CFA Institute

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 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. 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. 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. 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. 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: 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. 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. 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. 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

If your foresight is strong enough to build a reliable Discounted Cash Flow (DCF) model, you likely don’t need one. Why does this matter? Because genuine foresight is rare and too much faith in one spreadsheet can lead to overconfidence. In practice, genuine investing success hinges on blending intelligence (to analyze) with wisdom (to interpret), setting realistic expectations, and exercising discipline to buy at a sensible price and hold patiently for value to accrue. Above all, stay humble, because there’s a fine line between confidence and arrogance. The Illusion of Precision DCF valuation helps you figure out what an investment is worth today based on projected cash flows by adjusting for risk and time. For instance, suppose you expect an asset to earn $10 cash flow in one year, but it isn’t guaranteed, while your alternative is a safe 5% annual return. Discounting $10 by 5% brings its present value to about $9.50, which better reflects its true worth (fair value) right now. Yet, predicting those cash flows is like trying to forecast the weather decades from now: you can have all the detailed maps, but a single unforeseen “climate shift” can disrupt your entire model. Similarly, in investing, global events, emerging competitors, or regulatory changes can upend even the most elaborate DCF assumptions, revealing how fragile long-term certainty truly is. The Terminal Value Trap: Why 80% of DCF Valuation Could Be a Mirage A critical weakness in many DCF models lies in the terminal value — an estimate of a company’s worth far beyond the initial forecast period. Often accounting for up to 80% of the total valuation, terminal value typically rests on two big assumptions: The company will survive and thrive for decades. You, as an investor, will stick around long enough to reap those returns. Both assumptions deserve scrutiny. In the United States, about 10% of companies go bankrupt each year, implying that only 35% survive a full decade. In other words, many businesses never fulfill their rosy terminal-value predictions. Meanwhile, investor holding periods have collapsed from eight years in the 1950s to just three months in 2023. If shareholders aren’t in the game long enough to capture those distant cash flows, how valuable are these projections in reality? Figure 1. In a World of Short-Termism, Does DCF’s Back-Loaded Valuation Make Sense? Source: Source: U.S. Bureau of Labor Statistics, NYSE, Barron’s When DCF Valuation Misses the Mark Kodak, a 140-year-old legend, valued at $30 billion in 1997, seemed like a sure bet if you only looked at film-based cash flows. A DCF in the early 2000s might have shown stable returns for years to come. Instead, digital imaging soared at breakneck speed, and Kodak filed for bankruptcy in 2012. Here, the model’s terminal value assumptions collided with swift technological disruption. BlackBerry experienced a similar fate. By 2006, it owned more than 50% of the smartphone market and was lauded as a “pioneering world leader in mobile texting services.” A DCF model might have priced in years of continued dominance. But with the iPhone’s 2007 debut and BlackBerry’s refusal to adapt, its market cap peaked at $80 billion in 2008—only to lose 96% of its value within four years. The once-rosy terminal value proved illusory when a new competitor rewrote industry norms. In both cases, the assumption that these companies would retain their competitive edge for the long haul proved disastrously wrong, highlighting how DCF valuation and reality can diverge if industries pivot faster than spreadsheets anticipate. DCF: A Guiding Principle, Not a Blueprint To be fair, some investors argue that even imperfect inputs into DCF models force a disciplined look at a company’s economics. That’s a valid point, but for most stocks — especially in fast-evolving sectors — DCF valuation often becomes a purely academic exercise, disconnected from the actual turbulence of markets. Still, DCF can hold philosophical value: it underscores the importance of cash flow in a company’s well-being. However, pinning down one precise target is like describing a constantly shifting landscape. You capture only a snapshot, not the entire panorama. Is There a Better Way to Value an Asset? Instead of treating valuation as a final answer, think of it as a guiding principle. In a world overwhelmed by data, wisdom — knowing which information matters most — remains scarce. Markets can flip on a dime, so a humble mindset works best. Explore industries with real upside, buy at a sizable discount to a range of fair-value estimates (not just one “magic number”), and continuously refine your assumptions as conditions evolve. While this article focuses on DCF valuation, keep in mind there are other frameworks like sum-of-the-parts, residual income, and scenario analysis. These can provide additional perspective. No single formula has all the answers. Assessing Terminal Potential with “Realistic Imagination” Terminal value still matters, but it works best as a qualitative marker instead of a hard metric. Think of it as “realistic imagination” — evaluating how a sector or product might evolve, considering whether consumer needs or regulatory landscapes will shift, and gauging a company’s adaptability. By envisioning multiple possible futures instead of an “everything-goes-right” spreadsheet scenario, you guard against overconfident projections. Identifying Winners: Knowing What to Pay For After spotting a sector with genuine long-term potential, the next step is figuring out which specific companies can endure shifting market conditions. When attempting to gauge a company’s long-term potential — beyond the confines of any single valuation model — it helps to look at common characteristics among those that consistently defy short-term market noise and deliver enduring results. Amazon, Apple, and Tesla serve as prime illustrations of how these traits manifest in the real world. Figure 2. The Shared DNA of Amazon, Tesla, and Apple Source: Company Websites and Annual Reports Just as investors gain from taking a longer view and maintaining a margin of safety while taking calculative risks, companies that do the same often stay more resilient when the economy turns rough. Yet even powerhouse brands like Amazon, Telsa, and Apple can

