Should Young Investors Use Leverage? Ayres and Nalebuff Re-Tested Through 2025

In 2008, two Yale professors argued that the standard advice for young savers gets the risk backwards. Ayres and Nalebuff reported that buying stock on margin when young, then shifting to a more conservative mix later, would have produced 19% more average retirement wealth than holding 100% stocks throughout, and 90% more than a typical target-date glide path, in U.S. data back to 1871. In their historical cohorts the leveraged strategy came out ahead at every percentile, a property called first-order stochastic dominance.¹ They published a revised version in 2013 and a book in 2010.²³

Those numbers are often repeated without the conditions behind them. The paper assumed a borrowing rate close to the long-term bond rate, a worker who saves through every crash, and a strategy rebalanced every month for 44 years. Its own Monte Carlo test does not show dominance. What follows rebuilds the test, extends it through 2025, and changes one assumption at a time to see which ones the result depends on.

The rule: a fixed share of lifetime savings in stocks

Paul Samuelson and Robert Merton showed in 1969 that, under their assumptions, an investor should hold a constant fraction of total wealth in stocks regardless of age. Ayres and Nalebuff point out that a 25-year-old’s total wealth is mostly savings that have not happened yet. Investing 100% of a small account still leaves that worker with little money exposed to the market, while a 60-year-old with the same allocation has decades of savings at stake. Their rule sets the dollar amount in stocks as a share of current savings $S_t$ plus the present value of planned future contributions $PV_t$, limited by the 2:1 borrowing that Regulation T allows:⁴

With $\lambda = 88\%$, the paper’s target for an investor with a relative risk aversion of 2, a new worker hits the 2x cap immediately. In our runs the median worker stayed at full leverage until about age 31, carried some borrowing until about 50, and held 88% of a growing account in stocks after that. A worker who owns a home already does something similar with a mortgage, and Ayres and Nalebuff make that comparison.

The chart shows what the rule changes. With 100% stocks, about 75% of a career’s real dollars in stocks sat in the 15 years before retirement, when the account is largest. The leveraged rule lowered that to about 67%, a modest shift, because even at 2x a young worker’s account is small. Ayres and Nalebuff measure this with an inverse Herfindahl index of dollars in stocks by year, which gives the number of equally weighted years the exposure is equivalent to. In our 112 cohorts, 100% stocks used the equivalent of 21.7 of 44 years and the leveraged rule 25.3. The 90/50 glide path scored 26.7 by holding less stock throughout.

This differs from the claim that stocks become safer over long horizons, which Samuelson called a fallacy in 1963.⁵ Ayres and Nalebuff argue that spreading equal dollars across many years diversifies across those years’ returns, the way spreading dollars across stocks diversifies across companies. Samuelson still objected to their strategy; the authors wrote in 2010 that he had read only their abstract.⁶

What the papers reported

The 2008 paper simulated 94 workers who started at 21 between 1871 and 1963, saved 4% of a Social Security “scaled medium earner” wage, paid a 0.30% annual fee and retired at 65. Against 100% stocks, the 88% leveraged rule raised mean retirement wealth 19.3%, the median 27.0% and the worst cohort 7.4%, and finished ahead in 89 of 94 cohorts.¹ Two caveats sit in the same tables. Every percentile rose, but the standard deviation rose too (+6.6%), so the gap between good and bad outcomes widened in dollars. And the cohorts overlap: neighbors share 43 of 44 years, and the authors estimate the effective number of independent histories at about three.

Their strongest evidence for diversification across time holds the average fixed. A leveraged rule with a 74.2% target matched the mean of 100% stocks with a standard deviation more than 25% lower (Table VII). The 2013 article makes the same comparison with a 200%-to-50% rule, which matched the mean of a constant 75% portfolio with a 21% lower standard deviation.²

The paper’s Monte Carlo section reaches a weaker conclusion. Drawing 44 annual returns at random from the historical record, 10,000 times, the leveraged rule still raised the mean and median, but dominance disappeared. The worst draw fell from $22,533 with 100% stocks to $14,286, and certainty-equivalent wealth, which penalizes bad outcomes according to risk aversion, was 10.9% lower for an investor with a relative risk aversion of 4 and 33% lower at 8 (Table XV). Lowering the target for more risk-averse investors restored the gains against the two benchmarks (Table XVI).¹

