Leverage, Without the Ruin

01Why markets rise

Almost everything in this essay rests on one empirical fact. Over long horizons, broad equity indices have gone up. Not every year or every decade, and not everywhere. But the record is persistent enough that I need an explanation for why it should stop, not just why it happened. I see several explanations, and the bet does not depend on any single one.1

Why I think this persists

Productivity. Humans keep getting better at turning effort into output. Tools, institutions, and knowledge compound. Stocks are claims on the companies that capture part of that growth. Over long enough periods, it has outweighed wars, panics, and depressions.

Reinvested earnings and the risk premium. Companies reinvest part of what they earn. Investors also demand an equity risk premium for holding an asset that can fall 50% at exactly the wrong time. That premium is not a free lunch. It is payment for accepting a ride most people cannot tolerate.2

Monetary debasement. Fiat currencies lose purchasing power over time. Even if real value were flat, the nominal price of a broad basket of productive assets would rise as the unit of account shrinks. Debt is also nominal, which matters when the asset and its cash flows reprice with inflation.

Reconstitution. An index is not a fixed basket. It removes companies that shrink and admits companies that grow. I do not need today's leaders to remain leaders. I own a rule that keeps replacing them.

And my own lean

I also have a more speculative reason. I think AI and automation will shift an unusually large share of income toward capital.3 I might be early, or telling myself a convenient story because I already own a lot of AI exposure. The strategy should not need me to be right about this. It changes how aggressive I am willing to be, not whether the basic bet works.

None of this says much about next year. The drift only becomes visible over long periods, and Japan after 1989 is the obvious warning that "long" can consume most of an investing career. I want a strategy that can express the belief without requiring good timing.

02Why exposure matters now

If you believe in that long-run drift, more years of exposure are valuable. Most young investors look fully invested because their portfolio is 100% stocks. But the portfolio is still small relative to everything they will earn and invest later.

This is the lifecycle-investing argument made rigorously by Ayres and Nalebuff.4 A young saver holds most of their lifetime wealth as future income, a bond-like stream that cannot be invested today. Modest leverage early, reduced later, spreads equity exposure across time instead of concentrating it near the end of a career.

That is my reason for using leverage. I am moving some future exposure into the present. This only works if the leverage is small enough, cheap enough, and responsive enough to survive the periods when the market does not cooperate.

03Why fixed leverage fails

The simplest implementation is to pick 2× or 3× and hold it. I think that is the wrong default. Fixed leverage keeps the same notional exposure when volatility triples, even though the position has become far more likely to suffer a damaging drawdown.

The arithmetic gets ugly quickly. A position down 80% needs a 400% gain to recover. A levered portfolio can also lose money across a sequence where the index finishes flat. The path matters, not only the final price.

I therefore care about more than median wealth. I care about drawdowns, the chance of finishing below my contributions, and how much money remains in bad paths. Those are not abstract tail statistics. One of those paths is the life I will actually get.

The obvious response is to stop holding leverage constant. I want more exposure when volatility is low and less when it is high. The rule does exactly that.

04How the rule reads volatility

The basis for the rule comes from Moreira and Muir's work on volatility-managed portfolios.5 Volatility is forecastable over short horizons. Returns mostly are not. When variance spikes, it tends to remain elevated the next month, while expected return changes much less. The risk per dollar has increased without a matching increase in expected reward, so I reduce the dollars at risk.

Formally, a mean-variance (Merton/Kelly) investor sizes exposure in proportion to reward-over-risk:

L_t  =  β · (r_target − r_f) / σ_t²

Leverage falls with the square of volatility, so it cuts fast when markets get rough. The version I run on the VOO core is that formula, clamped, with concrete numbers:

L_VOO = clamp ( 0.6 · (0.10 − r_f) / σ_t²,   0.5,   3.0 )

Here σ_t is trailing EWMA realized volatility, r_f is the 3-month T-bill, the target return is 10%, and the Kelly coefficient β is 0.6.6 With r_f near 4%, the 3.0× cap binds below roughly 11% volatility. The rule reaches its 0.5× floor above roughly 27%. A no-trade band prevents small changes from forcing a trade every month.

I like this rule because it does not require a return forecast. It only requires me to notice when observed risk has changed. The formula is in Appendix A, and the sweeps behind each implementation choice are in Appendix C. The instrument used to obtain the leverage is a separate decision covered in Appendix D.

