Choosing Portfolio Weights to Maximize Positive Return Days

Summary

The document poses a portfolio-weighting problem: combine the returns of several models so that the resulting portfolio has as many positive periods as possible. Its objective is the fraction of periods in which the weighted sum of model returns exceeds zero. The question asks whether this problem has a standard name and whether research addresses it.

The only response recommends solving the problem numerically and imposing realistic constraints on the weights so the optimization can converge. It does not identify a formal problem class, propose a specific algorithm, or cite research. Because the objective counts threshold crossings, it is discontinuous in the weights and can be difficult for standard smooth optimization methods; the response does not discuss that challenge or specify constraints such as weight bounds or a budget condition. The document therefore introduces an objective that may be useful when the frequency of gains matters, but provides little practical guidance for solving or evaluating it.

Key ideas

• The objective maximizes the share of periods when a weighted combination of model returns is positive.
• The return series of each model enter through the portfolio’s weights.
• The response advises numerical optimization with realistic constraints but gives no specific solver.
• The discontinuous positive-day count can make the optimization difficult for common smooth methods.

Tags

# optimization to maximize number of positive days


# optimization to maximize number of positive days












suppose I have $N$ models, with returns $r_{n,t}$ over $1,...,T$ periods ($T>>N$). I want to find weights $w_n$ for model $n \in 1,...,N$ such the final model $p$, whose returns will be

$r_{p, t} = \sum_{n=1}^{N} w_n * r_{n, t}$

has the maximum number of positive days, i.e. I want to maximize

$\frac{\sum_{t=1}^{T} 1\{ r_{p,t} > 0\}}{T}$

Has can I solve this kind of optimization problem? Does it have a name? Are there any papers written about this?

## Answer by Thomas Maloney (score -1)

https://quant.stackexchange.com/a/20786

I would solve it numerically. You are trying to solve for N variables, you'll want to specify appropriate (and realistic) constraints such that your optimization procedure converges.

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