Our re-test, 1871 to 2025

We rebuilt the simulation from public data: Shiller’s monthly S&P Composite total return, bond returns and CPI;⁷ NBER call money rates, the broker loan rate Ayres and Nalebuff use, through June 1926;⁸ and one-month T-bills from the Kenneth French data library after that.⁹ The wage profile is the Social Security Administration table the paper cites, with SSA’s projected real wage growth, which puts the peak at $58,782 at age 51 as in the paper.¹⁰ Run on the authors’ posted workbook for the book version, with the workbook’s own monthly timing, our code reproduces every summary statistic to the dollar.³

On public data the medians, means, 10th percentiles and win counts line up with the published table. The worst cohort and standard deviation differ by a few points, which is expected when one or two extreme cohorts drive a statistic and the bond series differs. Reproducing Table V required one undocumented choice: the published numbers match only when future savings are discounted at 6.35%, the blended return the paper lists under Table IV, instead of the 2.63% risk-free rate its text describes. The higher rate makes the worker’s future savings look smaller and calls for less borrowing. We keep it for comparability; discounting at 2.63% instead raises the leveraged median gain at a 1.5% spread from +28% to +36%.

Extending the cohorts and pricing the loan

The extension adds every career that ended by 2025, 112 in all, and replaces the call money rate with T-bills plus a stated spread. Call money ran 1.4 points above T-bills on average from 1926 to 1970, so a 1.5% spread over bills is close to the paper’s own assumption and to what Interactive Brokers charges today. Before 1926, when there were no Treasury bills, bills are proxied by call money minus that average gap.

At box-spread rates the leveraged rule beat 100% stocks in every cohort. At 1.5% over bills it lost in 5, all retiring between 1999 and 2004, after the 1990s rally, when the leveraged rule had already cut back to 88% stocks and missed part of the gain. The worst cohort at 1.5% still ended +12% ahead of the worst 100%-stock cohort. Each extra point of spread cut the median advantage by roughly 4 to 6 percentage points. The break-even spread over T-bills was 6.5 points for the median, 5.1 for the mean, 4.7 for a risk aversion of 4 and 3.4 for the worst cohort.

The gain comes from the borrowing

The leveraged rule does two things at once: it borrows early and it de-risks late. Running the same 88% target with the cap set at 100% of savings separates them. Without borrowing, the rule holds 100% stocks until the target falls below the account balance, then trims. Against 100% stocks it finished with a mean -4.6%, median -1.3%, worst cohort +0.7% and -15% standard deviation. The late de-risking reduced dispersion and cost a little return. Nearly all of the paper’s gain over 100% stocks came from the borrowing.

Holding the average fixed tells the same story. A leveraged target of 75% matched the mean of 100% stocks with a -26% standard deviation, a +13% 10th percentile and a +4% worst cohort, close to the paper’s Table VII. The unleveraged version of the same comparison, the no-borrowing rule against a constant share of savings with the same mean, cut the standard deviation by only 6%. Spreading exposure across a career requires money to spread, and a young worker can get it only by borrowing.

Margin calls, paused savings and resampled history

Margin calls. FINRA Rule 4210 requires equity of at least 25% of a margin account’s value, and brokers can set higher house requirements.¹¹ Using daily U.S. market closes from 1926, a position re-levered to at most 2x at each month-end never fell below 25% within a month. At 30% maintenance it would have been called in 21 of 23,154 levered cohort-months, all in October 1929, September 1931 or October 1987. At 35% the count rose to 59, across six calendar months. These counts assume the monthly rebalancing the paper uses and ignore intraday lows; a buy-and-hold margin position that lets leverage drift up after a decline gets called sooner. The Personal Leverage guide covers how brokers handle calls.

Paused savings. The rule sizes the loan from savings the worker expects to make. We stopped contributions for 24 months after every 30% fall in real stock prices while the worker kept planning on them. Every cohort hit at least one pause. Because the pause cut contributions for every strategy, the leveraged rule still finished ahead of 100% stocks in 109 of 112 cohorts at a 1.5% spread. The test does not capture the harder case, a worker who has to sell investments to cover living costs, or a forced sale at the bottom after a margin call.

