Long short direct indexing > White paper
White paper: Long short direct indexing
14 min read
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140/40 long short direct indexing is now available. You can get started here or reach out to us at help@frec.com for assistance.
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Introduction
This white paper explores an investment strategy that combines factor-based investing, leveraged long short portfolio construction, and a tax-efficient direct-indexing process. The strategy is designed to track a benchmark index, such as the Russell 1000, while maintaining excess exposure to selected factors such as growth and value. This approach allows investors to express their views on factor exposures in a tax-aware manner, potentially generating pre-tax alpha and significantly improving after-tax returns.
Factor-based investing has become a cornerstone of systematic equity strategies, allowing investors to tilt portfolios toward characteristics such as value, size, momentum, quality, and growth [1, 2, 3]. However, many traditional implementations, including factor ETFs (exchange-traded funds), are typically long-only and invest in a narrower segment of the investable universe. Additionally, their structure generally lacks the flexibility to fine-tune factor exposures or efficiently harvest tax losses. By contrast, a direct indexing approach allows for broader market access, more precise control over factor tilts, and improved tax efficiency through ongoing, systematic loss harvesting.
Building on this insight, the strategy presented in this paper takes full advantage of direct indexing while incorporating a persistent tilt toward the selected factors. Unlike long-only tax loss harvesting, which becomes less effective over time due to gradual reduction in a portfolio’s ability to realize capital losses as individual positions accumulate unrealized gains—the long short structure enhances the ability to generate tax losses in various market conditions [3, 4].
Overview
Let’s examine a 140/40 growth-tilted portfolio that tracks the Russell 1000 index and break down what each term entails.
The growth factor, as defined by the Barra Global Total Market Equity Model for Long-Term Investors (GEMLT), captures characteristics of companies expected to grow their sales and earnings at an above-average rate. It incorporates multiple signals including analyst forecasted long-term earnings growth and historical sales and earnings growth. Later in this white paper, we will also introduce a value-tilted strategy, where the tilt is based on the book-to-price factor, defined as the most recently reported book value of common equity divided by the company’s current market capitalization.
A 140/40 long short portfolio is structured by taking a 140% long position in selected securities and a 40% short position in others. The proceeds from the 40% short sale fund the additional 40% long exposure, keeping the net market exposure close to 100%—consistent with the benchmark index. This structure provides greater flexibility to express factor tilts without increasing the investor’s overall market risk.
The long short design also enhances the potential for tax loss harvesting in a variety of market environments. When markets decline, the long side of the portfolio tends to accumulate losses that can be harvested. Conversely, in rising markets, short positions can generate realized losses as prices move against them—providing opportunities to offset capital gains elsewhere in the investor’s portfolio. This dual-sided mechanism greatly enhances the consistency and volume of tax loss harvesting compared to long-only strategies.
Methodology
Our strategy builds upon the framework developed in our prior white papers, where rebalancing a direct-indexing portfolio is formulated as a constrained optimization problem. The core objective remains the same: to efficiently trade off tracking error minimization against tax-loss harvesting opportunities and transaction costs.
As in the earlier approach, we define a composite objective function incorporating a factor-based risk model, expected tax outcomes, and estimated trading costs. This function is minimized subject to additional constraints, which we will outline later, using a state-of-the-art numerical solver. The objective function is defined as follows:
Recall that the objective function consists of three key components:
The first component quantifies the expected tracking error, defined as the forecasted variance of the portfolio’s return relative to that of the benchmark. Minimizing this term ensures the portfolio remains closely aligned with the benchmark, maintaining similar performance over time.
The second component captures the net tax impact of rebalancing trades. Loss-generating trades contribute negatively to the objective function, thereby encouraging tax-loss harvesting, while gains are penalized to discourage tax liabilities.
The third component models estimated trading costs, such as bid-ask spreads. Including this component discourages unnecessary turnover.
While the core optimization framework remains consistent with our previous long-only direct indexing approach—including constraints such as wash-sale avoidance—the key distinction in this factor-tilted long short strategy lies in an expanded constraint set that enables more sophisticated portfolio positioning. Specifically, we introduce new constraints to implement factor tilts, manage leverage, and control risk exposure, while still preserving tax efficiency and benchmark alignment.
