CFA Institute

When we talk about stock returns, most people assume that individual stocks should yield positive returns. That’s because the stock market has historically outperformed other asset classes like bonds. But surprisingly, the median monthly return for a large sample of individual stocks is — drumroll, please – zero. That’s right. A study conducted by Henric Bessembinder and published in the Financial Analysts Journal in April 2023 found that on a monthly basis, individual stocks generate returns centered around zero. In fact, this paints a “half-full, half-empty” scenario. Half the stocks produce positive returns, while the other half have negative returns. As an investor or advisor, how do you and your clients react to this? If this zero-median return statistic were the only way to look at stock performance, it would be hard to justify investing in stocks at all. Convincing clients to invest in equities would be an uphill battle, especially if they’re seeking short-term gains. Volatility In fact, there are many ways to evaluate stock returns beyond just focusing on median monthly performance. One common approach is to measure stock returns in terms of volatility. Volatility refers to how much a stock’s price fluctuates, and it’s often measured using standard deviation. On average, the annual standard deviation for stock returns is about 50%, which means that the price of an individual stock can swing wildly throughout the year. If we apply the 95% confidence interval often used in statistics, this implies that an individual stock’s return could vary by roughly +/- 100% in a given year. This is huge. Essentially, an individual stock could double or lose all its value within 12 months. This level of uncertainty can make stocks seem daunting, especially for those looking for stability. The idea that individual stocks are a “half-full, half-empty” proposition monthly, and are even more volatile annually, can scare away potential investors. But it’s important to remember that stocks are primarily intended to be long-term investments. The short-term ups and downs, while nerve-wracking, are part of the journey toward long-term wealth creation. So, what happens when we shift our focus to long-term individual stock returns? Shouldn’t we expect more consistency over time? Bessembinder also looked at long-term stock performance, and the findings weren’t exactly comforting. Over the long run, 55% of US stocks underperformed US Treasury Bill returns, meaning that more than half of individual stocks did worse than the safest government-backed investments. Perhaps even more alarming is the fact that the most common outcome for individual stocks was a 100% loss — complete failure. These findings suggest that investing in individual stocks is a high-risk endeavor, even when taking a long-term approach. Typically, when investors and financial analysts assess stock performance, they focus on two key statistical measures: central value (such as the mean or median return) and volatility (as measured by standard deviation). This traditional method of analysis often leads to a negative or at least discouraging narrative about investing in individual stocks. If returns are largely zero in the short term, highly volatile in the medium term, and risky in the long term, why would anyone invest in stocks? The answer, as history shows, is that despite these challenges, stocks have significantly outperformed other asset classes like bonds and cash over extended periods. But to truly understand why, we need to look beyond the typical first two parameters used in analyzing stock returns. The Third Parameter for Assessing Stock Performance: Positive Skew While traditional analysis focuses heavily on the first two parameters — central value and volatility — it misses a crucial component of stock returns: positive skew. Positive skew is the third parameter of stock return distribution, and it’s key to explaining why stocks have historically outperformed other investments. If we only focus on central value and volatility, we are essentially assuming that stock returns follow a normal distribution, similar to a bell curve. This assumption works well for many natural phenomena, but it doesn’t apply to stock returns. Why not? Because stock returns are not governed by natural laws; they are driven by the actions of human beings, who are often irrational and driven by emotions. Unlike natural events that follow predictable patterns, stock prices are the result of complex human behaviors — fear, greed, speculation, optimism, and panic. This emotional backdrop means that stock prices can shoot up dramatically when crowds get carried away but can only drop to a limit of -100% (when a stock loses all its value). This is what creates a positive skew in stock returns. In simple terms, while the downside for any stock is capped at a 100% loss, the upside is theoretically unlimited. An investor might lose all their money on one stock, but another stock could skyrocket, gaining 200%, 500%, or even more. It is this asymmetry in returns –the fact that the gains can far exceed the losses — that generates positive skew. This skew, combined with the magic of multi-period compounding, explains much of the long-term value of investing in stocks. Learn to Tolerate Tail Events If you examine stock return distributions, you’ll notice that the long-term value from investing in the market comes primarily from tail events. These are the rare but extreme outcomes that occur at both ends of the distribution. The long, positive tail is what produces the outsized returns that more than make up for the smaller, frequent losses. For stocks to have generated the high returns we’ve seen historically, the large positive tail events must have outweighed the large negative ones. The more positively skewed the return distribution, the higher the long-term returns. This might sound counterintuitive at first, especially when traditional portfolio management strategies focus on eliminating volatility. Portfolio construction discussions often center around how to smooth out the ride by reducing exposure to extreme events, both positive and negative. The goal is to create a more-predictable and less-volatile return stream, which can feel safer for investors. However, in avoiding those unnerving tail events, investors eliminate both the

The size factor is among those equity risk factors that have provided a premium over the longer term. Recently, however, some researchers have expressed doubt about its utility based on a comparison of its performance with other well-known factors. For example, Ron Alquist, Ronen Israel, and Tobias Moskowitz as well as Noah Beck, Jason Hsu, Vitali Kalesnik, and Helge Kostka have argued that there is neither strong empirical evidence nor robust theoretical support for a persistent size premium. But there are reasons why most investors should question the relevance of these conclusions. Statistical analyses by Joel L. Horowitz, Tim Loughran, and N.E. Savin show that the stand-alone outperformance of small-cap stocks over large-cap stocks is weak and may even disappear when exposure to the market factor is taken into account. In particular, augmenting the set of independent variables with the lagged market return, in addition to the contemporaneous market return, leads to an insignificant size premium. While of marginal statistical interest, this result has little if any practical implication for investors. Indeed, the lagged market “factor” is an artificial construct that investors cannot hold in their portfolios and so has only hypothetical statistical applications. As such, measuring the alpha of such a non-investable factor does not make economic sense. For us, the more important question is: Does the size factor add value to an investor’s portfolio? Factor performance should be assessed from a portfolio perspective The simplest way to determine whether a factor adds value to a portfolio is to compare the portfolio’s Sharpe ratio with and without the factor. The higher the Sharpe ratio, the higher the risk-adjusted return of the overall portfolio. A stand-alone factor premium will not answer this