Why Portfolio Risk Criteria May Select Different Efficient Allocations

Summary

The document asks why portfolios selected using three risk or performance criteria—the Sharpe ratio, ulcer performance index, and serenity ratio—appear at the same point on separately constructed efficient frontiers. It states that the risk-free rate is zero and reports that both the maximum-Sharpe and minimum-variance selections, along with their counterparts under the other criteria, coincide in the user's results.

The included answer says that using the same dataset across the frontiers leads to the same efficient combination and Sharpe ratio, while allocations should differ when minimizing measures such as the ulcer index. This is a brief response rather than a derivation or empirical demonstration. The result cannot be generalized from the information given: frontier construction, objective definitions, constraints, and implementation details are unspecified. Different risk measures can rank portfolios differently, so coincident selected points may reflect particular data or setup choices and warrant checking how each objective was calculated.

Key ideas

• The post reports coincident selected portfolios across frontiers built using three criteria.
• The reported setup uses a zero risk-free rate and the same underlying dataset.
• The answer suggests that minimizing downside-oriented measures may lead to different allocations.
• The document does not explain the frontier calculations or demonstrate why the points coincide.
• Different objective definitions and portfolio constraints can affect which allocation is selected.

Tags

# efficient frontiers are equal


# efficient frontiers are equal












I created 3 different efficient frontiers with 3 different risk factors(sharpe ratio, ulcer performance index and serenity ratio) and I wanted to find both MSR and GMV(and their equivalent for the other two risk factors) on each one. But all 6 points are the exact same point. I wanted to know if it has a meaning behind it. Does anyone know what it means? (Rf=0)

## Answer by Guido (score 0)

https://quant.stackexchange.com/a/69993

If you use the same dataset across all three portfolios you will find the same efficient combination across all three. Ergo, your sharpe ratio will be the same, because it basically uses the same tools. Instead, the allocation should be different in cases where you are going to minimize the ulcer index etc.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.