Portfolio Optimization Calculator
Optimize your investment portfolio for maximum risk-adjusted returns
Market Parameters
Treasury bill or government bond yield
Expected return of market benchmark (e.g., S&P 500)
Portfolio Assets
Portfolio Optimization Results
Risk-Adjusted Performance
Market Comparison (CAPM)
Normalized Asset Allocation
Portfolio Insights
📊 Your portfolio has an expected return of 8.30% with a volatility of 7.59%.
📈 The Sharpe Ratio of 0.698 indicates good risk-adjusted returns.
🎯 Portfolio beta of 0.945 suggests lower volatility compared to the market.
💎 Alpha of -1.31% indicates underperformance relative to market expectations.
Example Portfolio Optimization
Sample Portfolio
Tech Stock: 40% weight, 12% return, β=1.3, 18% volatility
Blue Chip: 35% weight, 8% return, β=0.9, 12% volatility
Bonds: 25% weight, 4% return, β=0.4, 6% volatility
Risk-Free Rate: 3% | Market Return: 10%
Calculated Metrics
Portfolio Return: (0.4×12%) + (0.35×8%) + (0.25×4%) = 8.6%
Portfolio Beta: (0.4×1.3) + (0.35×0.9) + (0.25×0.4) = 0.935
Sharpe Ratio: (8.6% - 3%) / Portfolio Volatility
Higher Sharpe Ratio indicates better risk-adjusted returns
Optimization Tips
Diversify across asset classes to reduce risk
Higher Sharpe Ratio indicates better risk-adjusted returns
Positive alpha suggests outperformance vs. market
Consider correlation between assets for true diversification
Rebalance periodically to maintain target allocation
Understanding Metrics
Sharpe Ratio
Measures excess return per unit of risk. Higher is better.
>1 = Excellent | 0.5-1 = Good | <0.5 = Poor
Portfolio Beta
Measures systematic risk vs. market.
>1 = More volatile | <1 = Less volatile
Alpha
Excess return over market expectations.
Positive = Outperformance
Volatility
Standard deviation of returns (risk measure).
Lower = Less risky
Asset Class Typical Ranges
Understanding Portfolio Optimization
What is Portfolio Optimization?
Portfolio optimization is the process of selecting the best combination of assets to maximize returns for a given level of risk, or minimize risk for a target return. It considers expected returns, volatilities, and correlations between assets.
Key Concepts
- •Risk-Return Tradeoff: Higher returns typically require accepting higher risk
- •Diversification: Spreading investments to reduce unsystematic risk
- •Efficient Frontier: Set of optimal portfolios offering maximum return for risk level
Key Formulas
Portfolio Return
Rₚ = Σ(wᵢ × Rᵢ)
Weighted average of asset returns
Sharpe Ratio
SR = (Rₚ - Rf) / σₚ
Risk-adjusted return measure
CAPM Expected Return
E(R) = Rf + β(Rm - Rf)
Expected return based on systematic risk
Alpha
α = Rₚ - [Rf + β(Rm - Rf)]
Excess return over CAPM prediction
Optimization Strategies
Maximum Sharpe Ratio
Optimize for best risk-adjusted returns
Minimum Volatility
Minimize portfolio risk while maintaining returns
Target Return
Achieve desired return with minimum risk