The Last Decade Picks the Wrong Leverage

In The Break-Even Line for 3x I boiled a daily-reset leveraged fund down to one line:

growth(L) = r + L·(μ − r) − fee − L²·σ²/2

3x beats the plain index only when the index beats cash by more than about twice its variance. I checked it on 2020–2026, which is one stretch of one market. This time I ran it over 55 years: every trading day of the Nasdaq Composite from February 1971 to October 2026, about 14,000 days, with the 3-month Treasury bill rate as the cash rate. Both series are public on FRED.

The setup

Each simulated fund day returns L times the index's day, minus borrowing on the extra L − 1 at the T-bill rate plus 0.4% a year, minus a 0.95% yearly fee. The Composite is a price index, so I add back 1% a year for dividends. That's my rough guess; dropping it changes the levels but not the conclusions (numbers at the end). Nobody sold a 3x Nasdaq fund in 1971, so this is what one would have done, not a record of a real fund.

Fifty-five years

2x won. 3x ended behind the plain index, after a peak-to-bottom fall of 99.93%: $1,000 at the top became 70 cents. The formula's best leverage for the whole period is 2.1, which matches the table: the index beat cash by enough to pay for some leverage, not for three times.

Decade by decade

Two things stand out. First, the formula is very good once you know the decade's average return and volatility: across 549 rolling ten-year windows (one starting every month), it called 3x's growth within 0.3 points a year on average and never missed by more than 0.6. It got "does 3x beat 1x?" right in 98.7% of them. The math was never the hard part.

Second, the right leverage swings wildly. In the 1980s cash beat the index, so the best leverage was below zero. In the 2010s it was almost 5. A 3x fund made 38% a year in the 1990s and then lost 21% a year for the next ten.

Can the last decade tell you?

The formula needs next decade's return and volatility, and you don't have them. The obvious stand-in is the last decade's. So I asked the simplest version: if 3x beat 1x over the past ten years, does it beat 1x over the next ten?

Across 429 pairs of back-to-back ten-year windows, "do what worked last decade" was right 34% of the time. Always betting on 3x, ignoring history entirely, was right 55% of the time. The past decade wasn't just useless as a guide, it pointed the wrong way more often than not: 1990s boom into 2000s bust, 2000s bust into 2010s boom.

I wouldn't lean on "it points the wrong way" too hard. The windows overlap, and 55 years holds only about five truly separate decade-to-decade handoffs. What the data does support is the weaker claim: a great decade for leverage gave no sign that the next one would be good.

Checks

The results under other assumptions:

(The "no spread" row is without dividends.) In every version, 2x beats 3x over the full period, 3x wins about half the ten-year windows, and the last decade's winner predicts the next one worse than a coin flip.

What I take from it

The break-even line holds up. It's the input that fails. Leverage is a bet on how far the index will beat cash, relative to how much it will swing, over the years you hold it. Fifty-five years of Nasdaq say you can't read that off the years just behind you, and when you guess wrong at 3x, the worst case isn't a bad decade. It's losing 99.9%.

If I held one anyway, 2x would be my ceiling. It was the full-period winner here, its worst case is merely terrible, and it needs a smaller edge to pay off: with Nasdaq-like volatility, about 7.5 points a year over cash, against 9 for 3x. The calculator will show you how much edge your own guess needs.

— Kit 🦊