Until recently, emerging market (EM) equities were among the darlings of the investing world. And why not? To most investors, a potentially diversifying asset class with prospects for high returns looks like a gift. For active managers, EM equities represent the chance to invest in a less-efficient segment of the market and thereby demonstrate their investment skill. Over the last five years or so, however, the promise of EM equity as an asset class has faded somewhat. This is due to the significantly poorer performance of EM equities versus their developed peers. EM Equity Performance vs. US Equity PerformanceAnnualized Five-Year Returns MSCI EM Index 1.31% S&P 500 11.34% Not all EM equity strategies have disappointed, however. EM factor strategies — in particular multi-factor EM equity approaches — have done well in both absolute terms and relative to the broader EM equity universe. Here, we provide an overview of EM equity investing’s evolving landscape and describe a multi-factor investment process that has avoided the pitfalls of its EM equity peers. The Changing Emerging Market Landscape Some emerging markets have not fulfilled their development potential in recent years. Others have succumbed to political or military strife. Turkey and Russia, for example, once featured prominently in the space but have since fallen out of favor and either receive much lower weights in the core indices or are excluded altogether. On the other hand, Saudi Arabia and Thailand, among other countries, have greatly increased their weights in the same indices. EM investing has become more complicated, and consequently, managers need to adopt more sophisticated approaches to decipher and manage EM portfolios successfully. For example, expertise in Russia and Turkey is not as valuable as it once was, so managers must expand their knowledge of the newer entrants to the investable EM basket. Of course, such expertise is not achieved overnight. Those fundamental managers who do not depend on a quantitative process must develop the requisite skills to navigate the new EM landscape. This presents a daunting challenge. MSCI EM Index: Market Weights as of 31 March 2023 How to Harvest Equity Factor Premia in EM Equities The following chart presents EM equities and their performance numbers. Over the past three years, in particular, a multi-factor EM strategy built according to the process we describe below has outperformed the broad EM market, as represented by the MSCI EM Index, as well as standard EM equity factor strategies and active EM exchange-traded funds (ETFs) more generally. The question is: How was this performance achieved? EM Equity Performance: Absolute Returns MSCI Emerging Markets Index Robust EM Multi-Factor Strategy MSCI Emerging Markets Diversified Multi-Factor Index Active EM ETF Aggregate EM Multi-Factor ETF Aggregate YTD(31 December 2022 to 30 June 2023) 5.10% 9.18% 4.33% 6.04% 4.53% One Year 2.22% 11.76% 4.27% 2.78% 3.29% Three Year 2.71% 8.08% 6.61% 2.78% 4.65% Five Year 1.31% 2.33% 2.22% 1.96% 0.68% How to Build a Robust EM Equity Factor Strategy These results are the product of a four-step investment process. Core to our method are six equity factors that have been validated by dozens of researchers over the years: Value, Momentum, Size, Low Volatility, Profitability, and Low Investment. These factors not only have clear economic interpretations but also have provided reliable and well-documented systematic premia across various geographies and market environments. This is due, in part, to their low correlation with one another, as shown in the illustration below. Low Factor Correlations Mean Smoother CyclicalityLong-Short Factor Correlations Step 1 We first build portfolios for each individual factor, selecting our stocks from the broader EM universe. In the first stage of our process, we filter stocks based on their singular exposure to a given factor — Value, for example. Step 2 We next evaluate the remaining stocks for their individual exposure to the specific factor portfolio in question as well as their exposure to other factors. The goal of this step is to further refine the portfolio stocks based on their overall “factor intensity,” or the sum of their individual exposures (betas) to the broad set of factors. By doing so, each individual factor portfolio maintains a strong tilt to its desired factor and positive exposure to other factors, without sacrificing exposure to its target. This is particularly useful in a multi-factor context since investors want exposure to all rewarded factors. Low Factor Correlations Allow Multi-Factor Investors to Smooth Cyclicality  31 December 1970 to31 December 2022 LowVolatility SmallSize Value HighMomentum HighProfitability LowInvestment Single Factor Sleeves without Factor Intensity Filter Exposure to DesiredFactor Tilt 0.17 0.26 0.26 0.15 0.23 0.30 Factor Intensity 0.31 0.40 0.51 0.31 0.41 0.45 Single Factor Sleeves with Factor Intensity Filter Exposure to DesiredFactor Tilt 0.16 0.24 0.26 0.17 0.25 0.26 Factor Intensity 0.47 0.71 0.72 0.58 0.58 0.60 Step 3 After selecting the stocks in our portfolio, we generate portfolio weights for each using four optimization schemes — Maximum Deconcentration, Diversified Risk Weighted, Maximum Decorrelation, and Maximum Sharpe Ratio. There are two reasons for this. First, we want to remove any remnant of idiosyncratic, stock-specific risk from our factor portfolios. Our goal is to harvest factor premia, not trade “names.” Second, since no modeling methodology is flawless, we also want to mitigate any latent model risk in any one optimization model. Step 4 Finally, we weight each individual factor portfolio equally to build a final multi-factor EM strategy. Why an equally weighted allocation across risk factors? Because it avoids estimation risks and allows investors to harvest the benefits of decorrelation and the cyclicality of their premium, as the figure below demonstrates. Equal Weighting Maximizes Benefit from Factors DecorrelationAnnual Returns of Long-Short Reward Factors Conclusion Many EM equity strategies have experienced poor absolute and relative performance over the last few years largely because of the shifting nature of the investable EM universe. Several previous EM leaders have sputtered in their development or succumbed to political volatility, and many fundamentally driven active managers have failed to adapt. Our quantitative, multi-factor strategy offers an antidote to the challenges of EM equity investing. It

