Robustness of CVaR-Minimizing Dynamic Allocation: Evidence from Multi-Asset Portfolios Through 2025

Abstract

Traditional risk parity approaches rely largely on volatility measures, which may not fully capture asymmetric risk profiles. This study examines a dynamic allocation approach that minimizes portfolio-level Conditional Value-at-Risk (CVaR). The CVaR-Minimizing Dynamic Allocation (CVaR-DA) approach is intended to manage tail-risk events more effectively than traditional variance-based methods. We conducted an out-of-sample rolling-window simulation for the dynamically re-estimated strategies, covering different market conditions from 2015 to early 2025. Two investment universes were examined: a concentrated equity–gold portfolio and a multi-asset portfolio comprising global equities, sovereign bonds, commodities, and gold. Variance-based DRP generated higher Sharpe ratios than Static Risk Parity in both universes while maintaining low portfolio turnover. The CVaR-DA approach provided better downside protection, particularly in the multi-asset universe, but produced higher turnover. Bootstrap inference yielded positive mean differences in Sharpe ratios between DRP and Static Risk Parity. However, the confidence intervals included zero, indicating that the differences were not statistically significant at conventional levels. The favorable drawdown results nevertheless suggest that dynamic risk allocation may improve portfolio resilience when risk conditions change. Moving from static, volatility-based allocation toward adaptive strategies that account for tail risk may therefore support capital preservation for institutional investors and fund managers.

1. Introduction

Portfolio construction has moved well past return maximization as its organizing principle. Risk Parity (RP) has become an important approach in institutional asset management, shifting the focus from capital-based allocation to a logic of risk budgeting: each asset class is sized so that it contributes an equal share of total portfolio risk. The intent is to reduce the portfolio’s exposure to idiosyncratic shocks in any single market. Classical Mean-Variance Optimization (MVO) offers a useful contrast here, since its sensitivity to estimation noise in expected returns is well documented. RP sidesteps that weakness by relying primarily on second-moment estimates, which is a large part of why it has proven durable in practice.

The conventional implementation carries an assumption that rarely survives contact with data, namely that asset covariance structures hold constant through time. The 2008 financial crisis and the market shocks of 2020–2023 both argue otherwise. Correlations are not stationary and may change sharply under systemic distress, while diversification benefits erode alongside pronounced volatility clustering. A static RP allocation can therefore concentrate risk at exactly the moment diversification matters most.

A second limitation concerns the risk proxy itself. Variance weights gains and losses symmetrically and does not directly capture the asymmetric fat tails that characterize financial returns. This paper takes up both gaps. We first examine a Dynamic Risk Parity (DRP) framework in which a rolling-window adaptive mechanism lets the allocation track shifting market conditions rather than remain fixed. We then propose a CVaR-Minimizing Dynamic Allocation (CVaR-DA) approach that targets portfolio-level Conditional Value-at-Risk directly, relocating the optimization objective from dispersion to the mitigation of catastrophic tail risk. The motivation is practical. For institutional investors, the binding cost of risk is seldom moderate fluctuation; it is the extreme, nonlinear losses that sit in the left tail of the return distribution. The evolution of Quantitative Asset Allocation (QAA) has reached a critical juncture where theoretical elegance meets changing market conditions. MVO has been the cornerstone of portfolio theory for more than 70 years, but it is still very sensitive to estimation error, with even small input errors producing extremely unstable and uninvestable weights. MVO is vulnerable because of this sensitivity, especially in multi-period settings where the future seldom resembles the historical mean.

This study’s primary issue is two-dimensional. The first is temporal instability: a portfolio designed for average conditions is often unsuited for extreme regimes, and markets are intricate adaptive systems where risk relationships are constantly changing. The second is symmetry bias: conventional models ignore the fact that investors are disproportionately hurt by downside volatility in comparison to the utility gained from upside gains, treating risk as a symmetric concept through variance.

While Static Risk Parity solves the capital concentration problem, it remains a halfway solution that fails to address the dynamic nature of risk. There is a clear rationale for a framework that is both Adaptive (to capture regime shifts) and Downside-Oriented (to protect against tail events). This study develops and validates a model that navigates these complexities, using bootstrap-based statistical inference to assess the robustness of the observed performance differences.

1.1. Research Objectives

This study is built around five strategic objectives to narrow the gap between financial theory and institutional robustness:

• Benchmark Adaptive Efficiency: To compare MVO, Static RP, and Dynamic RP over the period through 2025, using out-of-sample evaluation for the dynamically re-estimated strategies and a full-sample fixed-weight SRP benchmark.
• Quantify Regime Responsiveness: To estimate the extent to which a dynamic rolling-window DRP methodology succeeds in detecting and responding to sharp increases in systemic correlation compared with static benchmarks.
• Formalize Downside Optimization: To develop the CVaR-DA extension and evaluate its particular relevance to reducing drawdown severity.
• Validate Scalability across Heterogeneous Assets: To identify whether the advantages of dynamic risk management apply across asset classes or only to certain asset classes, such as concentrated and multi-asset universes.
• Establish Statistical Robustness: To use bootstrap resampling to assess whether the Sharpe ratio differences between DRP and Static RP are statistically significant.

1.2. Research Hypotheses

H1. 

(Performance): DRP should deliver better risk-adjusted returns than static risk parity, since static weights reflect a long-run average of the covariance structure rather than the regime actually prevailing.

H2. 

(Operational Stability): Turnover under DRP is expected to fall between the two benchmarks: lower than MVO, which reacts sharply to estimation error, but more responsive to regime shifts than static RP.

H3. 

In stressed periods, particularly 2020–2024, DRP should record smaller maximum drawdowns as the risk-budgeting mechanism cuts exposure when realized volatility rises.

H4. 

(Tail-Risk Reduction): The CVaR-minimizing dynamic allocation extension is expected to reduce realized tail-risk exposure relative to variance-based allocation, consistent with the value of accounting for non-normal return distributions in dynamic risk management.

