Portfolio Management Simulation

Asset Correlations

Stocks ↔ Bonds -0.20

Stocks ↔ Gold 0.10

Risk-free rate 2.0%

Simulation

Show efficient frontier

Max-Sharpe Portfolio

Return

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Volatility

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Sharpe ratio

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Stocks 33% Bonds 33% Gold 34%

How it works

Three assets — Stocks (μ=9%, σ=18%), Bonds (μ=4%, σ=6%) and Gold (μ=6%, σ=15%) — are combined into thousands of random long-only portfolios with weights w_i ≥ 0, Σw_i = 1 (drawn from a Dirichlet distribution so every point on the simplex is equally likely).

Portfolio return:   R_p = Σ w_i μ_i
Portfolio variance: σ_p² = Σ_i Σ_j w_i w_j Cov(i,j)
Cov(i,j) = ρ_ij σ_i σ_j
Sharpe ratio:       S = (R_p − R_f) / σ_p

Correlation sliders — reshape the covariance matrix Cov(i,j); more negative Stocks↔Bonds correlation bends the cloud left, shrinking achievable risk for the same return (the diversification effect).
Risk-free rate — shifts which portfolio maximises the Sharpe ratio (the tangency portfolio on the Capital Market Line).
Cloud axes — X = volatility (risk), Y = expected return, Z = Stocks weight; colour ramps blue → gold with the Sharpe ratio.
Efficient frontier line — for each volatility bucket, the highest-return portfolio found in the sample; the true frontier is the smooth curve this scatter approximates as N grows.
Gold marker — the single portfolio in the current sample with the highest Sharpe ratio (best risk-adjusted return).

Max-Sharpe portfolio Efficient frontier Colour: low → high Sharpe

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