Putting It All Together
Every framework from Parts I–IV applied to three concrete investor profiles. The synthesis the series has been building toward.
April 8, 2026
Marek Pawlowski
16 min read
Part V of The Mathematics of Diversification — the finale
TL;DR
I
The system so far
Across four articles, this series has built a complete mental model for investing. Before we apply it, let’s compress the whole system into a single page.
I
Variance is the enemy of compounding
Geometric returns are always lower than arithmetic ones. The gap scales with volatility. Kelly sizing maximizes geometric growth.
II
Diversification has a ceiling
Unsystematic risk can be diversified away. Systematic risk cannot. Correlation quality matters more than position count.
III
Asset classes have personalities
Real estate is efficient. Stocks are the benchmark. Tech is levered stocks. Bitcoin pays a huge variance tax.
IV
Entry price determines return
Valuation at purchase is one of the largest predictors of forward returns. The premium for buying cheap is real and durable.
V
Time changes the game
Long horizons collapse variance into near-certainty. Short horizons amplify it. Sequence risk makes the early years of withdrawal matter most.
VI
Selling is appropriate
When the horizon shortens, when valuations are extreme, when the thesis breaks, or when you need to fund your life. Almost never because of a crash.
Now the question the series has been implicitly building toward: what do I actually do with this? The answer depends entirely on who you are. Three profiles below cover the most common cases, with specific allocations and rationale drawn from every prior part.
II
Profile one: the young accumulator
Age 25–35, 30+ year horizon
Accumulation phase · No withdrawals · High human capital
| Broad equity index (VT / VWCE) | 75% |
| Real estate (REITs or primary residence) | 10% |
| Bitcoin | 10% |
| Cash / emergency fund | 5% |
Part I — variance is your friend here. Over 30+ years, the variance of a broad equity index collapses into a near-guaranteed positive geometric return.
Part II — concentration is fine. 75% in a single asset class sounds dangerous until you remember that a broad global equity index is already diversified across thousands of companies, sectors, and geographies.
Part IV — no sequence risk, no glidepath concerns. You’re not withdrawing. A 40% drawdown at age 30 is an opportunity to buy more, not a crisis.
The 10% Bitcoin allocation is deliberate Kelly sizing — small enough that a total loss is survivable, large enough to matter if the asymmetric thesis plays out.
III
Profile two: the mid-career builder
Age 40–55, 15–25 year horizon
Peak earning years · Family obligations · Growing portfolio
| Broad equity index | 55% |
| Real estate (home + possible investment) | 20% |
| Bonds / fixed income | 10% |
| Bitcoin | 5% |
| Cash / short-term needs | 10% |
Part I — variance still works for you, but less. You have 15–25 years, not 40. Kelly sizing adjusts downward.
Part II — real correlation matters now. Real estate becomes the most valuable true diversifier. Its correlation to equities (~0.3) is the key reason to hold it.
Part IV — sequence risk is starting to matter. The 10% bonds and 10% cash are sequence-risk insurance that gets deployed to buy equities after a crash.
Bitcoin trimmed from 10% to 5% — not because the thesis is weaker, but because your ruin tolerance has narrowed.
IV
Profile three: the near-retiree / early retiree
Age 60+, withdrawing or about to
Capital preservation · Sequence risk · 20–30 year remaining horizon
| Broad equity index | 40% |
| Real estate (primary + yield-generating) | 20% |
| Bonds / fixed income | 25% |
| Bitcoin | 2% |
| Cash (2–3 years of expenses) | 13% |
Part I — variance is now the primary enemy. You need the money soon. Every percentage point of volatility translates into geometric drag at exactly the moment you can least afford it.
Part II — diversification’s most important job is tail protection. The 25% bonds and 13% cash exist so that a major equity drawdown cannot force you to sell stocks at the bottom to fund living expenses.
Part IV — sequence risk is the whole game. The 2–3 years of cash is not an emergency fund — it is a sequence-risk buffer. This single structural decision is the difference between the Trinity Study’s 95% success rate and failure.
Bitcoin at 2% — essentially symbolic. At this life stage, a 90% Bitcoin drawdown should not change your retirement outcome.
V
The pattern across profiles
Compare the three allocations side by side and a clear pattern emerges. As the horizon shortens and withdrawals approach, equity exposure declines, defensive assets grow, and the allocation to high-variance bets shrinks sharply.
Allocation evolution by life stage
| Asset class | Young (25–35) | Mid-career (40–55) | Near-retiree (60+) |
|---|---|---|---|
| Equities | 75% | 55% | 40% |
| Real estate | 10% | 20% | 20% |
| Bonds | 0% | 10% | 25% |
| Bitcoin | 10% | 5% | 2% |
| Cash | 5% | 10% | 13% |
What’s striking is what doesn’t change. Real estate stays roughly constant around 10–20%. Cash grows modestly. The big shifts are between equities and bonds — and in the tapering of the Bitcoin allocation as ruin tolerance narrows.
Good portfolio construction is not a secret recipe. It is a thermostat — responsive to the same few inputs, adjusting steadily as your life changes.
VI
What's not in any of these portfolios
Individual stock picks. Concentrating in individual names is an expressive choice, not a mathematical one. It belongs in a separate “play money” bucket capped at a size where a total loss would not affect your long-term outcome.
Sector bets and thematic funds. No dedicated tech allocation, no AI fund, no clean energy theme. The broad equity index already holds them in market-cap weights.
Alternatives beyond real estate and a small crypto slice. No gold, no private equity, no hedge funds. Simplicity is an asset — every additional position adds monitoring cost, tax complexity, and behavioral temptation.
Market timing overlays. Part III showed that valuation matters, but Part IV showed that timing is hard. Rebalancing is the timing you need.
The series in one sentence
Investing is the discipline of making decisions today whose correctness depends on time you cannot yet see — and the math gives you the tools to make those decisions as rationally as possible given that uncertainty.
Parts I through IV built the framework: variance as the invisible tax, diversification as the one free lunch that has a ceiling, asset personalities as the inputs to portfolio construction, valuation as the largest predictor of forward returns, and time as the variable that changes everything. Part V shows how these fit together for real people at real points in their lives.
No framework survives contact with the future intact. But the point of a framework is not to predict outcomes — it is to give you a principled way to respond when the unpredictable happens.
The last most dangerous sentence in investing: "I’ll figure out my portfolio later." Later is never more rational than now.
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