question, since this does not account for the factors’ risk characteristics, namely the correlations between the factor under consideration and the other factors in the portfolio. Furthermore, gauging exposure to the market factor alone does not give a complete picture of how the factor will impact the portfolio because it ignores correlations with other factors. Adding the lagged values of the market factor in the regression does not resolve this problem and also assumes that an investor’s choice is limited to holding only the market or holding the market and size. To properly analyze the size factor, we must evaluate its utility within a set of economically relevant factors. Examining the size factor alongside economically meaningless or redundant factors hardly yields any statistical or economic insight. Consequently, to determine whether size adds value and improves the Sharpe ratio of a portfolio, we need to integrate exposures to all these other factors into our analysis. In work previously published in The Journal of Beta Investment Strategies, Scientific Beta researchers Mikheil Esakia, Felix Goltz, Ben Luyten, and Marcel Sibbe conducted several tests to determine whether the size factor does indeed improve the Sharpe ratio of a multi-factor investor. The results presented in the chart below illustrate that it clearly does and are consistent with findings from other researchers. The graph shows the factor weights that maximize the Sharpe ratio of an investor who can choose from a factor menu featuring the market, size, value, momentum, low-risk, high-profitability, and low-investment factors, which have been widely used in both academic and practitioner research. This is a straightforward way to assess a factor’s impact on the risk/return characteristics of a portfolio. Any deviation from these weights would lower the Sharpe ratio. The size factor received a weight of more than 9% in the portfolio, which is greater than that of value (2.9%) and close to those of momentum (11.4%) and low risk (11.7%). Weights in Mean-Variance Optimal Portfolio, July 1963 to December 2018 In the same study, the researchers also reported that the stand-alone size factor had the lowest return among the factors on the menu over the analysis period. Momentum and low risk had average stand-alone premia that were about three times as high. However, the weights of the momentum and low-risk factors in the optimal portfolio are not much higher than that of the size factor. What explains these results? Ultimately, optimal factor weights depend on more than just returns. They also rely on risk properties, notably factor volatilities and the correlations of each factor with factors other than the market factor. Taking these risk properties into account is particularly useful since we can measure them with a fair degree of reliability, while expected returns are notoriously hard to estimate. The size factor’s positive weight in the optimal portfolio demonstrates that including exposure to size improves the risk/return profile of a multi-factor portfolio. In particular, the size factor contributes to the Sharpe ratio because it has a particularly low correlation with other traditional factors, which makes it an effective diversifier of the portfolio. Indeed, its diversification benefits are so strong that even with close to no premium, the size factor would still be a valuable addition to a multi-factor portfolio. The size factor may not have stellar returns, but it is a valuable addition to a portfolio When a portfolio’s exposures to factors other than the market factor are taken into account, adding the size factor clearly improves the portfolio’s risk/return characteristics. Size is a strong diversifier of other traditional factors and consequently adds value to a multi-factor portfolio. Analysis that doesn’t consider exposures to momentum, profitability, and other factors is of little use to investors. Finally, there is a size effect. Claiming otherwise contradicts the various academic asset pricing models that show the size factor adds explanatory power in the cross-section of returns. These models, by including factors other than the market, provide meaningful conclusions for investors and bear out the size factor’s important contribution to portfolio diversification and risk control. If you liked this post, don’t forget to subscribe to 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 /Liudmila Chernetska Professional Learning for CFA Institute Members CFA Institute

The euro’s value relative to the US dollar (EUR/USD) recently dipped below parity for the first time since 2002. So precipitous and rapid has been the decline in EUR/USD over the past year that many mean reversion/short gamma funds have had to liquidate and return the remaining capital to investors. Hence the question posed in the title above. While charged buzzwords like “uninvestable” should be used with caution, the Russia–Ukraine war has clearly exposed and exacerbated the eurozone’s vulnerabilities. But to answer the underlying question, we need first to explore the literature on exchange rates and see what explanatory model (or models) works best. The Suite of Models: Different Horses for Different Courses Is there an overarching gestalt framework for currencies? Or do distinctions among developing and emerging markets, major and minor markets, and reserve currencies like the USD and the EUR necessitate multiple frameworks? The balance of payments (BOP) method offers key insights in all cases, with its classic accounting identity for economic adjustment: Savings − Investment = Income − Expenditure = Exports – Imports.  But the differences in the financial/capital accounts — mobile vs. restricted as allowed by regulations — and the nature and scope of monetary policies, from the traditional to the unconventional, make certain models more applicable in some domains than others. What does the purchasing power parity (PPP) approach, which measures the relative price of goods, tell us about the EUR? Could the portfolio balance approach, which gauges the relative price of assets, help us understand how quantitative easing (QE) has affected the transmission channel of international portfolio investments?  A Hamstrung ECB  Needless to say, the eurozone, currently comprising 19 member states that have adopted the EUR, is far more complex to analyze than a single sovereign state. Importantly, the eurozone is a monetary union without a fiscal union. Given the lack of a federal fiscal authority, the European Central Bank (ECB), along with its  price stability mandate, has also assumed de facto responsibility for countering financial fragmentation risk through containing core-periphery credit spreads. Then-ECB president Mario Draghi made that especially explicit in his famous “Whatever It Takes” speech of July 2012. Indeed, the interest rate spread between the German and Italian bonds, or the Bund–BTP spread, is currently a top concern. The ECB’s added role in reducing the redenomination risk premia on the periphery gives it extra leeway during easing cycles but makes it harder to tighten amid resurgent inflation. REER vs. NEER vs. EUR/USD  FX professionals gauge the value of one currency against a set of other currencies. So, the question is not so much whether the EUR is uninvestable but, rather, how well the EUR compares with other currencies — USD, JPY, GBP, CHF, CNH, etc. With multiple crosses available for trading, FX, as an asset class, seeks to monetize relative value. In popular parlance, the search is for the cleanest dirty shirt. Broad trade-weighted real effective exchange rate (REER) readings for the eurozone show that the EUR has been significantly undervalued since mid-2014 and remains so today. It currently stands at 92, with a reading below 100 indicating the currency is undervalued. What are we to make of this? To assume that the EUR is the currency of the future and always will be is not enough. Rather, we need to explore how the ECB’s unconventional monetary policies contributed to this outcome. Since mid-2014, the EUR’s trade-weighted nominal effective exchange rate (NEER) has shown a flattish return, and the EUR/USD pair has fallen by 27%. To be fair and consistent, we must compare REER to NEER trade-weighted indices, not bilateral EUR/USD performance. Still, this begs the question: Are there structural reasons for the EUR’s outsized underperformance compared with the USD? That depends on how the ECB’s policies have affected the eurozone’s balance of payments (BOP) through its current and financial accounts. Portfolio Rebalancing as a QE Transmission Channel The ECB’s balance sheet has more than tripled, to 82% of the eurozone’s GDP since 2015, due to both QE and targeted longer-term refinancing operations (TLTROs). By comparison, the US Federal Reserve’s balance sheet stands at 36.5% of GDP. The ECB now owns about 30% of all outstanding sovereign bonds as well as a sizeable share of private-sector bonds through the corporate sector purchase programme (CSPP). The ECB’s buying spree has had such a profound effect that net sovereign issuances were consistently negative from 2015 to 2021. The ECB effectively pushed the nominal long-term risk-free rates in the eurozone much lower. For example, the 10-year German Bund yield fell from 1.40% in mid-2014 to an all-time low of –0.85% in 2020.  