Advanced Mean Variance Optimizer Calculator

Balance return targets with variance-aware portfolio allocation models. Compare weights, volatility, and estimated portfolio efficiency. Turn matrix inputs into clear allocation insights for planning.

Calculator Inputs

Overall page flow stays single-column. The calculator fields use a responsive three, two, and one column grid.

Investment Amount

Target Portfolio Return (%)

Risk-Free Rate (%)

Asset 1 Name

Asset 2 Name

Asset 3 Name

Asset 1 Expected Return (%)

Asset 2 Expected Return (%)

Asset 3 Expected Return (%)

Asset 1 Std. Deviation (%)

Asset 2 Std. Deviation (%)

Asset 3 Std. Deviation (%)

Correlation 1-2

Correlation 1-3

Correlation 2-3

Display Precision

Example Data Table

Asset	Expected Return (%)	Std. Deviation (%)
System A	8.00	10.00
System B	12.00	16.00
System C	15.00	22.00

Example correlations: 1-2 = 0.25, 1-3 = 0.10, 2-3 = 0.35

Example target return: 10.00% with an investment amount of 100,000

Formula Used

Portfolio return: Rp = w1r1 + w2r2 + w3r3

Portfolio variance: Var(Rp) = w^T Σ w

Covariance: Cov(i,j) = ρij × σi × σj

Sharpe ratio: (Rp − Rf) / σp

Target-return optimizer: w = Σ^-1(λ1 × 1 + λ2 × μ)

The calculator builds a 3x3 covariance matrix from the standard deviations and correlations. It then inverts that matrix and solves the Lagrange multiplier system for the minimum-variance portfolio meeting the chosen target return.

A, B, and C frontier coefficients are computed from 1^TΣ^-11, 1^TΣ^-1μ, and μ^TΣ^-1μ. Those values also generate the efficient frontier curve shown in the chart.

How to Use This Calculator

Enter the total investment amount.
Provide a target portfolio return in percent.
Enter the risk-free rate for Sharpe ratio comparison.
Type names for the three assets or systems.
Enter each asset’s expected return and standard deviation.
Fill in the pairwise correlations between the assets.
Choose the output precision you prefer.
Click Optimize Portfolio to generate weights, allocations, summary metrics, and the efficient frontier plot.
Use the CSV or PDF buttons to export the visible results.

Frequently Asked Questions

1. What does this optimizer calculate?

It calculates the minimum-variance portfolio for a chosen target return using three assets, their expected returns, volatilities, and correlations.

2. Why can some weights be negative?

Negative values mean the unconstrained solution is using short exposure. This often appears when the target return is aggressive or correlations favor hedged combinations.

3. What is the efficient frontier?

The efficient frontier is the set of minimum-risk portfolios for different target returns. Points above it are infeasible, and points below it are inefficient.

4. What does the Sharpe ratio show?

It compares excess return against portfolio volatility. Higher values generally indicate better return earned per unit of total risk.

5. Why do correlations matter so much?

Correlations control diversification benefit. Lower or negative correlation can reduce overall portfolio variance even when individual assets are volatile.

6. Is this a long-only optimizer?

No. This version solves the unconstrained target-return problem. It does not impose a no-short-selling restriction or upper weight bounds.

7. Can this model be used outside finance?

Yes. Engineering teams can adapt it for risk-return style allocation problems involving projects, systems, energy mixes, or uncertain resource plans.

8. What causes optimization errors?

Invalid correlations, zero volatility, or a singular covariance matrix can break the inversion step. Small input adjustments usually resolve the issue.