Resampled history. With 3.5 independent careers in the record, the historical cohorts cannot show how often the strategy fails. We built 10,000 simulated careers from randomly drawn 5-year blocks of the 1871-2025 monthly data, keeping stocks, bonds and bills from the same months together and keeping any momentum or reversal inside each block.

At a 1.5% spread the leveraged rule ended ahead of 100% stocks in 85% of simulated careers, with a median gain of +20%. The worst of the 10,000 leveraged careers ended 36% below the worst 100%-stock career. For an investor with a risk aversion of 2, the 88% target was worth +14% in certainty-equivalent wealth. At 4 the gain was +2% with 5-year blocks and -6% with 1-year blocks; at 8 it was a loss of about a quarter to a third. These results match the paper’s Monte Carlo: the 88% target suits a fairly risk-tolerant investor, and a more cautious one needs a lower target, which means less borrowing and a smaller gain.

What other research finds

The models agree that young workers who can only invest current savings are often constrained, and disagree about how much borrowing helps once the borrowing is priced realistically.

• Bodie, Merton and Samuelson (1992) showed that a worker with safe earnings holds too little stock as a share of total wealth and may optimally borrow.¹²
• In Choi, Liu and Liu’s 2025 approximation of the optimal lifecycle portfolio, which does not allow borrowing, the stock allocation of a moderately risk-averse worker “is very frequently at the 100% upper boundary.”¹³ Duarte, Fonseca, Goodman and Parker find the 90th percentile household at 100% until just before retirement in a model capped at 100%.¹⁴ A binding cap is consistent with a desire for leverage.
• Willen and Kubler (2006) model consumption and collateralized borrowing together and conclude that unconstrained models “dramatically overstate the gains to holding equity.” Ayres and Nalebuff summarize Willen and Kubler’s estimate of the gain from 2:1 leverage over 100% stocks as 1.2% in lifetime utility.¹⁵¹
• Benzoni, Collin-Dufresne and Goldstein (2007) find that when wages and stock prices move together over the long run, young workers may optimally hold no stock or short it, because their earnings already behave like equity.¹⁶ Scott, Shoven, Slavov and Watson (2026) find that income risk correlated with stocks and Social Security replacement rates move optimal portfolios a long way from target-date funds, especially for lower earners.¹⁷
• Anarkulova, Cederburg and O’Doherty price the borrowing directly in a lifecycle model built on 39 developed markets. At 6.50% over bills, near the median broker margin spread in April 2024, the optimal household does not borrow. At 1.40%, the lowest broker spread then, gross exposure runs from 132% to 200% of wealth over the lifecycle, and at 0.37% borrowing hits the 200% cap at every age.¹⁸
• The one published outside test of the Ayres-Nalebuff rule we found, Wang, Li and Liu (2017), used U.S. data from 1900 to 2011 with margin at the risk-free rate plus 1 to 2 points. They found its risk reduction “relatively insignificant” and its outcomes inferior to conventional and dynamic lifecycle strategies.¹⁹

What leverage costs in October 2026

At a small-balance rate from a large broker, the historical result reverses: the strategy trailed 100% stocks in 92 of 112 careers at 8 points over bills. At Interactive Brokers or Robinhood rates it sits near our 1.5% case. Box spreads, index futures and deep in-the-money index options price financing close to Treasury rates; Ayres and Nalebuff estimated that one-year S&P 500 calls at 1x to 2x effective leverage implied 0.53 points over the one-year Treasury from 1996 to 2006, with no margin call possible on the purchased call.¹ Each brings its own work: option approval, rolls, expiration dates, and the difference between notional exposure and cash at risk. The box spread guide covers the cheapest of these.

A 2x leveraged ETF needs no margin account, but it resets its leverage every day instead of following a declining glide path, so holding one means adjusting the position size yourself as savings grow. The daily-reset guide tests what the daily reset costs.

