Dear Quants!
Having worked in the industry for over a decade and taught numerous young professionals and students, I have decided to launch a foundational series for aspiring analysts and quants. You will find abundant research criticizing the assumptions surrounding these concepts and efforts to advance them further. Some are solid approaches, while others are marketing ideas that work well in a sales pitch but lack lasting value in our pursuit of sustainable returns. Like any machine learning scientist or professional financial analyst, you might reach a decent level in your career by simply ‘driving’ the tools in front of you, be it Python libraries to build your ML models or using Bloomberg or other providers to build financial models. However, at some point, you will need to look under the hood and understand the engine to truly add value. Like Ken Miles in ‘Ford vs Ferrari’, you will need to become an excellent mechanic to become a professional driver. This series is not designed to make you a professional but will provide an initial understanding of the theories many of us still work with and ultimately will come to realize the limits to your potential to generate alpha.
At this point, I don’t even know when this series will end, but I know at some point, we will start diving deeper into certain topics, leveraging my network in the professional and academic spaces. So, I’m really looking forward to what this could become in 6–12 months from now.
After a long preamble, let’s dive into our first topics! Here is what you can expect in the Part 1:
- Capital Market Theory (CMT)
- Efficient Market Hypothesis (EMH)
- Modern Portfolio Theory (MPT)
Capital Market Theory
Understanding Capital Market Theory (CMT) is the first step toward your career in financial economics and investment research. It explains how securities are priced, the relationship between risk and return, and how investors behave in capital markets. This theory aids in understanding how capital markets function, including how resources are allocated, how assets are priced, and how returns are generated. CMT is particularly important for quantitative analysts (quants) and investors because it provides a theoretical foundation for making informed investment choices, assessing assets, and developing strategies for managing portfolios. For quants, CMT is useful in developing models that predict asset prices and manage risk through mathematical and statistical methods. It helps us gain insights into market behavior and deal more effectively with the complexities of the financial market.
Efficient Market Hypothesis
The Efficient Market Hypothesis (EMH) is the foundational layer on which all investment strategies are based, knowingly or not. Understanding the core concepts and statistical tools to test the extent to which the EMH applies to certain markets or asset classes can better guide your research and assess the sustainability of your investment model. From a high-level view, the EMH formulates how and to what level information is integrated into asset prices.
EMH categorizes market efficiency into three distinct forms: weak, semi-strong, and strong, each representing different degrees of market information absorption. The weak form asserts that all past trading information is reflected in stock prices, suggesting that technical analysis cannot consistently lead to superior returns. During my early days as a quantitative analyst on the sales side, mentored by technical analysts, I quickly realized the limitations of relying solely on past price movements and volume data to predict future stock prices. This was a practical introduction to the weak form efficiency of markets.
The semi-strong form of EMH takes this a step further by asserting that all publicly available information is reflected in asset prices, not just past trading information. Consequently, all publicly accessible information, including financial statements, news releases, and other public disclosures, is immediately and fully reflected in asset valuations. This assertion has profound implications for investment strategies, as it suggests that it is impossible to consistently achieve higher returns through fundamental analysis or by trading on public information. Research across various asset classes supports this assertion, showing that markets quickly adjust to new information, rendering traditional forms of fundamental analysis less effective in predicting future price movements. Studies in equity markets have demonstrated that stock prices adjust almost instantaneously to earnings announcements and macroeconomic news, indicating a high level of market efficiency. Similarly, in bond markets, research findings suggest that interest rate changes and monetary policy announcements are rapidly incorporated into bond prices. Even in less traditional asset classes, such as commodities and real estate, the impact of relevant economic indicators and geopolitical events on prices tends to affirm the semi-strong form of EMH in most developed and emerging markets.
Finally, the strong form of EMH claims that all information, public and private, is fully reflected in stock prices. This would imply that even insider information cannot be used to achieve consistent excess returns. While the strong form is more theoretical and less observed in practice, it serves as a reminder of the profound efficiency of capital markets and the challenges faced by those attempting to outperform them.
As a result, the EMH implies that active management strategies aimed at outperforming the market are often less effective than expected, leading many investors to prefer passive management approaches, such as index fund investing, which aims to mirror the performance of a market index at a very low cost point, as we can see in the massive growth of the mostly still passive ETF market over the past two decades.