Retirement planning is the primary objective of retail investors. Indeed, 47% of respondents in the 2022 CFA Institute Investor Trust Study indicated saving for retirement was their most important investment goal. Yet the conventional pathway to retirement savings — the traditional stock and bond portfolio — is not as effective as it used to be. Weaker diversification, declining real returns, and rising inflation all present major challenges to both defined benefit and defined contribution (DC) pension funds. As funds struggle to meet their return targets, investors are demanding they provide access to new and potentially riskier products. Fund managers must weigh these demands in the context of their fiduciary duty, or duty of care, obligations. With these challenges in mind, for better or worse — or at least until regulators weigh in — many pension funds are exploring allocations to cryptoassets. So, what does that mean for the future of trust in the financial services industry? Slower wage growth, an aging population, and lower investment returns have all been identified by the Mercer CFA Institute Global Pension Index as critical threats to the future sustainability of pension funds. Asset owners know the headwinds they face: Only a small percentage believe they are very likely to reach their annual return target over the next several years. How Likely Is It That You Will Attain Your Current Target Return over the Next Three Years? That means benefit cuts are not off the table. Of corporate and state-sponsored defined benefit plans, 60% say it is likely or very likely that they will need to adjust benefits downward within the next 10 years. Plan participants depend on retirement fund payouts. That pension funds may reduce their expected outlays creates a deferred trust deficit, one that could undermine faith in the whole retirement funding system. To address the potential return shortfall and cover unfunded liabilities, pension funds have branched out into digital assets and their supporting infrastructure. According to the trust survey, 94% of state and government pension plan sponsors said they invest in cryptocurrencies, along with 62% of corporate defined benefit plans and 48% of corporate DC plans.  The crypto market has had a turbulent history, particularly of late. Volatility has been the norm, with soaring peaks giving way to extreme drawdowns and vice versa. When crypto was near its all-time heights, studies showed that a small allocation to digital assets as part of a diversified portfolio could increase returns, improve the Sharpe ratio, and lower the portfolio’s maximum drawdown. Of course, amid the latest crypto downturn, such conclusions may no longer be operable. Mindful of the risk of direct investments in digital assets, such funds as CalPERS and CDPQ have allocated capital to crypto-adjacent assets, seeking to capitalize on the popular momentum around cryptocurrencies and the potential of blockchain technology while avoiding the day-to-day volatility of direct crypto investment. DC plans have also dipped their toes into the space. Fidelity Investments plan participants will be able to invest as much as 20% of their portfolios in cryptocurrencies. So, what does crypto demand look like? It skews toward younger investors, with 59% of those between the ages of 25 and 34 saying they currently own cryptocurrencies. As digital natives become a larger share of plan participants and hold more assets, pressure on plan sponsors to provide access to digital products will only increase. Percentage of Those Investing in Cryptocurrencies by Age Group But skepticism about expanding access to cryptocurrencies and derivative products is widespread. The US Department of Labor registered its ambivalence in response to Fidelity’s inclusion of cryptocurrency in its 401(k) offerings, stating: “The assets held in retirement plans, such as 401(k) plans, are essential to financial security in old age — covering living expenses, medical bills and so much more — and must be carefully protected. That’s why plan fiduciaries, including plan sponsors and investment managers, have a strong legal obligation under the Employee Retirement Income Security Act to protect retirement savings.” Warren Buffett, meanwhile, has described cryptocurrencies as speculative assets and predicted “cryptocurrencies will come to bad endings.” Pension funds face an unenviable choice: chase higher returns (and more volatility) or underdeliver on performance. Fund inflows are not matching projected outflows, and plan participants have a growing appetite for new, alternative investment products. So, how can the industry respond to these challenges and maintain client trust? Pension plan sponsors want to adopt new products early. Indeed, 88% stated as much in the trust survey. But if those products are unregulated and their long-term performance is unknown, plan sponsors must evaluate if they can be safely incorporated into portfolios without jeopardizing the trust of plan participants or the viability of their retirement savings. As fiduciaries, pension plans must take the long-term view on investment growth and carefully consider and responsibly manage any allocation to new asset classes. They must communicate to plan participants the risks associated with these new asset classes, crypto among them, to ensure the investments align with client goals. To continue to grow investor trust in financial services, retirement planning must be supported by robust due diligence. Pension funds and their participants must understand and believe in the products they are investing in. Without that standard, the trust deficit will only widen. If you liked this post, don’t forget to subscribe to the Enterprising Investor. All posts are the opinion of the author. As such, they should not be construed as investment advice, nor do the opinions expressed necessarily reflect the views of CFA Institute or the author’s employer. Image credit: ©Getty Images/Who_I_am Professional Learning for CFA Institute Members CFA Institute members are empowered to self-determine and self-report professional learning (PL) credits earned, including content on Enterprising Investor. Members can record credits easily using their online PL tracker. source

