Comparison report

Walk-forward on 5 years, Nov 2001 to Oct 2026
6 methods · 5 assets · monthly · rebalanced quarterly · 10 bp trading costs · risk-free T-Bills

Summary

Each method, scored out of sample

Highest Sharpe ratio

0.55

Equal weight; next risk parity 0.54

Smallest drawdown

−17.3%

Hierarchical risk parity

Lowest turnover

10% a year

Equal weight

Largest fall out of sample

0.64 → 0.44

Maximum Sharpe, Sharpe ratio

Out of sample, Nov 2001 to Oct 2026

Method	Return	Volatility	Sharpe	Sortino	Drawdown	CVaR 95%	Turnover
Equal weight	7.7%	11.4%	0.55	1.17	−37.8%	6.9%	10%
Minimum variance	5.8%	8.4%	0.50	1.20	−22.3%	4.7%	15%
Maximum Sharpe	6.1%	10.6%	0.44	0.97	−40.8%	6.6%	35%
Maximum diversification	6.0%	8.4%	0.52	1.23	−23.6%	4.8%	14%
Risk parity	6.2%	8.4%	0.54	1.26	−24.3%	5.0%	10%
Hierarchical risk parity	4.8%	6.6%	0.47	1.23	−17.3%	3.7%	13%

Return, volatility and turnover are a year; drawdown is the largest fall; CVaR is the average loss in the worst 5% of months. Bold marks the best in each column. Limits: at most 40% in any asset. Equal weight, risk parity and hierarchical risk parity: fully invested and long only; the limits on weights do not apply. Maximum Sharpe found no weights at 6 refits, from Jun 2008 to Sep 2009 (infeasible); it kept the weights it held.

Performance

Growth and returns by year, out of sample

Growth of 100

Equal weight 646Minimum variance 410Maximum Sharpe 443Maximum diversification 431Risk parity 449Hierarchical risk parity 323

Calendar-year returns

	Equal weight	Minimum variance	Maximum Sharpe	Maximum diversification	Risk parity	Hierarchical risk parity
2001 from Nov	0.4%	0.7%	0.3%	0.7%	0.5%	0.6%
2002	3.4%	2.9%	2.2%	4.4%	5.6%	9.8%
2003	22.2%	12.3%	11.0%	13.5%	15.7%	10.7%
2004	9.1%	4.5%	11.4%	5.5%	6.4%	3.9%
2005	7.0%	−2.6%	12.0%	−1.6%	1.4%	−0.2%
2006	−11.2%	−8.3%	−7.0%	−10.2%	−8.3%	−6.9%
2007	−3.6%	−1.5%	−3.3%	−1.1%	−1.1%	0.8%
2008	−22.1%	−9.8%	−27.8%	−10.9%	−12.8%	−8.0%
2009	41.6%	29.9%	36.7%	30.4%	29.7%	22.1%
2010	19.4%	4.9%	14.6%	6.7%	7.3%	−2.5%
2011	24.3%	17.1%	13.6%	17.1%	21.2%	19.4%
2012	20.7%	12.5%	8.1%	12.7%	12.5%	5.3%
2013	10.8%	−1.2%	4.3%	0.6%	5.0%	2.2%
2014	−4.0%	0.3%	0.5%	0.7%	0.4%	5.1%
2015	18.1%	17.3%	14.0%	18.4%	17.5%	16.8%
2016	17.0%	14.6%	13.2%	14.5%	14.0%	11.4%
2017	18.0%	16.0%	12.8%	14.3%	13.0%	8.1%
2018	29.6%	24.3%	25.8%	22.2%	21.6%	13.3%
2019	7.6%	4.6%	7.6%	4.4%	4.5%	2.2%
2020	1.1%	9.1%	6.7%	10.3%	6.3%	9.2%
2021	−10.1%	−9.7%	−9.1%	−9.4%	−8.5%	−6.9%
2022	−10.5%	−6.2%	−7.8%	−6.5%	−8.0%	−5.8%
2023	21.0%	17.2%	20.7%	16.3%	16.7%	12.1%
2024	33.9%	24.5%	26.2%	24.8%	25.5%	17.9%
2025	−15.4%	−8.3%	−5.5%	−8.1%	−11.7%	−8.0%
2026 to Oct	−4.4%	−4.8%	−6.2%	−4.2%	−3.9%	−3.2%

