Risk Diversification Calculator 🧩
Analyze the benefits of **diversification** by calculating the **Expected Return** and **Portfolio Risk (Standard Deviation)** for a two-asset portfolio.
Modern Portfolio Theory Formulas
This calculator is based on the core mathematics of **Modern Portfolio Theory (MPT)** for a two-asset portfolio.
1. Expected Portfolio Return ($$E(R_p)$$)
The portfolio's return is the weighted average of the individual asset returns.
E(Rₚ) = (wₐ × Rₐ) + (wᵦ × Rᵦ)
2. Portfolio Standard Deviation ($$\sigma_p$$) - Risk
The portfolio's risk is calculated using the weights, individual risks, and the correlation coefficient (ρ).
$$\sigma_p = \sqrt{ w_A^2\sigma_A^2 + w_B^2\sigma_B^2 + 2w_A w_B \rho \sigma_A \sigma_B }$$
Where:
- $$w_A$$ and $$w_B$$ are the weights of Asset A and Asset B ($$w_A + w_B = 1$$)
- $$R_A$$ and $$R_B$$ are the expected returns
- $$\sigma_A$$ and $$\sigma_B$$ are the standard deviations (risk)
- $$\rho$$ (rho) is the correlation coefficient
Master Portfolio Management with the Risk Diversification Calculator
Risk management is paramount in investing. The primary goal of smart **portfolio management** is not just to maximize returns, but to achieve those returns with the lowest possible level of risk. Our **Risk Diversification Calculator** is an essential tool for applying the principles of **Modern Portfolio Theory (MPT)**, allowing you to quantify the precise benefits of combining different assets.
Understanding Portfolio Risk: Standard Deviation
In finance, **risk** is defined as volatility, or the tendency of an asset's return to deviate from its expected value. This is mathematically measured by the **Standard Deviation**. A higher standard deviation means higher risk and greater unpredictability. By using this calculator, you can see how blending two volatile assets can result in a final portfolio with surprisingly low volatility—the magic of diversification.
The Key to Diversification: The Correlation Coefficient (ρ)
The entire benefit of diversification hinges on the **Correlation Coefficient (ρ)**. This metric measures how two assets move in relation to each other, ranging from -1.0 to +1.0:
- ρ = +1.0 (Perfect Positive Correlation): The assets move in lockstep. There is **no diversification benefit**.
- ρ = 0 (No Correlation): The assets move independently. There is a significant risk reduction benefit.
- ρ = -1.0 (Perfect Negative Correlation): The assets move in exactly opposite directions. This offers the **maximum diversification benefit** and the greatest reduction in **portfolio standard deviation**.
By inputting a low or negative correlation (like blending stocks and bonds), you can see how the portfolio's total risk can be lower than the risk of either asset individually, allowing you to build a true optimal portfolio.
Calculating the Diversification Effect
The calculator provides a unique metric: the **Diversification Effect**. This shows the actual amount of risk reduction (in percentage points) achieved by your chosen asset mix and correlation, compared to a simple weighted average of the two assets' risks. This quantified risk reduction demonstrates the non-linear benefit of combining assets with less-than-perfect correlation. Use this tool to test various asset allocations—from 100% Asset A to 100% Asset B—and identify the combination that lands on the **efficient frontier**, giving you the best return for a given level of risk.