This calculator gives estimates for education and planning. It is not investment, tax or legal advice; for decisions about your own situation, talk to a qualified financial professional.
Why mixing assets lowers risk
When two investments do not move exactly together, their ups and downs partly cancel out. A portfolio of the two can then be less volatile than the weighted average of its parts. This diversification effect, formalized by Harry Markowitz in 1952, is the foundation of modern portfolio theory and of the classic 60/40 stock and bond portfolio.
The formulas
For weights w₁ and w₂ = 1 − w₁:
- Expected return: R = w₁R₁ + w₂R₂
- Volatility: σ = √(w₁²σ₁² + w₂²σ₂² + 2w₁w₂ρσ₁σ₂)
- Sharpe ratio: (R − risk-free rate) ÷ σ
The correlation ρ ranges from −1 to +1. At +1 there is no diversification benefit; at −1 risk could be eliminated entirely; between the two, the lower the correlation, the larger the benefit.
The weight of asset 1 that gives the lowest possible volatility is:
w_min = (σ₂² − ρσ₁σ₂) ÷ (σ₁² + σ₂² − 2ρσ₁σ₂)
Example
A 60/40 portfolio of stocks (8% expected return, 16% volatility) and bonds (4%, 6%), with a correlation of 0.2 and a 3% risk-free rate:
- Expected return: 6.4%
- Volatility: 10.35%, below the weighted average of 12%
- Sharpe ratio: 0.33
- A bad year, two standard deviations below the mean: about −14%
- Minimum-variance mix: about 7% stocks, with a volatility of 5.9%
Reading the results
- Volatility is the standard deviation of annual returns. In about two years out of three, the return falls within one volatility of the expected return.
- The bad-year figure is a rough guide only. Real markets have fatter tails: in 2008, a 60/40 portfolio lost about 20%.
- The Sharpe ratio compares the extra return over cash with the risk taken, which helps compare mixes.
Choosing assumptions
Long-term US stock returns have averaged about 10% a year before inflation, with a volatility near 15 to 20%. Investment-grade bonds have had lower returns and a volatility of 4 to 7%. Forecasts for the next decade from large asset managers are often lower than history. Use a range of assumptions rather than a single guess.
Limits
The model uses two assets, one period and fixed inputs. Correlations tend to rise during crises, exactly when diversification is needed most. Taxes, fees and rebalancing also affect real results. Use the calculator to understand the trade-offs, not as a promise of future returns.