To implement a factor tilt and control the portfolio’s exposure to each factor, we impose the following constraints for each factor:
![\[ \text{lower bound of factor $f$} \le X_f^T(h_0 + \Delta) \le \text{upper bound of factor $f$}. \]](https://freccom.blog/wp-content/ql-cache/quicklatex.com-b81c3157f86af026a8ccd186fe262ac8_l3.svg "Rendered by QuickLaTeX.com")
To manage leverage, we constrain the gross exposure—the sum of the absolute portfolio weights—to a target level. In the case of a 140/40 portfolio, the short exposure is denoted by (L), where (L= 0.4), and the long exposure is (1+L= 1.4), resulting in a gross exposure of (1+2L= 1.8):
![\[ \sum_i |(h_0 + \Delta)_i| = 1 + 2L. \]](https://freccom.blog/wp-content/ql-cache/quicklatex.com-8e430c5f6f4aac55cc01d582a9c80225_l3.svg "Rendered by QuickLaTeX.com")
To ensure the rebalanced portfolio maintains a consistent level of market exposure, we constrain the portfolio beta relative to the benchmark index. Beta is a measure of a portfolio’s sensitivity to market movements; a beta of 1 implies that the portfolio is expected to move in tandem with the market, while values above or below 1 indicate amplified or muted sensitivity, respectively. To enforce this, we impose the following constraint on the portfolio’s total beta exposure:
![\[ 1 - \text{$\beta$ slack} \le \beta^T (h_0 + \Delta) \le 1 + \text{$\beta$ slack}. \]](https://freccom.blog/wp-content/ql-cache/quicklatex.com-727f84738f3fe25f9bedb0e3984f6b05_l3.svg "Rendered by QuickLaTeX.com")
Here, is the vector of asset-level betas
![\[ \beta = \frac{(D + XFX^T)h_b}{h_b^T(D + XFX^T)h_b}, \]](https://freccom.blog/wp-content/ql-cache/quicklatex.com-3173ae906d27c2014d3b472f0946013b_l3.svg "Rendered by QuickLaTeX.com")
and is a small slack parameter that allows limited deviation. This ensures that the portfolio maintains a market exposure consistent with the benchmark.
Furthermore, to mitigate the risk associated with concentrated short positions, we impose concentration constraints that limit the size of individual holdings. Unlike long positions, where losses are capped at 100%, short positions can generate unbounded losses if not properly managed. To control this risk, we restrict the magnitude of each stock position:
![\[ \text{lower bound of stock $i$} \le (h_0 + \Delta)_i \le \text{upper bound of stock $i$}. \]](https://freccom.blog/wp-content/ql-cache/quicklatex.com-9eddc2e8f0cbef7f4f80a17bd4b2e727_l3.svg "Rendered by QuickLaTeX.com")
These constraints help reduce exposure to idiosyncratic risk.
Simulations
To evaluate the performance of our strategies, we conducted a series of historical simulations using overlapping 10-year periods from April 1, 2005 to February 13, 2025. Each simulation was launched on a quarterly basis between April 1, 2005 and March 16, 2015, using market, constituent, and risk data available through February 13, 2025.
In total, 41 simulations were performed. Each simulation begins with a one-time cash investment of $1,000,000 and proceeds with monthly rebalancing based on the respective strategy logic. The long-only strategy tracks the Russell 1000 via a direct indexing approach, while the long short strategies use a 140/40 structure with a tilt toward either the growth or value factor. All three strategies are implemented using a consistent optimization framework and point-in-time forecasts from a factor-based risk model, ensuring no look-ahead bias.
All simulation results are deterministic—they use fixed inputs and a non-randomized optimization process. This ensures that multiple runs of the same simulation will produce identical results, eliminating the need for repeated trials or averaging.
Each strategy incorporates the following cost assumptions. The long-only portfolio is subject to an annual AUM fee of 0.22%, while the long short portfolio carries a higher management fee of 0.50%, reflecting its increased complexity and operational cost.
Transaction costs are applied at a flat rate of 2 basis point (0.02%) of traded notional (see our prior discussion on direct indexing transaction costs), charged symmetrically on both buys and sells. This means that an annual turnover rate of 474.07% will result in a 0.09% annual transaction cost. In addition, the long short portfolio incurs a financing cost: a 1.25% annual spread applied to the net debit balance, which is typically 40% of the portfolio value, resulting in a total annual charge of 0.5%.
Results
The following table summarizes simulation results for the long-only and long short strategies, with annualized return and cost components presented on both a pre-tax and after-tax basis. For after-tax calculations, we assume a 42.3% short-term tax rate and a 28.1% long-term tax rate1. We assume that investors have sufficient long-term and short-term gains outside of the strategy, allowing losses to generate tax savings at the respective rates. Returns and fee rates are computed monthly and then annualized.
