Equal thirds in SPY, AGG and GLD (S&P 500, US aggregate bonds, gold) raise Sharpe from 60/40's 0.52 to 0.68 without an optimizer. The advantage survives only if the sample includes 2005 to 2009. The authors acknowledge the appeal of fixed weights, describing them as effective and extremely simple. Their optimized headline portfolios get their additional Sharpe with bitcoin and searched assets added to the mix.
What Edén Wallberg and Karolin built
The study takes the private investor's perspective. It covers 59 liquid US-listed ETFs in equities, bonds and alternatives, with monthly rebalancing. Shorting and leverage are ruled out. Cash earns the federal funds rate, and trades incur a 5bp spread. The daily backtest spans 2005-01-01 to 2025-01-01, or 5,032 trading days. Diversification supplies the return: combine assets whose drawdowns occur at different times, then move into cash as forecast risk rises to cap volatility at 8%.
The tests cover two families. Risk-only rules make up the first: equal weights, volatility control, inverse volatility, minimum volatility, risk parity and maximum diversification. The last rule maximizes weighted-average asset volatility divided by portfolio volatility. These rules operate on three-to-five-ETF subsets. For equal weights and inverse volatility, the subsets come from an exhaustive search across 23 ETFs. All were listed when the backtest began; single-country and futures funds were excluded. The optimizer tests add assets such as IBIT by hand.
The second family puts one-month momentum, or a 50-day moving-average signal, into a constrained Markowitz problem spanning whole asset categories. Turnover is capped at 10% per rebalance and any weight at 10%. A ten-factor statistical model fitted by EM supplies the covariance estimates.
The authors are frank about the forecasts. Ridge regression using three price features delivers negative out-of-sample R² throughout: "at no level of regularization does the model beat the zero forecast for a single asset." The factor model's advantage over sample covariance is narrow, with normalized Frobenius error of 0.221 against 0.228. To measure consistency, they use LQ, the 25th percentile of the twenty calendar-year Sharpe ratios.
Gold takes 60/40's Sharpe from 0.52 to 0.68
Trading costs pose little threat here. Annual turnover for equal-weight SPY/AGG/GLD is 0.17, versus 0.12 for 60/40. A 5bp spread puts the annual drag below a basis point.
The paper's final table reports everything net of that spread. The three-ETF portfolio earns an 8% excess return, versus 7% for 60/40. Volatility is 9% against 10%. Its Sharpe is 0.68 against 0.52, maximum drawdown is 24% against 30%, and LQ is 0.49 against 0.13.
The search supports the same explanation. GLD appears in every top-fifteen portfolio at every size, although GLD was the only alternative with enough history to qualify. A weight sweep uses SPY, AGG and GLD as representatives of the three asset classes. Its best allocation is 30/40/30, with Sharpe 0.67. Owning all three matters more than the precise split.
The introduction and the sweep give 60/40 a Sharpe of 0.51 and a 36% drawdown; the final table gives 0.52 and 30%. We did not find an explanation reconciling those figures.
How much does maximum diversification contribute to SPY/TLT/GLD/IBIT's 0.90 Sharpe?
Maximum diversification on SPY/TLT/GLD/IBIT is the headline portfolio. It records Sharpe 0.90, a 28% drawdown and 0.42 turnover. Compared with the three-ETF portfolio, it makes three changes together: TLT replaces AGG, bitcoin enters, and the allocation rule changes. Comparing 0.90 with 0.68 cannot identify which change earned the difference.
The paper's tables let us separate some of those effects. They give the optimizers more credit than we expected. Equal-weight SPY/TLT/GLD is absent from the top-60 three-ETF list, where the cutoff is 0.68. Using those same three assets, minimum volatility achieves 0.87, maximum diversification 0.82 and risk parity 0.79. Risk weighting plainly helps when AGG gives way to a long bond with 15%-volatility. Maximum diversification still trails the best rule for those assets.