2. Literature Review

2.1. The Mean-Variance Paradigm and the Estimation Fragility of Optimization

Markowitz (1952) established the conceptual bedrock of modern quantitative finance, giving the risk–return trade-off a precise mathematical language for the first time. MVO locates portfolios along the efficient frontier that maximizes expected utility, conditional on returns being Gaussian. The move from theoretical elegance to empirical implementation, however, has proved far less clean. What Michaud (1989) termed the Markowitz optimization enigma has drawn sustained attention since (Kuhn et al., 2009; Lai et al., 2011), and the central critique concerns estimation risk. MVO treats historical means (µ) and covariances (Σ) as deterministic parameters rather than as stochastic estimates, so the optimizer behaves as an error maximizer: capital flows disproportionately toward the assets carrying the most estimation noise (Cousin et al., 2023; Kan & Zhou, 2007). Classical MVO is also myopic and static, presuming a stationary world. Financial markets are not stationary. They exhibit volatility clustering, which leaves single-period optimizations obsolete when regimes shift rapidly (D. Li & Ng, 2000).

2.2. From Capital Allocation to Risk Budgeting: The Equal Risk Contribution (ERC) Evolution

Risk parity (RP), and specifically the equal risk contribution (ERC) principle, has gained institutional prominence as an alternative to MVO. Where MVO chases expected returns and is sensitive to forecast error, RP shifts attention to the balance of risk exposure across holdings. Maillard et al. (2010) formalized the ERC approach, showing that equalizing the total risk contribution of each asset produces a diversification profile with a better risk–return trade-off than the naive equally weighted (EW) portfolio. What gives RP its mathematical footing is that it accounts for standalone volatility and cross-asset correlations together. A gap remains in static implementations. These typically rely on long-horizon covariance estimates, which leave investors exposed during correlation breakdowns, when assets that are ordinarily uncorrelated, such as stocks and bonds, begin to move in tandem under systemic liquidity shocks or inflationary pressure (Asness et al., 2012; Maewal & Bock, 2019).

2.3. Dynamic Adaptation and the Intertemporal Nature of Risk

The shift from static allocation to Dynamic Risk Parity (DRP) is an important development in tactical asset allocation. The idea is related to the multiperiod portfolio-selection literature, in which allocation decisions are considered over time rather than at a single point (D. Li & Ng, 2000). DRP follows this logic by estimating the covariance matrix Σ over a rolling window, so portfolio weights reflect recent market conditions (Roncalli, 2014). It can therefore be viewed as a regime-aware strategy rather than merely an optimization method. Regular weight updates allow the portfolio to reduce risk exposure as sustained increases in volatility begin to emerge.

Despite these advantages, two gaps remain. First, relatively little attention has been given to rolling-window DRP in broad multi-asset portfolios containing commodities and inflation-hedging assets. Earlier studies have focused more heavily on the construction and performance of conventional risk parity portfolios (e.g., Chaves et al., 2012). Second, few studies have directly compared rolling-window adaptation with formal regime-detection techniques. Costa and Kwon (2019), for example, formulate risk parity using a Markov regime-switching framework. It therefore remains unclear whether the simpler rolling-window approach captures changes in market regimes as effectively as an explicit switching model.

2.4. Beyond Variance: CVaR and the Management of Non-Linear Tail Risks

The sharpest critique of MVO and traditional RP alike concerns their reliance on variance as the sole proxy for risk. Variance presumes a symmetric distribution, one in which upside deviation counts the same as downside deviation. That presumption sits awkwardly with the evidence: financial returns are skewed and leptokurtic, and for institutional practitioners the two directions carry very different consequences. Risk management has accordingly shifted toward coherent risk measures, among them Conditional Value-at-Risk (Rockafellar & Uryasev, 2000). CVaR offers a sharper lens for portfolio construction because it looks only at expected loss in the worst outcomes, that is, at the left tail. J. Li and Xu (2013) examined mean-CVaR models, but the integration of CVaR into a dynamic risk parity framework has received far less attention. We address that gap by developing a dynamic allocation approach that shifts its optimization objective from minimizing average fluctuations, measured by variance, to minimizing extreme loss, measured by CVaR, so that the resulting portfolio is structurally more resilient to tail events.

2.5. Synthesis and Research Gap

The literature covers static risk parity thoroughly, and the theoretical case for CVaR is well established. Empirical work bringing the two together, however, is scarce, particularly work that combines three elements:

• Dynamic rebalancing. Rolling-window adaptation to capture regime shifts.
• CVaR Minimization: Shifting from variance-based risk allocation toward portfolio-level tail-risk minimization.
• Multi-asset implementation. Diversification across heterogeneous and non-linear assets through 2025.

This study addresses that gap with a framework tested across the market conditions of the past decade, responding to the estimation fragility of MVO and the myopia of static RP, and offering a more robust basis for wealth preservation under uncertain market conditions.

3. Methods

This section describes the data construction, portfolio optimization frameworks, and empirical testing design employed in this study. Particular attention is paid to ensuring strict out-of-sample evaluation of the dynamically re-estimated strategies and comparability across portfolio strategies.

3.1. Data and Asset Universes

The empirical analysis uses monthly return data spanning January 2015 to January 2025. Asset prices are obtained from publicly available market data sources and converted to monthly returns using month-end prices. We chose a monthly frequency for two reasons: it matches the rebalancing horizon that institutional risk parity implementations typically adopt, and it dampens microstructure noise and short-horizon autocorrelation present in higher-frequency data. All returns are computed as simple percentage returns and aligned across assets. Two distinct universes are examined, which allows us to assess both robustness and practical relevance.

For full reproducibility, Universe A comprises the following eleven tickers: AAPL, MSFT, AMZN, GOOG, TSLA, JNJ, JPM, NVDA, META, XOM, and GLD (SPDR Gold Shares, used as a liquid, exchange-traded proxy for physical gold). Universe B comprises seven tickers: SPY (U.S. equities), VEA (developed-market equities ex-US), VWO (emerging-market equities), TLT (long-term U.S. Treasuries), IEF (intermediate-term U.S. Treasuries), GLD (gold), and DBC (a broad commodities index), each used as a liquid ETF proxy for its respective asset class rather than direct holdings of the underlying instruments. All price series were obtained from Yahoo Finance using adjusted closing prices denominated in U.S. dollars and sampled at month-end frequency. Missing values in the underlying daily price series, where present, were handled using forward-fill followed by backward-fill before resampling to monthly frequency. We note that backward-filling addresses isolated non-trading-day misalignments across the different exchanges represented in the multi-asset universe and was applied only to single-day gaps; no multi-day gaps were present in the data. Given the monthly frequency of the subsequent analysis, any resulting look-ahead effect from this daily-level adjustment is immaterial to the reported monthly returns.

