The impact of regulation-based constraints on portfolio selection: The Spanish case

Portfolio selection has been a topic that gained traction since the 1950s with Markowitz's portfolio theory (1952), which provided a foundation for future research. His work was further extended and other theories, such as Sharpe's diagonal model (1963) were huge advancements for the portfolio selection problem, and most importantly, the Capital Asset Pricing Model (CAPM) (Lintner, 1965; Mossin, 1966; Sharpe, 1964) and the Arbitrage Pricing Theory (APT) (Ross, 1976) provided some of the most used models nowadays.

In the last decades, there has been a noticeable increase in the number of research papers where the main focus is constrained portfolio selection (see, for example, Asanga et al., 2014; Clarke et al., 2002; Basak and Croitoru, 2000; Pavlova and Rigobon, 2008; Detemple and Murthy, 1997; Cornet and Gopalan, 2010 among others), in order to obtain either more efficient sets, or portfolios that resemble reality better, but most of the constraints applied are observed in the market and the way it operates.

In this paper, we use an existing regulation regarding Spanish investment funds and use it as the constraining item over a set of simulated portfolios, to comprehend the difference law can make in terms of efficiency. We try to obtain evidence of whether the regulations imposed on investment funds translate into greater protection for investors or if, on the contrary, they are totally inefficient.

One of the motivations to test the Spanish investment funds regulation is the performance of these entities in Spain. Between 2005 and 2020, the returns showcased by the Spanish funds were relatively low, and worse than the IBEX 35 index, during the mentioned time-lapse the average annual returns were 1.9 percent (Fernandez et al., 2021). This low performance could have its source for multiple reasons, although as it is mentioned in Fernandez et al. (2021), management fees could be shrinking the funds' portfolio returns. However, we cannot rule out the fact that it could be due to an improper regulation in terms of constraints, which instead of protecting the investors, provides them with worse performances than the ones they would get without any regulation.

The main contribution of this work is to study the efficiency of the regulatory constraints imposed on Spanish investment funds, providing results from two different scenarios where the results from a group of constrained portfolios are compared to their non-constrained counterparts. In this way, we propose to advance in the study of the possible causes of the low performance that these investment products had over the last decade in comparison with other investment strategies, revealing whether the core issue is located in the corresponding regulation applied, or whether the results can be attributed to other factors.

The rest of the paper is organized as follows. Section "Constrained portfolio selection: a literature review" includes a literature review of the most popular constraints used by the financial literature. Section "Investment funds and portfolio selection" includes an overview of the Spanish investment funds, and their regulation and performance. Section "Constraints, data, and simulated scenarios" includes the data and constraints we used for the study and the created scenarios. Section "Results" presents the results of our tests, and finally, these results are discussed in section "Conclusions and future research lines".

The paper surveys constraints commonly applied to portfolio selection to improve realism and efficiency beyond classical mean-variance optimization. It revisits the Markowitz model with non-negativity and full-investment constraints, then focuses on the cardinality constraint (Limited Assets Markowitz, LAM), which limits the number of assets and imposes buy-in thresholds. LAM transforms the problem into an NP-hard one; exact methods (branch-and-cut, tailored pivoting, Lagrangian methods) and numerous heuristics (genetic algorithms, tabu search, simulated annealing, local search, perspective cuts) are reviewed with references (Bienstock, 1996; Bertsimas and Shioda, 2009; Li et al., 2006; Shaw et al., 2008; Schaerf, 2002; Chang, 2000; Frangioni and Gentile, 2006; Cesarone et al., 2007; Le Thi and Moeini, 2014). Studies applying cardinality to mutual fund portfolios and probabilistic models with multiple constraints (e.g., Yusuf et al., 2019) generally report improved outcomes.

Short-sales constraints are discussed as a classical restriction. Prior work shows that permitting short sales can increase returns but also risk substantially; no-short-sale constraints often reduce diversification and can still yield portfolios with smaller actual risk (Pogue, 1970; Green and Hollifield, 1992; Board and Sutcliffe, 1994; Jagannathan and Ma, 2003; Fan et al., 2012; Alexander et al., 2009; Kim et al., 2016).

Other market-inspired constraints include leverage limits (which alter risk allocations between risky and risk-free assets), transaction costs, VaR and chance constraints, liquidity and return-risk control, and sector or lot-size constraints (Bradfield and Raubenheimer, 2001; Chen et al., 2018, 2020; Grauer and Shen, 2000; Soleimani et al., 2009; Xue et al., 2019; Kaucic, 2019). Fees and costs are highlighted as key determinants of mutual fund performance (Fama and French, 2008). The literature also notes regulatory or life-cycle constraints used in pension systems (e.g., Mexico’s Retirement Savings System) and MIFID risk-profiling context, though these are outside this paper’s scope (García-Medina et al., 2021).

Regulatory constraints: The study applies Spain’s Real Decreto 1082/2012 (Article 50) as binding diversification constraints. At inception, all simulated portfolios satisfy: (i) any single asset ≤ 5% of portfolio value (implying at least 20 assets), and (ii) up to 10% per asset allowed provided the sum of weights exceeding 5% does not exceed 40% (minimum 16 assets: typically twelve ≤5% and up to four ≤10%). A 0.5% transaction cost per trade is included to reflect market frictions.