The ECB has effectively created a shortage of EUR-denominated bonds and compressed the nominal long-term risk-free rates in the eurozone. Cross-border portfolio rebalancing has been a key transmission channel for these unconventional policies. In fact, in mid-2014, historic portfolio outflows commenced as both resident and non-resident investors moved out of EUR-denominated debt securities and into the closest substitutes outside the EU. The largest cumulative net purchases were of long-dated debt securities issued by US entities. The Portfolio Balance Approach  The portfolio balance approach focuses specifically on the bond market as a driver of exchange rates. The model is better suited to currency pairs in developed markets, such as EUR/USD, since portfolio flows are very sensitive to market variables. In this model, monetary and fiscal conditions lead to changes in the supply and demand for domestic currency bonds relative to foreign currency bonds, which in turn, impacts the FX rate. Given the relative size and scale of the ECB’s unconventional monetary policies and the historic levels of cross-border portfolio rebalancing, the portfolio balance approach provides an elegant explanation for the massive collapse in EUR/USD between 2014 and 2015 — a peak-to-trough depreciation of 25% — and marks the inflection point where the EUR/USD gapped away from the EUR NEER. Fast forward to today: With the widening divergence between the ECB and the Fed responses to inflationary pressures, another dramatic period in the EUR/USD pair has begun. In the past 12 months, the EUR has depreciated by 16% against the USD but only by about 6% in NEER terms. Although

Convertible Securities: A Complete Guide to Investment and Corporate Financing Strategies. 2022. Tracy V. Maitland, F. Barry Nelson, CFA, and Daniel G. Partlow. McGraw Hill. Professionals who contemplate investing in, hedging, or issuing investment-grade or speculative-grade convertible bonds or preferreds in the public or private market in North America, Europe, or Asia will find just about everything they need to know in Convertible Securities: A Complete Guide to Investment and Corporate Financing Strategies. Pointers on such matters as using convertibles to diversify a portfolio or to optimize a capital structure are meticulously supported with empirical data and amplified with case studies. If, on certain subjects, readers desire more details than even the book’s 560 pages could accommodate, they can follow up on handy references to material on the website of Advent Capital Management, where Tracy V. Maitland, F. Barry Nelson, CFA, and Daniel G. Partlow apply their expertise in managing convertibles. In addition, the book recounts the asset class’s evolution from its 19th century origins right through the investment implications of the Tax Cuts and Jobs Act of 2017 and recent modifications of accounting standards for convertible issuers. The authors address a broad audience. Lay investors can apply basic financial theory, presented by way of background, to activities well outside the convertible market’s confines. At the same time, the book presents quantitatively sophisticated valuation methods and trading strategies, invoking terms of art that will be new even to many seasoned practitioners — for example, “ASCOTs,” “zomma,” “nuking,” and “happy meal.” It is incumbent on the reader to pay strict attention to the authors’ carefully considered wording throughout. Recollecting his introduction to financial markets in the 1980s, Advent founder Tracy Maitland mentions in his preface “long-term returns from convertibles that were equivalent to the returns from common equities, but with significantly less risk.” Bringing the story up to date in the main text, the authors state that “convertibles historically have returned approximately as much as common stocks over the long-term.” Careful to avoid overstating matters, they write at another point, “Convertibles typically provide less volatility than stocks.” Equally circumspect is this comment: “The record of convertible indices essentially matching the returns of equity indices over the decades may partly reflect the superior growth of convertible issuers relative to the growth of companies found in the equity indices” (italics added in the preceding sentences). One message that comes through clearly is convertibles’ asymmetric behavior, capturing much of the associated stocks’ upside while cushioning the downside via the bond side of their nature. Among many useful observations that are tangential to the main topic, two call for a bit of annotation. First, the authors state that “because risk increases with respect to time, longer-term securities tend to have wider credit spreads than shorter-term securities.” Records from ICE Indices, LLC, confirm that except from December 2007 to March 2009, the option-adjusted spread (OAS) on 10- to 15-year US investment-grade corporate bonds has consistently exceeded the OAS on 3- to 5-year issues. For high-yield bonds, however, the 3- to 5-year OAS has usually exceeded the 10- to 15-year OAS. Second, the authors state that “entities that have the ability to print money are considered to be completely risk-free because under any circumstances they can repay their debt with currency that they alone can create.” Actually, control of a currency is a necessary but not a sufficient condition for posing zero risk of default. History records a number of sovereign defaults on debt denominated in the home currency, such as Russia’s 1998 default on its ruble debt. Also worth keeping in mind in this connection is the fact that the US Treasury has a Standard & Poor’s rating of only AA+, not the agency’s highest rating (AAA). “Busted” (out-of-the-money) convertibles represent another time-honored topic in fixed-income circles. Some bond salesmen have promoted the belief that these issues invariably get neglected once they cease to be of interest to convertible investors, consequently becoming bargains with yields higher than the yields on comparable straight (nonconvertible) bonds. Maitland, Nelson, and Partlow judiciously state that convertibles priced at discounts to par merely “have the potential to significantly outperform non-convertible bonds” (italics added). As with most books, a few minor items in Convertible Securities bear cleaning up in a future edition. The book refers to the ICE BofA US High Yield Corporate Index by its former name, the “High Yield Master II Index.” Other editorial slips include mentions of the BlackRock “Alladin” fund, the “Capital Assets Pricing Model,” and the “Discounted Dividend Model.” These stylistic peccadillos do not detract from the many delights awaiting readers of Convertible Securities. One does not expect to discover in a weighty tome on finance the Latin antecedent of the saying, coined by Shakespeare, “It’s Greek to me.” Similarly serendipitous is a Talmudic commentary on the symbolism of the Hebrew analogues of the Greek letters gamma and delta. Most important, though, are the original research contributions that enrich the coverage of every aspect of the convertible ecosystem. York Capital Management CEO Jamie Dinan is right to call Convertible Securities a “remarkably comprehensive book.” Full disclosure: The reviewer is mentioned in this book’s acknowledgements and in an endnote. 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. 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

