Calculate Volatility of Equally Weighted Portfolio | Financial Risk Tool
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Accurately calculate volatility of equally weighted portfolio allocations using our professional-grade financial tool. Understand how diversification reduces unsystematic risk and visualize the impact of asset correlation on your total portfolio variance.
Portfolio Volatility (σp)
12.17%
Diversification Benefit
7.83%
Risk removed
Systematic Limit
10.95%
Min possible risk (N→∞)
Variance Ratio
37.0%
Portfolio Var / Asset Var
Formula Used: σp = σ × √ [ (1/N) + ((N-1)/N) × ρ ]
Figure 1: Portfolio Volatility vs. Number of Assets (Diversification Curve)
| Scenario |
Correlation (ρ) |
Number of Assets |
Resulting Volatility |
Table 1: Sensitivity Analysis based on current inputs
What is "calculate volatility of equally weighted portfolio"?
To calculate volatility of equally weighted portfolio implies determining the standard deviation of returns for a portfolio where every asset holds the same monetary value. In modern portfolio theory, this calculation is crucial because it quantifies the benefits of diversification.
This metric is widely used by risk managers, quantitative analysts, and individual investors who maintain "naive" diversification strategies (1/N portfolios). Unlike market-cap weighted indexes, an equally weighted approach gives every stock equal influence on the total risk. Understanding how to calculate volatility of equally weighted portfolio helps investors realize that adding more assets reduces risk, but only up to a certain floor defined by the average correlation.
Formula and Mathematical Explanation
The standard formula to calculate volatility of equally weighted portfolio simplifies the complex matrix algebra of variance-covariance into a manageable equation, assuming average variances and correlations.
The General Formula:
σp = σ × √ [ (1/N) + ( (N – 1) / N ) × ρ ]
Where:
| Variable |
Meaning |
Typical Unit |
Typical Range |
| σp |
Portfolio Volatility |
Percentage (%) |
5% – 50% |
| N |
Number of Assets |
Integer |
2 – 500+ |
| σ |
Avg Asset Volatility |
Percentage (%) |
10% – 100% |
| ρ (Rho) |
Avg Correlation |
Decimal |
-1.0 to 1.0 |
Table 2: Variables Definition for Volatility Calculation
Practical Examples
Example 1: The Diversification Benefit
An investor holds 25 stocks. The average volatility of a single stock is 30%, and the average correlation between them is 0.4.
- Inputs: N = 25, σ = 30%, ρ = 0.4
- Calculation: Using the tool to calculate volatility of equally weighted portfolio, the term under the square root becomes (1/25) + (24/25)*0.4 = 0.04 + 0.384 = 0.424.
- Result: σp = 30% × √0.424 ≈ 19.53%.
The risk dropped from 30% to 19.53% simply by diversifying, without reducing expected returns (assuming equal expected returns).
Example 2: High Correlation Market Crash
During a market panic, correlations often rise. Suppose correlation (ρ) jumps to 0.9.
- Inputs: N = 25, σ = 30%, ρ = 0.9
- Result: σp jumps to approximately 28.6%.
This demonstrates that diversification fails when correlations approach 1.0, a key insight when you calculate volatility of equally weighted portfolio.
How to Use This Calculator
- Enter Number of Assets: Input the total count of distinct positions in your portfolio.
- Input Average Volatility: Estimate the average annualized standard deviation of the individual assets (e.g., 20% for large-cap stocks).
- Set Average Correlation: Input the pairwise correlation coefficient. A value of 0 implies no relationship, while 1 implies they move perfectly in sync.
- Analyze Results: The tool will instantly calculate volatility of equally weighted portfolio.
- Systematic Limit: This is the theoretical minimum risk you can achieve with infinite assets given the current correlation.
- Diversification Benefit: The difference between the average asset risk and the portfolio risk.
Key Factors That Affect Results
When you calculate volatility of equally weighted portfolio, several financial dynamics influence the output:
- Correlation Coefficient (ρ): This is the most sensitive variable. A lower correlation dramatically increases the effectiveness of diversification. If ρ = 0, risk decreases with the square root of N.
- Number of Assets (N): Adding assets reduces risk quickly at first (e.g., going from 1 to 10 stocks), but the marginal benefit diminishes rapidly. The calculator visualizes this "elbow" in the chart.
- Individual Asset Volatility (σ): If the underlying assets are highly volatile (e.g., crypto or small-cap stocks), the portfolio floor will naturally be higher.
- Market Regimes: In normal markets, correlations might be 0.3. In crises, they converge to 1.0. You should calculate volatility of equally weighted portfolio under different regime assumptions.
- Weighting Scheme: This calculator assumes Equal Weighting (1/N). If you use Capitalization Weighting, a few large assets dominate the risk, usually resulting in higher volatility than the "ideal" diversified model.
- Time Horizon: Volatility scales with the square root of time. Ensure your inputs (annualized volatility) match your desired output timeframe.
Frequently Asked Questions (FAQ)
Why calculate volatility of equally weighted portfolio instead of market weighted?
Equally weighted portfolios often outperform market-weighted ones over long periods due to the "size factor" and rebalancing effects. Calculating its risk ensures you aren't unknowingly taking on excessive volatility.
What happens if Correlation is 1.0?
If ρ = 1.0, there is no diversification benefit. The portfolio volatility will exactly equal the average asset volatility, regardless of how many assets you own.
What is the "Systematic Limit"?
As N approaches infinity, the term (1/N) vanishes, and the formula simplifies to σ × √ρ. This is the non-diversifiable market risk that cannot be eliminated.
Does this apply to bonds and crypto?
Yes. As long as you have the average volatility and correlation estimates for those asset classes, you can calculate volatility of equally weighted portfolio for any asset type.
How do I find the average correlation?
You can calculate a correlation matrix of your assets and take the average of the off-diagonal elements. For US equities, 0.3 to 0.5 is a common historical range.
Is standard deviation the same as volatility?
In finance, volatility usually refers to the annualized standard deviation of returns. The terms are often used interchangeably in this context.
Can correlation be negative?
Yes. If ρ is negative, assets move in opposite directions, providing a "hedge" that reduces risk even faster than uncorrelated assets.
Why is the chart curved?
The chart is a hyperbola-like decay curve. The benefit of adding the 2nd stock is massive compared to adding the 100th stock. This is the law of diminishing returns in diversification.
Related Tools and Internal Resources
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{ name: "High Correlation (ρ=0.8)", r: 0.8, assets: n, v: calculateVol(n, vol, 0.8) },
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