Which accounts can hold it

Ayres and Nalebuff wanted their strategy inside 401(k) plans, where most young workers save, and noted that the law effectively prevents it. That is still true. Using part of an IRA as security for a loan is treated as a distribution of that part,²⁹ and limited-margin IRAs do not lend. Leverage in a retirement account means a leveraged ETF, or futures and options where the custodian allows them. In a taxable account, margin interest is deductible only against net investment income and only if you itemize; qualified dividends and long-term gains count toward that limit only if you give up their lower tax rate. Index futures and broad index options are taxed under Section 1256 as 60% long-term and 40% short-term gain, marked to market each year.³⁰

Try it: replay every career

The replay runs the same rule in your browser over all 112 cohorts. Change the borrowing cost, the target, the cap, or lower future stock returns, and compare the leveraged rule with the same rule that never borrows.

Who might reasonably borrow

• Workers whose pay does not move with the stock market: tenured or civil-service jobs, licensed professions with steady demand. Ayres and Nalebuff use assistant professors as their example.
• People who already hold 100% stocks in their retirement accounts, save consistently, keep six months or more of expenses in cash, and carry no debt above the rate they would borrow at.
• Investors who can borrow within about 2 points of T-bills, through a low-cost broker, box spreads, futures or index options, and who will follow a written rule to cut leverage as the account grows.
• Anyone who would accept losing their first few years of savings, with decades of contributions ahead to rebuild.

Who should skip it

• Anyone paying a large-broker margin rate. Historically that cost erased the gain.
• Workers in finance, technology, real estate or a small business, whose bonus, equity grants or job security fall with the market. The human capital guide covers this risk.
• Anyone saving for a home purchase, carrying credit card debt, or without an emergency fund.
• Anyone who sold during 2020 or 2022, or expects to. The historical results assume the worker kept buying through 1929, 1974, 2000 and 2008 at full leverage.

Key takeaways

• Ayres and Nalebuff’s rule holds a fixed share of lifetime savings in stocks, which means borrowing up to 2x early in a career and paying it down by about age 50.
• In 112 historical U.S. careers retiring 1915 to 2025, borrowing at T-bills plus 1.5% beat 100% stocks in 107 with a median +28%; at 8 points over bills it trailed in 92.
• The gain came from borrowing. The same rule without borrowing ended close to 100% stocks.
• The historical break-even borrowing cost was about 5 points over T-bills for average wealth and 3.4 for the worst cohort.
• Overlapping cohorts amount to about 3.5 independent careers. In resampled histories the worst outcomes were worse than 100% stocks’, and investors more risk-averse than the paper’s baseline gained little or lost.
• For most young investors, 100% stocks and a higher savings rate come first. Leverage on top requires cheap financing, steady income unrelated to the market, and a plan to pay it down.

Frequently asked questions

Does buying stock on margin when young reduce retirement risk?

In the historical cohorts, with cheap borrowing, it raised the worst and 10th-percentile outcomes compared with 100% stocks. In resampled histories the worst outcomes were worse, and the risk-adjusted gain depended on how risk-averse the investor is. At typical large-broker margin rates it lowered most outcomes.

What borrowing rate makes lifecycle leverage worth it?

In our 112-cohort test the leveraged rule matched 100% stocks on average wealth at about 5.1 points over T-bills, and on the worst cohort at 3.4 points. Rates within 1 to 2 points of bills were available in October 2026 at Interactive Brokers, Robinhood, and through box spreads and futures.

Is a 2x leveraged ETF a good way to do this?

It avoids margin calls and works in an IRA, and its cost is close to a low-cost margin loan. It holds a constant 2x exposure reset daily, so following the rule means holding a shrinking share of the account in the 2x fund as savings grow.

What did Ayres and Nalebuff recommend for risk-averse investors?

A lower target. Their Table IV gives 88% for a relative risk aversion of 2, 44.6% for 4 and 22.4% for 8. A lower target reaches its dollar goal sooner, so the worker borrows for fewer years.

Why not just hold 100% stocks?

For most young savers that is the better first step. In our test the no-borrowing version of the rule ended close to 100% stocks with less dispersion, and 100% stocks avoids margin, taxes on interest and the work of managing a loan. Target-date funds hold less stock than either when young; Poterba, Rauh, Venti and Wise found typical lifecycle funds produce retirement wealth similar to a constant allocation with the same average stock share.³¹

Related guides

• Personal Leverage: margin mechanics, the drawdown that triggers a call, and a stress test calculator.
• Lifecycle Asset Allocation: human capital and why young investors can hold more stock.
• The Merton Share: the formula behind a target share of wealth in stocks.
• Do Daily Resets Hurt Leveraged ETFs?: 100 years of 2x and 3x data.
• Box Spread Loans: borrowing near Treasury rates with index options.
• Stocks Are Always Risky: why long horizons do not remove stock risk.
• 60/40, Target-Date Funds, or 100% Stocks Forever?: what each approach is solving for.
• Life-Cycle Finance: planning saving, spending and risk across a whole life.

