Smart Factor Mixing: Dynamic Allocation of Value and Momentum

Value and Momentum are among the most extensively documented and empirically validated factor strategies in the asset pricing literature. As demonstrated in the seminal work by Asness, Moskowitz, and Pedersen (2013) titled “Value and Momentum Everywhere”, these two factors have delivered robust performance across asset classes and geographies.

Importantly, their historically negative correlation offers a compelling rationale for combining them in multi-factor portfolios to improve risk-adjusted returns. A naïve equal-weighted blend of Value and Momentum, as proposed in the aforementioned study, has proven remarkably resilient and difficult to outperform consistently.

However, this static allocation may not fully exploit the time-varying risk characteristics of the individual factors. Momentum strategies, in particular, are known to exhibit crash risk during periods of market stress. Barroso and Santa-Clara (2015) introduce a risk-managed version of Momentum, demonstrating that scaling exposure inversely with recent realized volatility can significantly reduce downside risk while preserving performance. Building on this insight, Sandberg (2019) proposes a dynamically weighted Value–Momentum combination, where the allocation to Momentum decreases as its short-term volatility increases, thereby improving portfolio stability.

In this article, we extend this line of research by introducing an optimization-based framework for dynamically blending Value and Momentum signals. Rather than relying on heuristic or backward-looking rules, we utilize forward-looking risk estimates to determine the optimal factor weights at each point in time. Specifically, we consider two strategies:

1. Minimum Variance Blend: selects the combination of Value and Momentum that minimizes the ex-ante portfolio variance.

2. Risk Parity Blend: allocates weights such that each factor contributes equally to the predicted portfolio risk.

We evaluate both approaches using a comprehensive backtest on the universe of the 1,000 largest U.S. equities by market capitalization. Our results indicate that these dynamically adjusted blends outperform, on average, the static 50/50 allocation in terms of realized information ratio (IR), with the minimum variance strategy outperforming in approximately 80% of rolling out-of-sample periods.

This framework illustrates how optimization and forward-looking risk models can enhance traditional factor-investing approaches by adapting to evolving market conditions in a disciplined and systematic manner.

Following are details of the framework, the intuition, and the numbers behind this optimization-based “smart mix” of Value and Momentum.

Optimization-Based Signal Mixing: From Raw Signals to Portfolio Weights

Signal definitions

• Value (Earnings-to-Price). For each stock i at time t we compute a forward-looking version of the traditional earnings-yield metric:

• Momentum (12-month return, 1-month skip). We measure past performance as the cumulative raw return over months t-12 to t-2, omitting the most recent month to mitigate the well-documented one-month reversal effect.

Standardization
To render the two characteristics comparable and robust, we apply the following cross-sectional transformation at every rebalancing date:

1. Winsorization at the 1st and 99th percentiles to remove outliers

2. De-meaning: subtract the cross-sectional mean of each signal

3. Scaling to unit variance, producing z-scores

The resulting vectors and each have mean zero and variance one.

Portfolio construction
Treating every standardized signal as a score that ranks stocks, we translate scores into positions through a dollar-neutral score-proportional scheme:

The weights rescaled to achieve a gross exposure of 100% (50% long, 50% short), yielding two fully diversified, dollar-neutral factor portfolios. Unlike the conventional decile or quintile portfolios prevalent in the literature, this full-cross-section approach:

• Uses information from every security.

• Produces smoother return series.

• Lends itself naturally to subsequent optimization because each factor can be treated as a single tradable portfolio with a well-defined risk-return profile.

These signal-derived portfolios constitute the inputs for the optimization framework described in the next section, where their weights are dynamically combined to create the final Value-Momentum mix.

Framing signal mix as an optimization problem

Having constructed standardized, dollar-neutral, long-short portfolios for the Value and Momentum signals, we proceed to combine these two strategies through a dynamic and risk-aware optimization framework.

Let and ​ denote the returns of the Value and Momentum strategies at time t as described above. Our goal is to construct a composite portfolio as a convex combination of the two strategies; its return is thus a convex combination of the two:

where is the time-varying weight on the Momentum portfolio.

