Equal weight 1/N
Equal Weight 1/N across asset classes
Where it stands today
Our calculation, 1984-02 – 2026-09
Growth of $10,000
Where it came from
The 1/N rule says: with N assets, put 1/N of the money in each and ignore estimates of returns and risk. It is the simplest possible allocation and has been used by ordinary savers for a very long time. Our encyclopedia already contains older equal-split ideas (the Talmud rule of thirds and the five-equal-slices Ivy Portfolio); this model is the academic version.
The reference paper is 'Optimal Versus Naive Diversification: How Inefficient is the 1/N Portfolio Strategy?' by DeMiguel, Garlappi and Uppal, Review of Financial Studies 22(5), pp. 1915-1953, May 2009 (an earlier discussion paper circulated from 2005). The authors compare 14 optimisation models (the sample mean-variance portfolio and extensions meant to reduce estimation error) with 1/N on several datasets.
Their finding: out of sample, none of the 14 models consistently beat 1/N on Sharpe ratio, certainty-equivalent return or turnover. The reason is estimation error: expected returns and covariances have to be estimated from limited history, and the error cancels the gain from optimising. In simulations calibrated to US equities the sample mean-variance strategy needs about 3,000 months of data to beat 1/N for 25 assets, and about 6,000 months for 50 assets.
The result does not say 1/N is optimal. It says that for asset allocation based on historical estimates, the naive rule is hard to beat; the authors also flag that much work remains to realise the promised gains of optimisation. A later critique (R-bloggers, 2013) argues that the datasets and short monthly history in the paper do not settle the question and notes that the Sharpe ratio differences were not tested for significance (a blog, not peer reviewed).
The choice of N and of which assets count is itself a view. In the paper the assets are mostly equity portfolios or indices of one asset class; here we apply the rule across asset classes, which is a different use (my reading; the paper's datasets are not confirmed in this research).
What is in it
| Each of N assets | 10% | Rule: 1/N. Our definition uses N = 10 (the paper itself does not fix a list of asset classes) |
How we model it
| US large companies (S&P 500) | 10% |
| US small companies | 10% |
| Developed markets outside the US | 10% |
| Emerging markets | 10% |
| Real estate (REITs) | 10% |
| US bond market (aggregate) | 10% |
| Inflation-protected bonds (TIPS) | 10% |
| Cash (Treasury bills) | 10% |
| Gold | 10% |
| Commodities | 10% |
For a euro investor
How to build it with European funds
| Part | Share | Example funds (ISIN) |
|---|---|---|
| US large companies (S&P 500) | 10% | iShares Core S&P 500 UCITS ETF USD (Acc) IE00B5BMR087Vanguard S&P 500 UCITS ETF (USD) Distributing IE00B3XXRP09 |
| US small companies | 10% | SPDR Russell 2000 U.S. Small Cap UCITS ETF IE00BJ38QD84iShares MSCI USA Small Cap ESG Enhanced CTB UCITS ETF USD (Acc) IE00B3VWM098 |
| Developed markets outside the US (closest match) | 10% | iShares Core MSCI Europe UCITS ETF EUR (Acc) IE00B4K48X80iShares Core MSCI Japan IMI UCITS ETF IE00B4L5YX21 |
| Emerging markets | 10% | iShares Core MSCI Emerging Markets IMI UCITS ETF (Acc) IE00BKM4GZ66 |
| Real estate (REITs) | 10% | iShares US Property Yield UCITS ETF IE00B1FZSF77iShares Developed Markets Property Yield UCITS ETF IE00B1FZS350 |
| US bond market (aggregate) (closest match) | 10% | iShares Core Global Aggregate Bond UCITS ETF EUR Hedged (Acc) IE00BDBRDM35iShares Core Global Aggregate Bond UCITS ETF USD (Dist) IE00B3F81409 |
| Inflation-protected bonds (TIPS) | 10% | iShares USD TIPS UCITS ETF USD (Acc) IE00B1FZSC47 |
| Cash (Treasury bills) | 10% | Xtrackers II EUR Overnight Rate Swap UCITS ETF 1C LU0290358497iShares USD Treasury Bond 0-1yr UCITS ETF (Acc) IE00BGSF1X88 |
| Gold | 10% | Invesco Physical Gold ETC IE00B579F325Xetra-Gold DE000A0S9GB0 |
| Commodities | 10% | iShares Diversified Commodity Swap UCITS ETF IE00BDFL4P12 |
The idea
If forecasts of returns and risk are noisy, equal weights avoid the estimation error and need no inputs. Applying it to asset classes spreads money across equities, bonds, cash and real assets without opinions on which will do best.
How people buy it
One broad low-cost index fund per class, equal amounts, rebalanced to 10% each. Examples: total/large US stock fund, small-cap fund, developed ex-US, emerging markets, REIT fund, aggregate bond fund, TIPS fund, T-bill or money-market fund, gold ETF, commodity ETF (examples are mine, not the authors').
Rebalancing as published
The paper's 1/N strategy is a constant-weight rule, which means rebalancing to 1/N every period of the test (the paper's rebalancing frequency is not confirmed in my sources). We assume annual rebalancing in the encyclopedia unless the engine says otherwise.
Variants
- 1/N across all 17 classes (5.88% each).
- 1/N across a shorter list (for example 5 classes as in the Ivy Portfolio: 20% each).
- 1/N with bond_mid in place of tips to get a longer history.
Criticism
- What counts as an asset class (and N) decides the real weights; 1/N is not neutral. With ten classes above, 30% sits in real assets and only 20% in bonds.