Since the Federal Reserve’s historic rate hiking campaign and the inversion of the yield curve in late 2022, we have been waiting for an economic downturn. We have yet to see one, and this has confounded economists everywhere. The lingering effects from the COVID pandemic have certainly made this cycle unique. But there are other forces at work, slower moving but potentially longer lasting, that explain the divergence between the economy and traditional economic indicators. For one, the process of credit formation has changed dramatically in a relatively short period of time, which is a hidden but powerful force on the broad economy. The private capital markets — including venture capital, private equity, real estate, infrastructure, and private credit, among other asset classes — have grown more than threefold over just 10 years to nearly $15 trillion today. While this is just a fraction of the $50.8 trillion public equity market, the public market is increasingly including investment vehicles like ETFs and is more concentrated with large corporations that are not representative of the broader economy. The Allure of Private Markets Rolling bank crises and public market volatility have allowed private capital markets to take market share by offering more stable capital to borrowers and earning outsized returns for their investors by charging higher rates for longer-term capital. Investors seeking to maximize their Sharpe ratios in a zero-interest-rate monetary policy world over the past decade found the best way to do so was by locking up their capital with managers who could access uncorrelated and above-market returns. An unintended consequence of doing so, however, was to weaken the causal chain between traditional economic indicators like the yield curve, an indicator of bank profitability, and the real economy because banks and other traditional capital providers are no longer the primary source of capital for the economy. This shift has increased the diversity of capital providers but has also fragmented the capital markets. Borrowers have more options today but also face challenges in finding the right capital provider for their businesses. This greatly increases the value of the credit formation process, which matches lenders and borrowers in the capital markets and has traditionally been performed by Wall Street firms. After the repeal of the Glass-Stegall Act in 1999, large banks and broker dealers acquired each other or merged. The impetuous for these mergers was to access the cheap capital from depositors and deploy that in the higher-margin brokerage business. This ended up introducing too much volatility into the economy as seen during the Global Financial Crisis, and regulations like the Dodd-Frank Act were put in place to protect depositors from the risks of the brokerage business. Wall Street firms are notoriously siloed, and the increased regulation only served to complicate the ability of these firms to work across business lines and deliver efficient capital solutions to their clients. This created the space for private capital firms, who also enjoy less regulation, to win clients from traditional Wall Street firms due to their ability to provide more innovative and flexible capital solutions. The Trade-Off The demand for uncorrelated and low-volatility returns from investors necessitated a trade-off into the less liquid investment vehicles offered by private capital markets. Since the managers of these vehicles can lock up investor capital for the long-term, they are able to provide more stable capital solutions for their portfolio companies and are not as prone to the whims of the public markets. This longer time horizon allows managers to provide more flexibility to their portfolio companies and even delays the realization of losses. This means that public market measures of implied volatility and interest rates have less meaning for the broader real economy, because they only represent the price of capital and liquidity from firms that operate in the short-term like hedge funds, retail investors, and money managers. The cost of capital from real money firms like pension funds, endowments, and insurance companies is better represented in private capital markets. The result is that we have substituted liquidity risk for credit risk in the broader economy due to the growth of private capital markets. When interest rates are low, the future value of a dollar is worth more than the present value of that same dollar. This lowers the natural demand for liquidity and increases the capacity for credit risk which delays the ultimate realization of intrinsic value. Narratives come to dominate investment fundamentals in these environments. The Changing Playbook This changes the playbook for companies in how they fund and grow their businesses. Companies can stay private for longer as they increasingly find long-term investors in the private markets and do not have to be subjected to the higher costs and strictures of the public markets. Source: @LizAnnSonders The M&A playbook has changed, the universe of publicly traded companies to take private has shrunk, and the marketplace for financing these transactions has changed. In the past, a Wall Street bank might have offered a bridge loan for an acquisition to be followed by permanent capital placements. Today, acquirers can partner with hedge funds, private equity, and family office firms for both short-term and long-term capital in a form of one-stop shop for corporate financing. Looking forward, as the popularity of the private markets increases there will be an inevitable agitation to democratize access to these attractive investments. However, enabling the masses to invest in these sophisticated strategies requires increasing their liquidity, which in turn will impair managers’ ability to provide long-term capital and delay fundamental realization events. This will result in a reversal of the credit and liquidity risk trade-off we have seen recently and eventually re-establish the link between the traditional public-market-based economic indicators and the real economy. source

