White paper: Using risk models to enhance direct indexing
Since the launch of the Frec Direct Indexing strategy, we have made numerous improvements to our tax-loss harvesting algorithm. Additionally, we have expanded our product offerings and research to include various popular indices beyond the S&P 500©. One notable improvement is the employment of a commercial risk model that captures constituents’ volatility and correlation. This model enables us to forecast and better manage each portfolio’s tracking error and further improve loss harvesting performance. This white paper details recent improvements and expands on the simulation results in our previous white paper to demonstrate the performance of direct indexing across a broader range of indices.
Understanding risk models
Risk models are financial tools that assist investors in managing the risks and returns of stocks and portfolios. These models can help investors assess equity risk and understand the relationships between securities and returns to guide their investment decisions.1
In this section, we’ll explain the importance of risk models in direct indexing and the factor-based risk model we’ve selected to optimize portfolio performance and tax efficiency.
Risk models in direct indexing
In direct indexing, a risk model can provide each constituent’s2 volatility and the correlation between pairs of constituents. This information allows us to forecast the tracking error of a portfolio, enabling informed decisions when balancing tracking error against tax-loss harvesting benefits. To better understand this approach, let’s examine how volatility and correlation contribute to forecasting tracking error.
Volatility, defined as the standard deviation of a stock’s return, measures the extent of a stock’s price fluctuations. Higher volatility leads to greater variability in a stock’s returns. As a result, deviations in allocation involving high-volatility stocks can lead to larger fluctuations in the portfolio’s overall performance relative to the benchmark, compared to similar deviations involving lower-volatility stocks.
The accuracy of tracking error forecasts can be further improved by considering the correlation between pairs of constituents. Many stocks historically demonstrate a high correlation with one another; selling shares of one stock to harvest tax losses and replacing them with a highly correlated stock can help reduce tracking error, provided the correlation remains stable over time.
Factor-based risk model3
We have licensed the Barra Global Total Market Equity Model for Long-Term Investors from MSCI, an industry leader in factor risk modeling. A factor-based risk model attributes the risk (tracking error) to specific factors that systematically influence constituents’ returns. These include style factors, such as value, momentum, and quality, as well as regional and industry factors.
Methodology
We follow the methodology outlined in our previous white paper to formulate rebalancing a direct-indexing portfolio as an optimization problem. This approach balances the trade-offs between minimizing tracking error and maximizing tax loss harvested by defining a scoring function and using a state-of-the-art numerical solver to minimize the scoring function with respect to various constraints (e.g. avoiding wash-sales). The scoring function, with a factor-based risk model is given as follows:
The scoring function consists of three key components.
The first term of the scoring function is the risk term; it measures the forecasted annualized variance of the difference in return between the rebalanced portfolio and the benchmark portfolio, which is the squared tracking error.
The second term measures the tax benefits and liabilities due to rebalancing trades. If the trades result in a taxable loss, this term will be negative, reducing the scoring function, and it will be positive if the trades result in capital gains. Recall that we aim to minimize the scoring function; therefore, the optimal solution will favor generating taxable losses.
The third term measures estimated transaction costs. Minimizing this term avoids excessive trading and reduces slippage due to bid-ask spreads and transaction fees.
Please refer to our previous white paper for a detailed analysis of transaction costs in direct indexing.
Performance analysis
We applied the same simulation methodology described in our previous white paper to evaluate the performance of our direct indexing implementation. With the expansion of our direct indexing products to indices beyond the S&P 500©, we now showcase its performance on these additional indices. However, due to limited historical constituent data for some indices, we conducted simulations using 10 years of historical data instead of the 20 years used for the S&P 500 analysis.
Simulation methodology
To demonstrate the performance of direct indexing with the addition of a factor-based risk model, we analyzed results from multiple historical simulations using overlapping 5-year periods. These simulations had start dates spaced 90 days apart, spanning from November 2013 to January 2024. For instance, the first simulation covered the period from October 30, 2013, to October 25, 2018, while the second simulation ran from January 28, 2014, to January 25, 2019, and so on. In total, 21 simulations were conducted.
Importantly, the results of these simulations are deterministic, meaning multiple runs for the same time period yield identical outcomes, rendering additional runs unnecessary. Each simulation began with a one-time cash deposit of $50,000 and progressed weekly, applying the direct indexing algorithm and simulating the resulting trades. The risk model provides a point-in-time forecast, using only the data available at the time of reference.