Our understanding of financial markets is inherently constrained by historical experience — a single realized timeline among countless possibilities that could have unfolded. Each market cycle, geopolitical event, or policy decision represents just one manifestation of potential outcomes. This limitation becomes particularly acute when training machine learning (ML) models, which can inadvertently learn from historical artifacts rather than underlying market dynamics. As complex ML models become more prevalent in investment management, their tendency to overfit to specific historical conditions poses a growing risk to investment outcomes. Generative AI-based synthetic data (GenAI synthetic data) is emerging as a potential solution to this challenge. While GenAI has gained attention primarily for natural language processing, its ability to generate sophisticated synthetic data may prove even more valuable for quantitative investment processes. By creating data that effectively represents “parallel timelines,” this approach can be designed and engineered to provide richer training datasets that preserve crucial market relationships while exploring counterfactual scenarios. The Challenge: Moving Beyond Single Timeline Training Traditional quantitative models face an inherent limitation: they learn from a single historical sequence of events that led to the present conditions. This creates what we term “empirical bias.” The challenge becomes more pronounced with complex machine learning models whose capacity to learn intricate patterns makes them particularly vulnerable to overfitting on limited historical data. An alternative approach is to consider counterfactual scenarios: those that might have unfolded if certain, perhaps arbitrary events, decisions, or shocks had played out differently To illustrate these concepts, consider active international equities portfolios benchmarked to MSCI EAFE. Figure 1 shows the performance characteristics of multiple portfolios — upside capture, downside capture, and overall relative returns — over the past five years ending January 31, 2025. Figure 1: Empirical Data. EAFE-Benchmarked Portfolios, five-year performance characteristics to January 31, 2025. This empirical dataset represents just a small sample of possible portfolios, and an even smaller sample of potential outcomes had events unfolded differently. Traditional approaches to expanding this dataset have significant limitations. Figure 2.Instance-based approaches: K-nearest neighbors (left), SMOTE (right). Traditional Synthetic Data: Understanding the Limitations Conventional methods of synthetic data generation attempt to address data limitations but often fall short of capturing the complex dynamics of financial markets. Using our EAFE portfolio example, we can examine how different approaches perform: Instance-based methods like K-NN and SMOTE extend existing data patterns through local sampling but remain fundamentally constrained by observed data relationships. They cannot generate scenarios much beyond their training examples, limiting their utility for understanding potential future market conditions.  Figure 3: More flexible approaches generally improve outcomes but struggle to capture complex market relationships: GMM (left), KDE (right).   Traditional synthetic data generation approaches, whether through instance-based methods or density estimation, face fundamental limitations. While these approaches can extend patterns incrementally, they cannot generate realistic market scenarios that preserve complex inter-relationships while exploring genuinely different market conditions. This limitation becomes particularly clear when we examine density estimation approaches. Density estimation approaches like GMM and KDE offer more flexibility in extending data patterns, but still struggle to capture the complex, interconnected dynamics of financial markets. These methods particularly falter during regime changes, when historical relationships may evolve. GenAI Synthetic Data: More Powerful Training Recent research at City St Georges and the University of Warwick, presented at the NYU ACM International Conference on AI in Finance (ICAIF), demonstrates how GenAI can potentially better approximate the underlying data generating function of markets. Through neural network architectures, this approach aims to learn conditional distributions while preserving persistent market relationships. The Research and Policy Center (RPC) will soon publish a report that defines synthetic data and outlines generative AI approaches that can be used to create it. The report will highlight best methods for evaluating the quality of synthetic data and use references to existing academic literature to highlight potential use cases. Figure 4: Illustration of GenAI synthetic data expanding the space of realistic possible outcomes while maintaining key relationships. This approach to synthetic data generation can be expanded to offer several potential advantages: Expanded Training Sets: Realistic augmentation of limited financial datasets Scenario Exploration: Generation of plausible market conditions while maintaining persistent relationships Tail Event Analysis: Creation of varied but realistic stress scenarios As illustrated in Figure 4, GenAI synthetic data approaches aim to expand the space of possible portfolio performance characteristics while respecting fundamental market relationships and realistic bounds. This provides a richer training environment for machine learning models, potentially reducing their vulnerability to historical artifacts and improving their ability to generalize across market conditions. Implementation in Security Selection For equity selection models, which are particularly susceptible to learning spurious historical patterns, GenAI synthetic data offers three potential benefits: Reduced Overfitting: By training on varied market conditions, models may better distinguish between persistent signals and temporary artifacts. Enhanced Tail Risk Management: More diverse scenarios in training data could improve model robustness during market stress. Better Generalization: Expanded training data that maintains realistic market relationships may help models adapt to changing conditions. The implementation of effective GenAI synthetic data generation presents its own technical challenges, potentially exceeding the complexity of the investment models themselves. However, our research suggests that successfully addressing these challenges could significantly improve risk-adjusted returns through more robust model training. The GenAI Path to Better Model Training GenAI synthetic data has the potential to provide more powerful, forward-looking insights for investment and risk models. Through neural network-based architectures, it aims to better approximate the market’s data generating function, potentially enabling more accurate representation of future market conditions while preserving persistent inter-relationships. While this could benefit most investment and risk models, a key reason it represents such an important innovation right now is owing to the increasing adoption of machine learning in investment management and the related risk of overfit. GenAI synthetic data can generate plausible market scenarios that preserve complex relationships while exploring different conditions. This technology offers a path to more robust investment models. However, even the most advanced synthetic data cannot compensate for naïve machine learning implementations. There is no safe