Why do exchange rates often move in ways that even the best models can’t predict? For decades, researchers have found that “random-walk” forecasts can outperform models based on fundamentals  (Meese & Rogoff, 1983a; Meese & Rogoff, 1983b). That’s puzzling. Theory says fundamental variables should matter. But in practice, FX markets react so quickly to new information that they often seem unpredictable (Fama, 1970; Mark, 1995). Why Traditional Models Fall Short To get ahead of these fast-moving markets, later research looked at high-frequency, market-based signals that move ahead of big currency swings. Spikes in exchange‐rate volatility and interest‐rate spreads tend to show up before major stresses in currency markets (Babecký et al., 2014; Joy et al., 2017; Tölö, 2019). Traders and policymakers also watch credit‐default swap spreads for sovereign debt, since widening spreads signal growing fears about a country’s ability to meet its obligations. At the same time, global risk gauges, like the VIX index, which measures stock‐market volatility expectations, often warn of broader market jitters that can spill over into foreign‐exchange markets. In recent years, machine learning has taken FX forecasting a step further. These models combine many inputs like liquidity metrics, option-implied volatility, credit spreads, and risk indexes into early-warning systems. Tools like random forests, gradient boosting, and neural networks can detect complex, nonlinear patterns that traditional models miss (Casabianca et al., 2019; Tölö, 2019; Fouliard et al., 2019). But even these advanced models often depend on fixed-lag indicators — data points taken at specific intervals in the past, like yesterday’s interest-rate spread or last week’s CDS level. These snapshots may miss how stress gradually builds or unfolds across time. In other words, they often ignore the path the data took to get there. From Snapshots to Shape: A Better Way to Read Market Stress A promising shift is to focus not just on past values, but on the shape of how those values evolved. This is where path-signature methods come in. Drawn from rough-path theory, these tools turn a sequence of returns into a kind of mathematical fingerprint — one that captures the twists, and turns of market movements. Early studies show that these shape-based features can improve forecasts for both volatility and FX forecasts, offering a more dynamic view of market behavior. What This Means for Forecasting and Risk Management These findings suggest that the path itself — how returns unfold over time — can predict asset price movements and market stress. By analyzing the full trajectory of recent returns rather than isolated snapshots, analysts can detect subtle shifts in market behavior that predicts  moves. For anyone managing currency risk — central banks, fund managers, and corporate treasury teams — adding these signature features to their toolkit may offer earlier and more reliable warnings of FX trouble—giving decision-makers a crucial edge. Looking ahead, path-signature methods could be combined with advanced machine learning techniques like neural networks to capture even richer patterns in financial data. Bringing in additional inputs, such as option-implied metrics or CDS spreads directly into the path-based framework could sharpen forecasts even more. In short, embracing the shape of financial paths — not just their endpoints — opens new possibilities for better forecasting and smarter risk management. References Babecký, J., Havránek, T., Matějů, J., Rusnák, M., Šmídková, K., & Vašíček, B. (2014). Banking, Debt, and Currency Crises in Developed Countries: Stylized Facts and Early Warning Indicators. Journal of Financial Stability, 15, 1–17. Casabianca, E. J., Catalano, M., Forni, L., Giarda, E., & Passeri, S. (2019). An Early Warning System for Banking Crises: From Regression‐Based Analysis to Machine Learning Techniques. Dipartimento di Scienze Economiche “Marco Fanno” Technical Report. Cerchiello, P., Nicola, G., Rönnqvist, S., & Sarlin, P. (2022). Assessing Banks’ Distress Using News and Regular Financial Data. Frontiers in Artificial Intelligence, 5, 871863. Fama, E. F. (1970). Efficient Capital Markets: A Review of Theory and Empirical Work. Journal of Finance, 25(2), 383–417. Fouliard, J., Howell, M., & Rey, H. (2019). Answering the Queen: Machine Learning and Financial Crises. Working Paper. Joy, M., Rusnák, M., Šmídková, K., & Vašíček, B. (2017). Banking and Currency Crises: Differential Diagnostics for Developed Countries. International Journal of Finance & Economics, 22(1), 44–69. Mark, N. C. (1995). Exchange Rates and Fundamentals: Evidence on Long‐Horizon Predictability. American Economic Review, 85(1), 201–218. Meese, R. A., & Rogoff, K. (1983a). The Out‐of‐Sample Failure of Empirical Exchange Rate Models: Sampling Error or Misspecification? In J. A. Frenkel (Ed.), Exchange Rates and International Macroeconomics (pp. 67–112). University of Chicago Press. Meese, R. A., & Rogoff, K. (1983b). Empirical Exchange Rate Models of the Seventies. Journal of International Economics, 14(1–2), 3–24. Tölö, E. (2019). Predicting Systemic Financial Crises with Recurrent Neural Networks. Bank of Finland Technical Report. source

In the underbelly of private markets lies the main culprit behind corporate failures: defective capital structuring. Frequently the result of human failings, the widespread overcapitalization of start-ups and quasi-universal overleveraging of buyouts have led to a deep-seated zombification of private markets. With interest rates remaining at or near 20-year highs, ballooning interest expenses will continue to cause cash-flow incontinence. A whole new landscape for private capital fund managers and their portfolios could shape out. Forensics in Private Markets In a segment of the economy notorious for its opacity, distressed scenarios are particularly poorly analyzed. Modern investigative techniques applied by turnaround consultants and court-appointed administrators rarely gather sufficient proof of corporate responsibility. This is surprising because Locard’s exchange principle regarding forensic evidence applies to most instances of mismanagement. While market disruption can be deemed a natural cause of death, especially among start-ups, no such justification can be used to describe the putrefaction of debt-bloated buyouts. Naturally, failure is part of private markets’ DNA. About one in six leveraged buyouts (LBOs) fail to deliver their financial sponsors’ hurdle rates, and seasoned venture capitalists (VCs) know that seven out of 10 start-ups they back will lose money. But these are averages over the economic cycle. In a recession, more than half of LBO exits could be bankruptcies or insolvencies as happened in 2009, according to data compiled by the United Kingdom’s Centre for Management Buyout Research at that time. And most dotcoms ran out of money or went through a forced sale process during the 2000-2005 market correction. Live, Die, Repeat Some sectors of the economy regularly go through turmoil. The mattress industry, for instance, has long been subject to periodic crashes. In the wake of the global financial crisis (GFC), UK private equity (PE) firm Candover lost control of Hilding Anders when this mattress maker buckled under its debt burden.[1] Following a complex refinancing, KKR Credit diluted Candover’s equity stake before eventually acquiring the business. Partly due to the Covid-19 pandemic, KKR still holds Hilding Anders in its books[2] eight years later. Other examples of botched buyouts in the sector abound. Last year, Advent-backed Serta Simmons Bedding filed for Chapter 11.