Portfolio Optimization Model Calculator

Balance risk and return with flexible inputs. Compare efficient portfolios, target returns, and Sharpe ratios. Plan better mixes using clear graphs and simple reports.

Calculator Inputs

Use the responsive grid below. It shows three columns on large screens, two on smaller screens, and one on mobile.

Use Refresh Asset Grid after changing this value.
Unchecked mode clips negative weights and renormalizes them.

Asset Assumptions

Asset 1

Asset 2

Asset 3

Asset 4

Correlation Matrix

Enter only the upper triangle. The lower triangle mirrors those values automatically.

Asset Equity Fund Bond Fund REIT Fund Gold Fund
Equity Fund
Bond Fund
0.20
REIT Fund
0.35
0.15
Gold Fund
0.10
0.05
0.12

Example Data Table

Use this sample set if you want a quick demonstration before entering your own expected returns, volatilities, and correlations.

Asset Expected Return (%) Volatility (%)
Equity Fund 9.20 18.00
Bond Fund 4.80 7.00
REIT Fund 7.10 14.00
Gold Fund 5.20 12.00
Correlation Example Equity Fund Bond Fund REIT Fund Gold Fund
Equity Fund 1.00 0.20 0.35 0.10
Bond Fund 0.20 1.00 0.15 0.05
REIT Fund 0.35 0.15 1.00 0.12
Gold Fund 0.10 0.05 0.12 1.00

Formula Used

This calculator follows mean-variance portfolio theory and builds a covariance matrix from your volatility and correlation inputs.

1) Covariance between two assets

Cov(i,j) = Vol(i) × Vol(j) × Corr(i,j)

2) Portfolio expected return

E(Rp) = Σ [w(i) × E(Ri)]

3) Portfolio variance and volatility

Var(Rp) = w' × Σ × w and σp = √Var(Rp)

4) Minimum variance weights

w = Σ⁻¹1 / (1'Σ⁻¹1)

5) Maximum Sharpe ratio weights

w = Σ⁻¹(μ - rf1) / [1'Σ⁻¹(μ - rf1)]

6) Target return weights

The target-return model uses the closed-form efficient frontier solution with constants A, B, C, and D.

Important note for no-short mode

When short selling is disabled, negative weights are clipped to zero and the remaining weights are renormalized. That is practical for planning, but it is not a full quadratic-programming solver.

How to Use This Calculator

  1. Choose how many assets you want to include, then refresh the asset grid.
  2. Enter a total investment amount, risk-free rate, optimization goal, and target return if needed.
  3. Add each asset name, expected annual return, and annual volatility.
  4. Fill the upper half of the correlation matrix. The lower half mirrors those entries.
  5. Decide whether short selling should be allowed.
  6. Press Optimize Portfolio to calculate the best weights.
  7. Review the summary, allocation table, model comparison, and Plotly charts.
  8. Download the result as CSV or PDF for reporting or later review.

FAQs

1) What does this calculator optimize?

It estimates portfolio weights using mean-variance theory. You can solve for minimum variance, maximum Sharpe ratio, or an efficient portfolio that aims for a chosen expected return.

2) Why do I need both volatility and correlation?

Volatility measures each asset’s individual risk. Correlation shows how assets move together. The model combines both to build covariance values and estimate total portfolio risk.

3) What does the Sharpe ratio mean?

The Sharpe ratio compares excess return against volatility. A higher value means the portfolio is expected to produce more return for each unit of total risk taken.

4) What happens when short selling is disabled?

The calculator removes negative weights and rescales the remaining positions to sum to 100%. This creates practical long-only weights, though it is an approximation rather than a strict optimization routine.

5) Why can my target return miss slightly?

That usually happens when short selling is turned off. After clipping negative weights, the model renormalizes the portfolio, so the achieved return can move a little away from the requested target.

6) Can I use monthly assumptions instead of annual values?

Yes, but keep all inputs on the same time scale. If you use monthly returns, monthly volatilities, and a monthly risk-free rate, the model stays internally consistent.

7) What does risk contribution show?

Risk contribution estimates how much each asset adds to total portfolio variance. It helps identify whether a small position is actually contributing a large share of portfolio risk.

8) Is this enough for real investment decisions?

It is a strong planning tool, but real decisions should also consider fees, taxes, liquidity, turnover, constraints, and scenario testing. Use it as an analytical model, not as sole advice.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.