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

Leverage = using borrowed money to invest more than you could with just your own cash

I feel like the stock market keeps going up in dollar terms over time

Line goes up and to the right, for a few reasons

And if that's a positive-expected-value game, i want my lifetime's money to spend as much time in it as possible

reasons like what?

economies grow. better tools let us make more stuff with less effort, and each breakthrough makes the next one easier

and i don't have to pick the next winner. i buy an index where bigger companies get bigger weights, so it shifts toward whoever's doing well

then there's money printer go brrr. as dollars lose purchasing power, the same assets can cost more dollars even without becoming more valuable

i also think we're still early on AI making the economy more productive. though that's probably the first point again, just moving faster

most speculative one: if AI can do almost all the work, maybe owning the companies doing it matters a lot more than earning a salary

A lifetime of earnings arrives too late

okay, but aren't those all arguments for just buying an s&p 500 fund and leaving it alone? aka voo and chill

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

but if you're young, most of the money you'll ever earn hasn't arrived yet. by the time you invest it, it has fewer years to grow

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 toward more bonds as you near retirement. extend that same logic earlier in life, and you go beyond 100% stocks by borrowing

What fixed leverage costs

well, okay. so just take on leverage according to what your future income looks like? buy a leveraged s&p 500 fund and leave it alone? aka upro and chill

Tempting, but there's a catch: the 3× in UPRO is for the S&P 500's daily return, not whatever it makes over the years you hold it

on each individual day, it just mirrors the s&p's move at three times the size. up 1% means up 3%, down 1% means down 3%

but let's put a couple of days together. say the market drops 5%, then gains 5%: 0.95 × 1.05 = 0.9975, so the index is down 0.25%. you're not quite back where you started, because the gain is on a smaller amount

But at 3× you drop 15%, then gain 15%: 0.85 × 1.15 = 0.9775, so you're down 2.25%. the same two days cost you nine times as much

that's volatility decay. those up-and-down moves eat into your money, and leverage magnifies the effect. it keeps happening through every choppy stretch, not just those two days

huh, so even if the index ends up almost 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 with losses that could take years to recover from

the main takeaway is: 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

jumpy markets tend to stay jumpy, and calm markets tend to stay calm (aka, volatility clusters). that's easier to predict than whether prices go up or down

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, you're taking more risk without a corresponding increase in returns

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

More leverage when markets are calm, less when they're jumpy. and less when borrowing gets expensive

okay, but how much?

There's a formula for sizing bets called the Kelly criterion. i use a scaled-down version, with settings that worked well in my experiments

L_{t} = \frac{0.6 \cdot (0.10 - r_{f})}{σ_{t}^{2}}

σ = how jumpy the market's been
r_f = short-term interest rate (3-month T-bill rate)

then i keep the result within a reasonable range: no lower than 0.5×, no higher than 3×

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

so i ran a simulated portfolio through historical s&p 500 data, adjusting its leverage with this rule

One backtest isn't enough

how did it do? did it hold up through the crashes?

Yeah, it held up on the S&P 500 from 1993 to 2026, which covers the dot-com crash, the 2008 financial crisis, 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? and less painful crashes than fixed leverage?

Yeah, though the last ~15 years have been super kind to any levered strategy. years of near-zero interest rates and a market that mostly kept climbing (ZIRP-era bull run)

The promising bit is that dynamic strat survived dot-com and the 2008 financial crisis, 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 a few different versions of the world: like an AI boom, a slow bleed, a jump in interest rates, an AI bust, a geopolitical freeze etc

Then I randomly stitch stretches of those together into 15-year futures. each version moves returns, how jumpy markets are, and interest rates together

And then I run every strategy through the same futures and compare how they do, from the bad outcomes to the good ones

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, meaning how far your portfolio falls from a previous high, 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 I run this strat in the tax-deferred part of my portfolio

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