The Vault

THE GEOMETRY OF WEALTH | Episode 14 of 15: Portfolio Construction for the Multiplicative World

The question is not whether to include trend following in a portfolio. The question is how much compounding you are willing to sacrifice by not including it

The previous thirteen episodes built the intellectual case, deployed the evidence, quantified the costs, and provided the evaluation toolkit. This episode assembles everything into a practical construction guide: how much to allocate, how to rebalance, how to implement, and how to think about the allocation in the context of an existing portfolio.

The central finding of Episode 9 bears repeating: a blended portfolio of equities and trend following produces more terminal wealth than either component alone, with a maximum drawdown smaller than either component alone. This is not a theoretical prediction. It is what happened over 313 months of real returns. The construction question is how to capture that geometric synergy in practice.

The Allocation Frontier

Figure 1 maps every 5% allocation increment from 100% S&P 500 to 100% TF Index, plotting CAGR against maximum drawdown. This is the geometric efficient frontier: the set of all portfolios available to an investor combining these two return streams.

Figure 1: The allocation frontier. Each point is a 5% increment of TF allocation, coloured from red (0% TF) to green (100% TF). The curve bends up and to the left: adding TF raises CAGR and reduces maximum drawdown through the 40% TF level. Peak CAGR of 8.41% occurs at 60/40 S&P/TF (40% TF). All blends are rebalanced monthly, net of fees.

The frontier has three critical features. First, it curves up and to the left through the first 40% of TF allocation. This is the geometric synergy: the blend produces higher CAGR and lower drawdown at the same time. The investor is not trading return for safety; the investor is getting both. This is only possible because the two return streams are negatively correlated during crises, so their combination avoids the deep drawdowns that destroy geometric return.

Second, the marginal improvement is not linear. The first 10% TF allocation reduces the maximum drawdown by 5.9 percentage points (from 50.9% to 45.0%) while increasing CAGR by 0.17 points. The next 10% reduces drawdown by a further 6.5 points while adding 0.12 points of CAGR. Each increment of TF reduces drawdown substantially while the CAGR cost is minimal, and by the time the allocation reaches 40% TF the maximum drawdown has compressed from 50.9% to 24.8% while CAGR has actually risen from 8.02% to 8.41%. The marginal arithmetic is striking: each 10% increment of TF buys roughly 6 percentage points of drawdown reduction while costing essentially nothing in CAGR through the first 40%. The drawdown reduction is not free because trend following is free; it is free because the geometric synergy from the negative crisis correlation more than offsets the lower standalone return. The investor is not paying an insurance premium. The investor is capturing a structural feature of the geometry of blended return streams.

Third, the frontier identifies three distinct optima, as documented in Episode 9: maximum CAGR at 60/40 S&P/TF (8.41%), maximum Sharpe near 50/50 (about 0.67), and maximum MAR at 40/60 (0.702). All three sit between 40% and 60% TF. The geometric answer to “how much trend following?” is not the 5% or 10% of typical institutional practice. It is 40% to 60%.

Table 1: Allocation blends of S&P 500 and TF Index, monthly-rebalanced, Jan 2000 to Jan 2026, net of fees. Notation is S&P/TF, so 60/40 is 40% TF. The GFC column is the cumulative Nov 2007 to Feb 2009 return. Peak CAGR sits at 60/40; peak MAR at 40/60.

Figure 2 isolates the MAR ratio across the same allocations. The relationship is nearly monotonic through 60% TF, with each increment adding geometric efficiency. The peak MAR of 0.702 at 40/60 is about 4.5 times the pure-equity MAR of 0.157, and every allocation above roughly 25% TF exceeds Berkshire’s 0.240.

Figure 2: MAR ratio by TF allocation. The dashed line marks Berkshire (0.240) and the dotted line the S&P (0.157). Bars turn green once the blend clears Berkshire, from roughly a quarter TF onward. Peak MAR 0.702 occurs at 40/60 (60% TF), about 4.5x the pure-equity MAR.

The frontier above uses the TF Index, a composite of many programs. An institutional allocator does not invest in the composite; they select programs. Episode 13 demonstrated what happens when the geometric toolkit makes that selection: a disciplined walk-forward process, choosing a ten-manager ensemble each year by MAR from the eligible long-record universe using only data available at the time, compounded at roughly 7.1% with a maximum drawdown near 11.5% and a MAR in the region of 0.6, well above the S&P’s 0.157, with no look-ahead at any decision. The evaluation framework does not merely describe managers. It selects the ones that improve the portfolio.