Data: Constituent stocks of the S&P 500 (NASDAQ and NYSE) are used, chosen for high liquidity suitable for large funds. The sample spans 1995–2020 (25 years). Simulations are run over rolling multi-year windows of 5 years (six samples: 1995–2000, 2000–2005, 2002–2007, 2007–2012, 2009–2014, 2015–2019) and 10 years (three samples: 1995–2005, 2002–2012, 2009–2020).

Simulation design: For each window, 1,000 random portfolios are generated that satisfy the regulatory constraints at time 0. Two evolution scenarios are compared, starting from the same initial weights:

• Unconstrained (buy-and-hold): No rebalancing to maintain constraints; weights drift freely. Portfolio is liquidated at the end of 5 or 10 years.
• Regulation-constrained (monthly monitoring and rebalancing): Each month, constraints are checked and enforced via minimal trades: (a) any asset exceeding 10% is sold down to 9%, proceeds redistributed among remaining assets while respecting all limits; (b) if the sum of weights of assets exceeding 5% surpasses 40%, assets in that set are sequentially reduced to 4.5% until the 40% cap is met. All trades incur 0.5% costs.

Evaluation metrics: For each portfolio and scenario, the end value of 1 invested dollar and the Sharpe ratio of monthly returns are computed. Scatter plots compare constrained (x-axis) vs. unconstrained (y-axis) outcomes; histograms display the distribution of Sharpe ratio differences (unconstrained minus constrained) to visualize which scenario performs better. Summary statistics report the percentage of cases where constrained portfolios outperform in total return and Sharpe ratio (Tables 2 and 3).

Five-year windows (1995–2000; 2000–2005; 2002–2007; 2007–2012; 2009–2014; 2015–2019):

• End value: In all six periods, most portfolios lie below the 45-degree line, indicating higher end values under constraints. Periods around the global financial crisis show lower end values overall, with recovery in 2009–2014.
• Sharpe ratio: Even stronger dominance of constrained portfolios; many points below the line, especially in 1995–2000 and 2009–2014. Histograms show the peak Sharpe ratio advantage typically between 0.15–0.20 in favor of constrained portfolios (≈0.4 in 1995–2000).
• Percent outperforming (constrained vs. unconstrained): Total return: 88%, 80.4%, 83.7%, 88.4%, 89.2%, 86.4% for the six 5-year windows. Sharpe ratio: 98.9%, 88.5%, 90.8%, 88.6%, 94.1%, 91.6%.

Ten-year windows (1995–2005; 2002–2012; 2009–2020):

• End value: Constrained portfolios generally attain higher terminal value; though more unconstrained portfolios appear close to the frontier than in 5-year tests, differences are often small (notably in 2009–2020).
• Sharpe ratio: Constrained portfolios dominate in 1995–2005 and 2002–2012; 2009–2020 shows a narrower margin with more unconstrained portfolios slightly ahead, consistent with a prolonged bull market benefiting buy-and-hold concentration in strong performers. Sharpe ratios trend lower across later samples.
• Percent outperforming (constrained vs. unconstrained): Total return: 86.6% (1995–2005), 75.4% (2002–2012), 72.2% (2009–2020). Sharpe ratio: 99.4% (1995–2005), 83.1% (2002–2012), 63.7% (2009–2020).

Overall: Across 9 samples (5- and 10-year windows), regulatory constraints consistently improve risk-adjusted performance and often improve end value. Advantages are largest in volatile or crisis-affected periods; advantages narrow in extended bull markets. Diversification enforced by constraints lowers volatility, yielding higher Sharpe ratios even when unconstrained portfolios occasionally achieve higher raw returns.

The study’s core question—whether regulatory diversification constraints improve long-term portfolio efficiency—is supported by simulations: constrained portfolios most often deliver higher Sharpe ratios and frequently higher terminal values. The constraints enforce diversification (minimum breadth, caps on concentration), which reduces volatility and downside risk. This risk reduction translates into superior risk-adjusted returns, addressing the hypothesis that regulation can protect investors and enhance efficiency. The periods surrounding crises show especially strong benefits, while long bull markets (2009–2020) diminish the edge for constraints as concentrated winners in buy-and-hold portfolios can dominate.

These findings imply that Spain’s regulatory limits are not the source of historically low mutual fund performance; rather, other factors such as management and transaction fees likely play larger roles, aligning with prior literature. The results also suggest that individual investors could emulate such regulatory diversification rules to improve portfolio efficiency.

The paper shows that applying Spain’s investment fund regulatory constraints (Real Decreto 1082/2012, Article 50) to equity portfolios generally improves efficiency: constrained portfolios outperform in total return for a large majority of cases and in Sharpe ratio across most simulated 5- and 10-year windows between 1995 and 2020. Benefits are robust across market regimes, with especially strong gains in turbulent periods. The findings indicate that regulatory diversification constraints are not responsible for the low historical returns of Spanish funds; management fees and other costs are more plausible drivers.

Future research directions include: testing the same regulation on European and other regional markets (e.g., Asia-Pacific, Japan), evaluating other regulatory frameworks (e.g., U.S. Investment Company Act), varying threshold levels to probe the diversification-performance trade-off, and extending beyond large-cap universes to assess liquidity constraints and market breadth effects.

The main limitation is the asset universe: only current S&P 500 stocks are used, chosen for liquidity, which may not reflect smaller-cap opportunities or the exact Spanish market universe. Results derive from simulated random portfolios with assumed monthly rebalancing and a fixed 0.5% transaction cost; management fees typical of mutual funds are not incorporated (beyond trading costs). The findings for 2009–2020 warrant further analysis given the long bull market dynamic that can favor buy-and-hold concentration.