Universe A (equity and gold). The first consists of ten large-cap U.S. equities together with gold, an equity-dominated portfolio augmented by a defensive asset. It serves as a controlled setting in which the effects of dynamic covariance estimation can be isolated among relatively homogeneous holdings.

Universe B (multi-asset portfolio). The second comprises a diversified set of asset classes: U.S. equities, developed and emerging market equities, government bonds across maturities, gold, and broad commodities. This composition reflects canonical risk parity implementations used by institutional investors and permits an assessment of dynamic risk parity in a realistic multi-asset setting.

It is possible to distinguish clearly between outcomes that are influenced by asset selection and those that are related to the portfolio development process itself by using two universes. The 2018 stock correction, the 2020 COVID-19 shock, and the 2022–2023 inflationary tightening cycle are just a few of the market regimes that were included in the sample period. This allowed for a thorough out-of-sample analysis of the dynamically re-estimated strategies under both stable and volatile market conditions.

Return series are computed from Yahoo Finance’s adjusted closing prices, which incorporate adjustments for stock splits and cash dividend distributions under the data provider’s default settings. Reported returns therefore approximate total returns rather than price-only returns.

3.2. Empirical Design and Out-of-Sample Framework

All dynamically re-estimated strategies (MVO, Dynamic RP, and CVaR-DA) are implemented using a rolling-window estimation framework to ensure strict out-of-sample evaluation. The Static Risk Parity (SRP) benchmark, by contrast, is estimated once using the full-sample covariance matrix and held fixed thereafter; it is therefore not out-of-sample in the strict sense used for the dynamic strategies; instead, it represents a fixed-weight benchmark against which the value of dynamic re-estimation can be assessed. For the dynamically re-estimated strategies, portfolio weights at time (t) are estimated using information available up to (t-1), and portfolio performance is evaluated at time (t). As is customary in dynamic risk parity research, a rolling window of 12 months is used for covariance and risk estimates across these strategies. This window is chosen to strike a balance between estimation stability and reactivity to shifting market conditions (Roncalli, 2014). The sensitivity of CVaR-DA to different window lengths and CVaR confidence levels is examined in Section 4.6.

For the dynamically re-estimated strategies, this design eliminates look-ahead bias and avoids overlapping estimation and evaluation periods. Portfolio rebalancing is conducted at a monthly frequency, consistent with the return measurement interval and common practice in empirical portfolio studies.

3.3. Mean–Variance Optimization (MVO)

Mean–Variance Optimization follows the classical Markowitz framework. At each rebalancing date, portfolio weights are determined by minimizing portfolio variance subject to a minimum expected return constraint and standard investment constraints. Formally, the optimization problem is given by

$$\underset{\mathrm{w}}{\mathrm{m}\mathrm{i}\mathrm{n}}{\mathrm{w}}^{\mathrm{\top }}\mathsf{\Sigma }\mathrm{w}$$

(1)

subject to

$${\displaystyle \sum _{i=1}^N}{w}_i=1,w_i\ge 0,{\mathrm{w}}^{\mathrm{\top }}\mu \ge \overline{\mu }$$

(2)

where w denotes the vector of portfolio weights; Σ is the estimated covariance matrix of returns; μ is the vector of expected returns; and $\overline{\mu }$ is a target return equal to the cross-sectional mean of estimated returns. Long-only constraints are imposed to ensure comparability with risk parity strategies. The MVO portfolio is estimated using the same rolling-window framework as other strategies, allowing for a fair out-of-sample comparison.

3.4. Static Risk Parity

Static Risk Parity portfolios are constructed using the Equal Risk Contribution (ERC) principle. The objective is to allocate portfolio weights such that each asset contributes equally to total portfolio risk, measured by portfolio variance (Fisher et al., 2015). Let total portfolio risk be defined as

$${\sigma }_p=\sqrt{{\mathrm{w}}^{\mathrm{\top }}\mathsf{\Sigma }\mathrm{w}}$$

(3)

where w denotes the vector of portfolio weights, and Σ is the covariance matrix of asset returns.

The risk contribution of asset i to total portfolio risk is given by

$$R{C}_i={\displaystyle \frac{w_i(\mathsf{\Sigma }\mathrm{w}{)}_i}{{\sigma }_p}}.$$

(4)

The Equal Risk Contribution condition requires that

$$R{C}_i=R{C}_j\forall i,j.$$

(5)

Equivalently, the ERC portfolio can be obtained by solving the following optimization problem

$$\underset{\mathrm{w}}{\mathrm{m}\mathrm{i}\mathrm{n}}{\displaystyle \sum _i^N}{\displaystyle \sum _{j=1}^N}{\left(R{C}_i\left(\mathrm{w}\right)-R{C}_j\left(\mathrm{w}\right)\right)}^2$$

(6)

subject to

$${\displaystyle \sum _{i=1}^N}{w}_i=1,w_i>0\forall i$$

(7)

The unit-sum constraint ensures full capital allocation, while the optimization objective enforces equality of risk contributions across assets. At the interior solution, the first-order optimality conditions of Equation (6) imply that all assets contribute equally to total portfolio variance, thereby satisfying the ERC condition.

The static Risk Parity portfolio is estimated once using the full-sample covariance matrix and held constant over time. Instead of using a rolling or expanding-window estimate, this design decision reflects the standard definition of a static risk parity benchmark in the literature, which is a single fixed-weight allocation that an investor commits to for the whole period. We observe that because SRP’s weights implicitly represent the full-sample covariance structure, which includes information not available in real time, it has an informational advantage over truly out-of-sample dynamic techniques. This means SRP should be understood as an ex-post fixed-weight comparator that benefits from look-ahead information, rather than an implementable real-time strategy. We do not assert a specific direction for how this affects the comparison with the dynamic strategies, as future information does not necessarily translate into improved realized performance in every evaluation period; we simply note this as an important interpretive caveat when comparing SRP against the genuinely out-of-sample dynamic strategies. To clarify the link between the optimization problem and the ERC condition, consider the associated Lagrangian formulation. The first-order optimality conditions at the interior solution imply that each asset’s total risk contribution (RC_i, the product of its weight and marginal contribution to portfolio variance) is equalized, consistent with Equation (5); marginal contributions themselves need not be equal across assets. Consequently, the solution of Equation (6) satisfies the Equal Risk Contribution condition stated in Equation (5). This approach serves as a benchmark to assess the incremental value of dynamic risk adjustments.

