Diversification is a core principle in portfolio management, aimed at reducing risk by spreading investments across multiple instruments. However, while adding assets initially provides substantial risk reduction, the benefits begin to diminish as more instruments are included. This article explores the mechanics behind the diminishing marginal benefits of diversification, the impact of correlation among assets, and practical considerations for traders and investors.
Theoretical Foundation of Diversification
The concept of diversification stems from Modern Portfolio Theory (MPT), which suggests that combining assets with low or negative correlation reduces portfolio risk without necessarily sacrificing return. The standard deviation of a portfolio’s returns (a measure of risk) is influenced by:
- The standard deviations of individual assets
- The correlations between asset pairs
- The weight allocations assigned to each asset
In Python, the portfolio variance can be calculated as follows:
import numpy as np
def portfolio_variance(weights, std_devs, correlation_matrix):
weights = np.array(weights)
std_devs = np.array(std_devs)
covariance_matrix = np.outer(std_devs, std_devs) * correlation_matrix
return np.dot(weights, np.dot(covariance_matrix, weights))
The Diminishing Effect of Additional Instruments
Initially, adding an instrument to a portfolio significantly lowers overall risk, especially if it has low correlation with existing holdings. However, as more instruments are added, the incremental reduction in risk diminishes due to the following factors:
1. Correlation Among Instruments
As more instruments are added, the likelihood of introducing additional assets that are highly correlated with existing ones increases. When correlations are high, the new asset contributes little to further risk reduction. In contrast, uncorrelated or negatively correlated assets provide substantial diversification benefits, but such opportunities are limited in real-world markets.
2. Converging Portfolio Risk Toward Systematic Risk
Total risk comprises both idiosyncratic (asset-specific) risk and systematic (market) risk. Diversification effectively reduces idiosyncratic risk, but systematic risk remains unavoidable. As the number of instruments increases, portfolio risk asymptotically approaches systematic risk, limiting further reduction.
3. Practical Constraints: Execution and Costs
While adding assets theoretically improves diversification, practical constraints such as transaction costs, liquidity, and execution complexity counteract benefits. Managing too many instruments may lead to inefficiencies, slippage, and increased exposure to operational risks.
4. Law of Diminishing Marginal Returns
Empirical studies show that substantial diversification benefits can be achieved with a relatively small number of assets. For example, a well-chosen portfolio of 10–20 instruments captures a significant portion of achievable diversification benefits, while adding more beyond this point yields progressively smaller risk reduction.
Empirical Example: Diversification in Equity Markets
A simple empirical test can illustrate this effect. Consider constructing portfolios with increasing numbers of randomly selected stocks. Studies suggest:
- A portfolio of 1 stock carries full idiosyncratic risk.
- Expanding to 5 stocks can reduce volatility by over 50%.
- A 20-stock portfolio achieves about 90% of maximum diversification benefits.
- Beyond 30 stocks, additional diversification provides marginal improvements.
This pattern holds true in various asset classes, including equities, commodities, and forex pairs and is demonstrated with the following python code and graph:
import numpy as np
import matplotlib.pyplot as plt
def diversification_effect(n_max=50, base_risk=1.0, avg_correlation=0.2):
n_values = np.arange(1, n_max + 1)
portfolio_risk = base_risk * np.sqrt((1 + (n_values - 1) * avg_correlation) / n_values)
plt.figure(figsize=(8, 5))
plt.plot(n_values, portfolio_risk, marker='o', linestyle='-', color='b', label='Portfolio Risk')
plt.axhline(y=base_risk * np.sqrt(avg_correlation), color='r', linestyle='--', label='Systematic Risk Limit')
plt.xlabel("Number of Instruments")
plt.ylabel("Portfolio Risk (Normalized)")
plt.title("Diminishing Diversification Benefits")
plt.legend()
plt.grid()
plt.show()
Graph: Diminishing diversification benefits over number of instruments traded simultaneously
Implications for Traders and Portfolio Managers
Understanding diminishing diversification benefits helps traders and portfolio managers optimize their strategies:
- Prioritize Asset Selection: Instead of indiscriminately adding instruments, focus on those with low correlation to existing positions.
- Balance Between Diversification and Concentration: While reducing risk is essential, over-diversification can dilute potential returns.
- Consider Factor Exposure: Assets influenced by similar risk factors (e.g., interest rates, economic cycles) may not provide meaningful diversification.
- Monitor Market Conditions: Correlations can change dynamically, especially during financial crises when traditionally uncorrelated assets may move in tandem.
Diversification is a powerful risk management tool, but its benefits are not unlimited. The incremental risk reduction diminishes as more instruments are added due to correlation effects, systematic risk, and practical constraints. A strategic approach—balancing sufficient diversification with focused asset selection—can enhance portfolio efficiency and improve risk-adjusted returns.
