ARTIFICIAL INTELLIGENCE

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Comprehensive Definition

Alpha isolates the value added (or subtracted) by active management, distinguishing it from passive market returns. It quantifies performance on a risk-adjusted basis, accounting for systematic risk via beta, which reflects an asset’s volatility relative to the market. A positive alpha signals outperformance—meaning the manager has skilfully selected securities or timed markets to exceed expectations—while a negative alpha indicates underperformance, often failing to justify management fees.^1,3,4,5 An alpha of zero implies returns precisely match the risk-adjusted benchmark.^3,5

In practice, alpha applies across asset classes:

• Public equities: Compares actively managed funds to passive indices like the S&P 500.^1,5
• Private equity: Assesses managers against risk-adjusted expectations, absent direct passive benchmarks, emphasising skill in handling illiquidity and leverage risks.¹

Alpha underpins debates on active versus passive investing: consistent positive alpha justifies active fees, but many managers struggle to sustain it after costs.^1,4

Calculation Methods

The simplest form subtracts benchmark return from portfolio return:

• Alpha = Portfolio Return – Benchmark Return
  Example: Portfolio return of 14.8% minus benchmark of 11.2% yields alpha = 3.6%.¹

For precision, Jensen’s Alpha uses the Capital Asset Pricing Model (CAPM) to compute expected return:
\alpha = R<em>p - [R</em>f + \beta (R<em>m - R</em>f)]
Where:

• ( R_p ): Portfolio return
• ( R_f ): Risk-free rate (e.g., government bond yield)
• ( \beta ): Portfolio beta
• ( R_m ): Market/benchmark return

Example: ( Rp = 30\% ), ( Rf = 8\% ), ( \beta = 1.1 ), ( R_m = 20\% ) gives:
\alpha = 0.30 - [0.08 + 1.1(0.20 - 0.08)] = 0.30 - 0.214 = 0.086 \ (8.6\%)^3,4

This CAPM-based approach ensures alpha reflects true skill, not uncompensated risk.^1,2,5

Key Theorist: Michael Jensen

The foremost theorist linked to alpha is Michael Jensen (1939–2021), who formalised Jensen’s Alpha in his seminal 1968 paper, “The Performance of Mutual Funds in the Period 1945–1964,” published in the Journal of Finance. This work introduced alpha as a rigorous metric within CAPM, enabling empirical tests of manager skill.^1,4

Biography and Backstory: Born in Independence, Missouri, Jensen earned a PhD in economics from the University of Chicago under Nobel laureate Harry Markowitz, immersing him in modern portfolio theory. His 1968 study analysed 115 mutual funds, finding most generated negative alpha after fees, challenging claims of widespread managerial prowess and bolstering efficient market hypothesis evidence.¹ This propelled him to Harvard Business School (1968–1987), then the University of Rochester, and later Intech and Harvard again. Jensen pioneered agency theory, co-authoring “Theory of the Firm” (1976) on managerial incentives, and influenced private equity via leveraged buyouts. His alpha measure remains foundational, used daily by investors to evaluate funds against CAPM benchmarks, underscoring that true alpha stems from security selection or timing, not market beta.^1,4,5 Jensen’s legacy endures in performance attribution, with his metric cited in trillions of dollars’ worth of evaluations.