For nearly thirty years, William Sharpe’s influential work, Arithmetic of Active Management, has become a cornerstone of passive investment philosophy. Published in the Financial Analysts Journal in 1991, Sharpe, a Nobel Prize laureate under the mentorship of Harry Markowitz, presented a compelling argument that has shaped how investors perceive market returns.
Sharpe’s central premise was straightforward: the costs associated with active management lead to underperformance when compared to passive strategies.
He argued that, prior to accounting for fees, both active and passive portfolios yield equivalent market returns; however, once fees are factored in, the arithmetic suggests that active management becomes a zero-sum game—often resulting in a negative-sum scenario.
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Challenging the traditional view of active management
This framework has significantly influenced the rise of index funds and led many investors to question the value of paying for supposed expertise in active management. Why pay for skill when the average market return is readily available without additional costs? While Sharpe’s insights were groundbreaking, they presented a somewhat static view of the market. Subsequent scholars, notably Lasse Heje Pedersen, have illustrated that active management can drive market evolution rather than merely redistribute returns among investors.
Understanding the limitations of Sharpe’s thesis
Sharpe’s depiction of passive investing captures its essence: it offers effortless exposure to the collective market wisdom. In a capitalization-weighted index, the portfolio composition adjusts automatically in response to price fluctuations, eliminating the need for constant trading. Each active investment decision is countered by an opposing position, creating a balance that reflects the consensus of market participants. Tracking an index allows the market to determine which strategies are effective.
However, if Sharpe’s model were entirely accurate, we would expect to see the eventual disappearance of active management, rendering markets incapable of functioning effectively. This notion contradicts earlier findings by economists Sanford J. Grossman and Joseph Stiglitz, who argued in their 1980 paper, On the Impossibility of Informationally Efficient Markets, that markets reward those who incorporate information into asset pricing.
The dynamic nature of markets
Sharpe’s arithmetic holds true only if we disregard the economic forces that underpin market operations. What if, instead, we viewed markets as dynamic entities where active management not only redistributes wealth but actively creates it?
Consider a hypothetical scenario involving a hundred investors, each owning an equal slice of the market. Among them, half are passive investors who simply hold their shares, while the other half engage in active trading, incurring annual management fees of approximately 2%. After one year, the active investors, burdened by fees, end up with diminished overall returns. This narrative, echoed by renowned figures like Warren Buffett, illustrates that increased trading activities often lead to reduced returns.
Redefining the narrative around active management
Yet, this interpretation of Sharpe’s arithmetic fails to recognize the evolving nature of markets. Sharpe’s assumptions reflect a static snapshot of market dynamics, neglecting the reality that companies continuously issue new shares, buy back existing ones, merge, and fail. Markets are vibrant systems that mirror the complexities of human behavior and economic trends, with indexes adapting to reflect these changes.
In his 2018 article, Sharpening the Arithmetic of Active Management, Pedersen emphasized that active management is essential for the evolution of markets. He presented compelling data indicating that the annual turnover rate of U.S. equities hovers around 7.6%, while bonds exhibit a turnover rate nearing 20%. Even in a scenario where all investors ceased trading, market dynamics would continue to shift, driven by the need for passive investors to periodically rebalance their portfolios.
The constructive role of active management
Active management does more than just shuffle shares; it plays a vital role in reallocating capital towards its most productive applications. When active managers identify inefficiencies or misallocations of resources, they are not merely engaging in trades but are instead facilitating a more efficient flow of capital. Through participation in corporate governance and investment decisions, they influence which firms expand, which contract, and how resources are allocated across the economy.
Sharpe’s central premise was straightforward: the costs associated with active management lead to underperformance when compared to passive strategies. He argued that, prior to accounting for fees, both active and passive portfolios yield equivalent market returns; however, once fees are factored in, the arithmetic suggests that active management becomes a zero-sum game—often resulting in a negative-sum scenario.0
Sharpe’s central premise was straightforward: the costs associated with active management lead to underperformance when compared to passive strategies. He argued that, prior to accounting for fees, both active and passive portfolios yield equivalent market returns; however, once fees are factored in, the arithmetic suggests that active management becomes a zero-sum game—often resulting in a negative-sum scenario.1