| Long-only | Long short (Growth) | Long short (Value) | |
| After-tax excess return | 1.34% | 3.00% | 2.93% |
| Tax alpha | 1.27% | 3.64% | 3.77% |
| Pre-tax excess return | 0.30% | 0.45% | 0.24% |
| Management fee | -0.22% | -0.50% | -0.50% |
| Transaction cost | -0.01% | -0.09% | -0.08% |
| Financing cost | 0.00% | -0.50% | -0.50% |
| Loss harvested | 3.09% | 8.47% | 8.82% |
| Tracking error | 0.70% | 1.58% | 1.49% |
On an after-tax basis, both the growth-tilted and value-tilted long–short strategies deliver superior performance relative to a long-only direct indexing approach, with annualized after-tax excess returns of 3.00% and 2.93%, respectively, compared with 1.34% for the long-only portfolio. This outperformance is driven largely by tax efficiency. The long short strategies realize substantially more harvested losses (8.47% for growth and 8.82% for value, versus 3.09% for long-only), which translate into tax alpha of 3.64% and 3.77%, respectively. Despite its higher transaction costs (0.09% for growth and 0.08% for value, versus effectively 0.01% for long-only) and a financing cost of 0.50% (which the long-only strategy does not incur), the long short strategies’ enhanced tax benefits more than compensate for these implementation frictions.
The following figure shows the mean cumulative losses harvested—as a percentage of initial capital invested—by both the long-only and long short strategies over a 10-year period.
The bars represent the average outcome across simulation runs, while the error bars capture the standard deviation, indicating the level of variability in loss harvesting performance from one simulation to another due to different market conditions. By year 10, the long–short strategies have harvested cumulative losses exceeding the originally invested capital—118% for the growth tilt and 120% for the value tilt—more than three times the cumulative harvest of the long-only Russell 1000 strategy, which levels off at approximately 30%. The results illustrate the tax-efficiency advantage of the long short strategy, which consistently harvests more capital losses each year compared to its long-only counterpart.
The error bars (standard deviation) provide insight into how consistent these results are across different market conditions. While both strategies exhibit some variation, the long-only strategy shows relatively higher dispersion in later years. This is likely due to the declining availability of loss-harvesting opportunities over time, which makes its outcomes more dependent on the specific return path of each simulation. Conversely, the long short strategy maintains more stable performance, with variability increasing more gradually and remaining narrower relative to its mean.
Higher leverage
To explore the impact of increased leverage, we also conducted simulations for 200/100 and 250/150 strategies. These used a similar setup to the 140/40 portfolio but incorporated higher associated costs: management fees of 1.0% (for 200/100) and 1.5% (for 250/150), and financing costs of 0.8% and 1.2%, respectively. The primary motivation for higher leverage is the potential for enhanced pre-tax returns, achieved by amplifying exposure to desired factors through more extended long and short positions. As a beneficial side product, this increased gross exposure can also lead to greater tax efficiency. This strategy intentionally takes on a commensurately higher risk profile in pursuit of higher after-tax returns, which in turn justifies the higher fee structure. However, investors must be aware of the associated trade-offs. With this higher-leverage approach, pre-tax returns are more likely to be driven by factor performance. It will also exhibit more volatility from short-term, stock-specific returns, though this idiosyncratic risk is expected to diversify away over the long term. This combination will naturally result in higher tracking error, with performance looking less like the benchmark compared to lower-leverage options. Therefore, these more aggressive strategies are most suitable for investors who are comfortable with the additional risk in exchange for the potential for higher excess returns over time.
The following table demonstrates this trade-off by comparing the annualized simulation results for the growth-tilted 140/40 strategy against the higher-leverage 200/100 and 250/150 variations.
| 140/40 (Growth) | 200/100 (Growth) | 250/150 (Growth) | |
| After-tax excess return | 3.00% | 5.42% | 6.63% |
| Tax alpha | 3.64% | 6.83% | 8.60% |
| Pre-tax excess return | 0.45% | 0.63% | 1.10% |
| Management fee | -0.50% | -1.02% | -1.53% |
| Transaction cost | -0.09% | -0.20% | -0.32% |
| Financing cost | -0.50% | -0.81% | -1.22% |
| Loss harvested | 8.47% | 15.64% | 19.16% |
| Tracking error | 1.58% | 3.04% | 4.13% |
As illustrated, increasing leverage scales the strategy’s outcomes. The 250/150 strategy, for example, generates a significantly higher pre-tax excess return (1.10%) and a much larger volume of realized losses (19.16%), leading to the highest after-tax excess return net of fees (6.63%). This outperformance, however, is accompanied by a proportional increase in costs and a materially higher tracking error (4.13%), underscoring the direct relationship between the magnitude of the leverage, implementation costs, and the portfolio’s deviation from the benchmark.