3.5. Dynamic Risk Parity

Dynamic risk parity extends the static framework by letting portfolio weights evolve in response to changes in asset risk characteristics. At each rebalancing date, we re-estimate the covariance matrix over a rolling 12-month window and recompute the ERC weights accordingly. The portfolio can therefore adapt to time-varying volatility and correlation structures, which matter most during market stress or regime shifts. Updating risk estimates at every step allows the strategy to hold risk contributions in balance while remaining more robust than a static allocation. What makes the approach dynamic, then, is the combination of time-varying parameter estimation with systematic re-optimization and rebalancing at each date.

3.6. CVaR-Minimizing Dynamic Allocation

To explicitly address downside risk, we introduce a CVaR-Minimizing Dynamic Allocation (CVaR-DA) framework. Instead of equalizing variance-based risk contributions, this approach focuses on minimizing tail risk as measured by Conditional Value-at-Risk (CVaR). For a confidence level α, CVaR is defined as the expected portfolio loss conditional on losses exceeding the Value-at-Risk (VaR) threshold. The optimization problem is formulated as

$$\underset{\mathrm{w},\mathrm{VaR},\mathrm{z}}{\mathrm{m}\mathrm{i}\mathrm{n}}\mathrm{VaR}+{\displaystyle \frac{1}{(1-\alpha )T}}{\displaystyle \sum _{t=1}^T}{z}_t$$

(8)

subject to

$$z_t\ge -{\mathrm{w}}^{\mathrm{\top }}{\mathrm{r}}_t-\mathrm{VaR},z_t\ge 0,{\displaystyle \sum _{i=1}^N}{w}_i=1,w_i\ge 0$$

(9)

where r_t denotes asset returns in the rolling estimation window. CVaR-DA portfolios are estimated dynamically using the same rolling-window framework as variance-based DRP.

According to the formulation of Rockafellar and Uryasev (2000), the optimization problem in Equations (8) and (9) is a linear program in (w, VaR, z) with a linear objective and linear (in)equalities for all constraints. Because it is convex, a globally optimal solution for this problem class was ensured by applying the SCS conic solver via the CVXPY interface at each rebalancing date.

We note an important finite-sample limitation of this specification: a 12-month rolling window contains an expected 0.6 observations in the lower 5% tail at the 95% confidence level, and only 0.12 observations at the 99% level. The empirical CVaR estimate at each rebalancing date is therefore necessarily dominated by one or very few realized returns, making the objective highly sensitive to individual monthly outcomes. This finite-sample constraint likely contributes to the elevated turnover documented in Section 4.3 and examined further in Section 4.6; conclusions regarding CVaR-DA’s tail-risk properties under this primary specification should accordingly be interpreted with this limitation in mind.

3.7. Leverage and Volatility Targeting

We also consider leverage-adjusted portfolios with a volatility targeting mechanism to represent realistic risk parity implementations. With a maximum leverage cap of three, portfolio returns are scaled to reach a target annualized volatility of 10%. Instead of using an internal calibration or optimization process, these parameter values were chosen to mirror standard industry practice among institutional risk parity implementations, which typically target a volatility level of 8–10% (ReSolve Asset Management, 2020). Leveraged positions have an annual borrowing cost of 2%. This extension allows for a realistic assessment of Dynamic Risk Parity under conditions commonly encountered in institutional portfolio management.

3.8. Performance Evaluation and Statistical Inference

Portfolio performance is evaluated using annualized return, volatility, Sharpe ratio, and maximum drawdown. In addition, portfolio turnover is computed to assess the stability and implementability of each strategy. To assess the robustness of differences in risk-adjusted performance, we employ bootstrap-based statistical inference. Sharpe ratio differentials between Dynamic Risk Parity and benchmark strategies are evaluated using resampled return series, allowing for inference without relying on parametric distributional assumptions.

Reported turnover is the time-series average of Σ_i |w_i,t − w_i,t−1|, which is the sum of absolute weight changes across assets at each rebalancing date without being divided by two. Since leverage rescales portfolio exposure rather than reallocating among assets, turnover for the volatility-targeted variant is calculated on the underlying Dynamic RP weight vector before the leverage scalar is applied in Section 3.7.

We use a moving block bootstrap approach with 2000 replications and a block duration of 6 months to evaluate the robustness of variations in risk-adjusted performance while maintaining the serial dependence pattern found in monthly returns. Resampled return series are used to assess Sharpe ratio differences between Dynamic Risk Parity and benchmark strategies, and the 5th and 95th percentiles of the resulting bootstrap distribution are used to create 90% confidence intervals.

The moving block bootstrap resamples blocks directly from the realized monthly strategy-return series produced by the rolling-window estimation, rather than resampling underlying asset returns and re-optimizing portfolio weights within each replication; it therefore tests the robustness of the Sharpe ratio differential to the sampling distribution of realized strategy returns, holding estimated weight paths fixed. Sharpe ratios throughout this study assume a risk-free rate of zero. Annualized return is the arithmetic mean of monthly returns multiplied by 12 (not a geometric or CAGR calculation), and annualized volatility is the standard deviation of monthly portfolio returns multiplied by √12. Transaction costs (Section 4.8) are deducted as cost_t = Turnover_t × (cost in basis points/10,000) applied to each month’s portfolio return, where Turnover_t follows the Σ_i|w_i,t − w_i,t−1| convention defined above; the quoted one-way cost is applied directly to this summed quantity without halving.

4. Results

This section presents the empirical performance of five strategies: mean–variance optimization (MVO), static risk parity (SRP), dynamic risk parity (DRP), leverage-adjusted DRP, and CVaR-Minimizing Dynamic Allocation (CVaR-DA). Results appear separately for each universe, which lets us judge robustness alongside practical relevance.

4.1. Portfolio Performance: Equity-Dominated Universe (Universe A)

Table 1 reports portfolio performance over the evaluation period for Universe A, comprising U.S. large-cap equities and gold.

Table 1. Performance comparison—Universe A (equity + gold, 2015–2025).

Strategy	Annual Return	Volatility	Sharpe Ratio	Max Drawdown
Mean–Variance Optimization	0.1763	0.1407	1.2527	−0.1674
Static Risk Parity	0.2659	0.1861	1.4289	−0.2605
Dynamic Risk Parity	0.2803	0.1899	1.4756	−0.2589
Dynamic RP (Vol-Targeted)	0.1702	0.1167	1.4579	−0.1376
CVaR-Minimizing Dynamic Allocation	0.2349	0.1671	1.4052	−0.2180

Volatility and returns are annualized. The maximum drawdown is calculated as the cumulative portfolio value’s peak-to-trough decrease over the full out-of-sample period; it is not annualized. Vol-targeted portfolios have a maximum leverage of three and a 10% yearly volatility target.