We explore two optimization objectives that reflect distinct philosophies of risk management:

• Minimum variance (defensive blend): At each time t, we select to minimize the ex-ante variance of the combined strategy. This objective naturally leads to a more conservative allocation by minimizing exposure to the more volatile factor in a given period. Specifically, during episodes of elevated Momentum volatility, the optimizer tends to lower the weight on Momentum in favor of the more stable Value component. Due to the typically negative correlation between Value and Momentum portfolios, the diversification benefit allows the variance-minimizing weight to remain strictly positive—i.e., the solution rarely assigns a zero weight to Momentum. As the simulation results will show, the optimal weights are often well within the interior of the [0,1] range and in many cases are close to the equal-weight benchmark of 0.5.

• Risk parity (equal risk contribution): Alternatively, we solve for such that the Value and Momentum portfolios contribute equally to the total ex-ante volatility of the blended strategy. While this approach is generally less conservative, it still adjusts the Momentum weight downward in periods when its forecasted volatility increases,

As a baseline comparison, we also include the naïve Equal-Weight Mix where = 0.5 for all t.

To estimate the ex-ante variance of the blended strategy, we rely on a proprietary risk model that covers the universe of all tradable N stocks. Such models integrate both historical return dynamics and volatility forecasting techniques, ensuring responsiveness to changing market conditions.

From this model, we extract the 2 x 2 covariance matrix of the factor returns by calculating the ex-ante co-/variances of the two portfolios.

Empirical Results

We assess the performance of the optimization-based factor blending strategies using a comprehensive multi-horizon backtest on the universe of the 1,000 largest U.S. equities by market capitalization. The evaluation period spans from beginning of 2004 to end of 2024, covering nearly two decades of market regimes, including the Global Financial Crisis, post-crisis recovery, the COVID-19 shock, and the recent inflation-driven rate cycle. Rebalancing happens at the end of each month.

Risk estimates used in the optimization are derived from a proprietary forward-looking risk model, which is updated monthly and conditioned only on information available at the time of each rebalance, ensuring an entirely out-of-sample evaluation.

Full-period summary performance

The table below summarizes the annualized performance statistics for the five strategies under consideration.

The backtest results clearly demonstrate the advantage of the optimization-based strategies, particularly the Min Variance approach. With an annualized IR of 0.30, Min Variance outperforms both the static equal-weight benchmark and the Risk Parity strategy, each of which achieves an IR of 0.19, as well as the standalone Momentum (0.14) and Value (0.10) portfolios.

This superior risk-adjusted performance is driven not by dramatically higher returns, but by effective volatility suppression: Min Variance achieves a geometric return of 1.79% with an annualized volatility of only 6.76%, significantly lower than the 8.5% - 9.0% volatility levels observed in the other strategies.

It also exhibits the most favorable drawdown profile, with a maximum drawdown of 24.81%. Importantly, downside risk measures—including downside volatility (7.38%) and expected tail loss—also favor Min Variance over both the benchmark and standalone Momentum, highlighting its effectiveness in mitigating extreme losses.

Multi-horizon performance maps

To evaluate the performance of each approach, we compute information ratios over all possible start–end date combinations within the test period, yielding a full grid of evaluation windows. This multi-horizon analysis allows us to examine the consistency of outperformance across short-, medium-, and long-term investment horizons.

As a baseline, we compare both strategies to a static 50/50 equal-weighted blend. Our primary evaluation metric is the information ratio, measured over all combinations of start and end dates to capture short-, medium-, and long-horizon investment windows. This multi-horizon analysis produces a full grid of performance intervals for each strategy.

Minimum variance vs. equal weight

Figure 1 shows the difference of information ratios between the Min Variance strategy and the equal-weight benchmark. Green pixels indicate that Min Variance outperforms the benchmark while red pixels indicate underperformance, with the intensity reflecting the magnitude of the difference.

Figure 1: Min Variance vs. Equal Weights—Multi-Horizon Information Ratio Difference

• The dominance of green across most of the grid indicates that Min Variance outperforms over a wide range of horizons.

• Information ratio improvements are particularly pronounced during periods of elevated volatility (e.g., 2008, 2020).