The Right Tail and the Process That Preserves It

The allocation frontier tells the investor how much to allocate. It does not tell them what kind of trend following to allocate to. This distinction matters because not all implementations treat the right tail equally, and the right tail is where geometric wealth lives. Episodes 7 and 10 established two facts: terminal wealth is dominated by a small number of outlier months (remove the best 32 from the TF Index and the terminal value collapses), and the programs with the broadest market universes and the largest right tails dominate the top of the terminal-wealth rankings. The geometric engine runs on outliers. Any implementation choice that systematically reduces exposure to outliers is fighting the geometry.

This is precisely what aggressive volatility targeting and dynamic position sizing can do. These techniques adjust position size in response to realised or implied volatility: as volatility rises, exposure is cut; as it falls, exposure is added. The stated purpose is to stabilise the equity curve and control drawdowns. The unstated consequence is that the process reduces its exposure to the very conditions that produce the right tail. Consider a trunk-scale trend: crude oil collapsing in 2020, cocoa erupting in 2024, the yen repricing in 2024. In every case the move is accompanied by sharply rising volatility. That is not incidental; it is definitional. An outlier is a large move, large moves produce high volatility, and a system that cuts position size as volatility rises is cutting its exposure to the outlier as the outlier develops. It is selling the trunk while the trunk is still growing.

The classic trend-following process does not do this. It sets position size at entry based on prevailing conditions and then does not interfere. The position rides the trend for as long as the trend persists, regardless of how volatile the move becomes; if the trend accelerates, the position is fully exposed to the acceleration, and if it reverses, the exit logic executes the cut. The process does not predict and does not adjust. It lets the right tail express itself fully and relies on the cut to manage the left tail.

This is the distinction between smoothing the equity curve and maximising geometric wealth. They are not the same objective. A heavily volatility-targeted implementation produces a smoother path with fewer extreme months in either direction, and its Sharpe ratio may look better because the denominator, total volatility, is reduced. But its MAR typically looks worse, because the right tail, the source of the terminal wealth that drives the numerator, has been clipped. The process looks better by the wrong metric and worse by the right one. The pattern in the terminal-wealth rankings is consistent with this: the programs that let positions run at full exposure through extreme trends sit at the top, while the smoothest-equity-curve programs cluster lower, having paid for smoothness with the right tail. This divergence is not an accident of engineering. It is a response to incentives. Over the past two decades much of the industry has migrated toward heavier volatility targeting and dynamic position sizing, and that migration tracks what raises assets rather than what builds wealth. A smoother equity curve and a higher Sharpe ratio are easier to market, easier for an allocator to hold through a review cycle, and easier to defend to a committee. They are more palatable, but palatability and compounding are different objectives. The classic process is the medicine rather than the marketing: it accepts a lumpier path because the lumps are where the geometric wealth is made, and it has refused to bend to the investor appetite for smoothness even when bending would have raised more capital. In a multiplicative system that trade is expensive: every clipped outlier is a compounding step that never occurred, and every step that never occurred removes the platform from which all subsequent steps would have launched.

Episode 10 introduced the wide net: maximum diversification across uncorrelated markets to ensure intersection with the system’s structurally inevitable tail events. The wide net captures the outlier, but capturing it is only half the mechanism. The other half is letting it run. A maximally diversified portfolio that then clips its exposure to every outlier through aggressive volatility targeting has cast the wide net and pulled it in before the catch is complete. The two principles work together: the wide net finds the trunk, and the classic process lets the trunk grow.

There is a further refinement worth understanding, though it should be held more loosely than the results above because it rests on external research rather than the performance database. Markets do not move symmetrically. Equity bull markets tend to last far longer than bear markets, while bear markets deliver greater intensity per unit of time: prices take the escalator up and the elevator down. The structural reason is that the global capital base is overwhelmingly long-biased (passive funds, pensions, sovereign wealth, retirement accounts), so convergent pressure during uptrends builds gradually while divergent pressure during downtrends compounds through margin calls, stop-losses, and risk limits hitting at once. The qualitative implication for implementation is intuitive and is one that many long-surviving programs appear to have converged on: be slower to enter and exit long trends, and faster to cut on the short side, treating the long and short sides as independent signal processes rather than mirror images. The investor evaluating a trend follower can reasonably ask whether the system calibrates the two sides independently. What the investor should not do is over-weight any single precise calibration ratio, because the available evidence shows the geometric payoff to asymmetry is marginal rather than dramatic.