Among the unlevered strategies, dynamic risk parity records the highest Sharpe ratio, ahead of both static risk parity and MVO. The leverage-adjusted variant does not maximize returns, but it produces the lowest maximum drawdown in this universe, which illustrates the trade-off between amplifying returns and controlling downside. CVaR-DA shows smaller drawdowns than the variance-based risk parity strategies, in line with its explicit focus on tail-risk minimization.

4.2. Portfolio Performance: Multi-Asset Universe (Universe B)

Table 2 reports results for Universe B, a canonical risk parity setting spanning equities, bonds, commodities, and gold.

Table 2. Performance comparison—Universe B (multi-asset portfolio, 2015–2025).

Strategy	Annual Return	Volatility	Sharpe Ratio	Max Drawdown
Mean–Variance Optimization	0.0384	0.0614	0.6258	−0.1296
Static Risk Parity	0.0527	0.0918	0.5745	−0.1716
Dynamic Risk Parity	0.0693	0.0929	0.7455	−0.1718
Dynamic RP (Vol-Targeted)	0.0536	0.1189	0.4503	−0.2235
CVaR-Minimizing Dynamic Allocation	0.0558	0.0880	0.6339	−0.1562

Volatility and returns are annualized. The maximum drawdown is calculated as the cumulative portfolio value’s peak-to-trough decrease over the evaluation period; it is not annualized.

In the multi-asset universe, dynamic risk parity again posts a higher Sharpe ratio than static risk parity, so the benefits of dynamic risk allocation are not confined to equity-heavy portfolios. CVaR-DA improves downside protection further, with the lowest drawdown among the risk parity strategies. Volatility targeting, by contrast, underperforms here: leverage appears to amplify exposure to unstable correlation regimes when markets come under stress.

4.3. Portfolio Stability and Turnover

Turnover reflects two practical concerns: what a strategy costs to implement, and how stable its allocations are. Table 3 reports average monthly turnover for each strategy.

Table 3. Average portfolio turnover.

Strategy	Universe A	Universe B
Mean–Variance Optimization	0.4421	0.2998
Static Risk Parity	0.0000	0.0000
Dynamic Risk Parity	0.0037	0.0009
CVaR-Minimizing Dynamic Allocation	0.3386	0.3370

Turnover is calculated as Σ_i|w_i,t − w_i,t−1|, which is a percentage of the overall portfolio value for each rebalancing period (monthly).

Turnover under dynamic risk parity is very low, close to that of static risk parity, yet risk-adjusted performance improves substantially. Both MVO and CVaR-DA trade more heavily, which reflects their greater sensitivity to estimation noise and, in the CVaR case, to the tail observations that drive the optimization. The trade-off DRP strikes between adaptability and implementation stability is therefore a favorable one.

4.4. Bootstrap-Based Statistical Inference

We apply bootstrap resampling to the Sharpe ratio differences between dynamic and static risk parity, testing how robust those differences are. Table 4 reports the results.

Table 4. Bootstrap Sharpe ratio differences (DRP−SRP).

Universe	Mean Difference	5% CI	95% CI
Universe A	0.1182	−0.8473	1.0599
Universe B	0.2251	−0.6078	1.0253

Block bootstrap that accounts for serial dependence in monthly returns with a block length of 6 months and 2000 replications.

Block bootstrap confidence intervals, which take into consideration serial dependence in monthly returns, continue to include zero in both universes and are still larger than those derived under an i.i.d. resampling assumption. This demonstrates that gains in the Sharpe ratio are not statistically significant at traditional levels and that taking serial dependence into account results in a statistically more conservative evaluation that is suitably more cautious. Nevertheless, the consistently positive mean differences and improved downside risk metrics suggest that the primary advantage of Dynamic Risk Parity lies in enhanced robustness and drawdown control rather than strict mean–variance dominance.

Overall, the empirical evidence suggests that Dynamic Risk Parity offers meaningful improvements in portfolio robustness across different asset universes. Although Sharpe ratio gains are economically relevant, they are not statistically significant at conventional levels. Dynamic Risk Parity maintains stable portfolio weights, although its downside-risk performance varies across portfolio specifications. CVaR-DA further enhances tail-risk protection, albeit at the cost of higher turnover, reinforcing the value of incorporating downside-focused risk measures into dynamic allocation frameworks.

To complement maximum drawdown as evidence of tail-risk mitigation, we report realized (historical, non-parametric) 95% Value-at-Risk and Conditional Value-at-Risk of monthly returns for each strategy. In Universe A, CVaR-DA exhibits a realized monthly CVaR of −6.00%, compared to −9.93% for Dynamic RP and −9.94% for Static RP; in Universe B, CVaR-DA’s realized CVaR is −4.66%, compared to −5.44% for both RP variants. Realized skewness for CVaR-DA is positive in both universes (+0.63 in A, +0.35 in B), in contrast to negative skewness for Static RP and Dynamic RP (−0.12 to −0.28), providing direct empirical evidence—rather than a purely theoretical assertion—that the CVaR-minimizing objective produces a materially less negatively skewed, lower-tail-risk return distribution. Table 5 summarizes the tail-risk measures and return skewness for each strategy in both investment universes.

Table 5. Tail-risk measures and return skewness by strategy.

Strategy	VaR 95% (A)	CVaR 95% (A)	Skew (A)	VaR 95% (B)	CVaR 95% (B)	Skew (B)
Static RP	−8.46%	−9.94%	−0.12	−3.69%	−5.44%	−0.16
Dynamic RP	−8.85%	−9.93%	−0.19	−4.07%	−5.44%	−0.28
CVaR-DA	−4.86%	−6.00%	+0.63	−3.80%	−4.66%	+0.35

4.5. Analysis of Sensitivity

We performed a grid search across target volatilities of 8%, 10%, 12%, and 15%, paired with leverage caps of 2×, 3×, 4×, and unrestricted, to determine whether the reported performance depends on the particular choice of target volatility (10%) and leverage cap.