IBIT accounts for the final move from 0.82 to 0.90. LQ remains 0.54, while drawdown increases from 24% to 28%. IBIT uses bitcoin history backfilled to 2017. The authors generally limit crypto to small allocations, citing its 50%-plus annual run since 2017. For this max-diversification portfolio, however, they say the position has no cap. Scaling each asset by its own volatility is all that keeps it small.
The parameters are untuned. The assets were searched.
The portfolios work "without tuning to the backtest period," the paper says. For the numerical parameters, that description holds: the volatility target and turnover caps are round values drawn from the literature. Asset selection has a different history. Gold and long Treasuries qualified through an exhaustive search over 2005 to 2025, the window in which performance is then evaluated.
The authors acknowledge this for their best search result, QQQ/XLP/TLT/GLD/IBIT at 1.02, which they report "as a reference rather than propose it." The proposed portfolios use the same ingredients. The conclusion accepts that "some use of prior knowledge when defining the universe is unavoidable." Yet the abstract continues to advertise results "without tuning to the backtest period."
The momentum results show the size of the universe effect. Across the full universe, the portfolio produces Sharpe 0.43, LQ -0.03 and turnover 1.08. The authors then remove categories identified by an ablation, a test that drops categories to measure their effect. They call the remaining 26 ETFs the Momentum Universe. Performance rises to 0.78, with LQ 0.40, a 16% drawdown and 0.81 turnover. They describe the selection bias as "modest, though not zero," conceding that "some of the improvement is still due to selection." Their defence rests on structural arguments against Futures and Countries made before any backtest ran.
That defence accounts for two of the three removals. Subtracting 15 country and 7 futures funds from the 59-ETF universe leaves 37. Getting to the 26-ETF Momentum Universe also requires dropping the 11 sector funds. Removing sectors alone raises Sharpe from 0.43 to 0.47, which the authors say surprised them.
Taking crypto out of the full 59-ETF momentum run lowers Sharpe from 0.43 to 0.29. We did not find a crypto-free run of the 26-ETF Momentum Universe, which holds both IBIT and ETHA. Costs remain trivial: turnover of 0.81 at 5bp costs about 4bp a year.
Excluding 2005-2009 puts 60/40 ahead of equal-weight SPY/AGG/GLD
The authors retest the four proposed portfolios over 2010 to 2025 and over 2005 to 2020. They report that "the ordering between the portfolios holds."
Over 2010 to 2025, the benchmark beats the simplest portfolio.
The four proposed portfolios retain their order in both windows. The benchmark changes position. Over 2010 to 2025, 60/40 earns 0.78, ahead of equal-weight SPY/AGG/GLD at 0.75 and SPY vc8 at 0.70. The LQ difference is larger: 0.61 versus 0.26 for the three-ETF portfolio. The sentence about the ordering omits the benchmark, though the conclusion acknowledges the issue. Its full sentence says that "the proposed portfolios do not depend on a single market crisis, although the relative performance of the 60/40 improves when the Financial Crisis is excluded."
Maximum diversification reaches 1.02 in that window and the Momentum Universe 0.86. Both beat 0.78. Over 2005 to 2020, the three-ETF portfolio leads 60/40 by 0.71 to 0.58. The authors' defence therefore holds for those two portfolios and fails for equal-weight SPY/AGG/GLD (0.75 against 0.78), the portfolio our title addresses. The simplest portfolio owes its edge to 2005 to 2009. The two that stay ahead without 2005 to 2009 carry bitcoin or the ablation choices.
We could not test these results ourselves. Our ETF price history starts after 2010. Any run we made would therefore begin within the window where 60/40 outperforms the equal-weight three-ETF portfolio. We lack precisely the 2005 to 2009 history that determines the headline.
I would choose equal-weight SPY/AGG/GLD over plain 60/40 for its weak-year Sharpe: 0.49 against 0.13 over the full period. Over 2010 to 2025, though, that ranking reverses to 0.26 against 0.61. To change my mind about the optimized versions, I would want to see the four portfolios held unchanged from 2025 forward, beyond the period used to choose them.