The implication for the investor selecting trend-following exposure is the same one the whole series has built toward. The geometric framework does not favour the smoothest equity curve. It favours the return stream with the highest MAR, the most positive skew, and the longest right tail, because those properties are diagnostic of a process that lets outliers compound. An implementation that sacrifices right-tail exposure for short-term smoothness may look more comfortable on a quarterly report, but comfort and compounding are different objectives, and only one of them builds wealth.

The Rebalancing Question

The blended results throughout this series use monthly rebalancing: at each month-end the portfolio is reset to its target weights. This raises a fair question. Is calendar rebalancing consistent with a process designed to harvest outliers? Table 2 tests the 60/40 blend across four cadences.

Table 2: The 60/40 S&P/TF blend across rebalancing frequencies, Jan 2000 to Jan 2026, net of fees. Terminal wealth ranges from $8.09 to $8.60 and MAR from 0.339 to 0.425. The synergy is robust across cadences, with a slight edge to less frequent rebalancing.

The results are robust across all frequencies: terminal wealth between $8.09 and $8.60 and MAR between 0.339 and 0.425, regardless of cadence. The synergy is not an artefact of a specific rebalancing schedule. The direction is nonetheless revealing. Annual rebalancing, the least frequent option tested, produces both the highest terminal wealth and the highest MAR, because less frequent rebalancing lets the trend-following allocation grow during crisis periods, when it is producing the outlier returns that drive geometric wealth, before being reset to target. Monthly rebalancing interrupts that twelve times a year; annual rebalancing interrupts it once. The spread is modest, just 6% of terminal wealth, so the message is nuanced rather than categorical: more frequent rebalancing mechanically trims the component that is outperforming, the effect is real but not large, and the investor who rebalances less frequently gives the geometry slightly more room to express itself.

The practical solution is structural rather than calendar-based. The investor should maintain allocation bands rather than fixed targets. A 60/40 target with a 15-point band, for example, lets the TF allocation drift between 25% and 55% without intervention; within those bands the portfolio expresses the geometry naturally, growing the TF sleeve during crises and shrinking it during bull markets. The investor rebalances only when drift exceeds the band, and rebalances to the band edge rather than the midpoint. This preserves the process’s ability to compound through outlier periods while preventing extreme drift that would change the portfolio’s character. The takeaway is not that rebalancing is harmful. It is that the investor need not obsess over frequency: any reasonable cadence captures the synergy, and the less the investor engineers the rebalancing, the more the geometry compounds.

The Institutional Case

Most institutional portfolios allocate between 0% and 10% to managed futures or trend following. The frontier shows that this is too small to capture the full synergy. Why are institutions structurally underweight? Four reasons, three openly discussed and one rarely.

The first is the evaluation framework. As Episode 13 documented, the Sharpe ratio dominates institutional evaluation, and it penalises the upside volatility that generates trend following’s terminal wealth while ignoring the skewness and crisis performance that generate its portfolio value. An allocator evaluating through the Sharpe lens sees a strategy with modest risk-adjusted return; an allocator evaluating through the MAR lens sees one with geometric efficiency exceeding Berkshire. The second is the patience cost. Episode 12 documented that trend following underperforms equities on a rolling three-year basis 68.7% of the time, and institutional allocators are evaluated quarterly and annually. A 20% allocation that underperforms for three consecutive years is difficult to defend to a board or investment committee, even when the geometric case is compelling. The decision is made by a committee that evaluates on arithmetic horizons; the geometric payoff arrives on its own schedule.

The third reason is the benchmark. Most institutional portfolios are measured against a 60/40 equity/bond portfolio or a peer group, and trend following increases tracking error relative to both. The allocator who adds 20% trend following and then trails the peer group for five years faces career risk; the geometric case says the allocation will prove its value over the full cycle, but the career incentive says the allocator must survive until the cycle completes. The fourth reason is rarely discussed openly. The 60/40 equity/bond portfolio has been the dominant institutional framework for decades and is deeply embedded in risk models, consultant recommendations, board presentations, and regulatory guidance. Episode 9 showed that replacing the bond sleeve with trend following added terminal wealth, reduced the maximum drawdown, and roughly doubled the MAR relative to a traditional equity/bond 60/40. But replacing bonds with trend following is not merely an investment decision; it is an institutional transformation, and the inertia is substantial even when the geometric case is clear.