In Universe A, Sharpe ratios were frequently unaffected by the leverage cap. They ranged from 1.40 to 1.50 throughout the grid, which indicates that the results were more sensitive to the target volatility itself. Universe B showed a different picture: Sharpe ratios there ranged from 0.40 to 0.50, indicating that performance was more sensitive to both parameters. Even so, the relative ranking of the techniques listed in Section 4.2 did not change under any combination of parameters, which suggests that our primary findings are not a result of the particular parameter selections.

Table A1 (Appendix A) presents the results. The insensitivity of Universe A’s Sharpe ratios to the leverage cap arises because realized volatility rarely necessitated leverage greater than 2×.

4.6. Sensitivity to CVaR Confidence Level and Rolling-Window Length

Table 3 reports monthly turnover of roughly 34% for CVaR-DA against less than 0.4% for variance-based DRP. Earlier research on the stability of tail-risk estimates points to the estimation window as a likely source of that gap, so we examined whether the 12-month rolling window used in the main analysis accounts for it. Holding all other parameters constant, we recalculated CVaR-DA over rolling windows of 12, 24, 36, and 60 months, and across CVaR confidence levels of 90%, 95%, and 99%. Table A2 reports the results.

Turnover fell substantially in both universes as the estimation window grew, from roughly 34% at 12 months to 10–19% at 24 and 36 months, and to 4–10% at 60 months. Shorter windows leave a smaller number of effective tail observations available for CVaR estimation, and the pattern in Table A2 is consistent with that mechanism. The short rolling window therefore appears to contribute substantially to the turnover gap between CVaR-DA and variance-based DRP.

The relationship between window length and risk-adjusted performance is less straightforward. In Universe A, Sharpe ratios decreased monotonically as the window lengthened, from 1.40 at 12 months to roughly 1.00–1.14 at 36 and 60 months, which points to a trade-off between estimator stability and reactivity to shifting market conditions. Universe B behaved differently. Sharpe ratios first rose from 0.63 at 12 months to roughly 0.70 at 24 months under the 95% and 99% confidence levels, then declined at 36 and 60 months. The more diversified multi-asset setting thus appears to balance stability against responsiveness most favorably somewhere around 24 to 36 months. Across all window lengths and the three confidence levels examined, the broad pattern of results held, so the choice of α = 95% in the primary analysis is unlikely to drive the reported findings.

We nonetheless retain the 12-month window in our main specification for comparability with the variance-based Dynamic Risk Parity benchmark in Section 3.2, which employs the same window length. Granting CVaR-DA a longer window on its own would introduce a second source of asymmetry between the two dynamic strategies, on top of their different risk-measure specifications. The practical implications differ, however. Practitioners running CVaR-DA with transaction costs as the primary concern could lower turnover considerably by adopting a longer estimation window, at a slight cost to responsiveness in concentrated portfolios and with a potentially advantageous trade-off in more diversified multi-asset settings.

4.7. Portfolio Concentration Analysis

To further examine whether CVaR-DA produces genuinely diversified allocations, we computed the Herfindahl–Hirschman Index (HHI) of portfolio weights at each rebalancing date. Dynamic RP maintained near-equal weighting throughout the sample (mean HHI of 0.091 in Universe A and 0.143 in Universe B, both within 1% of the equal-weight benchmark of 1/N). CVaR-DA, by contrast, exhibited substantially higher concentration (mean HHI of 0.470 in Universe A and 0.536 in Universe B, roughly 3.7–5.2 times the equal-weight benchmark), with quarterly average weights in a single asset—typically gold or intermediate-term Treasuries—exceeding 90% in several periods (e.g., 97% in gold in Universe A during Q4 2022; 93% in IEF in Universe B during Q1 2016). This finding provides direct empirical confirmation that CVaR-DA, as formulated in Equations (8) and (9), converges toward a concentrated minimum-CVaR portfolio rather than a diversified, risk-contribution-equalized allocation. This is consistent with the choice made in Section 3.6 to characterize the method as CVaR-minimizing dynamic allocation rather than CVaR risk parity.

4.8. Transaction-Cost-Adjusted Performance

Given the substantially higher turnover of CVaR-DA relative to variance-based Dynamic RP (Table 3), we assessed performance net of transaction costs. Assuming one-way costs of 5, 10, and 20 basis points per unit of turnover—consistent with typical institutional trading costs for liquid ETFs and large-cap equities—CVaR-DA’s Sharpe ratio in Universe A declines modestly from 1.4053 (gross) to 1.3938–1.3604 (net), and in Universe B from 0.6335 to 0.6104–0.5401, across the cost range tested. Dynamic RP’s Sharpe ratio is essentially unaffected given its negligible turnover (Table 3). While transaction costs modestly erode CVaR-DA’s absolute performance, its risk-adjusted return remains above that of Static RP across all cost scenarios tested, indicating that the strategy’s tail-risk benefits are not fully offset by realistic implementation costs, though cost sensitivity should be weighed against turnover-averse institutional mandates.

5. Discussion

The results point to a shift away from static, variance-based allocation toward approaches that adjust as risk conditions change and place greater weight on downside losses. This section brings the findings together by comparing Dynamic Risk Parity (DRP) with benchmark methods and considering the role of CVaR-DA in a multi-asset setting.

5.1. The Adaptive Advantage: Temporal Robustness vs. Static Fragility

The consistent outperformance of DRP over its static counterpart (SRP) is consistent with the core hypothesis that financial risk is a non-stationary construct. Even when market correlations suddenly changed, SRP portfolios kept out-of-date risk estimations, which resulted in capital weights that were out of step with current circumstances. Our results show that compared to static allocation, DRP’s rolling-window mechanism enables the portfolio to identify and react to regime shifts more successfully. DRP decreased portfolio risk exposure during systemic shocks by adjusting weights in response to realized volatility and correlation spikes, such as the turbulence of 2020 and the inflationary regime of 2022–2023. This confirms that the primary value of dynamic allocation lies not in picking winners, but in the systematic avoidance of risk over-concentration during regime transitions.

Table 6 reports average Dynamic RP portfolio weights in Universe B across three representative periods. Weight allocations remained essentially equal-weighted across all three periods, with each asset’s average weight varying by no more than 0.002 across the calm (2019), crisis (2020), and inflationary (2022) sub-periods. This indicates that Dynamic RP’s risk-budgeting mechanism produces only marginal reallocation at the annual-average level even during periods of significant market stress.

Table 6. Average dynamic RP portfolio weights in Universe B across selected periods.

