Risk-Seeking Portfolio Optimization for Winner-Take-All Competitions

Summary

The document asks how portfolio choice changes when the objective is to win a winner-take-all competition rather than to balance expected return against risk. Its example contrasts maximizing expected return and variance with conventional mean-variance optimization, which penalizes variance. A high-variance portfolio could raise the chance of exceeding a difficult performance threshold, even if it is less likely to produce a merely strong rank.

The responses characterize this preference as risk seeking. Under idealized frictionless conditions, the suggested outcome is unbounded leverage in the tangency portfolio; with borrowing constraints, leverage would rise to the permitted maximum. Another response notes that maximizing a convex criterion is generally not an interesting standard portfolio optimization problem, while Kelly betting is suggested as a related concept. The exchange does not derive an objective for ranking against other participants or quantify winning probabilities. Its conclusions depend on idealized assumptions and do not account for practical constraints beyond borrowing limits.

Key ideas

• A winner-take-all objective can favor variance differently from conventional mean-variance optimization.
• Seeking high variance to maximize the chance of finishing first is a form of risk-seeking behavior.
• In a frictionless model, the response suggests unbounded leverage in the tangency portfolio.
• Borrowing constraints limit leverage and therefore change the implied risk-seeking allocation.
• Kelly betting is mentioned as a related concept, but the discussion provides no competition-specific derivation.

Tags

# Maximizing Mean+Variance in a Portfolio


# Maximizing Mean+Variance in a Portfolio












Mean-Variance optimization trades off expected returns with portfolio variance. The idea is that excess variance is not desirable.

But what if you weren't averse to high variance and you wanted to maximize both expected returns and variance. Has there been any research done on this or concepts similar to this?

As an example of a situation where this might be the case, think of a paper trading competition where there are 100 participants. The winner receives $100, and everyone else gains nothing. Ideally, you'd want your portfolio to be high variance, because in order to win you need to outperform 99 others. If you maximized mean+variance (or mean+std), you would be essentially maximizing the odds that you get above some threshold. Compare this with mean-variance optimization, which might improve the chance you place in the top 10, but not necessarily maximize the chances you get first place.

## Answer by phdstudent (score 3)

https://quant.stackexchange.com/a/74536

You would be risk loving. In a world with no trading frictions you would just take infinite leverage and invest in the tangency portfolio.

In a world where there are borrowing constraints you would take maximum leverage possible to invest in the tangency portfolio.

## Answer by DrShredz (score 1)

https://quant.stackexchange.com/a/74589

The problem is then a maximization of a convex criterion, which is not really interesting from the mathematical of economic viewpoint, at least not in portfolio optimization.

## Answer by IronMarshal (score 0)

https://quant.stackexchange.com/a/74542

I think the Kelly betting system might be a good place to start.

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