“Complexity is like energy. It cannot be created or destroyed, only moved somewhere else. When a product or service becomes simpler for users, engineers and designers have to work harder. [Donald A.] Norman writes, ‘With technology, simplifications at the level of usage invariably result in added complexity of the underlying mechanism.‘ For example, the files and folders conceptual model for computer interfaces doesn’t change how files are stored, but by putting in extra work to translate the process into something recognizable, designers make navigating them easier for users.” — Shane Parrish, Farnam Street Fitch Ratings’ downgrade of US sovereign credit from AAA to AA+ last week highlights a latent principal–agent problem in modern financial markets: Investors have outsourced much of their risk management to the rating agencies. But the problem goes beyond just risk management and the rating agencies. Before Standard & Poor’s reduced its US credit rating in 2011, financial contracts referred to “risk-free” or liquid assets as AAA-rated securities. Considered “good collateral,” these assets were a requirement in most financial transactions. When US credit became split-rated, the risk of forced liquidation of US Treasuries after another downgrade emerged as a clear and present danger. As Jim Bianco writes, “In the subsequent 12 years, most of these financial contracts have been rewritten to include ‘debt backed by the US Government’ or words to this effect.” But the financial position of the United States has deteriorated over the past decade, which explains why the Fitch downgrade was not a huge surprise. To be sure, some disagreed with the decision, while others felt it didn’t come soon enough, but most market participants greeted the news with a collective shrug. A strict financial analysis of US sovereign credit ignores the country’s strong geopolitical position. Its enviable geography and singular influence over global shipping lanes ensure a prominent place in the world economy and are vital inputs to its creditworthiness. This is the dilemma that Fitch and other rating agencies face when distilling a phenomenon as complex as a sovereign nation’s creditworthiness down to a simple designation. Such labels help keep the gears of commerce turning, but what they actually mean is growing cloudier and losing their informational value. Before 2011, two rating agencies could initiate a deleveraging and spark a panic in the financial markets. But thanks in part to the re-wording of financial contracts in the intervening years, Fitch’s decision failed to catalyze such an event. That counts as a present good. But what about the restorative effects a deleveraging could have on balance sheets or the fiscal discipline it could engender? What if policymakers need to be reminded that ongoing debt accumulation comes with a cost? In the past, the markets imposed that discipline. Market-imposed discipline meant greater financial market volatility and less financial intermediation. Of course, while that may have made for healthier balance sheets, it also meant less growth and lower living standards. The rating agencies and other financial market actors provide a form of third-party oversight. They apply a loose system of checks and balances to counter outsized risk accumulation. The Commodity Futures Trading Commission (CFTC) imposes position limits on investment firms, the US SEC fights securities fraud, and the US Federal Reserve regulates the banking system. These are all worthwhile functions. The question is: Does the increased functionality these efforts bring to the financial markets come with any hidden costs? This is the principal–agent problem in its purest form. Financial innovations increase intermediation, which makes capital cheaper and more readily available. This leads to economic growth and higher standards of living. Lower barriers to entry and seemingly reduced complexity encourage people to invest their savings in the markets. But beneath the surface, the underlying market complexity has never gone away; it has just been moved somewhere else. If the complexity of our financial system is constant, then where is it hiding and who is managing it? The dependency paradox suggests that as principals delegate responsibilities to others, they may inadvertently reduce their own capacity to make informed decisions, understand complex issues, and retain the necessary skills to perform those tasks well. Innovations like exchange-traded funds (ETFs) have opened up the financial markets in a cost- and tax-efficient way. Investors can now buy a well-diversified portfolio with the click of a mouse. But in the not-too-distant past, such an endeavor would have required teams of professionals to accomplish, and today the mechanism that transforms that mouse click into a portfolio remains a mystery to most. The complex algorithms, order routing, payment for order flow, and execution occurring behind the scenes go largely unnoticed until we read about the outsized profits that certain firms make by providing liquidity to the market. In a way, financial innovations are creating two classes of investors: those who merely consume the products and those who understand how the system that creates these products works. This goes to the heart of the principal–agent problem. Knowledge gaps between principals and agents can lead to, but don’t necessitate, conflicts of interest. With rating agencies, the conflict arises from the risk that they could pose to the financial system. On the one hand, if they stray from their disciplined analytical approach, their value as a market referee drops, but if they follow too strictly, they could cause a meltdown. To bridge the markets’ inevitable knowledge gap, we have to accept that complexity can only be transformed and that agents must be empowered to manage this complexity to increase the functionality of the markets. It is not enough for these agents to be transparent and accountable. It is on us, the principals, to monitor and participate in the financial markets and educate ourselves on how they work. While investing has gotten “easier,” beneath the simple mouse clicks and user-friendly interfaces lies a complex world that we cannot lose sight of or ignore. That complexity will inevitably reveal itself, and when it does, instead of panicking or assigning blame, we should look to understand it for what

Markets in Chaos: A History of Market Crises around the World. 2024. Brendan Hughes, CFA. Business Expert Press. Should history teach or merely inform? This question lies at the heart of Markets in Chaos, a broad yet succinct historical overview of macroeconomic crises around the world and across time. No mere exposition of financial market ructions in such places as Weimar Germany or Japan in the 1990s, this volume studies the mechanics of market disruptions in depth with a view toward educating the reader and investor. The writing is clear, and the case studies are well researched. The author’s discussion and analyses are not only instructive but also relevant. Many of the events reviewed will be familiar to finance and investment professionals. Nonetheless, this volume should be a part of any (aspiring) practitioner’s library, if for no other reason than to provide invaluable perspective on the context in which financial decisions are made and guidance on how best to navigate macroeconomic dislocations in the service of clients. Additionally, the case studies could supplement the CFA Program curriculum on the topics of macroeconomics and risk management. Financial market regulators, economists, policymakers, portfolio managers, and risk officers will find this book a timely and welcome refresher. As the author, Brendan Hughes, CFA, makes clear throughout, some decision makers will need to pay more heed than others. Market history, for want of a less hackneyed turn of phrase, often does rhyme, if not repeat, as the events analyzed between these pages make clear. Common themes arise time and again. Central banks print money, economies are financialized, fiat currencies hamper productivity growth, and government corruption places fragile economies in a doom loop. Cheap money leads to financial excess. Does no one learn? Throughout the narrative, Hughes draws frequent parallels between