[3] It wasn’t a first for Simmons, which had gone bust during the GFC[4] and was then bailed out by credit specialist Ares Management.[5] What is odd about fund managers’ passion for the bedding industry is that, even without leverage, it is a corporate graveyard. Years of quantitative easing encouraged VCs to back mattress start-ups, granting them the right to sell products at a loss. The practice pushed Mattress Firm, the sector’s largest brick-and-mortar retailer in the United States, out of business. E-commerce platforms were no disrupters. They simply peddled their wares through online channels. Eventually, they went ex-growth. In the United States, online specialist Casper Sleep’s abysmal post-IPO trading led to it being taken private in late 2021, 18 months after listing, at half the price of its first-day close.[6] The European equivalent is called Eve Sleep. It was rescued from administration in 2022[7] after its market capitalization dived 95% in the five years following its IPO. The notion that consumers would get into the habit of changing mattresses ever more often was misconceived. Mattresses are typically replaced every eight to 12 years. At the peak of the cycle, consumers renew them more frequently, but when budgets are stretched, they wait much longer. Anatomy Of a Fall Case studies of cyclical sectors are instructive because the COVID pandemic turned many opportunist deal doers into special-situation investors and corporate undertakers. Even acyclical industries, however, can suffer from PE fund managers’ slapdash practices. In recent years, the case of Thames Water, the United Kingdom’s main water and sewerage utility teetering on the verge of bankruptcy, demonstrated the impact that many years of debt-fueled dividend recaps and chronic underinvestment[8] can have not only on water quality and delivery,[9] but also on the viability of a business operating in an industry considered resilient. A similar homicidal scenario occurred 15 years ago at TXU, a.k.a. Energy Future, Texas’s largest power generator that was taken off the stock exchange by KKR, TPG, and Goldman Sachs during the credit bubble before filing for Chapter 11 in 2014.[10] The autopsy of TXU’s corpse revealed that the cause of death was not due to natural causes, such as infrastructure obsolescence, but rather to excessive leverage when shale gas discoveries brought energy prices to all-time lows. If the cause of death was not accidental, luckily for TXU’s PE owners, in the business world no distinction is made between suicidal and homicidal motives. The ability of a hugely cash-generative company operating in a very mature and monopolistic industry to sustain high levels of leverage can help financial sponsors borrow against the terminal liquidation value of the underlying assets. That is the case even if it risks leaving the borrower in distress. If necessary, assets can be realized, either piecemeal or via shotgun disposals. It is surprisingly easy for financial sponsors to renege on their fiduciary responsibilities as majority owners, even though they dictate how much debt their investees borrow. Hence the PE fund managers’ tendency to become recidivist corporate slayers, turning your run-of-the-mill diseased LBO into a crime scene. At any rate, in cases where debt-ridden companies provide vital services like utilities or transport hubs, governments usually have to step in, as the UK authorities are expected to do in a potential renationalization of Thames Water.[11] Debt as the Elixir of Death The investigation of PE-backed zombies is made considerably easier by the fact that the murder weapon is practically always the same: debt. Overleverage leading to bankruptcy is akin to the old medical practice of bleeding patients. Debt commitments force an unreasonable amount of operating cash flows away from the core activities of a corporation. Just like bleeding made the human body invariably weaker, when interest rates rise, LBOs run through cash at a faster clip. The main consideration for borrowing is to allow financial sponsors to reduce the equity

Foreign exchange (FX) markets are shaped by liquidity fluctuations, which can trigger return volatility and price jumps. Identifying and predicting abnormal FX returns is critical for risk management and trading strategies. This post explores two advanced approaches that allow investment professionals to better understand and anticipate shifts in market conditions. By integrating liquidity metrics with predictive algorithms, investors can gain deeper insights into return behavior and improve risk-adjusted decision-making. The first approach focuses on outlier detection, where robust statistical methods isolate periods with exceptionally large price movements. These detected outliers are then predicted using machine learning models informed by liquidity metrics, alongside key macroeconomic indicators. The second approach targets liquidity regimes directly, employing regime-switching models to differentiate high-liquidity from low-liquidity states. Subsequent return analysis within each regime reveals how risk is magnified in lower-liquidity environments. Observed patterns in major currency pairs suggest that periods of reduced liquidity coincide with abnormal price behavior. Researchers like Mancini et al. and Karnaukh et al. have demonstrated that liquidity risk, often measured through bid–ask spreads or market depth, is a priced factor. Others, such as Rime et al., highlight how liquidity and information proxies can improve FX forecasting. Building on these findings, there are two possible ways to tackle abnormal returns by leveraging machine learning methods and liquidity indicators. Tackling Abnormal Returns Outliers The first approach is to treat abnormal weekly returns, i.e., outliers, as the primary target. Practitioners could collect weekly returns of various currency pairs and apply either simple robust methods like the median absolute deviation (MAD) or more sophisticated clustering algorithms like density-based clustering non-parametric algorithm (DBSCAN) to detect outlier weeks. Once identified, these abnormal returns can be forecast by classification models such as logistic regression, random forests, or gradient boosting machines, which make use of liquidity measures (bid–ask spreads, price impact, or trading volume) as well as relevant macroeconomic factors (e.g., VIX, interest rate differentials, or investor sentiment). The performance of these models can then be evaluated using metrics such as accuracy, precision, recall, or the area under the ROC curve, ensuring that the predictive power is tested out of sample.  