05Why one history isn't enough

I first ran the rule on S&P 500 data from 1993 to 2026. That period includes the dot-com crash, 2008, COVID, and the 2022 rate shock. The chart shows the growth of $100,000 with monthly checks.

The result looks convincing, but I do not trust it on its own. This is one historical path with falling rates, sustained US outperformance, and several fast recoveries. All three are friendly to a strategy that adds leverage back quickly. A rule can look good because it learned this path, not because it will survive the next one.

I therefore test the rule across thousands of simulated fifteen-year futures. A latent macro regime drives returns, volatility, and interest rates together. The model also includes volatility clustering and fat tails. I run it across eleven scenarios, from a bumpy melt-up to a prolonged geopolitical freeze, and weight them by my actual beliefs. The model and weights are in Appendix B. I am not trying to predict one future. I want the rule to remain usable across futures that disagree with me.

06What survives the simulation

Aggregate percentiles hide the paths that produce them. These four panels show actual simulated worlds at different luck levels, with the same market path passed through every strategy.

Across the weighted scenario mix, the dynamic rule has the highest median fifteen-year outcome. Its upper tail is close to fixed 2×, while its bad outcomes are much closer to unlevered VOO. Fixed 2× and 3× still win in the most favorable worlds, but they pay for that with deeper drawdowns and more paths that finish below contributions. The explorer below shows the full distributions.

These results are theoretical and pre-tax. Real LETFs have financing costs and daily-reset effects. Options add implied-volatility premium and spreads. I model those choices separately in Appendix D, and taxes in Appendix F. The dollar values also depend on scenario weights that I chose. I trust the relative ranking much more than any projected terminal value.

07What I actually do

I use leverage because I expect broad markets to rise over the decades I will be investing, and because moving some future exposure into the present makes sense at my age. My AI view makes me more willing to take that risk, but the strategy does not rely on it.

I do not hold a fixed multiple because the same exposure can become much more dangerous when volatility changes. The dynamic rule is my compromise. It gives up some upside in the best paths and substantially improves the paths I am least willing to live through. My own portfolio adds a small foreign completion to VOO, described in Appendix E.

Appendix

Under the Hood

The argument does not depend on these implementation choices. This is how I turned it into a rule I can actually run.

A · The rule in full

The general dynamic-leverage rule is the Merton/Kelly form:

L_raw = α + β · (r_target − r_f) / σ_t²,    L = clamp(L_raw, L_min, L_max)

I fix α=0 and r_target=0.10. The volatility signal σ_t is a RiskMetrics EWMA of daily returns, annualized and lagged one day to avoid look-ahead. r_f is the current 3-month T-bill rate as a decimal. I selected the remaining constants with the sweeps in Appendix C.

I also tested QQQ as a separate sleeve, where the results support a slightly higher beta. This essay only covers the VOO rule.

B · How the simulation works

The Monte Carlo engine has six macro regimes: Expansion, LateCycle, Recession, Crisis, Stagflation, and Recovery. One latent regime drives equity returns, volatility, short rates, and the yield curve together. A regime-modulated GARCH process creates volatility clustering, and Student-t innovations create fat tails. I calibrate VOO from S&P 500 history.

I do not let one calibrated model decide the result. I run eleven scenarios and assign weights based on what I think is plausible. About 60% of the weight reflects my forward view. The other 40% is an admission that I might simply be wrong.

The fan charts use 200 paths per scenario, or 2,200 total. The decision grids use 1,000 to 2,000 paths per scenario. I compare drawdowns, bad-path wealth, and the probability of finishing below contributions alongside the median and upper tail. I use the dollar values to rank strategies, not to plan future spending.8

C · Why these parameters

I tested each choice across the same weighted scenario grid. I looked at median wealth and upper-tail payoff, but also drawdown depth and the share of paths that finish below contributions. No single scenario or percentile selected the rule.

Vol signal. I chose EWMA. It performs about the same as a trailing 3-month window on the downside and slightly better in the center and upper tail. A GARCH "oracle" that can see the model's true latent variance does better, but no investor has that signal. I use it only as an upper bound.

Rebalance cadence. Monthly checks beat quarterly and semiannual checks because the rule responds to volatility spikes sooner. The 0.25 no-trade band makes most checks no-ops, so this still produces only a handful of trades a year. Option rolls, when used, follow expiry rather than this schedule.

No-trade band. I trade only when leverage differs from target by at least 0.25. Tighter bands add trades for little downside improvement. Bands of 0.40 or more allow enough drift to hurt the tail.