macroeconomic events, comparing and contrasting policy decisions and market outcomes, emphasizing the missteps and the lessons learned. Some governments learn from their mistakes; others, not so much. Chile’s experience in the 1980s stemmed from a dearth of oversight and a surfeit of credit creation. The government’s lack of adequate foreign exchange reserves and overreliance on copper extraction for export revenue led the economy into recession once the commodity boom subsided. Similar circumstances were present in Iceland prior to the global financial crisis (GFC) and Indonesia in the late 1990s during the Asian financial crisis. Market shocks lay bare undiversified economies’ problems. Whereas Chile subsequently demonstrated fiscal probity and supported free trade, proper oversight, and more prudent bank lending policies that made its economy relatively stable in a region whose other economies are not, Iceland and Indonesia continue more or less on a path of economic fragility and volatility. The frequent cross-references in the book tie the narrative together and help reinforce critical concepts. While the chapters may be read in isolation, the discussion and analysis make for a smooth progression between them. Separated by time and region, the macroeconomic dislocations of the economies and markets that form the events in this volume share experiences and teachable moments. To paraphrase George Orwell, all markets and economies are alike — some more so than others. Hughes’s approach to the subject matter is instructive and well organized, allowing for ease of reference and understanding of how concepts interrelate. With the exception of the chapters that explore market dislocations in the farther reaches of history (18th century France, 19th century America and Europe, and Ancient Rome), where a lack of data from the time periods in question would preclude an assessment of how companies were affected, each chapter provides a background and market impact, the impact on businesses, and a review of how the disruptions affected the macroeconomy. The closing chapter offers useful, if familiar, guidance on how to apply financial history to everyday investment decisions: Stay invested, but prudently; diversify across both asset classes and countries, avoid market timing, do not invest in businesses that require leverage to achieve good returns, do invest in those that require little capital to operate and have pricing power. Thousands of years of history can improve investors’ understanding of possible outcomes and better inform their investment decisions. Hughes does not merely examine the historical record but weighs in on the implications of recurring themes at both a macroeconomic level and a microeconomic level. In his estimation, the US Federal Reserve has strayed from its mandate, for years creating cheap money that stokes inflation and provides fodder for speculation and inflated property markets. Fractional reserve banking only compounds the problem. A return to the gold standard in some measure — the author undertakes an informative and critical examination of its history — along with a link between money supply and GDP growth and full-reserve banking, which would better align the goals of central banks and private commercial banks, would alleviate the risks attached to fiat currencies and create conditions propitious for a more stable economy less prone to inflation. European monetary union, itself due in part to the eventuality of the United States’ abandonment of the price link to gold more than two decades earlier, presents a problem of mismatch between a shared currency and member countries’ economic and political circumstances. The disparate experiences of the Greek and German economies in the 2010s are telling. The euro’s longer-term prospects would appear questionable. Hughes puts the current state of financial services under the microscope. Banking has its rewards and risks, the latter giving rise in very recent history to new financial technologies that offer financial services with banking features — think Venmo, SoFi, and Credit Karma — but which lack proper surveillance. Regtech is still catching up to financial innovation. The jury is still out on the hidden risks that the emergence of shadow banking has created. Designed as an alternative to the risks of centralized finance, cryptocurrencies labor under flaws similar to those of commercial banks, as the fate of many cryptocurrency exchanges attests. Stablecoins look to be anything but stable. If we have learned nothing else, it is that the

In today’s investment landscape, the debate between active and passive management often misses a critical point: they aren’t mutually exclusive. Incorporating passive funds into actively managed portfolios can enhance diversification, reduce risk, and optimize returns. By leveraging a hybrid, “team of funds” approach, investors can capitalize on the strengths of both strategies, creating portfolios that achieve financial goals more efficiently. This post explores how passive investments complement active strategies, driving better results for clients and portfolios alike. Robust Portfolio Construction With a Team of Funds Approach A robust portfolio construction process should be customized to the client’s asset allocation and target excess return. It should also maximize alpha diversification across the portfolio. This approach provides these benefits: Minimizing tracking error by aligning the portfolio’s long-term effective exposures to its benchmark Equalizing each fund’s contribution to portfolio alpha and tracking error Capitalizing on the relationship between the portfolio’s active return and market return. Here is a case study that illustrates this approach. It tests results using all active funds versus using a combination of active and passive funds. I chose four asset allocation strategies across global equity and bonds to represent a set of client risk tolerances. I excluded real assets and illiquid investments in favor of publicly available funds that represent the core of most investment portfolios. Portfolio parameters: Strategies range from 50-50 to 80-20 mixes of equity and bonds Alpha targets range from a minimum 50 basis points (bps) to a maximum of 175 bps in 25 bps increments. This produced a set of 24 teams of funds. I maintained diversification and style characteristics across strategies, with global, developed equity balanced between value and growth styles. This produced a total of 11 minor asset segments. Table 1: Diversification across asset strategies. All-Active Fund Results The all-active performance results over a 12-year period are grouped by investment strategy. The hybrid, team of funds approach delivered enhanced returns with lower volatility than their benchmarks. This result was driven by two factors. First, alpha diversification removed most individual fund tracking error. Second, the slightly negative correlation of each portfolio’s excess return to the portfolio’s total return causes a portion of its tracking error to be subtracted from its volatility, given this relationship: Contribution to Volatility = Weight * Volatility * Correlation with Portfolio Return Chart 1: Team of Funds vs. Benchmarks. I repeated this approach, this time allowing passive funds into the mix. Each portfolio was free to hold any funds on our platform and an unlimited allocation of passive funds. The goal was to earn the target excess return while minimizing volatility risk. The surprising result — across all strategies and alpha targets — is that portfolios that held substantial exposure to passive investments replicated the returns of the portfolios that held all active funds. This result corrects the prevailing wisdom that passive funds dilute excess return. The passive-active hybrid portfolios had an average of 40% passive exposure and a range of about 10% to 65%, depending on the strategy and the alpha target. Chart 2: All-Active Portfolios vs Hybrid Portfolios. Passive Exposures Across Strategies and Alpha Targets Passive funds allow us to be more selective in our use of active investments, choosing only the best of the best. They eliminate