Which mix is efficient?
The optimizer looks for the weights that fit your goal: the most return per unit of risk, the lowest volatility or equal risk contributions. The efficient frontier shows every mix with the highest expected return for a given level of risk.
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How it works
It builds on Harry Markowitz's theory: expected return, volatility and correlations are estimated from the returns of the building blocks. Because the building blocks don't move in lockstep, a mix can swing less than any single one of them.
Options include max. Sharpe ratio (the most return above the risk-free rate per unit of volatility), min. variance (the lowest volatility), risk parity (every building block adds the same amount of risk) and Black-Litterman with your own market views. Limits per ETF prevent extreme positions.
Optimized weights are sensitive to the estimated returns. That's why there is shrinkage (the estimated covariance is pulled toward a calmer target), resampling (many optimizations on slightly changed data, averaged) and a walk-forward test that only uses data known at each point in time.
What a result looks like
Sample dataMade-up sample data, no real prices and no recommendation. Calculated with the same methods as the tool itself.
Inputs in this example
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Create accountEfficient Frontier
Return and volatility p.a. of the efficient portfolios; diamonds: the optimized portfolios.
Optimized portfolios
Weights and expected values p.a. from the estimates.
| Building block | Max. Sharpe ratio | Min. variance | Risk parity | Equal weight |
|---|---|---|---|---|
| Global equities | 31% | 14% | 17% | 25% |
| Equities emerging markets | 0% | 0% | 10% | 25% |
| Bonds | 59% | 86% | 57% | 25% |
| Gold | 10% | 1% | 17% | 25% |
| Return p.a. | 5.1% | 4.1% | 5.0% | 6.2% |
| Volatility p.a. | 5.5% | 4.6% | 6.0% | 9.9% |
| Sharpe ratio | 0.56 | 0.46 | 0.50 | 0.42 |
Estimates per building block
Average return and volatility p.a. from the monthly returns.
| Building block | Return p.a. | Volatility p.a. |
|---|---|---|
| Global equities | 7.9% | 14.3% |
| Equities emerging markets | 7.7% | 22.5% |
| Bonds | 3.5% | 5.1% |
| Gold | 5.6% | 14.6% |
Assumptions: Expected returns and covariances estimated from the made-up monthly returns 01/2006 to 12/2025 (sample), long positions only, adding up to 100%. The weights apply to these estimates, not to the future.
Frequently asked questions
What is the efficient frontier?
The line of all portfolios with the highest expected return for a given level of risk. Portfolios below the line are inefficient: there is a mix with more return for the same risk.
What is risk parity?
A weighting where every building block contributes the same amount to the portfolio's volatility. Low-volatility building blocks such as bonds therefore get more weight than stocks.
Why are optimized portfolios often so lopsided?
Because small differences in the estimated returns lead to large differences in the weights. Limits per ETF, shrinkage, resampling and Black-Litterman make the results more stable.
Will the best portfolio of the past also be the best in the future?
Not necessarily, because the estimates are based on the past. The walk-forward test shows how a strategy that is re-optimized regularly, without looking into the future, would have done.
Learn more in the knowledge base
- MethodologyOptimization methodology: estimation, objectives, Black-Litterman, resampling and walk-forward
- ArticleEfficient frontier: Markowitz portfolio optimization
- ArticleRisk parity: equal risk contributions instead of equal weights
- ArticleCovariance estimation: why optimizers need shrinkage
- ArticleBeyond Markowitz: estimation error, noise and true diversification
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