Risk

How far and how long each method fell

Drawdown

Equal weight −37.8% at worstMinimum variance −22.3% at worstMaximum Sharpe −40.8% at worstMaximum diversification −23.6% at worstRisk parity −24.3% at worstHierarchical risk parity −17.3% at worst

Sharpe ratio over the past 3 years

Equal weight 0.36Minimum variance 0.37Maximum Sharpe 0.40Maximum diversification 0.41Risk parity 0.30Hierarchical risk parity 0.23

In and out of sample

How much of each method's promise survived

In sample and out of sample

In sampleOut of sample

In sample, each method is fitted to the whole history and scored on the same periods: it sees the returns it is scored on, so it looks better than it can be. The gap to the out-of-sample point is the cost of estimating from the past.

What each method promised and delivered

Method	Sharpe in	Sharpe out	Change	Return in	Return out	Drawdown in	Drawdown out
Equal weight	0.55	0.55	0.00	7.7%	7.7%	−37.8%	−37.8%
Minimum variance	0.59	0.50	−0.09	6.5%	5.8%	−23.3%	−22.3%
Maximum Sharpe	0.64	0.44	−0.20	7.1%	6.1%	−25.8%	−40.8%
Maximum diversification	0.59	0.52	−0.07	6.6%	6.0%	−23.1%	−23.6%
Risk parity	0.59	0.54	−0.05	6.2%	6.2%	−22.6%	−24.3%
Hierarchical risk parity	0.55	0.47	−0.08	5.0%	4.8%	−16.7%	−17.3%

Weights

What each method held, and how often it traded

Weights at the last refit, Sep 2026

	US Equity	Intl Equity	Bonds	Gold	Real Estate
Equal weight	20%	20%	20%	20%	20%
Minimum variance	22%	4%	40%	28%	6%
Maximum Sharpe	33%	10%	–	40%	17%
Maximum diversification	14%	5%	40%	28%	14%
Risk parity	14%	13%	42%	19%	12%
Hierarchical risk parity	5%	5%	71%	13%	6%

Weights at each refit

Minimum variance · turnover 15% a year

Maximum Sharpe · turnover 35% a year

Maximum diversification · turnover 14% a year

Risk parity · turnover 10% a year

Hierarchical risk parity · turnover 13% a year

Darker is a larger weight, up to 74%. Equal weight kept the same weights throughout. Trading costs a year: Equal weight 0.02%; Minimum variance 0.03%; Maximum Sharpe 0.07%; Maximum diversification 0.03%; Risk parity 0.02%; Hierarchical risk parity 0.03%.

Method

How the comparison was run

How the methods were tested

Assets	US Equity, Intl Equity, Bonds, Gold and Real Estate; T-Bills as the risk-free asset, held as cash. Monthly returns, Nov 1996 to Oct 2026.
Validation	Walk-forward. At each rebalance from Nov 2001, each method is fitted to the previous 60 months of returns and its weights are held until the next. Every return scored is one the method had not seen when it chose its weights.
Estimates	Ledoit–Wolf covariance and historical mean returns, annualised by 12.
Limits	At most 40% in any asset; fully invested.
Rebalancing	Quarterly, to the targets; between rebalances the weights drift with prices.
Trading costs	10 bp of the value traded, paid from the next period's return.
In sample	The same methods fitted once to all the history and held over the same periods, for comparison.
Ratios	Sharpe and Sortino ratios against the T-Bills return over each period scored (1.8% a year over the test); value at risk and expected shortfall from history, at 95% over one month.

Every figure is computed by Finalytics 1.0.0-rc.1 from the assets' returns; the same inputs give the same report, identified by the input digest a78f1863f962.