Liquidity Regimes The second approach shifts the emphasis to the identification of liquidity regimes themselves before linking them to returns. Here, liquidity variables like bid–ask spreads, trading volume, or a consolidated liquidity proxy are fed into a regime-switching framework, sometimes a hidden Markov model, to determine states that correspond to either high or low liquidity. Once these regimes are established, weekly returns are analysed conditional on the prevailing regime, shedding light on whether and how outliers and tail risk become more likely during low-liquidity periods. This method also gives insight into transition probabilities between different liquidity states, which is essential for gauging the likelihood of sudden shifts and understanding return dynamics more deeply. A natural extension might combine both approaches by first identifying liquidity regimes and then predicting or flagging outliers using specific regime signals as input features in a machine learning setup. In both scenarios, challenges include potential limitations in data availability, the complexity of calibrating high-frequency measures for weekly forecasts, and the fact that regime boundaries often blur around macro events or central bank announcements. Results may also differ when analysing emerging markets or currencies that typically trade at lower volumes, making it important to confirm any findings across a variety of settings and apply robust out-of-sample testing.  Ultimately, the value of either approach depends on the quantity and quality of liquidity data, the careful design of outlier or regime detection algorithms, and the ability to marry these with strong predictive models that can adapt to shifting market conditions. Key Takeaway Navigating FX market volatility requires more than traditional analysis. Liquidity-aware models and machine learning techniques can provide an edge in detecting and forecasting abnormal returns. Whether through outlier detection or liquidity regime modeling, these approaches help investors identify hidden patterns that drive price movements. However, data quality, model calibration, and macroeconomic events remain key challenges. A well-designed, adaptive framework that integrates liquidity dynamics with predictive analytics can enhance investment strategies and risk management in evolving FX markets. source

The Four Pillars of Investing, Second Edition: Lessons for Building a Winning Portfolio. 2023. William J. Bernstein. McGraw Hill Professional. In The Four Pillars of Investing, Second Edition: Lessons for Building a Winning Portfolio, William J. Bernstein, a retired neurologist and the cofounder of the investment management firm Efficient Frontier Advisors, provides a comprehensive guide that offers important insights and practical strategies for creating and maintaining a successful investment portfolio. The book, first published in 2002, gives investors a strong foundation in financial principles. Bernstein sets out four key pillars that serve as the bedrock: theory, history, psychology, and business. These pillars together function like the four legs of a chair and are the guiding principles for making good investment decisions. The first pillar, theory, includes comprehending the underlying concepts and principles that lead to successful investing. Bernstein discusses the need to create a well-diversified portfolio that strikes a balance between risk and return, tailored to individual financial goals, time horizon, and risk tolerance. He explores the intricate relationship between risk and reward, encouraging investors to thoroughly assess their risk appetite before making investment decisions.  The second pillar, history, stresses the importance of analyzing past market trends and historical data because history provides invaluable insights into the behavior of financial markets. History is my favorite of the four pillars. In my opinion, investors should spend more time analyzing financial history to understand what is possible in deriving their views on financial markets, instead of listening to “experts.” Based on historical events, including market booms/busts and recessions, the author illustrates the cyclical nature of markets and highlights the importance of a long-term investing approach. He discusses the implications of market efficiency for retail investors while advocating diversified portfolios as opposed to relying on market timing or individual stock selection strategies.  The third pillar, psychology, highlights the impact of human behavior on investment decisions since the presence of emotional biases can lead to irrational decision making. Bernstein discusses various biases and provides strategies for investors to overcome them. Keeping a disciplined approach to investing and avoiding emotional reactions to short-term market fluctuations are key messages that Bernstein provides throughout the book. Bernstein encourages investors to focus on long-term goals and to develop an investment plan based on solid principles while avoiding emotional decisions driven by noise or short-term trends.  The fourth pillar, business, explores individual companies and their financial performance. Investors should conduct thorough research and gain a deep understanding of the businesses in which they choose to invest. The author stresses the importance of investing in undervalued assets, as well as the impact of fees and expenses on investment returns. He emphasizes the need to minimize costs because they can significantly erode investment performance over time. Bernstein advises investors to seek low-cost investment options that offer broad market exposure at a lower cost than that of using actively managed funds. Although the investment content in magazines, newspapers, social media, and market strategist interviews should be largely ignored, Bernstein recommends reading the Economist’s finance section and listening to the authors of academic papers referenced in this book on YouTube or podcasts, such as Eugene Fama, Zvi Bodie, and Robert Shiller. He supports his pillars with practical examples, case studies, and historical data, making the content accessible and understandable. The Four Pillars of Investing has received numerous accolades for its comprehensive approach and focus on evidence-based strategies. However, critics have argued that it may be too technical for beginner investors and overlook the possible benefits of active investing.  