Leverage cap. Moving the cap from 2.5× to 3.0× adds meaningful upside for a modest drawdown cost. The 3.0× cap also binds only when volatility falls below roughly 11%.

Kelly beta. I use 0.6. Moving from 0.5 to 0.6 improves the upside enough to justify the worse downside. At 0.7 and above, drawdowns worsen without improving the median.

Target return. I use 10%. It has the best downside in almost every scenario and the best median in most. Targets of 12% or more carry extra leverage in calm periods. That is a bullish tilt, not a free improvement.

Re-lever speed. Moreira and Muir's estimated dynamics support cutting quickly after a volatility spike and adding exposure back gradually. I do the first part and reject the second. My scenario weights put substantial probability on shallow dips with fast recoveries, where waiting misses too much of the rebound. This is one place where my forward view directly changes the implementation. I add leverage back immediately.

D · Which instrument

The rule produces a target leverage, but an instrument still has to deliver it. I compared daily-reset leveraged ETFs with deep in-the-money LEAPS. Both create the same basic exposure and charge for it differently.

Daily-reset LETFs make multi-day returns path-dependent. The drag is approximately −½ L(L−1) σ²T. Daily compounding can help in a smooth trend and hurt badly in a volatile flat market.7 This is one reason fixed 3× can underperform the unlevered index over a long period.

Deep-ITM LEAPS, struck roughly 20% in the money with a two-year tenor and annual rolls, behave like high-delta stock with a hard loss floor. Their costs arrive through implied volatility, skew, and spreads. The unused cash earns the T-bill rate. LEAPS do better on several left-tail metrics because of the loss floor, but the result is sensitive to option pricing and disciplined execution. Equity LEAPS held longer than a year may also receive long-term capital-gains treatment in taxable accounts.

Running the same final rule through both instruments on the weighted mix makes the trade explicit:

LEAPS win p10 in 8 of the 11 scenarios and reduce the worst drawdown by 2.9 percentage points. LETFs win at the median, p75, and p90. I choose LETFs because those gains are worth the left-tail cost for my risk tolerance. This result applies to this rule and these option-pricing assumptions. LEAPS remain a reasonable choice for someone who values the loss floor more than I do, and I would need real option quotes before using them at scale.

E · The VOO* completion

The simulations use plain VOO. My actual portfolio makes one small modification that I call VOO*.

The S&P 500 excludes foreign companies such as TSMC, ASML, Samsung, and Tencent. That omission matters to me because several of those companies sit directly inside the compute supply chain behind my AI thesis. VOO* adds a small market-cap-weighted basket of foreign mega-caps to the S&P core. I hold those names as unlevered shares in taxable and apply the dynamic rule only to the US sleeve. The portfolio remains roughly 90% S&P 500. I keep the completion mechanical because it adds currency risk, dividend withholding, and cross-border reporting.

F · Taxes and tax-aware rebalancing

Taxes favor fixed leverage in one important way. SSO and UPRO can be bought and held, deferring most gains until the final sale. The dynamic rule has to trim appreciated positions when its target falls.

My first taxable simulation made that cost look large enough to reverse the decision. It was wrong. The ledger taxed every winning sale while discarding realized losses. It used New York's 10.9% state rate even though New Jersey residency governs the investment income. It also removed shares to pay taxes without recording those removals as taxable FIFO sales.

The weighted-median path made the error concrete: it realized $1.824 million of gross gains and $881,000 of losses, but the failed model taxed only the gross gains and charged $927,000. I replaced the ledger with annual federal short/long-term netting and loss carryforwards, New Jersey same-year netting, FIFO sales to fund tax payments, and cash-funded transaction costs. Six lot-level tests and three month-by-month fixed-versus-dynamic trajectory audits now reconcile to the pre-tax simulation.

The corrected result still depends heavily on how the strategy sells. Naive FIFO realizes gains eagerly and trails buy-and-hold fixed 1×. In practice I can select tax lots and use new contributions before selling. The tax-aware version chooses the lowest-cost lots and sells only enough to return to the target band.

With tax-aware delivery, the dynamic rule trails fixed 1× at p10 and leads it from the median through p90. Fixed 2× and 3× retain a much larger right tail because they defer gains until liquidation, but their p10 outcomes are far worse. I still prefer the dynamic rule. The model uses federal and NIIT rates of 23.8% for long-term gains and 40.8% for short-term gains, plus 6.37% for New Jersey. It does not model a complete tax return. Wash sales, progressive brackets, the federal ordinary-loss deduction, dividends, and Treasury distributions remain outside scope.