- Equal weights ignore risk: commodities and emerging stocks add much more volatility than cash and TIPS but get the same dollar share.
- The paper's evidence is mostly for stock portfolios and a limited history; critics say the Sharpe differences were not tested for significance (R-bloggers, 2013).
Through the eras
| Era | Dates | Total | Per year | Worst drop | S&P 500 |
|---|---|---|---|---|---|
| Black Monday | 1987-08 – 1987-12 | −10.6 % | — | −14.8 % | −21.8 % |
| Savings-and-loan crisis and 1990 recession | 1990-07 – 1991-03 | +5.5 % | — | −5.5 % | +7.4 % |
| 1994 bond market massacre | 1994-02 – 1994-12 | −2.3 % | — | −4.1 % | −3.2 % |
| Asian and Russian financial crises | 1997-07 – 1998-10 | −1.8 % | −1.4 % | −12.6 % | +22.4 % |
| Dot-com bubble and crash | 2000-03 – 2002-10 | −3.4 % | −1.3 % | −9.7 % | −37.2 % |
| Recovery and housing boom | 2002-11 – 2007-09 | +126.7 % | +18.1 % | −4.5 % | +97.0 % |
| Global financial crisis | 2007-10 – 2009-03 | −26.4 % | −18.5 % | −34.1 % | −44.7 % |
| The decade after the crisis | 2009-04 – 2019-12 | +153.7 % | +9.0 % | −12.0 % | +411.2 % |
| Fourth-quarter 2018 sell-off | 2018-09 – 2018-12 | −8.3 % | — | −8.3 % | −14.4 % |
| Covid crash and stimulus boom | 2020-02 – 2021-12 | +27.8 % | +13.7 % | −14.7 % | +53.6 % |
| Inflation shock and rate hikes | 2022-01 – 2022-12 | −10.9 % | −10.9 % | −15.5 % | −19.9 % |
Calendar years
Any N-year period
| Any N-year period | Worst | 10 % worse than | Median | 10 % better than | Best |
|---|---|---|---|---|---|
| 1 y (501) | −31.4 % | −2.8 % | +9.6 % | +20.8 % | +43.8 % |
| 3 y (477) | −4.4 % | +2.8 % | +8.1 % | +15.0 % | +22.2 % |
| 5 y (453) | +1.7 % | +4.4 % | +8.3 % | +12.3 % | +18.8 % |
| 10 y (393) | +4.2 % | +5.2 % | +8.6 % | +10.6 % | +11.9 % |
| 15 y (333) | +4.6 % | +6.5 % | +8.5 % | +10.1 % | +11.0 % |
| 20 y (273) | +6.4 % | +7.1 % | +8.5 % | +9.9 % | +10.7 % |
| 30 y (153) | +7.2 % | +7.6 % | +8.1 % | +9.1 % | +9.8 % |
How it behaved in history
- 1929-2015 (why spread across classes). Stocks returned 9.9% a year versus 5.3% for bonds for 1927-2015, yet stocks lost over 80% in the Great Depression, and underperformed bonds for 20 years (1929-1949) and 40 years (1969-2009). This is the type of history the equal-split across classes is meant to survive (Faber, quoted in AAII). www.aaii.com
- 1966-1982, 1973-1974, 2000-2002, 2008, 2022. No published results for this exact ten-class equal-weight mix. Our engine will compute them. The composition (30% real assets, 10% cash) is the feature that decides behaviour in inflation eras. ideas.repec.org
Published results (by others)
- Across 14 optimisation models and seven datasets none consistently beats 1/N on Sharpe ratio, certainty-equivalent return or turnover (datasets of the paper (sample not specified in my sources)): qualitative ideas.repec.org
- Estimation window needed for sample mean-variance to beat 1/N (simulation calibrated to US stocks) (simulation): about 3,000 months for 25 assets, about 6,000 months for 50 assets ideas.repec.org
- 1/N typically had higher out-of-sample Sharpe ratio, higher certainty equivalent and lower turnover than optimal policies (earlier version, 2005 seminar abstract, ten datasets) (2005 draft): qualitative or.stanford.edu
What we could not verify
- The seven datasets of the published paper and the paper's rebalancing frequency were not read (the full text is behind a paywall; the NBER draft link returned 404). A 2006 draft refers to ten S&P 500 sector portfolios as one dataset (search summary).
- A claim that Harry Markowitz used 1/N for his own retirement savings is commonly attached to this paper; I did not verify it and do not use it.
- The list of ten asset classes is our own design, not from the authors.
- Datasets may differ between the 2005 draft (ten) and the 2009 version (seven): not verified.
Sources
- ideas.repec.org
https://ideas.repec.org/a/oup/rfinst/v22y2009i5p1915-1953.html - lbsresearch.london.edu
https://lbsresearch.london.edu/id/eprint/407 - or.stanford.edu
https://or.stanford.edu/seminars/demiguel_111105.html - academicnewsletter.sufe.edu.cn
https://academicnewsletter.sufe.edu.cn/info/355050 - www.r-bloggers.com
https://www.r-bloggers.com/2013/06/the-fallacy-of-1n-and-static-weight-allocation/ - www.aaii.com
https://www.aaii.com/journal/article/the-trinity-portfolio-combining-diversification-tilts-and-trend-following?printerfriendly=true
Calculated on historical data. Past results do not predict the future. Models before the 1990s use stand-ins for classes that had no index yet; fees, taxes and fund costs are not included. This is mathematics, not an investment recommendation.