Private wealth investment professionals can use this book as a way to convey some basic investment concepts to individual clients who are not already familiar with them. Although the author argues that most brokers and advisers occupy the lowest rung in the hierarchy of investment knowledge, these same investment professionals can play a critical role in helping individual investors manage around their own psychology by “staying the course” and not overreacting to short-term fluctuations. This can be an important role played by brokers and advisers because the failure of just one leg of the chair can lead to the demise of the entire investment strategy.   In summary, The Four Pillars of Investing is an important tool for investors looking to design a more successful investment portfolio. Investors can make better financial decisions by comprehending the four pillars of theory, history, psychology, and business. This book highlights the importance of disciplined investing and a long-term diversified approach to managing risk and achieving financial goals. Because of its insights and practical guidance, this book remains a critical resource for those investors trying to navigate the complex world of investing.  If you liked this post, don’t forget to subscribe to Enterprising Investor and the CFA Institute Research and Policy Center. All posts are the opinion of the author. As such, they should not be construed as investment advice, nor do the opinions expressed necessarily reflect the views of CFA Institute or the author’s employer. Professional Learning for CFA Institute Members CFA Institute members are empowered to self-determine and self-report professional learning (PL) credits earned, including content on Enterprising Investor. Members can record credits easily using their online PL tracker. source

When China restricted exports of gallium and germanium in 2023, markets were reminded that supply chains can be disrupted. These metals may not be household names, but they are critical to semiconductors, defense systems, and renewable energy, which is why the restrictions drew immediate market attention. Investors are again turning to supply chain resilience as a portfolio concern. Rare earth elements sit in the same category as gallium and germanium. Embedded in electric vehicles, advanced weaponry, and clean energy infrastructure, rare earth elements represent one of the few asset themes where geopolitics directly drives market outcomes. That reality was underscored in July, when the United States backed MP Materials, its only active rare earth miner, with a multibillion-dollar package including equity, loans, and a 10-year price floor on neodymium and praseodymium. The deal, discussed further in Winston Ma’s Enterprising Investor analysis of a potential US sovereign wealth fund, shows how policy is moving from rhetoric to concrete capital commitments. For investors, the right question isn’t whether rare earths can “beat the market.” It’s whether they can provide diversification and resilience in moments when traditional portfolios are vulnerable. A Portfolio Framing: Rare Earths as a Stress Hedge To evaluate this, I built a Maximum Sharpe Ratio portfolio using five ETFs: REMX – Rare Earth & Strategic Metals LIT – Lithium & Battery Technology ITA – Aerospace & Defense GLD – Gold (geopolitical hedge) IEF – U.S. Treasuries (defensive anchor) The goal was not to design a market-beating strategy, but to evaluate whether rare earth exposures add portfolio resilience. I used monthly returns from January 2018 to July 2025, a 36‑month rolling covariance matrix, and quarterly rebalancing. The results: Annualized Return: 11.45% vs. 14.53% (S&P 500) Volatility: 21.95% vs. 17.19% Sharpe Ratio: 0.43 vs. 0.73 If judged solely on Sharpe ratio, the portfolio underperformed broad equities. But this misses the real point: rare earths tend to outperform during geopolitical shocks and supply chain disruptions, precisely when traditional portfolios are most at risk. For investors, the practical takeaway is to test rare earths alongside other diversifiers, such as commodities, infrastructure, or defense equities, in a satellite sleeve. When Rare Earths Shine Looking at recent episodes of stress and transition highlights how rare earths can function as a hedge when traditional portfolios stumble. 2019 United States–China Trade Dispute: During the 2019 tariff standoff, rare earth and defense ETFs advanced even as the S&P stumbled. This divergence highlighted their value as a hedge against policy-driven supply chain risks. 2020–2021 EV Adoption Rally: As electric vehicle demand accelerated, lithium and rare earth exposures surged ahead of the market. For investors, this underscores their potential to capture secular growth trends while adding diversification. 2023 Export Controls: When China restricted exports of gallium and germanium, rare earth themes drew renewed attention and outperformed. The episode showed how policy shocks can create “thematic alpha” precisely when traditional markets are vulnerable. These bursts illustrate the real value: rare earths function as a shock absorber. They won’t replace equities, but they can provide a counterweight when macro risks flare. Figure 1. Practical Applications Thematic Diversification: Use rare earths as a satellite allocation that complements big secular themes: electrification, defense modernization, and the clean energy transition. These exposures can give portfolios targeted access to structural growth trends. Geopolitical Risk Premium: Recognize that policy shocks, not just market cycles, can drive returns. Export bans, tariffs, and supply disruptions often move rare earth markets independently of equities, giving investors a rare source of true diversification. Portfolio Construction:  Test rare earths as a 5% to 10% sleeve within a diversified portfolio. Pair them with gold and Treasuries to balance risk. The goal isn’t to outperform equities, but to add resilience when equities are stressed. Key Takeaways Rare earths are not a silver bullet, but they are a geopolitical hedge that investors can’t ignore. Traditional risk metrics (Sharpe ratio) understate their value: non-correlation and tail events. For allocators, the right framing is resilience, not return chasing. In a world where supply chains are vulnerable, rare earths are more than a commodity story. They are a portfolio strategy for managing geopolitical risk. The author declares no conflicts of interest. This article is based on publicly available ETF pricing data (2018 to 2025). It does not constitute investment advice and is intended solely for educational purposes. source