Given increased client interest in other factor exposures, we extended this high-leverage analysis to our quality-tilted strategy. The quality factor seeks to identify companies with stable earnings, high profitability and investment quality, and low debt. The results, summarized below, show a similar scaling relationship between leverage, risk, and return, consistent with the growth factor findings.
| 140/40 (Quality) | 200/100 (Quality) | 250/150 (Quality) | |
| After-tax excess return | 3.17% | 6.50% | 8.37% |
| Tax alpha | 4.04% | 7.98% | 10.46% |
| Pre-tax excess return | 0.23% | 0.53% | 0.93% |
| Management fee | -0.51% | -1.02% | -1.53% |
| Transaction cost | -0.08% | -0.18% | -0.26% |
| Financing cost | -0.51% | -0.81% | -1.22% |
| Loss harvested | 9.54% | 18.76% | 24.33% |
| Tracking error | 1.52% | 2.83% | 3.92% |
The results for the quality factor reinforce the same core trade-offs. While the excess returns and tax alpha differ slightly from the growth simulations—reflecting the distinct nature of the factor—the fundamental relationship holds: higher leverage offers a pathway to enhanced pre-tax and after-tax returns but requires investors to accept higher costs and a greater deviation from the benchmark.
The following figure shows the mean cumulative losses harvested—as a percentage of initial capital invested—across all three levels of leverage over a 10-year period. By year 10, the quality-tilted long–short strategies have harvested cumulative losses exceeding the originally invested capital—130% for 140/40, 265% for 200/100, and 337% for 250/150. The higher leverage strategy shows relatively higher dispersion in later years. This is likely due to the scaling effect of using leverage, which makes its outcomes more dependent on the specific return path of each simulation. The results illustrate the tax-efficiency advantage of using higher leverage, which consistently generates more capital losses on average each year compared to lower leverage options.
Discussion
Through historical simulations, we demonstrate that a factor-tilted long short direct indexing strategy can enable investors to express factor-based views in a tax-efficient way. By allowing investors to take on short positions, the strategy not only enhances flexibility in portfolio construction but also significantly increases the availability of loss-harvesting opportunities.
Compared to a traditional long-only direct indexing approach, the long short strategy offers substantially greater tax efficiency. Across all simulation periods, it consistently generated higher levels of harvested losses and post-tax returns, despite involving extra complexity and incurring additional costs. This strong tax alpha can be especially valuable for investors in high marginal tax brackets seeking to reduce their near-term taxable liabilities.
That said, the benefits of the long short approach come with important trade-offs. The inclusion of short positions introduces additional sources of risk, including higher tracking error and greater sensitivity to market volatility. Moreover, the strategy entails higher implementation costs, such as financing costs on short positions and a larger operational footprint. As our simulations of the 200/100 and 250/150 strategies demonstrate, these trade-offs are scalable. Increasing the portfolio’s leverage can further enhance potential pre-tax and after-tax returns, but it does so at the cost of proportionally higher fees and a materially higher tracking error. This highlights a clear spectrum of choice for the investor.
Nevertheless, our historical simulations show that across all leverage levels, the after-tax performance gains can more than offset the increased costs and risks, particularly over longer horizons. For investors with a strong preference for factor tilts and a high sensitivity to after-tax returns, the long short strategy offers a compelling extension of direct indexing. It provides a flexible framework where investors can select a leverage point—from the 140/40 structure to more aggressive options—that best aligns with their specific risk tolerance and after-tax return objectives, broadening both the investment and tax management toolkits.
Get started
140/40 long short direct indexing is now available. You can get started here or reach out to us at help@frec.com for assistance.
To get early access to 200/100 and 250/150 long short direct indexing, please enter the waitlist here.
References
- Fama, E. F., & French, K. R. (1992). The Cross-Section of Expected Stock Returns. The Journal of Finance, 47(2), 427–465.
- Fama, E. F. 1993. Common Risk Factors in the Returns on Stocks and Bonds. Journal of Financial Economics 33(1): 3–56.
- Goldberg, L., Lewis, C., & Zorn, T. (2024). The Enhanced Value of Tax-Loss Harvesting in Long-Short Portfolios. Research Paper.
- Sialm, H., & Sosner, S. (2018). Tax-Loss Harvesting and Portfolio Performance. Management Science, 64(2), 705–722.
- Khang, K., Cummings, A., Paradise, T., & O’Connor, B. (2022). Personalized Indexing: A Portfolio Construction Plan, https://corporate.vanguard.com/content/dam/corp/research/pdf/personalized_indexing_a_portfolio_construction_plan.pdf
All results in this white paper are hypothetical, do not reflect actual investment results, and are not a guarantee of future results.
This white paper describes implementation and performance details of a long short direct indexing approach similar to that used on the Frec platform at the time of writing (August 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.
This white paper is for information purposes only and is not intended as tax advice or a trade recommendation. Clients should consult with their personal tax advisers 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 purchased through the tax-loss harvesting service may be better or or worse than the performance of the securities that are sold for tax-loss harvesting purposes.
