Decoding Risk-Adjusted Returns - A Comprehensive Decade-Long Analysis

Investment success relies on the delicate balance between managing risk and achieving returns. Striking this equilibrium demands not only a thorough understanding of financial instruments but also an appreciation of the nuanced behaviours that underpin market performance. In a world of increasing economic complexity and uncertainty, investors must rely on robust data analysis and advanced metrics to navigate the intricate dynamics of risk and reward.

This article explores the performance of two prominent global indices - the FTSE 100 and the S&P 500 - alongside a weighted portfolio blending these indices, over a decade-long period. The dataset spans trading days from January 1, 2013, to December 31, 2022, capturing a diverse range of market conditions, including two of the most challenging periods in recent history: the economic upheaval caused by the Covid-19 pandemic and the geopolitical turbulence stemming from the Russia-Ukraine conflict. These crises serve as stress tests for the examined indices, highlighting their resilience and vulnerabilities under extreme conditions.

To gain a comprehensive understanding of performance, this study employs advanced statistical tools, including the Sharpe Ratio, kurtosis, skewness, and Value at Risk (VaR). The analysis provides insights into the drivers of returns, the risks associated with tail events, and the asymmetries in return distributions that challenge conventional assumptions of normality. By examining these metrics, the study sheds light on the relative strengths and weaknesses of each index and the stabilising benefits of portfolio diversification.

Through this quantitative framework, the article not only evaluates historical performance but also offers practical takeaways for investors seeking to optimise their portfolios in an increasingly volatile financial landscape. It bridges theoretical insights with actionable strategies, empowering investors to better understand risk-return dynamics and build resilient portfolios capable of withstanding future market uncertainties.

THE CONCEPT

Quantitative measures are essential tools for evaluating and comparing investments, offering a systematic approach to understanding performance and managing risk. These metrics enable investors to move beyond subjective judgments, providing objective criteria to assess the potential and suitability of various investment opportunities. Among these tools, the Sharpe Ratio, kurtosis, skewness, and Value at Risk (VaR) are particularly significant, each contributing unique insights into the risk-return characteristics of financial data.

The Sharpe Ratio is a cornerstone of investment analysis, measuring risk-adjusted returns by assessing the excess return generated per unit of risk. This metric helps investors determine which investments deliver the most efficient balance between reward and volatility, making it easier to identify those that optimise performance relative to the risks undertaken.

Kurtosis and skewness add depth to the analysis by examining the shape and behaviour of return distributions. Kurtosis highlights the frequency and impact of extreme events, shedding light on the potential for unexpectedly large gains or losses. Skewness, meanwhile, reveals asymmetry in the distribution of returns, indicating whether deviations from the average are more likely to be positive or negative. Together, these metrics challenge the assumption of normality often applied in financial modelling and provide a more detailed understanding of potential investment outcomes.

Value at Risk (VaR) further enhances the analytical toolkit by quantifying the likelihood of losses within a specified confidence level and time frame. This metric is particularly valuable for risk management, as it provides a clear estimate of the downside exposure associated with an investment. By identifying the potential for significant losses, VaR enables investors to align their strategies with their risk tolerance and financial goals.

These quantitative measures collectively form the backbone of this analysis, offering a holistic framework for evaluating investments. They provide investors with a comprehensive understanding of risk-adjusted returns, distributional nuances, and potential losses, helping to identify assets that deliver an optimal balance between risk and reward. This multidimensional approach ensures that decisions are informed by rigorous, data-driven insights, supporting effective portfolio construction and long-term investment success. By integrating these metrics into their evaluation processes, investors can navigate the complexities of financial markets with greater confidence and precision.

Sharpe Ratio

First introduced by William Sharpe in 1966, the Sharpe Ratio is a fundamental metric in finance that evaluates risk-adjusted returns, offering a standardised method to compare investments with differing levels of risk. By quantifying the amount of excess return generated per unit of risk taken, the Sharpe Ratio provides a clear and objective basis for assessing the efficiency of an investment. This measure allows investors to identify which assets deliver the most favourable balance between reward and volatility, making it an invaluable tool for portfolio optimisation and performance evaluation.

Sharpe Ratio = ( Rp−Rf ) / σp​​

Where:

• Rp​: Portfolio return
  

• Rf​: Risk-free rate, given at 3% annually or ~0.000082 daily
  

• σp​: Standard deviation of portfolio returns, representing risk

Kurtosis and Skewness

Kurtosis: Kurtosis measures the "fatness" or thickness of a distribution's tails, providing insight into the frequency and magnitude of extreme outcomes. High kurtosis indicates a greater likelihood of rare, extreme values compared to a normal distribution, emphasising the presence of tail risks. In financial analysis, this measure is crucial for identifying assets or portfolios exposed to significant volatility or extreme market events.