asset allocation constraints that limit efficiency in the selection of active funds. This drives greater “alpha diversification” and lowers active risk. Table 2: Passive Exposures. Key insight: Including passive funds drives a more efficient selection of active funds. Effect of Passive Investments on Active Risk Chart 3 compares the relationship between alpha and tracking error for all-active and hybrid portfolios. Tracking error increases modestly with total volatility in the all-active portfolios, until reaching an inflection point, when risk begins increases rapidly. The hybrid portfolios are dramatically more efficient. Active risk across the strategies is nearly identical, with differences only at the highest alpha targets. The return-to-risk line is nearly linear. Chart 3: Active results for All-Active and Hybrid Portfolios. Benefits of Lowering Active Risk Alpha diversification, the selective use of passive investments, and an unconstrained active fund team create a combination of factors that produce superior active results. These benefits are consistent across the strategies, with lower active risk increasing high-confidence minimum alpha in the hybrid portfolios. Chart 4 illustrates the 95% confidence level alpha across all portfolios. The trend lines for the all-active and the hybrid strategies summarize the improvement that passive funds contribute. On average, this is between 15 bps and 20 bps of excess return. Chart 4: High-Confidence alpha for All-Active and Hybrid Portfolios. Evaluating Hybrid Portfolio Performance I selected the 60-40 strategy with 100 bps target alpha to illustrate my hybrid performance evaluation approach. My decision-based approach focuses on an active component plus a passive component, in a hierarchical framework: Active vs. passive allocation Major asset segments Minor asset segments Funds My passive allocation is close to an 80-20 mix of stocks and bonds, while the active allocation is a nearly-even mix. This creates substantially different long-term allocation performance effects. Chart 5: Hybrid Portfolio Allocation to Asset Classes Within Passive and Active Components. The active and passive components also differ in their allocations within equity and bonds. This is primarily driven by the alpha opportunities found in the active funds. It is also influenced by alpha diversification across the active funds we include. Chart 6: Allocation to Major Asset Segments within Passive and Active Components. My most detailed passive and active allocations (at the style level) fully explain my allocation to more than 40% of the portfolio’s assets to passive investments. The total exposure in each asset segment matches the benchmark allocation. Table 3: Style-Level Allocations Across Passive and Active Components. Key Drivers of Hybrid Portfolio Return Chart 7 illustrates total return and volatility for each performance component. Relative to the benchmark return, the active allocation detracted from excess return while the passive allocation contributed to excess return. Chart 7: Return and Risk for Hybrid Portfolio Performance Components. The selection effect is evaluated by comparing

Our 4×4 Asset Allocation philosophy approaches every asset or strategy based on how it contributes to — or detracts from — four goals: Growth, Income, Preservation, and Liquidity. In particular, under the 4×4 Goal Parity framework, each of these goals has equal weight. So, what does a goals-based approach to equity factors look like from this perspective? The literature on equity factors, particularly Eugene F. Fama and Kenneth R. French’s extended family of factors, is deep and extensive. These include Small Minus Big (SMB) and High Minus Low (HML), which respectively describe the difference between returns of small- and large-cap stocks and high book-to-market and low book-to-market stocks. Among the factors of more recent vintage are Robust Minus Weak (RMW) and Conservative Minus Aggressive (CMA), or the difference in returns among companies with robust and weak operating profitability and between those that invest conservatively and aggressively. The Kenneth R. French Data Library also features Momentum (Mom), or the return spread between winners and losers over the last 12 months, as well as Short-Term and Long-Term Reversal factors (ST_Rev, LT_Rev). While many researchers focus on each factor’s stand-alone performance metrics, we are more concerned with the relationships among the factors themselves, their (non-linear) relationships with larger market and macroeconomic conditions, and ultimately each factor’s role in a goals-based, investor-specific portfolio. How do the simple correlations between factors compare? The market’s excess return (Mkt-RF) is negatively correlated with Mom, HML, and RMW, a frequent proxy for Quality. Mkt-RF is most negatively correlated, however, with CMA, which may be a “management behavior quality” factor and perhaps a quality or defensive factor. That is, aggressively investing executives engaged in empire-building activities may do well when capital is flowing but suffer in market downturns. Conservative firms, on the other hand, save cash for rainy days and rely less on external financing. HML and CMA have a 68% correlation. This could be because investors place higher valuation multiples on firms with fast-growing assets than on their slower-asset-growing peers. In any case, based on empirical correlations, HML is a defensive factor as well since Value tends to do well in recessions. Fama–French Factor Correlations, July 1963 to December 2022 Methodology: Standard Pearson correlation coefficients computed with monthly returns. But what does a non-linear analysis of the factors reveal when we compare their skewness and convexity with respect to major risk factors, such as Mkt-RF, monthly changes in 10-year Treasury yields, monthly changes in money-market or “risk-free” rates (RF), and month-on-month changes of the CPI-U index? Convexity reflects the co-skewness coefficient between a Fama–French factor and two instances of a risk factor squared. In particular, the co-skewness of Mkt-RF with itself is simply Mkt-RF skewness. If a Fama–French factor has positive co-skewness with a risk factor, it is convex with respect to that risk factor. If it has negative co-skewness, it is concave. For example, Mkt-RF is concave with respect to CPI MoM while CMA is convex with respect to Mkt-RF. Fama–French Factor Skewness and Convexity, July 1963 to December 2022 Red cells represent negative and blue cells positive co-skewness values.Skewness and co-skewness coefficients computed with monthly returns and bounded by [-0.5,0.5]. Convexity relative to a major risk factor indicates better performance in crises driven by rapid changes in interest rates, inflation, or sharp market declines. Heuristically, convexity should contribute to our (real capital) Preservation goal. Conversely, concave, negatively skewed assets and strategies may behave like income-generating corporate bonds and equities, delivering their best performance in placid environments but underperforming in crises. Convexity and Concavity: CMA vs. Mkt-RF and Mkt-RF vs. CPI MoM In 4×4 Goal Parity we quantify this intuition with two investor-specific parameters: strategic horizon and loss tolerance. In particular, we look at Fama–French factors from 1963 to 2022. Given a 10-year strategic horizon and a 15% loss tolerance, our methodology demonstrates the following: Value (HML) makes a significant Preservation contribution, providing some protection in recessions. CMA and LT_Rev factors are even better Preservation factors. In particular, HML, CMA and LT_Rev did very well in 2022 when both stocks and bonds declined. RMW overlaps with Quality and High Dividend equities and contributes more to Income. Twelve-month window Mom contributes to Income as well. Faster Mom would deliver more Preservation. 