Calculator inputs
Use two to six engineering projects, process options, or design paths. Returns and volatilities should use matching time units.
Example data table
This sample shows one engineering-style portfolio mix for design programs, capital projects, or research pathways.
| Project | Expected Return | Volatility | Example Notes |
|---|---|---|---|
| Grid Upgrade | 10.80% | 12.50% | Stable infrastructure program with moderate uncertainty. |
| Sensor Network | 13.20% | 18.30% | Higher upside but stronger deployment variability. |
| Efficiency Retrofit | 8.90% | 10.20% | Lower return with strong risk control. |
| Automation Line | 11.70% | 15.60% | Balanced option for cost and productivity gains. |
Formula used
The calculator converts each correlation input into covariance with this relationship:
Covariance(i,j) = Volatility(i) × Volatility(j) × Correlation(i,j)
Portfolio expected return is the weighted sum of asset returns:
E(Rp) = Σ wi μi
Portfolio variance is calculated with the covariance matrix:
σp2 = wT Σ w
The efficient frontier under unrestricted weights is generated with:
σp2(R) = (A R2 − 2 B R + C) / D
Where:
A = 1TΣ−11, B = 1TΣ−1μ, C = μTΣ−1μ, D = AC − B2
The maximum Sharpe portfolio uses the risk-free rate and normalizes:
w ∝ Σ−1(μ − rf1)
How to use this calculator
- Select the number of projects or assets you want to model.
- Enter a label, expected return, and volatility for each item.
- Fill the correlation matrix with values from -1 to 1.
- Provide a risk-free rate if you want a Sharpe ratio comparison.
- Enter a target return for a specific optimized portfolio solution.
- Press Build frontier to calculate portfolio mixes and frontier points.
- Review the chart, weight table, and covariance matrix.
- Download CSV or PDF outputs for reporting or documentation.
FAQs
1. What does an efficient frontier show?
It shows the best expected return available for each risk level. Portfolios below the frontier are inefficient because another mix offers more return for the same volatility.
2. Why use this in engineering decisions?
Engineering teams often compare projects with uncertain outcomes. This approach helps balance performance targets against variability, correlation, and portfolio-level diversification effects.
3. What inputs matter most?
Expected return, volatility, and correlation drive the model. Small correlation changes can significantly alter diversification benefits and the final frontier shape.
4. Does the calculator allow short positions?
Yes. The optimization uses unrestricted analytical formulas, so some weights may become negative. Negative values represent short exposure or an offsetting allocation.
5. What is the global minimum variance portfolio?
It is the portfolio with the lowest possible variance among all feasible weight combinations. It often becomes the starting point of the efficient branch.
6. Why can the matrix become singular?
A singular matrix usually appears when projects are nearly identical or perfectly correlated. The optimizer then cannot separate exposures cleanly, so inversion fails.
7. What does the maximum Sharpe portfolio mean?
It identifies the mix with the highest excess return per unit of total risk, using your risk-free rate as the baseline benchmark.
8. Should all inputs use the same period?
Yes. Returns, volatilities, and the risk-free rate must share the same annual, quarterly, or monthly basis for results to stay consistent.