Fee structure and benchmark ETFs
For all simulations, AUM fees were calculated based on Frec’s pricing as of January 9, 2025, as detailed in the accompanying table. The following table also includes the corresponding comparison ETF for each index.
| Benchmark Index | Annual AUM Fee | Comparison ETF |
| CRSP US Large Cap | 0.10% | Vanguard Large-Cap Index Fund ETF |
| CRSP Mid Cap | 0.14% | Vanguard Mid-Cap Index Fund ETF |
| CRSP Small Cap | 0.15% | Vanguard Small-Cap Index Fund ETF |
| CRSP Total Market | 0.13% | Vanguard Total Stock Market Index Fund ETF |
| Russell 1000 | 0.22% | iShares Russell 1000 ETF |
| Russell 2000 | 0.26% | iShares Russell 2000 ETF |
| Russell 3000 | 0.27% | iShares Russell 3000 ETF |
| S&P 500 | 0.10% | SPDR S&P 500 ETF Trust |
Performance results
The primary metric of interest in direct indexing is the potential capital loss that can be captured. The following graph and table compares our earlier target weight-based methodology with our new risk model-based approach in terms of the annualized tracking error and the total loss harvested over five years, expressed as a percentage of an initial $50,000 investment. The tracking error is calculated as the standard deviation of excess returns relative to the comparison ETF across the 21 historical simulations:
| Benchmark Index | Tracking Error (Risk Model) | Tracking Error (Target Weight) | Loss Harvested (Risk Model) | Loss Harvested (Target Weight) | Loss Harvested Improvement |
| CRSP US Large Cap | 0.88% | 0.59% | 18.66% | 17.06% | 9.38% |
| CRSP US Mid Cap | 0.66% | 1.17% | 28.22% | 22.58% | 24.97% |
| CRSP Small Cap | 0.88% | 0.92% | 40.43% | 33.54% | 20.56% |
| CRSP Total Market | 0.83% | 1.02% | 21.83% | 17.98% | 21.44% |
| Russell 1000 | 0.65% | 0.46% | 19.24% | 16.86% | 14.15% |
| Russell 2000 | 0.69% | 0.84% | 46.42% | 42.03% | 10.45% |
| Russell 3000 | 0.67% | 0.72% | 21.17% | 17.42% | 21.56% |
| S&P 500 | 0.82% | 0.61% | 16.83% | 15.65% | 7.54% |
Discussions
Our historical simulations demonstrate that a factor-based risk model can effectively harvest more losses across all indices while closely tracking the broader index performance. The improvement is particularly pronounced in small- and mid-cap segments of the market. However, it is important to note that direct indexing has been able to harvest significantly more losses in the small- and mid-cap segments compared to large-cap stocks. This is primarily due to the underperformance of small- and mid-cap stocks relative to large-cap stocks over the past 10 years, which has created more loss-harvesting opportunities in the small- and mid-cap markets. For example, the Russell 1000 returned 12.20% annually during the simulation period, while the Russell 2000 returned 7.66% annually over the same period.
While it has generally shown a positive impact to include factor-based risk models, they are not without limitations. The effectiveness of direct indexing using a risk model depends on the forecasting accuracy of the underlying model. To ensure optimal performance, we will collaborate closely with our risk data provider, MSCI, to continuously monitor and evaluate its accuracy.
If you have any questions about the details, feel free to reach out at help@frec.com or schedule a call here.
This white paper describes the implementation and performance details of a Direct Indexing approach similar to that used on the Frec platform at the time of writing (01/09/2025) details may differ from the implementation used in the product now and in the future. This paper may be amended at any time to reflect new findings, improve readability, or correct inaccuracies. The results in this white paper are hypothetical, do not reflect actual investment results, and are not a guarantee of future results.
This white paper is for information purposes only and is not intended as tax advice. Frec refers to Frec Markets, Inc. and its wholly owned subsidiaries, Frec Advisers LLC and Frec Securities LLC. Frec does not provide legal or tax advice and does not assume any liability for the tax consequences of any client transaction. Clients should consult with their personal tax advisors regarding the tax consequences of investing with Frec and engaging in these tax strategies, based on their particular circumstances. Clients and their personal tax advisors are responsible for how the transactions conducted in an account are reported to the IRS or any other taxing authority on the investor’s personal tax returns. Frec assumes no responsibility for tax consequences to any investor of any transaction.
The effectiveness of Frec’s tax-loss harvesting strategy to reduce the tax liability of the client will depend on the client’s entire tax and investment profile, including purchases and dispositions in a client’s (or client’s spouse’s) accounts outside of Frec, the type of investments (e.g., taxable or nontaxable) or holding period (e.g., short-term or long-term. The performance of the new securities purchases through the tax-loss harvesting service may be better or worse than the performance of the securities that are sold for tax-loss harvesting purposes.
The S&P 500© index is a product of S&P Dow Jones Indices LLC or its affiliates (“SPDJI”), and has been licensed for use by Frec Markets, Inc. S&P®, S&P 500®, US 500 and The 500 are trademarks of Standard & Poor’s Financial Services LLC (“S&P”); and these trademarks have been licensed for use by SPDJI and sublicensed for certain purposes by Frec Markets, Inc. Frec’s direct indexing strategy is not sponsored, endorsed, sold or promoted by SPDJI, Dow Jones, S&P, their respective affiliates and none of such parties make any representation regarding the advisability of investing in such product(s) nor do they have any liability for any errors, omissions, or interruptions of the S&P 500© index.
