about portfolio optimization.

Efficient Frontier Chart Calculations: https://docs.google.com/spreadsheets/d/1EKtydhCvPrYc7k0A8UB2q-xRIjyGRjJz/edit?usp=sharing&ouid=109840622104215188080&rtpof=true&sd=true  

2.4 CAPM-based Performance Estimation

(Daily returns for each of the 15 stocks in our portfolio over the October 18, 2024-November 18, 2024 period)

Based on the analysis and comparison of different portfolio models, several key insights emerge regarding the performance and efficiency of each approach. The Tangency Portfolio (Historical) stands out with the highest Sharpe Ratio of 0.6614, indicating that it is the most efficient portfolio in terms of risk-adjusted return. This suggests that, for investors seeking to balance return and risk, the Tangency Portfolio (Historical) would be the optimal choice. It achieves the best trade-off between risk and return, making it a strong candidate for those who prioritize an efficient investment strategy.

In contrast, the Tangency Portfolio (CAPM) excels in generating excess returns, as evidenced by its alpha of 0.2845, the highest among the portfolios analyzed. Alpha represents the ability of a portfolio to exceed the expected return based on its market risk exposure. This indicates that the Tangency Portfolio (CAPM) is particularly effective at producing returns beyond what is predicted by market risk factors. However, its Sharpe Ratio of 0.265 suggests that, while the portfolio generates strong excess returns, it is less efficient at converting risk into return compared to the Tangency Portfolio (Historical).

The portfolio's beta values provide additional insights into the portfolios' market sensitivity. The Tangency Portfolio (CAPM) exhibits the most negative beta value of -0.3819, signifying the strongest inverse relationship with the market. This implies that the Tangency Portfolio (CAPM) may provide protection in bearish market conditions, as it is less likely to correlate with market movements. However, it also faces challenges in benefiting from market upturns, making it a more conservative choice for investors looking to hedge against market downturns. In comparison, the Tangency Portfolio (Constrained) and the original portfolio (our Portfolio) both have negative beta values (-0.102 and -0.2196, respectively), suggesting lower sensitivity to market fluctuations. These portfolios provide more stability, although they may underperform in rising markets.

The Equal-Weighted Portfolio, with a Sharpe Ratio of 0.2978, falls in the middle in terms of performance. While it does not optimize for risk-adjusted returns as effectively as the Tangency Portfolio (Historical), it is a straightforward approach that treats all stocks equally without attempting to optimize for risk or return. This model offers a more diversified exposure across the assets, which may appeal to more risk-averse investors who prefer a simpler and more balanced strategy.

In conclusion, the analysis highlights that the choice of portfolio model depends on the investor's risk tolerance and investment objectives. For those seeking the highest risk-adjusted returns, the Tangency Portfolio (Historical) is the most efficient. However, for investors looking to achieve the greatest excess return beyond market predictions, the Tangency Portfolio (CAPM) would be more suitable. The portfolios with lower beta values, such as the Tangency Portfolio (Constrained) and Our Portfolio, offer more stability, which could be attractive for investors looking to minimize their exposure to market volatility. Ultimately, each model has its strengths and weaknesses, and the optimal choice will depend on the individual investor’s financial goals, risk appetite, and market outlook.

3. Performances

3.1 Performance Assessment of Our 15-Stock Portfolio vs Alternative Models

The analysis of our 15-stock portfolio, compared to other portfolio models, shows that our custom portfolio provided the highest return in the short term. This outcome suggests that the strategy we applied assigning more weight to larger, more stable companies and less weight to riskier ones  was effective in generating superior returns over the given period. Our portfolio achieved a return of 0.05368, which was higher than that of the Equal-Weighted Portfolio, the Tangency Portfolios (Historical, CAPM, and CAPM-Adjusted), and even the S&P 500 Index.

However, while our portfolio delivered the best performance in the short term, we acknowledge that this strategy may not be the most optimal in the long run. The lack of a formal model to support our weight allocation could lead to less favorable outcomes over time. A more structured approach, integrating various models and strategies, would likely yield more stable and favorable results in the future.

For the next time, we plan to combine different models and strategies to improve the allocation of weights in our portfolio. This will allow us to account for various risk-return scenarios and optimize the portfolio more effectively for better long-term results.

3.2 Evaluation of Portfolio Performance Using Daily Returns

In this analysis, we evaluate the performance of each portfolio using daily returns. This approach allows for a more precise assessment of risk and return by capturing short-term fluctuations in the market. By using daily returns, we can observe how each portfolio performs on a day-to-day basis, providing a clearer picture of volatility and portfolio stability. This method enables a better comparison between different portfolio models, ensuring that the results reflect the actual market conditions and performance investors might experience in real time.

From the portfolio performance evaluation, it is clear that our portfolio outperformed all the other portfolio models tested, achieving the highest average return of 0.0025. This result is reflected in the Sharpe ratio, which measures the return relative to the risk associated with an investment. Our portfolio achieved a Sharpe ratio of 0.16448, the highest among the portfolios tested, indicating that it offered a strong return for the risk undertaken. Furthermore, our portfolio outperformed the S&P 500 Index in terms of Sharpe ratio, highlighting its efficiency in balancing risk and return.

In terms of alpha, which measures the excess return above the expected market return, our portfolio also excelled. With an alpha of 0.002329, it showed 0.2% additional excess return compared to the S&P 500. This outperformance was especially evident when compared to the Tangency Portfolio (Constrained), which showed a negative alpha, indicating underperformance relative to the expected market return.

In summary, our portfolio demonstrated superior performance both in terms of average return and risk-adjusted return (as indicated by the Sharpe ratio). It also delivered excess returns, as seen in the positive alpha value, outperforming the S&P 500 and the other portfolios in the analysis. Although the portfolio worked well in the short term, it is important to note that a more systematic model may offer even better long-term results by optimizing the weight allocation and incorporating broader market factors.

4. Conclusion and Strategic Insights

This project has provided valuable insights into how portfolio risk and return are influenced by the weights assigned to each asset and the methods used for portfolio optimization. By analyzing different models, such as the Tangency Portfolio, Equal-Weighted Portfolio, and CAPM-based strategies, I have gained a deeper understanding of how various factors contribute to portfolio performance. This approach demonstrates that adjusting asset weights and selecting different models can significantly affect the risk-return trade-off.

In practice, there are many ways to construct and evaluate portfolios, and each method has its own advantages and limitations. The key takeaway from this analysis is not just about which model or strategy performs the best, but rather how to interpret the data accurately and apply this knowledge in real-world investment decisions. Being able to assess risk, understand market dynamics, and adjust strategies based on real data is crucial for successful investment management.

Ultimately, the ability to interpret portfolio data and apply it effectively to real-life scenarios is what will help investors make the correct decisions. While there are various strategies and models available, I believe that it is the combination of all these models, along with the ability to interpret the data and know how much weight to give to each model, that is key to building the perfect portfolio. Understanding the principles and adapting them to achieve optimal results in different market conditions is what will truly drive success in portfolio management.