Skewness: Skewness evaluates the asymmetry of a distribution of returns, shedding light on the direction and likelihood of deviations from the mean. Negative skewness implies that extreme negative outcomes are more probable than extreme positive ones—a characteristic often observed in financial datasets (Brooks, 2019). This metric is particularly valuable for risk management, as it highlights the potential for adverse market movements that could significantly impact investment performance.

Value at Risk (VaR)

VaR quantifies the potential for loss within a specified time frame and confidence level, providing a clear measure of downside risk. Widely utilised in financial markets, this metric helps investors and risk managers understand the extent of potential losses under adverse conditions (Gujarati and Porter, 2009). By offering a standardised approach to estimating risk exposure, VaR plays a pivotal role in aligning investment strategies with an investor's risk tolerance.

While each of these metrics - Value at Risk (VaR), Sharpe Ratio, kurtosis, and skewness - provides valuable insights when considered individually, their true power emerges through their combined application to real-world financial data as they collectively form a comprehensive framework that captures the complexities of performance, risk, and return distributions.

METHODOLOGY & DATASET

Data Overview

This analysis covers 2,470 trading days between January 1, 2013, and December 31, 2022, focusing on:

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FTSE 100

An index representing the 100 largest UK companies by market capitalisation

S&P 500

A benchmark for US equities, representing 500 of the largest companies in the US

Mixed Portfolio

A 70% allocation to the S&P 500 and 30% to the FTSE 100 to examine diversification effects.

> Key Metrics

Metric	FTSE 100	S&P 500	Portfolio
Mean Return (Daily)	~0.0000	0.0004	0.0002
Standard Deviation	0.0101	0.0113	0.0095
Sharpe Ratio	-0.012	0.025	0.016
Kurtosis	15.6	18.9	19.9
Skewness	-0.87	-0.80	-1.01

With this descriptive foundation, we can now explore how these metrics translate into actionable insights. The following section analyses the risk-return trade-offs and the implications of the statistical patterns observed in the data.With this descriptive foundation in place, the analysis can now shift towards uncovering actionable insights derived from these metrics.

By examining the interplay between risk and return, the next section delves into the trade-offs that these measures highlight, offering a deeper understanding of their practical implications. This exploration also considers the statistical patterns observed in the data, providing a basis for interpreting how these characteristics influence investment strategies and decision-making in real-world scenarios.

INTERPRETATION & VALIDATION

Superior Risk-Adjusted Performance

The analysis reveals a clear disparity in risk-adjusted performance between the indices. The S&P 500 achieved the highest Sharpe Ratio of 0.025, underscoring its superior risk-return profile and its ability to generate higher returns per unit of risk. Conversely, the FTSE 100 recorded a negative Sharpe Ratio of -0.012, highlighting its underperformance when adjusted for risk. This stark contrast not only illustrates the efficiency of the S&P 500 in compensating investors for the risks undertaken but also underscores the challenges faced by the FTSE 100 in delivering adequate returns relative to its volatility. These findings emphasise the importance of evaluating investments through the lens of risk-adjusted metrics to identify assets that align with an investor’s performance objectives.

Benefits of Diversification

The mixed portfolio demonstrated a notable reduction in risk, as evidenced by its lowest standard deviation of 0.0095. This outcome highlights the effectiveness of diversification in mitigating volatility, particularly when combining assets from different regions. By blending investments across varied markets, the portfolio benefits from reduced exposure to region-specific risks, achieving a more stable performance. This underscores the value of diversification as a fundamental principle in portfolio construction, enabling investors to manage risk more effectively while pursuing consistent returns.

Non-Normal Distributions

High kurtosis values indicate a higher frequency of extreme returns, suggesting that the data exhibit fatter tails than a normal distribution. This, combined with negative skewness, underscores the increased likelihood of significant downside risks. Such findings challenge the conventional assumption of normally distributed returns, which is often employed in traditional risk models (Brooks, 2019), highlighting the need for more robust methods to capture the true nature of financial data.

While these insights provide a strong foundation for assessing relative performance, they also emphasise the importance of quantifying potential losses. To address this, the next section focuses on applying Value at Risk (VaR) to evaluate downside risks specifically for the FTSE 100, offering a more detailed perspective on the scale and likelihood of adverse market movements.

