Problems with arithmetic means and alphas

In this episode, we welcome back return guest Hank Bessembinder for a deeply analytical conversation spanning leveraged ETFs, volatility, and the future of performance measurement. Hank walks us through his latest research on leveraged single-stock ETFs, clarifying the misunderstood concept of "volatility decay" and decomposing returns into rebalancing effects and frictions. The results are striking: meaningful underperformance relative to simple levered benchmarks, driven by both embedded costs and the mechanics of daily resets. In the second half, we shift gears to a more foundational question: What is a return, really? Hank challenges the dominance of arithmetic averages and even geometric means, arguing that neither truly captures the long-term investor experience. He introduces the concept of the sustainable return—a measure based on the cash flows an investment can support without depleting capital—and outlines how it could reshape academic finance and real-world financial planning.

Key Points From This Episode:

(0:01:03) Welcome back to Hank Bessembinder and overview of his recent research.

(0:06:16) What "volatility decay" really means—and why the term may be misleading.

(0:09:16) Why volatility does not necessarily reduce mean returns in constant leverage ETFs.

(0:10:11) Ex-ante decision-making and the wedge between mean and median outcomes.

(0:11:26) Single-stock vs. index leveraged ETFs: Similar mechanics, different magnitudes.

(0:12:52) Why past research has been so cautionary about long-term use of leveraged ETFs.

(0:15:53) How rebalancing costs differ for long and short leveraged products.

(0:16:57) The benchmark: Levered buy-and-hold versus constant daily rebalancing.

(0:19:46) Empirical results: Long funds underperform by ~0.8% per month; short funds by ~1% per month.

(0:21:10) Decomposing underperformance into rebalancing effects and frictions.

(0:24:15) The real (though rare) possibility of returns below –100% in leveraged products.

(0:27:04) Simulation results over 50 years: Skewness, negative medians, and rebalancing drag.

(0:28:38) Why volatility tends to coincide with reversals—and why reversals drive rebalancing costs.

(0:31:15) Practical guidance: Who, if anyone, should use leveraged single-stock ETFs.

(0:34:58) The limitations of arithmetic means and single-period models.

(0:36:55) Why aggregate investors are not buy-and-hold investors.

(0:39:17) The shortcomings of arithmetic averages, alphas, and Sharpe ratios for long-horizon measurement.

(0:42:38) Why log returns don't solve the core measurement problems.

(0:44:56) The case for dollar-weighted returns and the limitations of IRRs.

(0:48:18) Modified IRRs and their role in capturing aggregate investor outcomes.

(0:50:14) Introducing the sustainable return: Measuring what can be withdrawn without depleting capital.

(0:53:22) Expected sustainable return and its close relationship to the geometric mean.

(0:56:09) Proportional sustainable return and withdrawal-based performance measurement.

(1:00:00) Individual stock returns through the lens of sustainable returns.

(1:00:53) Nudging academic finance beyond the "econometric streetlight."

Links From Today's Episode: Meet with PWL Capital: https://calendly.com/d/3vm-t2j-h3p

Rational Reminder on iTunes — https://itunes.apple.com/ca/podcast/the-rational-reminder-podcast/id1426530582. Rational Reminder on Instagram — https://www.instagram.com/rationalreminder/

Rational Reminder on YouTube — https://www.youtube.com/channel/ Benjamin Felix — https://pwlcapital.com/our-team/

Benjamin on X — https://x.com/benjaminwfelix

Benjamin on LinkedIn — https://www.linkedin.com/in/benjaminwfelix/

Cameron Passmore — https://pwlcapital.com/our-team/

Cameron on X — https://x.com/CameronPassmore

Cameron on LinkedIn — https://www.linkedin.com/in/cameronpassmore/

Editing and post-production work for this episode was provided by The Podcast Consultant (https://thepodcastconsultant.com)