Allocation explorer
See what your assumptions imply.
Enter your forecasts for each asset’s return and volatility, and for how the assets move together. The explorer plots the efficient frontier, the steadiest mix for each expected return. It also shows how far the frontier moves when you change one forecast.
Inputs changed. Update the frontier to see the new result.
Your assumptions, plotted
Your mix against the frontier
Your mix: 5.30% expected annual return and 10.64% annual volatility.
The frontier shows the lowest volatility for each expected return, within your limits.
Inspect a possible mix
A point on the frontier
Move from minimum volatility to maximum expected return. Arrow keys work too.
Expected return
Annual volatility
| Asset | Your weight | Selected |
|---|---|---|
| Global equities | 50.00% | 36.96% |
| Bonds | 35.00% | 28.26% |
| Real assets | 15.00% | 34.78% |
Efficient under these assumptions and limits.
Your weights fall outside the allocation limits. The frontier respects those limits; your mix is shown for comparison.
| Portfolio | Expected return | Volatility |
|---|---|---|
| Your mix · current assumptions | 5.30% | 10.64% |
| Selected frontier point | 5.17% | 9.91% |
“Keep as comparison” saves this frontier and your mix, so both stay on the chart while you change a forecast.
Show the frontier numbers
| Point | Return | Volatility | Weights |
|---|---|---|---|
| 1 | 3.35% | 5.57% | Global equities 0.00%; Bonds 82.61%; Real assets 17.39% |
| 2 | 3.44% | 5.59% | Global equities 0.82%; Bonds 78.86%; Real assets 20.33% |
| 3 | 3.53% | 5.66% | Global equities 2.72%; Bonds 76.20%; Real assets 21.09% |
| 4 | 3.62% | 5.74% | Global equities 4.62%; Bonds 73.53%; Real assets 21.85% |
| 5 | 3.71% | 5.86% | Global equities 6.52%; Bonds 70.87%; Real assets 22.61% |
| 6 | 3.80% | 6.00% | Global equities 8.42%; Bonds 68.21%; Real assets 23.37% |
| 7 | 3.90% | 6.16% | Global equities 10.33%; Bonds 65.54%; Real assets 24.13% |
| 8 | 3.99% | 6.34% | Global equities 12.23%; Bonds 62.88%; Real assets 24.89% |
| 9 | 4.08% | 6.54% | Global equities 14.13%; Bonds 60.22%; Real assets 25.65% |
| 10 | 4.17% | 6.75% | Global equities 16.03%; Bonds 57.55%; Real assets 26.41% |
| 11 | 4.26% | 6.99% | Global equities 17.93%; Bonds 54.89%; Real assets 27.17% |
| 12 | 4.35% | 7.24% | Global equities 19.84%; Bonds 52.23%; Real assets 27.93% |
| 13 | 4.44% | 7.50% | Global equities 21.74%; Bonds 49.57%; Real assets 28.70% |
| 14 | 4.53% | 7.77% | Global equities 23.64%; Bonds 46.90%; Real assets 29.46% |
| 15 | 4.63% | 8.05% | Global equities 25.54%; Bonds 44.24%; Real assets 30.22% |
| 16 | 4.72% | 8.34% | Global equities 27.45%; Bonds 41.58%; Real assets 30.98% |
| 17 | 4.81% | 8.64% | Global equities 29.35%; Bonds 38.91%; Real assets 31.74% |
| 18 | 4.90% | 8.95% | Global equities 31.25%; Bonds 36.25%; Real assets 32.50% |
| 19 | 4.99% | 9.26% | Global equities 33.15%; Bonds 33.59%; Real assets 33.26% |
| 20 | 5.08% | 9.59% | Global equities 35.05%; Bonds 30.92%; Real assets 34.02% |
| 21 | 5.17% | 9.91% | Global equities 36.96%; Bonds 28.26%; Real assets 34.78% |
| 22 | 5.27% | 10.24% | Global equities 38.86%; Bonds 25.60%; Real assets 35.54% |
| 23 | 5.36% | 10.58% | Global equities 40.76%; Bonds 22.93%; Real assets 36.30% |
| 24 | 5.45% | 10.92% | Global equities 42.66%; Bonds 20.27%; Real assets 37.07% |
| 25 | 5.54% | 11.26% | Global equities 44.57%; Bonds 17.61%; Real assets 37.83% |
| 26 | 5.63% | 11.61% | Global equities 46.47%; Bonds 14.95%; Real assets 38.59% |
| 27 | 5.72% | 11.96% | Global equities 48.37%; Bonds 12.28%; Real assets 39.35% |
