Can 20 whole-share stock positions replicate a momentum ETF?
A 100-stock replica tracked SPMO closely. A 20-stock basket using whole shares fell short in a separate account test. Here is where the target weights broke down.
English research archive · Japanese original
Can you reproduce an ETF with the position sizes and trading costs your account can support? We tried two historical simulations with different benchmarks.
- ETF tracking, 2016–2025. A standalone 100-stock replica using fractional shares tracked the S&P 500 Momentum ETF (SPMO) closely enough to meet both tracking criteria.
- Whole-account returns, 2005–2025. A model account using a 20-stock basket with whole shares missed both return criteria against the same account using a VOO proxy. At the median rebalance, the basket held 14 of its 20 targets.
The second test combines fewer holdings, trading costs, cash left after rounding and substitute data. It cannot tell us how much each factor contributed.
What we tested
SPMO tracks an S&P 500 momentum index, which selects stocks with stronger recent price performance and weights them using company size and momentum scores. The index rebalances in March and September. Our account could not buy SPMO through its broker at the time. If your brokerage offers the fund or fractional shares, you have different choices. Before building a replica, check whether your account can match the target weights after rounding and costs.
We selected 100 stocks using a momentum score. We calculated capped weights from company size and momentum, limiting each to the lower of 9% or three times its weight in the 100-stock set. We took the 20 largest weights and rescaled them to total 100%. At each semiannual rebalance we used closing prices, rounded each target holding down to whole shares, and kept the remainder in cash. Trades carried a 0.10% cost plus $1 per order.
We scaled modeled capital backward in line with the level of the S&P 500. From 2015 we used point-in-time S&P 500 membership and share counts. For 2005–2014, we used the 500 stocks with the highest dollar trading volume as a substitute for historical membership. The VOO proxy adds a hypothetical 0.065 percentage points per year to the dividend-inclusive series for SPY, an ETF that tracks the S&P 500. The adjustment is a modeling assumption. The series uses SPY history, and the study did not verify a current fee difference.
In the account comparison, we swapped only one portion of the model portfolio: half of its core allocation. The account also held SPY and cash and used a rule that responded to portfolio drawdowns.
A fractional-share replica tracked SPMO fairly closely
These are annualized returns for the standalone series, using 2016–2025 data.
| Standalone series | Annualized return |
|---|---|
| 100-stock replica with fractional shares | 17.41% |
| SPMO | 17.92% |
| Difference | −0.51 percentage points |
Monthly returns had a correlation of 0.970. We had set a maximum annualized return gap of two percentage points and a minimum correlation of 0.95. The replica passed both checks.
The 20-stock version fell behind inside the model account
The table shows the whole model account. Only the allocation described above was swapped between the replica and the VOO proxy.
| Criterion set before testing | Account with the 20-stock replica | Account with the VOO proxy | Result |
|---|---|---|---|
| Beat the VOO proxy account by at least 0.5 annualized percentage points over 2005–2025 | 8.90% | 9.71% | Failed. −0.81 points versus the proxy |
| Finish ahead in both 2005–2012 and 2013–2025 | 3.60% / 12.28% | 4.58% / 12.98% | Fell behind in both |
| Maximum drawdown no more than 3 percentage points deeper | −34.07% | −36.98% | Passed |
| Worst calendar year no more than 5 percentage points worse | 2008, −26.14% | 2008, −26.80% | Passed |
The model passed the two downside criteria and missed both return criteria. The early-period result relies on the substitute universe described above.
We also tested other position counts for context. They were outside the adoption criteria.
| Allocation used in the model account | Annualized, full period | 2005–2012 | 2013–2025 | Max drawdown |
|---|---|---|---|---|
| VOO proxy | 9.71% | 4.58% | 12.98% | −36.98% |
| 10 stocks, whole shares | 9.62% | 4.37% | 12.98% | −35.74% |
| 15 stocks, whole shares | 9.17% | 4.03% | 12.46% | −36.10% |
| 20 stocks, whole shares | 8.90% | 3.60% | 12.28% | −34.07% |
| 25 stocks, whole shares | 8.75% | 3.53% | 12.09% | −33.72% |
| 100 stocks, fractional shares | 10.03% | 4.54% | 13.55% | −37.61% |
Where the replica drifted
- Position sizes. The median rebalance could hold 14 of the 20 target stocks, and the minimum was seven. We added the absolute gap between each stock’s target and actual weight. The median was 34% before 2015 and 36% from 2015 onward. The two figures measure allocation mismatch. If one share costs 7% of the allocation, a 5% target cannot be filled with a whole share.
- Cash and stock coverage. Cash left after rounding changed the result. The study does not isolate it from the effects of costs, fewer holdings, or substitute data. In our preliminary work, the top 20 positions accounted for about 69% of SPMO's weights, so the replica omitted nearly a third from the start.
- Trading costs and historical scaling. Median one-way turnover was 46%, with 22 orders and a cost of 0.64% of the allocation per rebalance. The backward scaling of capital made high historical share prices, including pre-split prices, more consequential.
Before the account's drawdown rule was applied, annualized returns for the stock baskets alone were 10.82%, 8.78%, 7.63%, and 6.81% for 10, 15, 20, and 25 whole-share positions, respectively. The 100-stock fractional-share basket returned 11.32% annualized. These basket figures are separate from the account table.
Even the 100-stock fractional-share allocation led by just 0.32 annualized percentage points in the full account comparison, and it trailed in 2005–2012 at 4.54% versus 4.58%. A separate check, excluded from the adoption criteria, covered 126 trading days after the 2009 low. The account with the 20-stock replica gained 15.2%, compared with 20.3% for the account with the VOO proxy.
What to check in a replication study
Start with the account you could actually use. Can it buy the same stocks in the same weights? Are the returns after trading costs? Does the benchmark cover the same dates? Can your broker offer the fund? Which parts of the comparison rely on proxies?
This study covers one set of assumptions, including 20 stocks, semiannual rebalancing, the stated caps and costs, and a model account with a drawdown rule. The early universe and the VOO series are substitutes. Capital scaling is a modeling choice, and the direct check against SPMO covers 2016–2025 only. Actual execution prices and costs can differ.
The decision recorded in October 2026
AlpAI did not adopt this replica because it missed the return criteria. The policy recorded then was to hold half the core allocation in VOO.
Dated account observation. A record saved around 06:45 JST on October 17 showed VOO within the core allocation and listed October 16 as the acquisition date. It did not establish the fraction of the allocation already moved. That account observation is separate from the backtest figures above.
The study may be revisited if position sizes become easier to match, for example through fractional shares or a different capital base. The decision would still need evidence under those conditions.
This is research based on historical data. It does not recommend a product or promise future results.