• The frequency of outperformance is approximately 76.4%, as confirmed by the distribution summary.

• On average, the information ratio improvement in winning windows is +0.067, while the average underperformance in losing windows is similar at -0.078.

Risk parity vs. equal weight

Figure 2 provides the analogous plot for the Risk Parity strategy. While green areas still dominate:

• The grid is more mixed, with larger red regions, especially in the 2009–2020 interval.

• The frequency of outperformance drops to 55.7%, indicating a less consistent edge.

• On average, the information ratio improvement in winning windows is +0.027, while the average underperformance in losing windows is similar at -0.033.

These observations suggest that while Risk Parity achieves some degree of risk diversification, it lacks the sharper downside protection that characterizes the Min Variance strategy.

Figure 2: Risk Parity vs. Equal Weights—Multi-Horizon Information Ratio Difference

Despite their structural differences, both Min Variance and Risk Parity exhibit a shared strength: They successfully manage risk exposure during periods of elevated market stress, leading to superior performance relative to the static 50/50 mix. In times such as the Global Financial Crisis (2008–2009), the COVID-19 crash (2020), and the inflation-driven rate-hiking regime (2022–2023), both strategies dynamically adjust weights in response to rising volatility and seem to outperform in terms of information ratio.

Evolution of factor weights

To better understand the behavior of the two optimization frameworks over time, Figure 3 shows the time series of factor weights assigned to Value and Momentum by the Min Variance and Risk Parity strategies, respectively.

Figure 3: Progression of Factor Weights Over Time

The Min Variance strategy exhibits a highly responsive and adaptive allocation pattern, with factor weights fluctuating considerably over time. Notably, during periods of elevated market volatility—such as the 2008 financial crisis, the COVID-19 shock in early 2020, and parts of the rate-hiking environment post-2022—the optimizer consistently reduces exposure to Momentum, often pushing its weight close to zero.

In contrast, Value typically receives a higher allocation in these periods, reflecting its lower volatility and role as a stabilizing factor. The result is a dynamic risk control mechanism that rebalances aggressively to maintain portfolio stability during turbulent conditions.

In contrast, the Risk Parity allocation is far more stable, with weights hovering closer to 50/50 throughout most of the sample. Deviations from equal weighting do occur but are generally moderate, rarely exceeding a 20-percentage-point shift in either direction. While more refined than a naïve 50/50 mix, Risk Parity exhibits less responsiveness to sudden volatility spikes, which likely explains its weaker downside protection and lower outperformance frequency compared to the Minimum Variance approach.

Key Takeaways

This study proposes a practical and effective framework for dynamically blending Value and Momentum strategies using forward-looking risk optimization. We demonstrate that clear risk-aware allocation rules can significantly enhance portfolio outcomes.

Across nearly two decades of U.S. equity data, the Minimum Variance blend consistently outperforms the traditional 50/50 mix— achieving a higher information ratio, lower volatility, and smaller drawdowns. The Risk Parity strategy, while more conservative in its reallocations, also improves performance stability relative to the static benchmark, particularly in crisis environments.

Risk-aware blending helps avoid Momentum crashes, which frequently occur during episodes of market stress. Both optimization strategies dynamically reduce exposure to Momentum when its volatility spikes—most notably during the 2008 financial crisis, 2020 COVID shock, and the 2022–2023 rate hike cycle—thereby mitigating tail risk and preserving long-term capital.

Overall, these results highlight the importance of dynamic, forward-looking signal mixes. Rather than relying on fixed weights, even lightweight optimization routines can exploit evolving factor risk profiles to deliver more robust and resilient performance. This approach is flexible, scalable, and readily extendable to broader multi-factor or macro-driven allocation frameworks. 

References

Asness, C.S., Moskowitz, T.J., Pedersen, L.H., 2013. “Value and Momentum Everywhere.” The Journal of Finance 67, 3, 929-85.

Barroso, P., Santa-Clara, P., 2015. “Momentum has its moments.” The Journal of Financial Economics, 116, 111-20.

Sandberg, D.J., 2019. “Value and Momentum: Everywhere, but not all the Time.” S&P Global Intelligence, Market Intelligence Research 2019

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