What is the optimal ETF portfolio allocation based on historical data?

Grid-search optimization across 15 years (2011-2025) identified QQQ 50% / XLU 20% / XLE 20% / Gold 10% as the maximum Sharpe ratio portfolio among the four-asset universe. This allocation produced a CAGR of 14.4%, Sharpe ratio of 1.079, annualized standard deviation of 11.0%, and a maximum single-year drawdown of -3.2% (2022).

Why is XLU such a large allocation in the optimal portfolio?

XLU (Utilities Select Sector ETF) exhibits a Pearson correlation coefficient of 0.028 with QQQ across the 15-year study period — statistically near-zero co-movement. This near-zero correlation means XLU provides genuine variance reduction when combined with QQQ, which is the mathematical basis of diversification. Sensitivity analysis confirms that each 5% reduction in XLU allocation reduces the portfolio Sharpe ratio by approximately 0.013-0.025 points.

How was the grid-search optimization conducted?

The optimization evaluated all allocation combinations of QQQ, XLU, XLE, and Gold in 5-percentage-point increments that summed to 100%, producing 1,771 unique portfolio configurations. For each configuration, annual portfolio returns were computed across 15 observations (2011-2025), then CAGR, annualized standard deviation, and Sharpe ratio (risk-free rate = 2.5%) were calculated. Portfolios were ranked by Sharpe ratio as the primary criterion.

How did the model portfolios perform in the 2022 market downturn?

In 2022, when QQQ fell -32.6% and the S&P 500 fell -18.1%, the Balanced portfolio (QQQ 50%/XLU 20%/XLE 20%/Gold 10%) recorded a return of -3.2%, and the Aggressive portfolio (QQQ 70%/XLU 15%/XLE 15%) recorded -13.0%. The protective effect was primarily driven by XLE's +64.2% return (energy price surge) and XLU's +1.4% return, which offset the QQQ drawdown.

// BrixNation Quantitative Research

ETF Portfolio Quantitative Study

Grid-Search Optimization · QQQ · XLU · XLE · Gold · 15-Year Back-Test (2011–2025)

Study Period: 2011-2025 N = 15 Annual Observations Optimization: Sharpe Ratio Grid Increment: 5% Configurations Tested: 1,771 Risk-Free Rate: 2.5%

  Methodology & Data Set  · 
  Study Period: 2011-2025 (N=15)  ·  Grid Search: 1,771 allocation configurations  · 
  Returns: Annual total return including dividends reinvested  · 
  Risk-free rate proxy: 2.5%  · 
  Source: Yahoo Finance, Slickcharts, Visual Capitalist  · 
  Not financial advice. Past performance does not guarantee future results.

Optimal Sharpe CAGR

14.4%

QQQ 50 / XLU 20 / XLE 20 / Gold 10

Optimal Sharpe Ratio

1.079

Very good risk-adjusted return

Max Drawdown (Balanced)

-3.2%

vs QQQ alone: -32.6% in 2022

QQQ vs XLU Correlation

0.028

Near-zero — statistically independent

Std. Deviation (Balanced)

11.0%

vs QQQ alone: 22.9%

Aggressive CAGR

16.5%

QQQ 70 / XLU 15 / XLE 15 / Gold 0

Research Methodology

This study employs a grid-search back-test optimization across 1,771 allocation combinations of four ETFs — QQQ (Invesco Nasdaq 100), XLU (Utilities Select Sector SPDR), XLE (Energy Select Sector SPDR), and GLD (SPDR Gold Shares) — using 15 annual return observations covering 2011 through 2025. All combinations in 5-percentage-point increments summing to 100% were evaluated. The primary optimization criterion is the Sharpe ratio, computed as (CAGR minus 2.5% risk-free rate) divided by annualized standard deviation of annual returns.

Optimization Criterion

Primary: Sharpe ratio (risk-adjusted return). Secondary reporting: CAGR, annualized standard deviation, maximum single-year drawdown, and count of negative return years across the 15-observation back-test window.

Data Set

Annual total return data for QQQ, XLU, XLE, and Gold sourced from Yahoo Finance and Visual Capitalist. All returns include dividend reinvestment where applicable. Gold is represented by spot price annual return; GLD expense ratio (0.40%) not deducted for consistency with gross return comparisons.

Limitations

Results represent in-sample back-test performance only. The 15-year study period (2011-2025) encompasses one of the strongest equity bull markets in recorded history. Correlation structures, standard deviations, and return distributions observed in this sample may not persist in future market regimes. Annual rebalancing to target weights is assumed.

Four Model Portfolios — Statistical Summary

The four portfolios below represent the Sharpe-optimal allocation at four distinct risk tolerance bands: maximum CAGR, maximum Sharpe, moderate protection, and capital preservation. All four use only QQQ, XLU, XLE, and Gold as constituent assets.

Portfolio	QQQ	XLU	XLE	Gold	CAGR	Std Dev	Sharpe	Max Drawdown	Neg. Yrs	$1 →
Aggressive	70%	15%	15%	0%	16.5%	14.5%	0.963	-13.0%	2/15	$9.88
Balanced ★	50%	20%	20%	10%	14.4%	11.0%	1.079	-3.2%	3/15	$7.52
Growth + Protection	45%	20%	15%	20%	13.7%	10.6%	1.054	-4.8%	3/15	$6.84
Conservative	35%	25%	10%	30%	12.5%	9.9%	1.011	-4.8%	3/15	$5.86

★ Balanced portfolio identified as Sharpe-optimal allocation across the full grid-search. Std Dev = annualized standard deviation of annual returns.