Critics argue that EMH overlooks the psychological and behavioral aspects of market participants, which can lead to irrational trading and market anomalies… one of the several reasons why I remain very active in the constantly innovative and challenging industry of investment management and research.
Behavioral finance, for instance, provides numerous examples where investor psychology leads to patterns such as overreaction, underreaction, and other biases that EMH cannot fully account for. Additionally, the assumption that information is instantly and uniformly available to all investors overlooks disparities in access to information and the ability to process it efficiently. There are still so many investors out there who believe they can process, analyze, and act on information faster than a quantitative model can. In light of accessible AI, this is becoming a less and less defensible standpoint, in my view.
Besides this, real-world events such as market bubbles and crashes offer empirical challenges to the strong form of EMH, suggesting that prices do not always reflect underlying fundamentals. You will find enough examples out there, and I highly recommend making yourself familiar with them, starting with the Tulip Mania, the Volkswagen Short Squeeze in 2008 (I traded through this one in a high-frequency environment — a fascinating case!), cryptocurrencies, GameStop, and, more recently, Nvidia. Each of these instances provides a unique case study into how market sentiment, speculation, and investor behavior can deviate significantly from the rational, information-driven expectations posited by EMH.
Acknowledging these limitations is important for every quant, as it impacts our comprehensive understanding of market dynamics and the development of robust investment strategies that can adapt to the complexities of real-world financial markets.
Modern Portfolio Theory — The Efficient Frontier
How can investors construct a portfolio to maximize expected return for a given level of risk? This key question, posed by Harry Markowitz in his groundbreaking 1952 paper ‘Portfolio Selection’ and later recognized with a Nobel Prize in Economic Sciences, laid the foundation for Modern Portfolio Theory (MPT). Markowitz’s theory introduced the concept of diversification as a mathematical framework for assembling a portfolio of assets that collectively reduces risk more effectively than any individual investment within the portfolio could on its own. He proposed that by combining assets with varying levels of risk and return, and by considering their correlations, investors could construct an ‘efficient frontier’ — a set of optimal portfolios offering the highest expected return for a given level of risk. This innovative approach shifted the focus from selecting individual securities to designing a balanced, diversified portfolio that aligns with an investor’s risk tolerance and return objectives.
The MPT provides a systematic method for portfolio construction that emphasizes the optimization of a portfolio through diversification. It involves analyzing expected returns, variances, and correlations of various assets to find the efficient frontier, which shows the portfolios that offer the highest expected return for each risk level. Among these, the Global Minimum Variance Portfolio (GMVP) stands out as a key concept within Markowitz’s framework. The GMVP is the portfolio with the lowest possible risk (variance) for the given set of assets, regardless of return, and serves as a critical starting point for constructing efficient portfolios.
Within the framework of MPT, risks are categorized into systematic and unsystematic. Systematic risk, or market risk, affects the entire market and cannot be eliminated through diversification. Examples include economic recessions and geopolitical tensions, which tend to impact the broad market. For instance, the 2008 financial crisis exemplified systematic risk, affecting almost every asset class. Similarly, geopolitical events like the Brexit referendum in 2016 led to widespread market volatility, underscoring the pervasive nature of systematic risk.
Unsystematic risk, on the other hand, is specific to a particular company or industry and can be largely mitigated through diversification. A prime example of unsystematic risk is the bankruptcy of Enron in 2001, which devastated its shareholders but had a limited impact on the broader market. Another example is the 2018 Facebook data privacy scandal, which led to a significant drop in the company’s stock price but did not affect the entire tech sector or the market as a whole.
The efficient frontier represents portfolios that have optimized the balance between expected return and risk, minimizing unsystematic risk through diversification while accepting the unavoidable systematic risk that comes with the broader market. For someone who has been investing for European and US investment managers and constantly has the conversation around home bias, it is important to note that the efficient frontier is not limited to stock or sector allocations. In order to get even close to the theoretical framework of the efficient frontier, the investment universe must include different asset classes, geographies, and investment approaches.
To calculate portfolios that lie on the efficient frontier, we can employ various optimization techniques to identify the mix of assets that maximizes returns for a given level of risk or minimizes risk for a given level of return. This calculation is rooted in the foundational principles of Modern Portfolio Theory.
