Testing a Portfolio Reallocation Rule with ChatGPT
Using AI to search for a really high-return low-risk portfolio and allocation rule.
This experiment compares two approaches for the same four-fund portfolio: a simple buy-and-hold portfolio with no reallocation and a fully specified event-driven reallocation rule. The purpose is to test whether selective transfers after unusually large relative or absolute moves can improve long-run return and risk-adjusted performance without routine calendar rebalancing.
The initial portfolio is: IVV - 81 allocation units, VGT - 7 allocation units, VPU - 7 allocation units, and GLD - 7 allocation units
We are comparing two rules:
Rule 1 - Buy and hold. The portfolio is initialized at the January 2005 month-end observation and no subsequent reallocations are made. Each position is allowed to rise or fall with market performance for the entire test period.
Rule 2 - Full dynamic reallocation rule. The portfolio begins with the same initial allocation. No reallocations are made during 2005. Beginning with the January 2006 month-end observation, reallocations occur only when one of the events below is triggered. There is no routine annual rebalancing and no scheduled restoration of target portfolio weights.
VGT event. The VGT target begins at 10% of the portfolio. Each January, the target may increase according to the rise in the Information Technology weight of the S&P 500 since the starting date: VGT target = 10% + 12.5% × the increase in the S&P 500 Information Technology weight. The target cannot decline and is capped at 13%. If VGT reaches a month-end adjusted-price level at least 50% above a qualifying prior high established at least 12 months earlier and VGT is also above its current target weight, 25% of VGT’s dollar amount above the target is sold and invested in VPU.
GLD event. If GLD reaches a month-end adjusted-price level at least 30% above a qualifying prior high established at least 12 months earlier, 25% of the entire GLD position is sold and invested in IVV.
IVV outperformance event. Each month, the trailing three-month total return on IVV is compared with the trailing three-month total return on VPU. If IVV outperforms VPU by 20 percentage points or more and the differential freshly crosses that threshold, 10% of the current IVV position is sold and invested in VPU.
VPU outperformance event. If VPU outperforms IVV by 10 percentage points or more—equivalent to an IVV-minus-VPU differential of -10 percentage points or less—and the differential freshly crosses that threshold, 8% of the current VPU position is sold and invested in IVV.
After any event triggers a transaction, that same event cannot trigger another transaction for at least 12 months. If more than one event is triggered in the same month, each transaction amount is calculated from the portfolio immediately before that month’s trades and the transactions are then executed together.
Experiment design. The test uses 241 month-end observations from January 2005 through January 2025, producing 240 monthly return observations. Both portfolios begin with the identical 81 IVV / 7 VGT / 7 VPU / 7 GLD normalized allocation. The no-reallocation portfolio is held unchanged throughout. The full dynamic rule begins making eligible adjustments in January 2006.
Monthly adjusted prices are used for IVV, VGT, VPU, and GLD so that distributions are incorporated in returns. CAGR is calculated from terminal wealth. Annualized volatility is the sample standard deviation of monthly portfolio returns multiplied by the square root of 12. The Sharpe ratio uses monthly excess returns based on the FRED TB3MS three-month Treasury-bill series divided by 12 and is annualized by the square root of 12.
The test does not include taxes, bid-ask spreads, commissions, or other transaction costs. The thresholds are treated as a research specification rather than as optimized trading recommendations.
2. Results
Performance
CAGR. The no-reallocation portfolio produced a CAGR of 10.875%, compared with 11.207% for the full dynamic rule. The dynamic rule therefore increased CAGR by 0.332 percentage point, or about 3.1% relative to the no-reallocation result.
Annualized volatility. Annualized volatility was 13.545% with no reallocation and 14.010% under the full dynamic rule. The dynamic rule therefore increased volatility by 0.465 percentage point, or about 3.4%.
Sharpe ratio. The Sharpe ratio increased from 0.7155 with no reallocation to 0.7178 under the full dynamic rule, an increase of 0.0022, or about 0.31%.
Ending value of a $10,000 investment. A $10,000 equivalent investment grew to $78,829 with no reallocation and $83,686 under the full dynamic rule. The dynamic rule therefore produced about $4,857 more terminal wealth, an increase of about 6.2%.
The full dynamic rule produces the higher compound return and slightly higher Sharpe ratio, but it also produces higher volatility and a somewhat deeper maximum drawdown. Under the working success criterion used in this research - higher CAGR, higher Sharpe, and no increase in volatility - the full rule therefore does not qualify as an unambiguous improvement over no reallocation.
Ending Portfolio
No-reallocation portfolio. The portfolio ends with 75.42% in IVV ($606.39), 14.43% in VGT ($116.00), 4.83% in VPU ($38.80), and 5.33% in GLD ($42.87), for a total normalized value of $804.06.
Full dynamic-rule portfolio. The portfolio ends with 82.14% in IVV ($701.11), 13.08% in VGT ($111.65), 2.67% in VPU ($22.75), and 2.12% in GLD ($18.09), for a total normalized value of $853.60.
Allocation Activity
The corrected full rule generates 12 allocation transactions in 12 distinct months over the 20-year test: 3 GLD-to-IVV transactions under the gold rule, 1 VGT-to-VPU transaction under the technology rule, 8 VPU-to-IVV transactions under the three-month differential rule, 0 IVV-to-VPU transactions because the +20 percentage-point threshold is never reached.
The asymmetry of the three-month differential rule remains important to the final portfolio. The -10 percentage-point VPU-outperformance threshold produces eleven fresh crossings in the raw monthly data, but three occur during a 12-month same-event lockout and therefore do not generate transactions. The +20 percentage-point IVV-outperformance threshold is never reached. As a result, the rule progressively transfers capital from VPU into IVV, and the full-rule portfolio ends with 82.1% in IVV and only 2.7% in VPU.
Interpretation
The experiment shows that the event-driven rule can raise terminal wealth without frequent trading, but the gain is accompanied by greater equity concentration and somewhat higher risk. This specific full rule ends with about $4,857 more per $10,000 after 20 years and higher annualized volatility of 0.46 percentage rates. My search with the assistance of CHAT GPT for the holy grail, a portfolio and allocation strategy that beats the market by a lot with less risk has not succeeded, but I will persist.
Author’s Note: I publish a wide range of personal-finance, investing, economic, and policy material on my multi-topic blog, Economic and Political Insights. One example is The Sequence of Returns Puzzle: Why Timing Hurts Workers and Retirees in Opposite Ways, which uses simulations and retirement examples to demonstrate that the impact of the path of returns on terminal retirement wealth can often be more important than average returns.
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