Period	DBC	GLD	IEF	SPY	TLT	VEA	VWO
2019 Calm	0.143	0.143	0.144	0.142	0.144	0.142	0.142
2020 COVID crisis	0.142	0.143	0.144	0.142	0.144	0.142	0.142
2022 Inflation	0.143	0.143	0.143	0.142	0.143	0.142	0.143

5.2. Economic Utility vs. Statistical Conservatism

A key result from the bootstrap analysis is that an economically meaningful difference does not necessarily establish statistical dominance. DRP produced higher Sharpe ratio estimates than SRP in both universes, but the confidence intervals included zero. The results therefore do not establish a statistically significant performance advantage.

For institutional managers, however, portfolio performance is not judged by the Sharpe ratio alone. Large drawdowns may lead to redemptions and create additional fiduciary pressure. In this study, DRP maintained low turnover and relatively stable allocations, although its maximum-drawdown performance varied across the two portfolio specifications. Its practical value therefore lies in adaptive allocation and implementation stability rather than demonstrated return alpha or consistently lower tail risk.

5.3. CVaR-DA and the Limitations of Symmetric Risk Measures

One of the more significant contributions of this study is the empirical validation of the CVaR-DA extension. Variance-based DRP uses a symmetric second-moment risk measure that does not distinguish favorable from unfavorable return deviations or explicitly characterize tail-loss magnitude; this critique does not require an assumption of Gaussian returns, as covariance-based risk parity does not itself assume normality. Our results indicate that during systemic crises, variance cannot represent the negative skewness and fat tails that asset returns exhibit. The CVaR-DA framework performed better on tail-risk mitigation: by reducing projected loss in the worst 5% of scenarios, the model produced a more robust downside performance floor. That strengthens the hedge against extreme tail events, where volatility-based models may underestimate the magnitude of potential loss, particularly during periods of realized negative skewness.

5.4. Multi-Asset Complexity and the Leverage Paradox

The study highlights a paradoxical relationship between leverage and diversification. In the concentrated equity-gold universe, leverage was an effective tool for volatility targeting. However, in the diversified multi-asset universe, the application of leverage required extreme caution. We observed that during periods of correlation breakdown—when equities and bonds declined simultaneously—losses were higher in DRP portfolios with leverage adjustments. This pattern is in line with recent empirical data demonstrating that, due to concurrent monetary tightening pressures on both asset classes, the hitherto negative stock-bond correlation changed and turned positive during the 2022–2023 inflationary period (Molenaar et al., 2024). This suggests that in addition to Dynamic Risk Parity, multi-asset managers may need other systems for tracking correlation risk; this is a subject for further study. Our findings caution against careless use of leverage without taking systemic liquidity concerns into account because the benefit of diversification is not continuous and depends on the underlying macro-regime. This pattern is directly observable in our data using a broader and more stable equity–bond measure: the full-year correlation between SPY (U.S. equities) and TLT (long-term Treasuries) in Universe B was persistently negative in the years preceding the inflationary shock (−0.30 in 2018 and −0.60 in 2019), consistent with the conventional equity–bond diversification benefit. This relationship reversed sharply during the 2022–2023 inflationary tightening cycle, with the full-year SPY–TLT correlation turning strongly positive (+0.51 in 2022 and +0.88 in 2023), directly illustrating the breakdown of the traditional stock–bond hedge documented by Molenaar et al. (2024) and motivating the case for dynamic, rather than static, risk allocation.

6. Conclusions

This study compared MVO, Static Risk Parity, Dynamic Risk Parity, and CVaR-Minimizing Dynamic Allocation, using rolling-window out-of-sample evaluation for the dynamically re-estimated strategies and a full-sample fixed-weight SRP benchmark over the period from 2015 to early 2025. Two investment universes were considered: an equity–gold portfolio and a broader portfolio containing equities, sovereign bonds, commodities, and gold. The comparison was intended to examine whether updating risk estimates over time changes portfolio performance when volatility and correlations are not stable.

Variance-based DRP recorded higher Sharpe ratios than MVO and Static Risk Parity in both investment universes. It also maintained relatively low portfolio turnover. However, the block-bootstrap confidence intervals for the differences between the Sharpe ratios of DRP and Static Risk Parity included zero. The observed differences therefore cannot be treated as statistically significant. The maximum-drawdown results also differed across portfolio specifications, so the findings do not show that variance-based DRP consistently provides better drawdown protection than every benchmark.

CVaR-DA produced lower maximum drawdowns than the unlevered variance-based risk parity strategies in both investment universes. The reduction was more evident in the multi-asset portfolio. This result came with substantially higher turnover, indicating a practical trade-off between downside-risk control and portfolio adjustment. CVaR-DA should therefore be considered as a method for controlling portfolio-level tail risk rather than as a strategy that improves every performance measure.

Overall, the results suggest that rolling risk estimates can make portfolio allocations more responsive to changes in market conditions. Variance-based DRP offered higher point estimates of risk-adjusted performance with low turnover, whereas CVaR-DA placed greater emphasis on losses in the lower tail of the return distribution. The choice between these approaches depends on whether the investor gives greater weight to risk-adjusted return, drawdown control, or implementation costs.

There are several limitations that provide directions for further research. First, the CVaR-DA formulation used in this study minimizes portfolio-level CVaR rather than formally equalizing marginal CVaR contributions across assets. Second, the Static Risk Parity (SRP) benchmark was estimated using the full-sample covariance matrix and therefore was not strictly out of sample. Future research should construct the static benchmark using only information available before the evaluation period. Future research could develop a true CVaR-based equal-risk-contribution formulation analogous to the variance-based ERC conditions presented in Equations (4) and (5).

Appendix A.1

Table A1. Sensitivity analysis—Dynamic RP (vol-targeted) Sharpe ratio and maximum drawdown across target volatility and leverage cap. The volatility-targeting restriction was rarely enforceable at that target volatility level, according to leverage cap values with equivalent outcomes.