The 2022 experience should accelerate that transformation. The traditional equity/bond 60/40 suffered one of its worst years in a half-century as equities and bonds fell together, violating the core premise that bonds hedge equities. Over the same year the S&P 500 fell 19.0% and a 60/40 equity/TF blend lost only 6.0%. The crisis that the bond framework was supposed to protect against was the crisis that broke it, and the trend-following framework worked precisely as designed.

The geometric frontier says allocate 40 to 60 percent. Institutional practice says 0 to 10. The gap between the two is not ignorance. It is the distance between what the mathematics requires and what the institutional framework permits.

The Accessibility Question

The series has documented that trend following delivers geometric properties that transform portfolio efficiency. The honest question is whether ordinary investors can access it, and the honest answer has three parts.

The principle is fully accessible. The geometric properties, positive skew, crisis alpha, and negative equity correlation, are properties of the process rather than of any specific implementation. They arise from cutting losses and riding trends across diversified markets, the process is codifiable, and it has been implemented in ETFs, mutual funds, and retail managed-futures platforms available at modest minimums. The best specific implementations may not be accessible. Some of the programs documented in this series are closed to new investors, require minimums of a million dollars or more, or are reachable only through fund-of-funds structures with additional fee layers. The blueprint is open; some of the best-built houses are gated. This is a real limitation and should not be minimised.

But the structural properties persist across accessible vehicles. The key finding for the retail investor is that the geometric fingerprint is observable across a wide range of implementations, including lower-cost, widely accessible ones. The specific CAGRs of the top institutional programs may not be replicated, but the properties that make trend following valuable in a portfolio, documented in Episodes 7 through 9, belong to the process. An investor accessing trend following through an ETF or mutual fund captures the process properties even if the specific calibration produces different magnitudes, and the accessibility gap has narrowed since 2020 as diversified trend-following ETFs and mutual funds have multiplied at lower cost than traditional hedge-fund structures. They are not identical to the gated programs, but the Episode 11 finding applies: the fingerprint belongs to the process, not to any particular practitioner. All returns analysed in this series are net of fees.

The Hidden Trend Following in Your Portfolio

There is a final point that connects accessibility to the broader argument. The S&P 500 index, the benchmark most investors hold through index funds, already embeds a form of trend following in its construction. The index is not a static list; it is reconstituted regularly, adding companies that demonstrate sustained market-capitalisation growth (a form of momentum) and removing those that decline below the threshold (a form of the cut). The index systematically buys winners and sells losers. This is trend following at the security level, applied with a long lookback and slow rebalancing, and any investor who owns an index fund is already, unknowingly, benefiting from it.

The explicit trend-following allocation documented in this series provides three things the implicit equity momentum does not: diversification across asset classes (commodities, bonds, currencies, and equity indices rather than individual stocks); protection during equity crises (the implicit momentum in the S&P does not protect against a broad equity decline, because it operates within equities); and the negative equity correlation that produces the geometric synergy of Episode 9. The investor who holds only the S&P 500 has trend following in one dimension; the investor who adds explicit trend following has it in all dimensions. This reframes the question for the investor who asks why they should add something new. They are not adding something new. They are making explicit, diversified, and optimised a principle that already exists in their portfolio in an implicit, concentrated, and suboptimal form. The trend-following allocation does not change the philosophy of the portfolio. It completes it.

The Construction Checklist

The practical decisions for the investor building a geometric portfolio reduce to six.

Allocation size. The frontier identifies 40 to 60 percent TF as optimal; this is the data-driven answer. In practice most investors will allocate less, constrained by mandates, behavioural tolerance, or implementation costs. The minimum allocation that captures meaningful synergy is roughly 20%, which cuts the S&P’s maximum drawdown from 50.9% to 38.5% while lifting CAGR from 8.02% to 8.31%. Below 20%, the allocation is too small to materially change the portfolio’s geometry.

Implementation style. Favour classic implementations that hold full position exposure through trends over heavily volatility-targeted or dynamically-sized approaches that cut exposure as moves develop. The framework values right-tail preservation above equity-curve smoothness, so evaluate a vehicle’s skewness and MAR, not its Sharpe ratio or volatility; the implementations with the highest positive skew are those most likely to let the right tail compound.

Rebalancing. Any reasonable frequency works, with a slight edge to less frequent rebalancing. Structural allocation bands, for example a 15-point band around the target, let the portfolio express the geometry naturally during crisis and bull periods while preventing extreme drift; rebalance to the band edge, not the midpoint. The discipline of maintaining the allocation matters more than the frequency.