Risk Assessment

To thoroughly evaluate the downside risks associated with the FTSE 100, the Value at Risk (VaR) metric was calculated to quantify the potential for losses over a specified time frame and confidence level. This measure provides a precise estimate of the maximum expected loss under normal market conditions, offering valuable insights into the risk profile of the index. By incorporating historical data and statistical methods, the VaR calculation serves as a critical tool for understanding the likelihood and magnitude of adverse outcomes, enabling a more comprehensive assessment of the FTSE 100's vulnerability to market downturns.

Q0.05 = μ + z0.05 . σ

Where:

• z0.05 = -1.645 (critical value for the 5% lower tail)
  

• μ = 0
  

• σ = 0.0101

.: Q0.05 = 0 + (−1.645⋅0.0101) = −0.0166 or -1.66%

This indicates that there is a 5% probability of experiencing daily losses greater than -1.66%. In other words, under normal market conditions, the FTSE 100 is expected to incur losses exceeding this threshold only 5 out of every 100 trading days. This measure highlights the tail risk associated with the index and underscores the importance of incorporating such probabilities into risk management strategies to prepare for rare but significant adverse events.

With the relative performance and downside risks of these indices now thoroughly analysed, we are well-positioned to synthesise these findings into broader, actionable investment insights. This integration of performance metrics and risk assessments provides a deeper and more nuanced understanding of the risk-return trade-offs that each index embodies. Such an approach not only uncovers the comparative strengths and vulnerabilities inherent in each index but also offers a roadmap for tailoring investment strategies to align with diverse investor priorities.

For those prioritising capital preservation, this analysis identifies which indices offer lower volatility and downside risk. Conversely, for growth-oriented investors, it highlights opportunities where returns justify the associated risk. For those seeking a balanced approach, it offers a comprehensive view of how different indices contribute to diversification and long-term stability. By quantifying the dynamics between risk and return, this study equips investors with a clear framework for optimising their portfolios.

Additionally, this synthesis supports practical applications in portfolio diversification, guiding decisions on how to allocate assets across different regions and indices to minimise risk while maximising returns. It also informs strategies for asset allocation by highlighting how varying market conditions impact each index differently. These insights are invaluable for navigating the complexities of modern financial markets, where volatility and uncertainty demand well-informed, adaptive strategies.

This detailed understanding lays the groundwork for a forward-looking discussion, focusing on how these findings translate into effective risk management and portfolio optimisation. It ensures that investors are better equipped to make decisions in an environment where both opportunities and challenges are increasingly dynamic and interconnected.

In conclusion, this analysis highlights the intricate and multifaceted dynamics of risk and return in financial markets, offering key insights that bridge theoretical understanding with practical investment considerations. The S&P 500’s superior Sharpe Ratio demonstrates its strong appeal to growth-focused investors, balancing risk and reward more efficiently than its counterparts. Meanwhile, the mixed portfolio underscores the enduring value of diversification, which mitigates asset-specific volatility and fosters a more stable return profile - an invaluable trait in uncertain markets.

However, the findings also challenge conventional assumptions underpinning traditional risk models. The presence of high kurtosis and negative skewness across datasets reveals the heightened probability of extreme outcomes and asymmetric risks, which standard models based on normal return distributions fail to adequately capture. These challenges highlight the pressing need for advanced risk management strategies that go beyond static measures. Techniques such as stress testing, scenario analysis, and modelling of tail risks become indispensable for navigating the complexities of modern financial environments.

Ultimately, this analysis reinforces the importance of adopting a multidimensional approach to portfolio construction and risk assessment. Investors must balance the pursuit of returns with the realities of volatility and market irregularities, leveraging advanced tools to enhance resilience against unexpected shocks. By integrating these findings into their strategies, investors can better position themselves to navigate the evolving financial landscape, optimising portfolios that not only perform but endure in the face of uncertainty. This comprehensive perspective paves the way for smarter, more adaptable investment decisions in an era defined by both opportunity and risk.

Whether the focus is on optimising for growth, managing risk, or achieving a balanced portfolio, our evidence-based approach combines rigorous analysis with practical application.

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References:

• Brooks, C. (2019). Introductory Econometrics for Finance. 3rd ed. Cambridge: Cambridge University Press.

• Gujarati, D. N., and Porter, D. C. (2009). Basic Econometrics. 5th ed. New York: McGraw-Hill Education.

• Stigler, S. M. (1986). The History of Statistics: The Measurement of Uncertainty Before 1900. Cambridge: Harvard University Press.

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