From Sandpiles to Angel Investments

This article explores the dynamics of angel investing through the lens of celebrated mathematical theories of self-organized criticality (SOC) and fractal behavior. Return distributions from AngelList data highlight the presence of power law returns. This has significant implications for portfolio construction, investment strategies, and diversification; notably, the potential for significant contributions from a handful of angel investments.

Angel investing, known for its potential for extraordinary returns, mirrors natural phenomena characterized by SOC and fractal behavior. This exploration draws parallels to patterns and phenomena observed in nature like earthquakes, avalanches, and brain synapses.

Understanding these dynamics will provide unique insights and empower practitioners to create unique investment strategies that maximize returns.

Traditionally in the field of physics, criticality refers to the condition of a system at a critical point where it undergoes a phase transition, displaying unique properties and behaviors distinct from other states. In finance and angel investing, recognizing the significance of critical points may be helpful for understanding market behavior and extreme events. While the exact patterns can be complex and varied, the concept of criticality highlights the potential for sudden, large-scale changes. Such awareness can aid in developing strategies for risk management and decision-making, particularly in the high-risk, high-reward environment of angel investing, where market dynamics can shift rapidly.

Evidence of Self-Organized Criticality in Nature

SOC was first proposed by Per Bak et al. in 1987 through a simple toy model for sandpile dynamics. This development occurred after seminal work on critical phenomena led by 1982 Physics Nobel Laureate Kenneth Wilson. Critical phenomena provided a foundational understanding of phase transitions and scaling behavior through renowned renormalization group theory. Bak and his colleagues argued that certain dynamical systems naturally evolve without tuning a parameter to a critical state where a minor event can trigger a chain reaction, resulting in phenomena such as avalanches. SOC behavior has since been observed in various natural systems, including sandpiles, snowflakes, and many more over the past few decades.

Key Experimental Evidence

1. Avalanche Size Distribution: Both sandpile and snowflake experiments show that the distribution of avalanche sizes follows a power law, a hallmark of SOC. Small avalanches are frequent, but large avalanches also occur, and there is no characteristic size for avalanches.
2. Critical Slope and State: Sandpiles and snowflakes naturally evolve to a critical slope or state. When grains are added to a sandpile or snowflakes form, they accumulate until reaching a threshold, triggering an avalanche, and maintaining the system near this critical state.
3. Perturbation Length and Scale Invariance: The perturbation length, measuring how disturbances spread through the system, grows with the system size. This suggests that avalanches can propagate across the entire system, a feature of SOC. A wide variety of systems exhibit self-similarity, meaning patterns look similar at different scales, indicating fractal behavior.
4. Temporal Power Laws: Time intervals between avalanches and their durations also follow power law distributions, supporting the idea that these systems are in a critical state.
5. Universality: SOC behavior is robust and observed in different granular materials and setups, as well as snowflake formations, indicating it is a universal property of such systems.

Certain dissipative dynamical systems and growth models, including those based on Stephen Wolfram’s cellular automata, can exhibit SOC behavior. These models evolve through simple local interactions, leading to complex global patterns and self-organized critical states. Wolfram’s computational methods illustrate how such systems mirror the dynamics seen in the growth of natural phenomena and economic systems. SOC behavior is also recently observed in many natural biological systems, such as brain synapses, where neural activity shows power-law distributions. This reflects a few neurons firing extensively while most remain inactive, displaying avalanche-type dynamics, known as neuronal avalanches.

Implications for Angel Investments

Applying SOC to angel investments provides a new perspective on understanding market dynamics. Here’s how SOC concepts can help decode the complexities of angel investing:

1. Power Law Distribution of Returns: Like avalanches in sandpiles, the returns on angel investments follow a power law. That is, a small number of investments yield extremely high returns, while the majority may result in small returns or losses. This distribution lacks a characteristic scale, a hallmark of SOC.
2. Critical State of the Market: The market for angel investments can be seen as being in a critical state, where small changes (e.g., new technologies or market trends) can lead to significant shifts in investment outcomes. This sensitivity to initial conditions and potential for large-scale impact is reminiscent of SOC behavior.
3. Cascading Effects: A successful startup can trigger a cascade of positive effects, including follow-on investments, market growth, and increased valuations of related companies. These cascading effects are like the chain reactions in SOC systems.
4. Network Dynamics: Interactions among investors, startups, and markets form a complex network. Changes in one part of the network can propagate through the entire system, leading to large-scale shifts. This interconnectedness and potential for widespread impact align with SOC principles.

