leverage, without the ruin

Why I expect markets to keep going up

Ever since I fell down a rabbit hole on leveraged index investing, I've been trying to work out how to do leverage right in my own portfolio

wait what? i need more context

I feel like the stock market keeps going up in notional value over time

Line goes up and to the right, for a bunch of independent reasons

And if that's true, it's a positive-EV game, so you want to play it as much as you possibly can, with as much money as you can

independent reasons like what?

Economies grow. Since the industrial revolution, innovation has kept begetting more innovation, a la Kurzweil's law of accelerating returns

I buy a cap-weighted index, so I don't need to know where the next wave comes from, winners get bigger weights and losers fade out

Then there's money printer go brrr, fiat loses purchasing power, so assets priced in it drift up

AI productivity hasn't really hit the economy yet either, though that's probably just accelerating returns again

Most speculative one: if AI pushes the value of labor toward zero, returns flow to capital owners, and maybe capital ownership is all that matters in the far future

A lifetime of earnings arrives too late

okay, but aren't those all arguments for just VOO and chill?

VOO and chill is great, but it only puts the cash you have today into the game

And if you're young, most of your income arrives in the future, so it never gets enough time in this positive-EV game

Ideally you'd borrow against that future income and put it to work now, and leverage lets you do exactly that

Really it's just the classic glide from 100% stocks to bonds as you near retirement, extrapolated further back down your timeline

What fixed leverage costs

well, okay. so just take on leverage according to what your future income looks like and leverage accordingly? UPRO and chill instead of VOO and chill?

Tempting, but fixed leverage is the naive answer, and it can genuinely ruin you

If some instrument gave you 3× the S&P over fifteen years, we'd be done here, just max long that

But that's not how leveraged ETFs work, they target 3× the daily return, not your holding period

And that's where volatility decay comes from, say the market drops 5%, then gains 5% back, the index is only down 0.25%

But at 3× you drop 15%, then gain 15%: 0.85 × 1.15 = 0.9775, so you're down 2.25%, same round trip costs the 3× fund about nine times as much, and it keeps happening through every choppy stretch

huh, so even if the index is flat, you might still bleed out? especially if it stays choppy for years?

Pretty much, a choppy or drawn-out year or two can leave you in a genuinely unrecoverable state

So don't hold leverage fixed, lever up when we expect smooth sailing and cut it when we expect choppiness

Volatility decides the leverage

and how do you know when it'll be smooth vs choppy?

That's the key bit, volatility is way more predictable than direction

Volatility clusters, high-vol stretches tend to be followed by more high-vol, so guessing how turbulent next month is is way easier than guessing which way it goes

And we can leverage that (sorry)

The other half is that historically, more volatility hasn't paid off in proportionally bigger returns

So in a turbulent stretch, each dollar of exposure is making a worse bet than it is in a calm one

makes sense. how do you translate this into a leverage target?

Like this: L_t = clamp ( 0.6 · (0.10 − r_f) / σ_t², 0.5, 3.0 )

It's the Kelly criterion that determines the leverage, with constants plugged in that gave me good empirical results

σ_t is the volatility we've been talking about, and r_f is the 3-month T-bill rate. At today's 4%, the target looks like this

Dynamic target leverage 4% T-bill rate · 10% target return · β 0.6

One backtest isn't enough

did it actually hold up on real history?

Yeah, it held up on the S&P 500 from 1993 to 2026, which covers the dot-com crash, the GFC, COVID, and the 2022 rate shock

Growth of $100,000, 1993 to 2026 Monthly rebalancing · log scale

that's quite impressive, more than 5× the ending wealth of the S&P with smaller drawdowns than fixed leverage?

Yeah, though the last ~15 years have been super kind to any levered strategy. basically a ZIRP-era perma-bull run

The promising bit is that dynamic strat survived dot-com and the GFC, and was already well ahead by 2011, before aforementioned ~15 years

so, did you simulate it on more unfavourable paths?

Yeah, I ran it across thousands of simulated 15-year futures that don't all look like the last thirty years

I built multiple "regimes" of the world: like an AI boom, a slow bleed, rate shock, AI-bust, geopolitical freeze etc

I probabilistically sample these regimes that move returns, volatility, and rates together and construct these 15-year paths

And then I compare the strategies on all those paths and look at the broad distribution of outcomes

What the full distribution says

makes sense. the results?

15-year simulated outcomes $100k + $2k/month · pre-tax

On final return, dynamic matches fixed 2×'s upside while matching 1×'s downside

On drawdowns, it's much closer to 1× than 2×, and nowhere near as bad as 3×

So yeah, the sims are pretty convincing to me

What I actually do

have you already changed your portfolio based on this research?

Pretty much, but I had to factor in a lot of practicalities, like taxation, instrument choice, and what works in each account

So now I run dynamic leverage in my tax-advantaged accounts, my 401(k) and Roth IRA, and stick to fixed leverage in taxable to avoid the tax drag

And I build it around VOO*, a market-cap-weighted mix of VOO and foreign mega-caps like TSMC, ASML, Samsung, and Tencent, since a lot of the AI and tech value chain is international

some bits might feel counterintuitive in real life, like cutting leverage after the market has already crashed. you think you'll actually follow it?

I hope so. Having run the experiments and written the argument down should give me enough conviction to follow the rule even when it feels wrong in real time