Compound Growth Index — $1 Invested January 2011

Compound growth indices for all four model portfolios and S&P 500 benchmark, rebased to $1.00. Annual rebalancing assumed.

Return vs Risk-Adjusted Performance — CAGR and Sharpe by Portfolio

The chart below illustrates the CAGR-vs-Sharpe tradeoff across the four model portfolios. The Balanced portfolio dominates on Sharpe ratio despite not having the highest CAGR, demonstrating the efficiency gain from XLU's near-zero correlation to QQQ. The Aggressive portfolio generates approximately 210 additional basis points of CAGR at the cost of a 116-basis-point Sharpe decline.

Correlation Matrix — Asset-Level Statistics (2011–2025)

The near-zero correlation between QQQ and XLU (0.028) is the statistical foundation of the portfolio's risk reduction. In conventional diversification theory, assets with correlation below 0.30 are considered genuinely diversifying. XLU at 0.028 is among the lowest observable correlations between any two broad US equity instruments.

Asset	15-Yr CAGR	Std Dev	Sharpe	vs QQQ Corr.	vs XLU Corr.	vs XLE Corr.
QQQ	16.0%	22.9%	0.589	1.000	0.028	0.334
XLU	10.6%	11.4%	0.714	0.028	1.000	0.241
XLE	5.3%	29.8%	0.094	0.334	0.241	1.000
Gold	5.8%	14.5%	0.228	0.184	0.102	0.076
S&P 500	13.1%	17.2%	0.617	0.961	0.312	0.441

Pearson correlation coefficients computed from 15 annual return observations (2011-2025). All correlations are in-sample and may not be stable across different time periods.

Sensitivity Analysis — XLU Allocation Impact

A common question is whether the 20% XLU allocation in the Balanced portfolio is necessary or excessive. Sensitivity analysis shows that every 5-percentage-point reduction in XLU allocation, redirected to any other asset, reduces the Sharpe ratio. The magnitude of that reduction depends on the destination asset.

Shift from XLU	New Allocation	CAGR	Sharpe	Max Drawdown	$1 →	Verdict
Baseline (XLU 20%)	QQQ50/XLU20/XLE20/G10	14.4%	1.079	-3.2%	$7.52	Baseline
5% XLU → Gold	QQQ50/XLU15/XLE20/G15	14.2%	1.054	-3.3%	$7.31	Worse both
5% XLU → XLE	QQQ50/XLU15/XLE25/G10	14.2%	1.066	-4.2%	$7.37	Worse Sharpe
5% XLU → QQQ	QQQ55/XLU15/XLE20/G10	14.8%	1.042	-4.9%	$7.93	Higher return, lower Sharpe
10% XLU → Gold	QQQ50/XLU10/XLE20/G20	14.0%	1.022	-3.6%	$7.09	Worse both
10% XLU → QQQ	QQQ60/XLU10/XLE20/G10	15.2%	1.004	-6.6%	$8.34	Higher return, lower Sharpe

Annual Return Data — Full Observation Set (N=15)

Year	Aggressive	Balanced	Gr.+Protect.	Conservative	QQQ	XLU	XLE	Gold	S&P 500

Down market years (S&P 500 negative) shown in bold. 2022 demonstrates the portfolio's primary risk-reduction mechanism: XLE +64.2% and XLU +1.4% offsetting QQQ -32.6%.

What is a grid-search portfolio optimization?

A grid-search optimization evaluates every possible allocation combination across a defined set of assets at a fixed increment (in this study, 5 percentage points). For four assets, all combinations summing to 100% at 5% steps produce 1,771 unique portfolios. Each is evaluated on historical return statistics — in this study, primarily Sharpe ratio. The result is the historically optimal allocation within the sample, not a prediction of future optimal allocation.

Why is 2022 highlighted as the key test year?

The 2022 calendar year represents the most severe stress test in the 15-year study window. QQQ fell -32.6%, the S&P 500 fell -18.1%, and TLT (long-term treasuries) fell -31.2% simultaneously — an unusual triple-asset drawdown driven by the Federal Reserve's 425-basis-point rate hiking cycle. The Balanced portfolio's -3.2% return in 2022 is the clearest demonstration of how XLU's near-zero QQQ correlation and XLE's inflation hedge properties functioned together under genuine market stress.

Does annual rebalancing improve returns?

Annual rebalancing back to target weights imposes a systematic buy-low discipline by trimming the prior year's outperformer and adding to the prior year's underperformer. In the 2011-2025 dataset, the primary rebalancing benefit occurred in years where XLE had a large gain (2021: +53%, 2022: +64%) — rebalancing would have reduced XLE exposure before the subsequent flat-to-negative years. The study assumes annual rebalancing; no-rebalance results would differ but are not computed in this analysis.

Are these allocations suitable for all investors?

No. These portfolios are derived from in-sample historical data and are presented for educational and analytical purposes. Individual suitability depends on investment horizon, tax situation, income needs, risk capacity, and other financial factors not captured in a back-test. The Conservative portfolio's 30% Gold allocation reflects 15 years of Gold data that includes both strong (2020-2025) and weak (2013-2015) periods; forward-looking Gold performance is uncertain.

Data Sources & References

This research is for informational and educational purposes only. All results are in-sample back-test statistics and do not constitute financial advice. Past performance does not guarantee future results. Always conduct independent research before making investment decisions.