Method note

Monthly real returns run from January 1871 to May 2026: Shiller’s real total-return S&P Composite and real 10-year bond returns, deflated by his CPI over the same month; NBER call money rates to June 1926; and the Kenneth French one-month T-bill return, compounded from daily data, from July 1926. Each cohort starts in January and saves monthly for 528 months, 4% of the SSA 2004.3 medium-earner factors grown at 1.07% a year in real terms (3.9% wage growth over 2.8% CPI, the 2004 Trustees Report’s ultimate assumptions). Each month the contribution arrives, the stock share is set, and the month’s return accrues: the share times the stock return, plus one minus the share times the bond return (below 100%) or the borrowing rate (above), minus a 0.025% monthly fee. Wealth is floored at zero. The target rule sets stock dollars to 88% of savings plus the present value of planned contributions at a 6.35% real discount rate, capped at 2x savings; when that is less than savings, the share is the same fraction capped at 100%. The no-borrowing variant caps at 100% throughout. Borrowing costs T-bills plus the stated spread; before July 1926 bills are call money minus its 1926-1970 average gap over bills. The 2008 replication uses call money through November 1970 and bills plus that gap afterward. Certainty equivalents use constant relative risk aversion over the cross-section of terminal wealth. Margin calls compare each month’s lowest daily close of the French value-weighted market, relative to the prior month-end, with the threshold implied by that month’s leverage. The bootstrap draws 60-month blocks (12-month in the sensitivity row) with replacement from January 1871 to December 2025, seed 20261017. No taxes, trading costs or forced liquidations are modeled. The engine is nwtracker/lifecycle_leverage.py, tested in tests/test_lifecycle_leverage.py; the calculator runs the same equations in the browser and is checked against the Python output. Scripts, data and printed output are in the summitward-research repository. The Ayres-Nalebuff workbook used for the exact check is not redistributed.

