Time Arbitrage: Fractal Markets and Financial Chaos

I like to periodically reset my thinking and get back to basics — whether simplifying my exercise regimen or rehashing philosophical principles. Recently, I felt the call to strip down investing and revisit fundamentals — to forget about valuation metrics, alpha, beta, and Monte Carlo simulations and think about investing from the ground up. What is investing? Why has it worked for so long? Will it continue to work in the future?

This back-to-basics impulse coincided with reading Benoit Mandelbrot’s ‘The (Mis)Behavior of Markets.’ Mandelbrot is no ordinary investor. He’s a mathematician with a deep understanding of randomness who applies concepts from fractal geometry to financial markets. Rather than offering tactics, his book challenges prevailing assumptions in finance. It’s not a manual of strategies but a non-linear wrecking ball arguing that predominate financial models fail to account for the messy complexity of real markets. 

The notion that markets did not follow the neat Gaussian distributions I had learned about but were instead driven by wild, fractal geometries and uncertainty was both unsettling and exhilarating. His takedown of modern financial modeling raises more questions than answers —sowing productive doubt versus false confidence. One passage prodded foundational questions on investing’s essence: “The prime mover in a financial market is not value or price, but price differences; not averaging, but arbitraging. People arbitrage between places or times.”

Growth vs. Value

Investing is often framed as a battle between growth and value strategies. Growth investors relentlessly seek innovative companies on the path to rapid growth and market dominance. They’re willing to accept higher valuations based on the belief that earnings will eventually justify the multiple as these companies fulfill their potential.

In contrast, value investors focus on stocks overlooked by the broader market — hidden gems trading at seemingly bargain prices. They look to identify mispriced assets, believing the market has wrongly assessed their potential. Value investors seek to profit as the market eventually recognizes these companies’ true worth. Growth enthusiasts dismiss value investors for clinging to potentially outdated companies, while value proponents criticize growth investors for paying exorbitant prices detached from the underlying business fundamentals.

If the investing world were a clear-cut battleground, why do both growth and value strategies continue to garner followers? Wouldn’t adherents of the demonstrably inferior approach inevitably be driven out of the market? There must be more nuance to this story. The persistence of both growth and value investors hints that each strategy grasps part of a greater truth. We need to zoom out to make sense of this bigger picture.

Price Differences

For a moment, let’s return to the Mandelbrot quote that initiated my quest to distill my views on investing, this time with several keywords in bold: “The prime mover in a financial market is not value or price, but price differences; not averaging, but arbitraging. People arbitrage between places or times.”

Mandelbrot brings this concept to life through real-world examples. He tells of a graduate student who arbitraged locations — buying a used convertible cheaply in snowy Minnesota, repairing it, and selling at a premium in sunny California. The young man cleverly profited from price differences between geographic markets.

Mandelbrot points to ticket scalpers to illustrate time arbitrage. These merchants purchase tickets today, hoping to sell them at a higher price later when demand spikes. The savvy scalper exploits the price difference between present and future by locking in inventory early. In both the place and time arbitrage, Mandelbrot points out that both tactics “assume no ‘intrinsic’ value in the item being sold; they simply observe and forecast a difference in price, and try to profit from it.”

Consider the incredible range of time horizons within modern markets. Day traders focus on minute-by-minute fluctuations, hoping to profit from immediate price shifts. Swing traders broaden their outlook to days or weeks, seeking to ride larger trends. At the far end sits Warren Buffett, who famously quipped the 1988 Berkshire Hathaway letter to shareholders: “Our favorite holding period is forever.” Buffett’s Berkshire Hathaway embodies long-term, buy-and-hold investing, where forever means decades or more.

This spectrum demonstrates the arbitrary nature of time. No universal law says an hour is fast, a month slow, and 20 years long. These distinctions only emerge relative to other players and opportunities in the market ecosystem. But every participant, regardless of their preferred holding period, seeks price differences to exploit.

The Elusive Nature of Value

I don’t mean to diminish the role of value. However, estimating intrinsic value proves slippery, lacking a definitive formula. Investors employ various approximations to pin down this moving target. Book value offers a snapshot of assets from the balance sheet. Discounted cash flow projections bake in assumptions about future growth and discount rates. Market capitalization and enterprise value provide market-based assessments.

Yet no magic number emerges. The motley collection of valuation techniques betrays our yearning for a single, knowable, value-unlocking certainty. This desire for an unambiguous target propels the quest for newer, more comprehensive models.

But perhaps the assumption of fixed, rational value is itself misguided. Asset prices dynamically interact with human sentiment, biases, and randomness. Their so-called intrinsic value likely morphs minute to minute. By acknowledging the futility of false precision around value, we open ourselves to other perspectives. Rather than obsessing over an elusive target, we focus on the more reliable signposts of relative price differences. This liberation from the burden of fixed value judgment is itself a gift.

The Power of Time

Fair questions arise — what meaningfully guides us if value proves so dynamic and investors are essentially arbitrageurs? Are we all just ticket scalpers guessing at prices?

The scalper analogy holds insight. As with investing, buying low and selling high sounds straightforward yet proves quite tricky in practice. An inexperienced operator hitting the streets would lack key judgment — when do prices hit resistance levels? How long before late-arriving fans stop overpaying? Even armed with a simple framework, real-world nuance overwhelms novices.

Yet the seasoned scalper develops an intuitive feel for pricing cycles, consumer psychology, and unpredictable swings. Through hard-won experience, they cultivate judgment around dynamic variables. Rather than seeking fixed formulas, the veterans artfully ride waves and ripples.

Similar principles apply in investing. Understanding that prices lack precision liberates us to hone judgment. Developing a multi-dimensional perspective, an intuition for cycles, and a stomach for uncertainty counts more than uncovering “true” value. The world is messy, but therein lies the opportunity.

Now, imagine a scalper buying 2024 Super Bowl tickets back in 1990. Despite risks like rival league innovation or waning interest, the time arbitrage potential proved immense. According to GoBankingRates, average Super Bowl tickets cost $125 in 1990. Fast forward to 2022, and prices hit $8,869 — a staggering 7,000% increase.

My Views

This example highlights the exponential opportunity from long time horizon arbitrage and how I think about investing at Vermillion Private Wealth. Despite inherent uncertainties over decades, the long-term investor who can ride out dips and turbulence can harness time to compound modest gains into exponential returns.

Rather than obsessing over elusive absolute value, I focus on the reliable relativity of price differences over time. 

Zooming out, growth and value strategies both seek a flavor of arbitrage. Growth investors hope to ride a valuation escalator into the future. Value players wait patiently for their analysis to be proven right. And both can be successful, so I use concepts from both schools in my analysis and strategies. By granting opportunities long horizons, I harness investing’s potential.