Implementation vehicle. Options run from institutional-quality single managers and multi-manager platforms with high minimums to trend-following ETFs and managed-futures mutual funds with low minimums and daily liquidity. The geometric properties are observable across the spectrum even though specific CAGRs differ; evaluate any vehicle with the Episode 13 toolkit.

Monitoring. Monitor skewness, MAR, and crisis performance, not Sharpe or rolling return relative to equities. Rolling underperformance during bull markets is expected and documented in Episode 12; it is not a signal to reduce the allocation. Deterioration in skewness or crisis performance is the signal that the process may have changed.

Time horizon and fees. The geometric advantage requires a full market cycle, including at least one significant (30%-plus) equity drawdown, to manifest, so the allocation should not be evaluated on a horizon shorter than seven to ten years; doing so is like judging fire insurance over a period without fires. And because all returns in this series are net of fees, the investor should confirm that the chosen vehicle does not consume the geometric edge in costs, applying the toolkit to net-of-fee returns.

The minimum viable allocation is 20%. The optimal allocation is 40 to 60 percent. The implementation should preserve the right tail. The rebalancing should respect the geometry. The minimum horizon is one full market cycle. And the discipline of maintaining the allocation through underperformance matters more than any other decision on this list.

The Bridge

The construction is complete. The investor now has the mathematical framework, the evidence, the cost accounting, the evaluation toolkit, and the construction guide. The portfolio can be built. But the series has been building toward something larger than a construction guide. Across fourteen episodes a pattern has emerged that challenges the foundational narrative of the investment industry. The industry says wealth comes from picking the right assets; the geometric evidence says wealth comes from the properties of the return stream, regardless of what produced it. The industry evaluates selection; the geometry evaluates path. The industry asks what you bought; the geometry asks what happened to your capital along the way. Episode 15 draws these threads together and addresses the largest question: not how to build a geometric portfolio, but what this investigation reveals about the nature of wealth creation itself. Wealth is geometry, not selection. The path determines the outcome. The process matters more than the pick.

Data and Sources

All performance data is drawn from the NilssonHedge Trend Following performance file for the period January 2000 to January 2026 (313 monthly observations), net of management and performance fees. Blended portfolios are weighted combinations of the S&P 500 Total Return and the TTU TF Index monthly series, rebalanced at the stated frequency. The allocation frontier (Figure 1, Table 1) uses 5% increments from 0% to 100% TF with monthly rebalancing; the GFC column is the cumulative return from November 2007 to February 2009. Figure 2 plots the MAR ratio (CAGR divided by absolute maximum drawdown) at each increment, with the Berkshire (0.240) and S&P (0.157) references; the blend’s MAR clears Berkshire from roughly 25% TF onward. The rebalancing-frequency analysis (Table 2) tracks the weight drift implied by each asset’s monthly return and resets to target at the stated interval. The wider manager universe referenced in this series is the 47-program TTU TF Index defined by a minimum 15-year track record, with per-program exhibits drawn from the 38 programs with 20-year-plus records, consistent with Episodes 10, 11, and 13. All headline figures were verified directly against the source monthly returns.

The walk-forward allocator result referenced from Episode 13 (a ten-manager ensemble selected annually by MAR over a rolling 15-year window, approximately 7.1% CAGR at an 11.5% maximum drawdown) is documented in that episode. The S&P 500 reconstitution discussion draws on S&P Dow Jones Indices methodology. The institutional-allocation discussion draws on Hurst, Ooi, and Pedersen, “A Century of Evidence on Trend-Following Investing” (AQR, 2017) and industry surveys of managed-futures allocation. The asymmetric-calibration and bull/bear-duration material draws on an external 68-market study of asymmetric trend calibration (whose asymmetric and symmetric ensembles produced near-identical MARs of approximately 0.615 and 0.616) and on Lunde and Timmermann’s work on bull and bear market durations; these external sources should be cited directly when this episode is published and are not reproducible from the performance database. The equity/bond 60/40 comparison figures are drawn from Episode 9.

Want the theoretical foundation for why markets adapt?

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Want the theoretical foundation for why trend following works?

The Fractals of Finance: Determinism, Adaptation and the Geometry of Markets

The book explores the full architecture of feedback, fat tails, and fractal structure in financial markets, and what it means for how we trade, invest, and understand risk.

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Want a practical field manual for trading trends and capturing outliers?

The Aussie Turtles Trend Following Guide: A Field Manual for Hunting Outliers adapts the timeless principles of the original Turtle traders into a systematic, rules-based approach for modern markets. Co-authored with Adam Havryliv.

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