Sources

1. Ian Ayres and Barry J. Nalebuff, “Life-Cycle Investing and Leverage: Buying Stock on Margin Can Reduce Retirement Risk,” NBER Working Paper 14094, June 2008 (Tables IV, V, VII, VIII, X, XII, XV, XVI). nber.org
2. Ian Ayres and Barry Nalebuff, “Diversification Across Time,” The Journal of Portfolio Management 39, no. 2 (2013): 73-86, doi:10.3905/jpm.2013.39.2.073. Figures quoted from the October 2010 working-paper version (Yale Law & Economics Research Paper No. 413). yale.edu (PDF)
3. Ian Ayres and Barry Nalebuff, Lifecycle Investing: A New, Safe, and Audacious Way to Improve the Performance of Your Retirement Portfolio (Basic Books, 2010); simulation workbooks posted at lifecycleinvesting.net. lifecycleinvesting.net
4. 12 CFR 220.12, Supplement: margin requirements (Regulation T). cornell.edu
5. Paul A. Samuelson, “Risk and Uncertainty: A Fallacy of Large Numbers,” Scientia 98 (1963): 108-113 (reprint). casact.org (PDF)
6. Ian Ayres and Barry Nalebuff, “Did Paul Samuelson Support Leveraged Lifecycle Investing?” Freakonomics, July 6, 2010. freakonomics.com
7. Robert J. Shiller, U.S. stock market data (ie_data.xls: real total return price, real total bond returns, CPI), monthly from January 1871, downloaded October 2026. shillerdata.com
8. NBER Macrohistory Database, series m13001, call money rates, mixed collateral, New York City, monthly 1857-1970. nber.org
9. Kenneth R. French Data Library, Fama/French 3 Factors [Daily] (market and one-month T-bill return), July 1926 to May 2026. dartmouth.edu
10. Michael Clingman and Orlo Nichols, “Scaled Factors for Hypothetical Earnings Examples Under the 2004 Trustees Report Assumptions,” SSA Actuarial Note 2004.3 (Table 6, medium earner). ssa.gov
11. FINRA Rule 4210, Margin Requirements. finra.org
12. Zvi Bodie, Robert C. Merton and William F. Samuelson, “Labor Supply Flexibility and Portfolio Choice in a Life Cycle Model,” Journal of Economic Dynamics and Control 16 (1992): 427-449. nber.org
13. James J. Choi, Canyao Liu and Pengcheng Liu, “Practical Finance: An Approximate Solution to Lifecycle Portfolio Choice,” NBER Working Paper 34166, August 2025. nber.org
14. Victor Duarte, Julia Fonseca, Aaron S. Goodman and Jonathan A. Parker, “Simple Allocation Rules and Optimal Portfolio Choice Over the Lifecycle,” NBER Working Paper 29559. nber.org
15. Paul Willen and Felix Kubler, “Collateralized Borrowing and Life-Cycle Portfolio Choice,” NBER Working Paper 12309, June 2006. nber.org
16. Luca Benzoni, Pierre Collin-Dufresne and Robert S. Goldstein, “Portfolio Choice over the Life-Cycle when the Stock and Labor Markets Are Cointegrated,” Journal of Finance 62, no. 5 (2007): 2123-2167. nber.org
17. Jason S. Scott, John B. Shoven, Sita N. Slavov and John G. Watson, “Life Cycle Portfolio Choice with Human Capital and Social Security,” NBER Working Paper 34966, March 2026. nber.org
18. Aizhan Anarkulova, Scott Cederburg and Michael S. O’Doherty, “Beyond the Status Quo: A Critical Assessment of Lifecycle Investment Advice,” working paper, August 27, 2026 (Internet Appendix C.9 on leverage). ssrn.com
19. Luo Wang, Bin Li and Benjamin Liu, “Understanding the Leveraged Life Cycle Investment Strategy for Defined-Contribution Plan Investors,” Financial Planning Research Journal 3, no. 2 (2017): 12-30, doi:10.2478/fprj-2017-0006. repec.org
20. Federal Reserve Bank of St. Louis, “Are U.S. Treasuries Still Convenient?” On the Economy, October 14, 2025 (box-spread minus Treasury yields at 6-, 12- and 18-month maturities). stlouisfed.org
21. Robinhood, margin rates, as of September 17, 2026. robinhood.com
22. Interactive Brokers, margin rates (USD, IBKR Pro and IBKR Lite), retrieved October 18, 2026. interactivebrokers.com
23. ProShares, Ultra S&P500 (SSO) fund page (daily 2x objective; gross expense ratio 0.88%, net 0.84% after a waiver through September 30, 2027), data as of October 16, 2026. proshares.com
24. Charles Schwab, margin rates and requirements (base rate 10.25%, last changed September 18, 2026), retrieved October 18, 2026. schwab.com
25. Fidelity Investments, margin rates (base rate 10.825%, effective September 18, 2026), retrieved October 18, 2026. fidelity.com
26. Vanguard, margin rates (base rate 9.75%, last changed September 18, 2026), retrieved October 18, 2026. vanguard.com
27. Board of Governors of the Federal Reserve System, 3-Month Treasury Bill Secondary Market Rate (DTB3), 4.10% on October 15, 2026, via FRED. stlouisfed.org
28. Chris Murray and Marco Sammon, “The Costs and Benefits of Leveraged ETFs,” working paper, August 24, 2026 (Table 2 expense ratios and funding spreads). ssrn.com
29. IRS Publication 590-B, Distributions from Individual Retirement Arrangements (pledging an IRA as security for a loan). irs.gov
30. IRS Publication 550, Investment Income and Expenses (investment interest; Section 1256 contracts). irs.gov
31. James Poterba, Joshua Rauh, Steven Venti and David Wise, “Lifecycle Asset Allocation Strategies and the Distribution of 401(k) Retirement Wealth,” NBER Working Paper 11974, January 2006. nber.org

Disclosure

The tables, charts and calculator are the author’s own calculations on public data under the stated assumptions. They describe past U.S. market paths and simulated paths built from them, and do not forecast returns or borrowing costs. Broker rates are as published on the dates given and change often. Nothing here is investment advice.