Convexity of a Weighted Sharpe and Information Ratio

Summary

The document asks whether a weighted combination of the Sharpe ratio and information ratio can be made convex, giving an example that assigns three times the weight to information ratio before averaging. It does not provide an answer, transformation, derivation, or evidence, so it offers no established method for converting the combined objective into a convex function.

The question highlights a modeling issue for portfolio optimization: convexity depends on how each ratio is defined, the variables being optimized, and any constraints imposed. Since these details and a proposed solution are absent, the document cannot establish whether the stated combination is convex or how to reformulate it. Readers would need additional assumptions and mathematical analysis before using the expression as an optimization objective.

Key ideas

• The document asks about convexity of a weighted combination of Sharpe and information ratios.
• It gives an example weighting information ratio more heavily than Sharpe ratio.
• No derivation or answer is supplied, so convexity and a possible reformulation remain unresolved.
• Any convexity assessment would require definitions, optimization variables, and constraints.

Tags

# Can I add Sharpe Ratio with information ratio in convex way


# Can I add Sharpe Ratio with information ratio in convex way












Sharpe Ratio can be turned into a convex function. And information ratio as well.

Supppose I add these ratios as follows:

(SR + 3 IR ) / 2

Can this function transfer into convex?

How should I do it?

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