SI411: Why the Best Portfolios Are Built to Be Wrong ft. David Dredge & Richard Brennan

The core argument. Dredge and Brennan converge from opposite disciplines — options/convexity and systematic trend-following — on one claim: markets are complex adaptive systems, not statistical distributions to be sampled. As Brennan puts it, paraphrasing his own framing, the future "isn't hidden, it hasn't been written yet." From that single premise both derive that risk is not volatility — it is the loss-absorbing capital behind a position and the stability of correlation assumptions, both of which conventional risk models (VaR, Sharpe, modern portfolio theory) treat as fixed when they are not.

The mechanism. Dredge frames markets as populated mostly by "rational accounting men" — banks, pensions, insurers, central banks, FX reserve managers — who are price-insensitive because they optimize to regulatory/accounting rules, not economic value, versus a smaller set of "boundedly rational" risk-takers with skin in the game. He argues the bond market went furthest through this imbalance by late 2020 (his "mother of all bubbles"), and that the 2022 rate shock was only the initial unwind — central banks, FX reserve managers, banks and insurers are still sitting on unrealized losses they haven't marked or cut. Brennan built an agent-based model with random, convergent (mean-reverting) and divergent (trend-amplifying, which includes passive flows) traders; pure randomness produced a clean Gaussian outcome, but once divergent participants crossed roughly 25% of the population, fat tails, volatility clustering and market memory appeared as a phase transition, not a gradual drift. Both attribute large moves primarily to endogenous buildup rather than news — Brennan cites Jean-Philippe Bouchaud's finding that news explains only a small fraction of tick-level moves — with risk accumulating quietly (thinning liquidity, rising position size) before a small trigger releases it, an idea both frame through Dredge's forest-fire/self-organized-criticality analogy: fire risk rises with unburned brush, and connectivity (leverage) determines whether a strike stays local or spreads.

Critically, both say the calmest regimes are the most dangerous, not the safest. Brennan's research finds risk events cluster after low-volatility periods because volatility-targeting models mechanically raise position size as measured vol falls, while investors behaviorally lever up to generate returns in dull markets. His example: the Japanese government bond market in 2018 had trailing volatility near 0.9%, implying leverage of roughly 16.4x; a subsequent 0.6% move erased about 9% of capital. Trend-following's own signature example is cocoa, which most diversified trend books held only because they were maximally diversified — not because anyone forecast the move.

What has to be true. Underpinning all of this is non-ergodicity — the idea that the arithmetic (ensemble) average and the geometric (time) average diverge once a path can end in ruin. Dredge invokes Ole Peters' ergodicity economics and Nassim Taleb's point that a 50% drawdown needs a 100% recovery to break even. Brennan reshuffled 40 years of return data, changing only sequence: standard metrics (Sharpe, Sortino, VaR, standard deviation) were unchanged, but terminal wealth outcomes ranged from a 30% decline to an 84% decline depending purely on path — the difference, he says, between a bad year and not being in business.

This is why both reject standard portfolio metrics. Brennan argues Sharpe conceals construction: two portfolios can share a 1.5 Sharpe while one is a single levered Kelly-sized bet (one failure mode) and the other is a thousand loosely related small positions (near-zero single-point failure), and Sharpe cannot distinguish them — it also penalizes convexity, noting trend-following's best month in 40 years, October 2008, added 3.4% to total portfolio wealth yet moved the Sharpe ratio from only 0.914 to 0.931. Both reject Kelly-optimal sizing for the same reason: optimal betting assumes perfect information, leaves no room for estimation error, and once fat tails are introduced the sample size needed for a reliable edge estimate explodes; Brennan says his own tests show simple equal-risk-weighted sizing outperforms Kelly-based sizing once regime change and noise are introduced, and cites Long-Term Capital Management as the canonical failure of trading at the optimal edge.

On diversification, both push back on the textbook view. Dredge says diversification only helps when downside is bounded; if any single position can go to infinite loss, diversifying across such positions doesn't help, whereas his book wants unbounded upside (his St. Petersburg paradox analogy: paying a fixed price to keep playing an infinite-upside game repeatedly is the trade). Brennan's research finds markets are permanently coupled through shared participant models (an agent diversified across a dozen markets creates coupling across all of them), and diversification does not thin tails — as sample size grows, exposure to the market's fractal structure increases, meaning bigger drawdowns and bigger gains both lie ahead as diversification widens, which is how a maximally diversified trend book ended up holding cocoa. This is why leverage on "concave" (correlation rising to bad markets) exposures compounds risk, while leverage on genuinely convex, negatively-correlating exposures reduces portfolio risk as it grows — the basis for portable-alpha and return-stacking structures, which Dredge frames as safe only if the added exposure (long vol, trend) is truly convex rather than simply additional leverage on concave risk.

Practical takeaways given. Dredge: change compensation from calendar-year arithmetic returns toward geometric wealth compounding; free capital tied up in weak diversifiers and redeploy into explicit convexity/loss-mitigation; build resilience through iterative learning rather than backward-looking optimization. Brennan: cap leverage in absolute terms to break the automatic link between quiet markets and large positions; size every market to equal risk rather than tilting toward recent strongest performers; grow exposure by widening the book (more markets, more diversification) rather than scaling existing bets; and always enter positions small, letting the market build the position out of open profit.