4×4 Asset Map: Investor Goals and Fama–French Factors, July 1963 to December 2022 Strategic horizon 𝑇=10 years, “substantial loss” barrier B=85%. The eight-factor portfolio includes equal weights of Mkt-RF, SMB, HML, RMW, CMA, Mom, ST_Rev, and LT_Rev. Sources: 4x4invest’s proprietary methodology; Kennneth R. French’s Data Library From our goals-based perspective (or a macro lens perspective), Fama–French factors play quite different roles. So, should investors build diversified factor portfolios balanced across all of our 4×4 goals? To start answering this question, we built an equal-weighted portfolio of eight Fama–French factors — Mkt-RF, SMB, HML, RMW, CMA, Mom, ST_Rev, and LT_Rev — and rebalanced it monthly. From 1963 to 2022, the eight-factor portfolio lags Mkt-RF during bull markets but does much better during bear markets and with lower volatility. The portfolio achieves a Sharpe ratio of 1.16 versus 0.42 for Mkt-RF without accounting for transaction costs. Perhaps excess equity market returns reflect GDP growth in the large and relatively closed US economy. From this perspective, the eight-factor portfolio’s performance pattern more resembles that of US nominal GDP, with a much lower “tracking error.” Mkt-RF and Eight-Factor Portfolio vs. US Nominal GDP Growth, July 1963 to December 2022 The eight-factor portfolio includes equal weights of Mkt-RF, SMB, HML, RMW, CMA, Mom, ST_Rev, and LT_Rev. 4x4invest’s calculations for illustration and educational purposes only. Past performance is not indicative of future results. The 4×4 Asset Map above shows that the equal-weighted eight-factor portfolio comes pretty close to a 4×4-optimal Goal Parity portfolio, with equal weight on Growth, Income, Preservation, and Liquidity. The relationships among the different factors vary over the six-decade examination period. Nevertheless, “powering” all four goals may have delivered the diversification benefits necessary to achieve resilient performance across the bear markets of 1972 to 1974, 2000 to 2002, and

Quantitative Risk and Portfolio Management: Theory and Practice. 2024. Kenneth J. Winston. Cambridge University Press. The field of textbooks on quantitative risk and portfolio management is crowded, yet there is a problem matching the right book with the appropriate audience. Like Goldilocks, there is a search for a book that is neither too technical nor too simple to reach a broad audience and have the most significant reader impact. The perfect quant text should be a mix of explaining concepts clearly with the right level of intuition and enough practicality, combined with mathematical rigor, so the reader can know how to employ the right tools to solve a portfolio problem. Although textbooks are not often reviewed for CFA readers, it is useful to highlight a book that fills a unique gap between the CFA curriculum and the growing demand to find model-driven investment management solutions. Quantitative Risk and Portfolio Management: Theory and Practice achieves that critical balance by providing an apt mix of intuition and applied math. Author Ken Winston, the author of Quantitative Risk and Portfolio Management, has had a distinguished career moving between industry and academic positions. He is well-placed to provide readers with the necessary tools to be an effective quant or a professional who needs to digest the output from quants. Winston’s book fills a niche between theory and practice; nevertheless, it is not the ideal text for every CFA charterholder. It places greater emphasis on the math and programming of solutions than most practical portfolio management books. Programming is currently a “hidden curriculum” item in investment risk and portfolio management education that goes beyond theory and research. Brad De Long, the University of California Berkeley economic historian, has conjectured that programming skills are like the fine chancery hand of medieval university graduates. Programming goes beyond the classic liberal arts or business education, showing your distinction as an educated man. In today’s world, it is not enough to say you know portfolio or risk management; you must be able to “do” it. Winston closely links quant concepts with Python programming to make the hidden curriculum of quant finance transparent and accessible. You will not become a quant programmer from studying this book, but Quantitative Risk and Portfolio Management enables you to more easily bridge the link between theory and critical quantitative analysis through programming. Quantitative Risk and Portfolio Management integrates Python code snippets throughout the text so that the reader can learn a concept and the foundational math and then see how Python code can be integrated to build a model with output. While this is not a financial cookbook, the close integration of code distinguishes it from others. That makes the book useful for sitting on the shelf as a reference for analysts and portfolio managers. For example, the reader can learn about fixed-income yield curves and then see how the code can generate output for different models. If you want to build a simple model, creating the basic code is not a trivial exercise. Exposure to Winston’s code snippets allows the reader to move more quickly from a risk and portfolio management learner to a doer. The book is divided into twelve chapters that cover all the basics of quantitative risk and portfolio management. The emphasis for many of these chapters, however, is significantly different from what many readers may expect. Winston often focuses on concepts not covered in more traditional or advanced texts by building on core math foundations. For example, there is a chapter on how to generate convex optimizations following the discussion on the efficient frontier. If you are going to run an optimization, this is critical knowledge, yet it is the first time I have seen an extensive review of optimization techniques in a finance text. At times, the chapter order may seem odd to some readers. For example, optimization and distributional properties come after equity modeling. However, this sequencing is not problematic and does not take away from the book. Winston begins with the basic concepts of risk, uncertainty, and decision-making, which are central issues facing any investor. Before discussing individual markets, the book focuses on risk metrics based on no-arbitrage models and presents the often-overlooked Ross Recovery Theorem. Quantitative Risk and Portfolio Management then focuses on valuation measurements for equity and bond markets. The author takes a unique presentation approach to discuss these core markets, which is a critical difference between this book and its competitors. For fixed income, he starts with classic discounting of cash flows but then layers in greater degrees of complexity so that readers can learn how more complex models are developed and extend their earlier thinking. I have not seen this done as effectively in any other portfolio management book, even ones that focus solely on fixed income. The same technique is used with the equity markets section. From a simple presentation of Markowitz’s efficient frontier, Winston adds complexities to show how the problem of uncertain expected returns is addressed to improve model results. He also effectively presents the complexities of factor models and the arbitrage pricing theorem. Again, this is not generally the approach presented in other texts. Quantitative Risk and Portfolio Management presents a focused chapter on distribution theory and a section on simulations, scenarios, and stress testing. These are important risk concepts, especially when the problem of risk management is placed in the context of controlling for uncertainty. The book then explains time-varying volatility measurement through current modeling techniques, the extraction of volatility from options, and the measurement of relationships across assets based on correlation relationships. While it is neither a math book nor one on econometrics, Quantitative Risk and Portfolio Management strikes a nice balance between the core concepts on measuring volatility and covariance with more advanced issues concerning risk forecasting. The book ends with a chapter on credit modeling and one on hedging, and in both cases follows Winston’s approach of layering in greater modeling complexity. Given his clear discussion of the difference between risk and uncertainty,