Theoretical and Empirical Support

• Power Law in Venture Capital Returns: Research shows that venture capital returns follow a power law, with a few investments generating the majority of returns.
• Market Sensitivity: The venture capital market is highly sensitive to trends and external factors, leading to rapid shifts in investment focus and valuations. This dynamic nature is characteristic of a system in a critical state.
• Network Effects: The success of certain startups often leads to increased investments in related areas, demonstrating the network dynamics and cascading effects typical of SOC.

Examples of SOC-Like Behavior in Angel Investments

• Tech Bubbles and Crashes: The dot-com bubble and subsequent crashes exemplify SOC, where the market reached a critical state, and small triggers led to significant market corrections.
• Innovation Waves: Waves of innovation, such as the rise of social media or blockchain technology or the recent innovation wave triggered by Gen-AI and variants, lead to large-scale changes in investment patterns, like avalanches in SOC systems.

Analyzing AngelList Data

Insights from AngelList data, examining 1808 investments prior to Series C, reveal a significant long tail in the return distribution. When plotted on a Log-Log scale, the returns follow a power law distribution, deviating from Gaussian or log-normal distributions. This behavior supports the existence of self-organized criticality in Angel Investments and venture capital portfolios, where a few significant events disproportionately influence the overall system.

Data Analysis and Findings

The analysis of AngelList data shows that the return distribution of angel investments has a “fat tail,” meaning that extreme returns occur more frequently than predicted by normal distributions. This indicates that a small number of investments generate most of the returns, while most investments yield modest or negative returns.

Figures and Interpretation:

Figure1. Return distribution from AngelList data, which indicates the presence of fat long tail to the right.

Figure 2. Log-log plot of the tail of the return distribution from AngelList data, which clearly deviates from standard normal distribution (solid red line) and tends towards a power law (dotted blue line).

These figures signal the possibility of power law distribution of returns in angel investing, highlighting the presence of outliers and the significance of identifying high-potential investments.

Understanding Power Law Distributions

Power law distributions are characterized by the presence of “fat tails,” where extreme values occur more frequently than predicted by normal distributions. In the context of angel investing, this means a few investments yield extraordinary returns, while the majority yield modest or negative returns. This phenomenon reflects the underlying dynamics of startup ecosystems, where innovation, market dynamics, and competitive pressures create a landscape dominated by outliers.

Implications for Investment Strategies

For angel investors, understanding power law distributions can be insightful. Investing in many startups increases the likelihood of capturing outliers. Investors should focus on identifying and supporting high-potential startups, because these will drive most returns.

Business Models in Early-Stage Investing

Many funds focus on early-stage investing in a diversified manner, leveraging systematic decision-making processes. This approach maximizes returns while managing risk, particularly for managers skilled at identifying and nurturing outliers. These funds often employ a portfolio strategy that includes many small investments, banking on the few that will achieve massive success to drive overall returns.

Diversified Investment Approach

A diversified investment approach involves spreading investments across many startups, industries, and stages. This strategy mitigates risks associated with individual investments and increases the chances of capturing high-return outliers. By diversifying, investors can better manage the inherent uncertainties in early-stage investing.

Systematic Decision-Making

Systematic decision-making processes help investors identify promising startups. This involves using data analytics, market intelligence, and experienced judgment to evaluate potential investments. A systematic approach reduces the risk of biased or emotional decisions, leading to more consistent and effective investment outcomes.

Strategies for Identifying Outliers

Identifying potential outliers requires a deep understanding of market trends, technological advancements, and the unique attributes of startup teams. Experienced investors often look for scalable business models, strong leadership, and products that address significant market needs.