Target Vol	Leverage Cap	Universe A Sharpe	Universe A MDD	Universe B Sharpe	Universe B MDD
8%	2	1.5008	−0.1079	0.5013	−0.1793
8%	3–∞	1.5008	−0.1079	0.4988	−0.1793
10%	2	1.4579	−0.1376	0.4640	−0.2235
10%	3	1.4579	−0.1376	0.4503	−0.2235
10%	4–∞	1.4579	−0.1376	0.4571	−0.2235
12%	2	1.4294	−0.1668	0.4447	−0.2659
12%	3	1.4294	−0.1668	0.4292	−0.2659
12%	4–∞	1.4294	−0.1668	0.4292	−0.2659
15%	2	1.3975	−0.2102	0.4812	−0.3088
15%	3	1.4008	−0.2102	0.4049	−0.3263
15%	4	1.4008	−0.2102	0.3985	−0.3263
15%	∞	1.4008	−0.2102	0.4014	−0.3263

Table A1. Sensitivity analysis—Dynamic RP (vol-targeted) Sharpe ratio and maximum drawdown across target volatility and leverage cap. The volatility-targeting restriction was rarely enforceable at that target volatility level, according to leverage cap values with equivalent outcomes.

Target Vol	Leverage Cap	Universe A Sharpe	Universe A MDD	Universe B Sharpe	Universe B MDD
8%	2	1.5008	−0.1079	0.5013	−0.1793
8%	3–∞	1.5008	−0.1079	0.4988	−0.1793
10%	2	1.4579	−0.1376	0.4640	−0.2235
10%	3	1.4579	−0.1376	0.4503	−0.2235
10%	4–∞	1.4579	−0.1376	0.4571	−0.2235
12%	2	1.4294	−0.1668	0.4447	−0.2659
12%	3	1.4294	−0.1668	0.4292	−0.2659
12%	4–∞	1.4294	−0.1668	0.4292	−0.2659
15%	2	1.3975	−0.2102	0.4812	−0.3088
15%	3	1.4008	−0.2102	0.4049	−0.3263
15%	4	1.4008	−0.2102	0.3985	−0.3263
15%	∞	1.4008	−0.2102	0.4014	−0.3263

Appendix A.2

Table A2. Sensitivity of CVaR-DA to rolling-window length and CVaR confidence level.

Window (Months)	α	Sharpe (A)	MDD (A)	Turnover (A)	Sharpe (B)	MDD (B)	Turnover (B)
12	0.90	1.4049	−0.2180	0.3386	0.6234	−0.1562	0.3384
12	0.95	1.4053	−0.2180	0.3387	0.6335	−0.1562	0.3370
12	0.99	1.4047	−0.2180	0.3387	0.6303	−0.1562	0.3414
24	0.90	1.1965	−0.1589	0.1735	0.5622	−0.1302	0.1324
24	0.95	1.1816	−0.1453	0.1851	0.6958	−0.1288	0.1124
24	0.99	1.1824	−0.1453	0.1859	0.6959	−0.1288	0.1125
36	0.90	1.0811	−0.1690	0.1136	0.4733	−0.1290	0.0675
36	0.95	1.0006	−0.1749	0.1010	0.6617	−0.1321	0.0439
36	0.99	1.0063	−0.1753	0.0985	0.6977	−0.1361	0.0476
60	0.90	1.1396	−0.1619	0.0950	0.2708	−0.1210	0.0488
60	0.95	1.0732	−0.1786	0.0735	0.4523	−0.1411	0.0483
60	0.99	1.1116	−0.1753	0.0518	0.5697	−0.1486	0.0441

Table A2. Sensitivity of CVaR-DA to rolling-window length and CVaR confidence level.

Window (Months)	α	Sharpe (A)	MDD (A)	Turnover (A)	Sharpe (B)	MDD (B)	Turnover (B)
12	0.90	1.4049	−0.2180	0.3386	0.6234	−0.1562	0.3384
12	0.95	1.4053	−0.2180	0.3387	0.6335	−0.1562	0.3370
12	0.99	1.4047	−0.2180	0.3387	0.6303	−0.1562	0.3414
24	0.90	1.1965	−0.1589	0.1735	0.5622	−0.1302	0.1324
24	0.95	1.1816	−0.1453	0.1851	0.6958	−0.1288	0.1124
24	0.99	1.1824	−0.1453	0.1859	0.6959	−0.1288	0.1125
36	0.90	1.0811	−0.1690	0.1136	0.4733	−0.1290	0.0675
36	0.95	1.0006	−0.1749	0.1010	0.6617	−0.1321	0.0439
36	0.99	1.0063	−0.1753	0.0985	0.6977	−0.1361	0.0476
60	0.90	1.1396	−0.1619	0.0950	0.2708	−0.1210	0.0488
60	0.95	1.0732	−0.1786	0.0735	0.4523	−0.1411	0.0483
60	0.99	1.1116	−0.1753	0.0518	0.5697	−0.1486	0.0441

Appendix A.3

Table A3. Portfolio concentration based on the Herfindahl–Hirschman Index (HHI).

Strategy	Mean HHI	Min HHI	Max HHI	Equal-Weight HHI (1/N)	Ratio
Dynamic RP—A	0.0910	0.0909	0.0911	0.0909	1.00×
CVaR-DA—A	0.4704	0.2039	0.9471	0.0909	5.17×
Dynamic RP—B	0.1429	0.1429	0.1429	0.1429	1.00×
CVaR-DA—B	0.5355	0.3146	0.9025	0.1429	3.75×

Table A3. Portfolio concentration based on the Herfindahl–Hirschman Index (HHI).

Strategy	Mean HHI	Min HHI	Max HHI	Equal-Weight HHI (1/N)	Ratio
Dynamic RP—A	0.0910	0.0909	0.0911	0.0909	1.00×
CVaR-DA—A	0.4704	0.2039	0.9471	0.0909	5.17×
Dynamic RP—B	0.1429	0.1429	0.1429	0.1429	1.00×
CVaR-DA—B	0.5355	0.3146	0.9025	0.1429	3.75×

Appendix A.4

Table A4. Net Sharpe ratios under alternative transaction-cost assumptions.

Strategy	Cost (bps)	Sharpe Net (A)	Sharpe Net (B)
Dynamic RP	5	1.4755	0.7454
CVaR-DA	5	1.3938	0.6104
Dynamic RP	10	1.4754	0.7454
CVaR-DA	10	1.3827	0.5870
Dynamic RP	20	1.4751	0.7453
CVaR-DA	20	1.3604	0.5401

Table A4. Net Sharpe ratios under alternative transaction-cost assumptions.

Strategy	Cost (bps)	Sharpe Net (A)	Sharpe Net (B)
Dynamic RP	5	1.4755	0.7454
CVaR-DA	5	1.3938	0.6104
Dynamic RP	10	1.4754	0.7454
CVaR-DA	10	1.3827	0.5870
Dynamic RP	20	1.4751	0.7453
CVaR-DA	20	1.3604	0.5401