The expected return of a portfolio is derived from the weighted average of the expected returns of each asset it contains. These weights are proportional to the amount invested in each asset relative to the total portfolio value. The expected returns of each asset are a critical input that I cannot cover in detail here. Most investors often look at historical data to estimate the average rate of return over a specific period. But as you can guess, the reality is that it’s not simply a matter of extrapolating past performance into the future. Financial analysts and quants use a variety of different approaches to forecast returns, including discounted cash flow analysis, option pricing models to assess potential movements of derivative investments, sentiment analysis that determines market mood from various sources of information, or machine learning models that account for the impact of dynamic factors.
Risk, the second key element in portfolio optimization, is evaluated by the expected portfolio’s variance, which is a measure of how much the returns of the portfolio can be expected to fluctuate. The correlation coefficient ρ plays a key role in this context, as it measures how the returns of two assets move in relation to each other. The goal in portfolio construction is often to select assets with low or negative correlations to enhance diversification and reduce overall risk. This is because a mix of assets with diverse performance characteristics can lead to a portfolio that performs more consistently over time, mitigating the impact of unsystematic risk.
Modern Portfolio Theory — Assumptions and Criticism
Despite the mathematical elegance of the efficient frontier and its utility in portfolio optimization, there are critical considerations and criticisms to be aware of. Correlations between assets can change, particularly during periods of market stress, potentially diminishing the expected benefits of diversification (Stable Correlation Assumption).
Other assumptions and practical considerations we must consider are:
- Model Risk from Historical Data: The reliance on historical data to estimate future returns, variances, and correlations can lead to model risk. Past performance is not always indicative of future results, yet MPT often uses historical data as a predictive tool, which may not always capture future market dynamics.
- Assumption of Normal Distribution: MPT assumes that the returns of assets are normally distributed, which simplifies the calculation of risk as variance. However, real-world data often exhibit skewness and excess kurtosis, leading to the underestimation of extreme events or tail risks.
- Assumption of Rational Behavior: MPT assumes that all investors act rationally, seeking to maximize returns for a given level of risk. This assumption overlooks the realities of behavioral finance, where investors’ decisions can be influenced by psychological biases and irrational behaviors.
- Necessity for Ongoing Reassessment: The efficient frontier is not static but dynamic. As market conditions vary, there is a clear need to regularly evaluate and adjust the portfolio.
- Single-Period Model Limitation: The theory typically applies to a single time period, which may not align with multi-period investment horizons. This misalignment can impact the optimal asset allocation for long-term investors.
- Ignoring Transaction Costs and Taxes: MPT calculations often do not account for transaction costs, taxes, and other market frictions that can significantly impact real-world portfolio performance and the feasibility of frequent rebalancing.
I want to outline again: As market conditions change, so too does the composition of the efficient frontier. This dynamic nature requires ongoing analysis to ensure that the portfolio remains as close as possible to the optimal frontier, adapting to new information and market movements. Moreover, considering alternative assets like real estate, commodities, and private equity can diversify a portfolio beyond the traditional 60/40 stocks and bonds approach, potentially enhancing the risk-return profile. Adopting a dynamic asset allocation strategy allows for more flexible adjustments to the portfolio in response to real-time market data and economic indicators, offering a proactive approach to portfolio management in the face of changing market conditions.
Understanding and predicting investor behavior through the lens of behavioral finance can lead to more realistic models of market dynamics and investor reactions. Tail risk hedging strategies, such as the use of derivatives, are extremely useful for protecting against extreme market movements, addressing the underestimation of tail risks inherent in MPT and the main risk factor that remains: systematic risk.
For all my students reading this… your midterm will include a question on the number of investments that, according to empirical evidence, are deemed sufficient to alleviate most unsystematic risks (review the link).
Further Readings
- https://www.jstor.org/stable/1831028
- https://econpapers.repec.org/article/blajfinan/v_3a47_3ay_3a1992_3ai_3a2_3ap_3a427-65.htm
- https://www.ivey.uwo.ca/media/3775518/the_cross-section_of_expected_stock_returns.pdf
- https://www.sciencedirect.com/science/article/abs/pii/0304405X77900095
- https://www.jstor.org/stable/4480206
- https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2325825