Key Factors for Identifying Outliers

1. Market Trends: Staying attuned to emerging market trends helps investors identify startups with high growth potential.
2. Technological Advancements: Understanding technological innovations allows investors to spot startups that are poised to disrupt industries.
3. Startup Teams: Strong leadership and cohesive teams are critical indicators of a startup’s potential for success.

Leveraging Networks

Building strong networks within the startup ecosystem provides access to high-quality deal flow and valuable mentorship opportunities. Collaborative investing with other experienced angels and venture funds can share due diligence insights and reduce individual risk.

In addition, leveraging networks and ecosystems to source deals and support portfolio companies, such as those facilitated by the Angel Capital Association (ACA) and Investment Networks such as the Angel Investor Forum (AIF), can enhance the likelihood of identifying and nurturing high-potential startups. Several thought leadership and knowledge sharing platforms including CFA Institute provide critical knowledge and resources that empower investors in making informed decisions.

Challenges to Traditional Portfolio Construction

The power law dynamics of angel investing challenge conventional portfolio construction wisdom. While successful founders and investors such as Peter Thiel may implicitly embrace the power law structure, focusing on only a few promising companies could often underperform market returns, highlighting the complexity of consistently identifying high-performing investments. Traditional diversification strategies, which spread risk across a wide array of assets, may not fully capitalize on the unique return characteristics of angel investing.

Rethinking Diversification

In the context of angel investing, diversification takes on a different meaning. Rather than merely spreading investments across many companies, effective diversification involves strategic selection of startups across various industries, stages, and geographies. This approach helps mitigate the risk of sector-specific downturns and increases exposure to diverse growth opportunities.

Strategic Diversification

Strategic diversification involves:

• Sector Diversification: Investing in startups across different industries to spread risk.
• Stage Diversification: Including startups at various stages of development, from seed to later stages.
• Geographic Diversification: Investing in startups from different regions to reduce exposure to local market risks.

Fees and Market Outperformance

Considering the fees charged by managers and platforms like AngelList, it is essential to evaluate their impact on net returns. Market returns often outperform hypothetical portfolios due to the cumulative effect of management and performance fees. According to a study by the Kauffman Foundation, management fees in venture capital funds combined with the performance fees (carried interest) on profits could consume gross returns, significantly reducing the overall profitability of investments. Therefore, angel investors must carefully evaluate fee structures and consider the net returns after fees when selecting investment opportunities. Platforms that offer lower fee structures with performance-based incentives can be more attractive, as they align with the interests of investors and managers, thereby enhancing the potential for higher net returns.

Implications for Angel Investors

Understanding power law dynamics in angel investing highlights parallels between economic growth and natural processes. Recognizing the SOC in venture capital, where a few standout investments significantly impact overall performance, angel investors can benefit from prudent diversification. Strategic systematic portfolio construction, considering fees and the fractal nature of economic growth in startups, can be advantageous.

Practical Investment Strategies

• Broad-Based Investment Approach: Investing in a large number of startups increases the likelihood of capturing outliers. Diversifying across sectors, geographies, and stages can mitigate risks and enhance returns.
• Leveraging Networks: Building strong networks within the startup ecosystem can provide access to high-quality deal flow and valuable mentorship opportunities. Collaborative investing with other experienced angels and venture funds can share due diligence insights and reduce individual risk.
• Data-Driven Decision Making: Utilizing data analytics and market intelligence can improve investment decisions. Identifying patterns in successful startups can inform future investments and enhance portfolio performance.
• Long-Term Perspective: Angel investing requires patience and a long-term view. Many successful startups take years to reach their full potential. Investors should be prepared for illiquidity and the potential for multiple rounds of funding before realizing returns.
• Active Involvement: Engaging with portfolio companies through mentorship and strategic guidance can increase the likelihood of their success. Active investors often contribute more than just capital, providing valuable industry connections and operational expertise.

Key Takeaway

The return profile of angel investing exhibits power law behavior like natural phenomena, reflecting the presence of self-organized criticality and fractal patterns. The power law distribution in returns underscores the outsized impact of outlier investments on overall economic growth in the venture capital ecosystem. The potential for a handful of investments to contribute significantly makes this asset class worthwhile. Investors should embrace these natural parallels, leveraging data-driven insights for informed decisions.