| 28 | 5.81% | 12.31% | Global equities 50.27%; Bonds 9.62%; Real assets 40.11% |
| 29 | 5.90% | 12.67% | Global equities 52.17%; Bonds 6.96%; Real assets 40.87% |
| 30 | 6.00% | 13.03% | Global equities 54.08%; Bonds 4.29%; Real assets 41.63% |
| 31 | 6.09% | 13.39% | Global equities 55.98%; Bonds 1.63%; Real assets 42.39% |
| 32 | 6.18% | 13.75% | Global equities 58.91%; Bonds 0.00%; Real assets 41.09% |
| 33 | 6.27% | 14.14% | Global equities 63.48%; Bonds 0.00%; Real assets 36.52% |
| 34 | 6.36% | 14.55% | Global equities 68.04%; Bonds 0.00%; Real assets 31.96% |
| 35 | 6.45% | 14.99% | Global equities 72.61%; Bonds 0.00%; Real assets 27.39% |
| 36 | 6.54% | 15.44% | Global equities 77.17%; Bonds 0.00%; Real assets 22.83% |
| 37 | 6.63% | 15.92% | Global equities 81.74%; Bonds 0.00%; Real assets 18.26% |
| 38 | 6.73% | 16.42% | Global equities 86.30%; Bonds 0.00%; Real assets 13.70% |
| 39 | 6.82% | 16.93% | Global equities 90.87%; Bonds 0.00%; Real assets 9.13% |
| 40 | 6.91% | 17.46% | Global equities 95.43%; Bonds 0.00%; Real assets 4.57% |
| 41 | 7.00% | 18.00% | Global equities 100.00%; Bonds 0.00%; Real assets 0.00% |
Show the assumptions behind this result
| Asset | Return | Volatility | Weight | Limits |
|---|---|---|---|---|
| Global equities | 7.00% | 18.00% | 50.00% | 0.00% to 100.00% |
| Bonds | 3.00% | 6.00% | 35.00% | 0.00% to 100.00% |
| Real assets | 5.00% | 12.00% | 15.00% | 0.00% to 100.00% |
| Asset pair | Correlation |
|---|---|
| Global equities / Bonds | 0.20 |
| Global equities / Real assets | 0.50 |
| Bonds / Real assets | 0.10 |
Try a change
How much rests on one forecast?
Keep the starting example as a comparison. Lower the expected return for global equities from 7% to 5%. Move the frontier point to the highest expected return with volatility under 10%. At 7%, that mix held 34.78% in real assets. At 5%, it holds 70.84%. The efficient frontier guide works through the 6% case too.
Then change the weights. Your point moves, but the frontier stays put: the set of possible portfolios still has the same forecasts and limits.
Read the result
What the frontier leaves out
The efficient frontier is the set of portfolios where you cannot improve expected return without accepting more volatility. This explorer starts at the minimum-volatility portfolio and ends at the highest permitted expected return.
It models one year, with weights adding to 100% and no short positions or borrowing. Return includes income and price changes, before taxes and costs. Volatility measures variation in returns; it does not tell you the maximum loss or the chance of meeting a financial goal.
Your own estimates may be wrong.
Method
What the explorer calculates
Expected portfolio return is the weighted average of the asset returns. Each covariance is correlation × volatility of asset A × volatility of asset B. Portfolio variance is the sum of every pair’s covariance multiplied by its two weights; volatility is its square root.
For each target return, the explorer finds the smallest variance allowed by your weight limits. The line connects 41 optimized portfolios, or a single point when the assumptions leave only one efficient choice. Displayed percentages are rounded; the download preserves the calculated values.
Correlations are checked as a complete matrix. A combination can be impossible even when each pair lies between −1 and +1. The explorer reports that conflict and leaves your inputs unchanged.
Method references: CVX portfolio optimization, Nick Higham on correlation matrices, and MOSEK on estimation error.