  This paper proposes a new method for financial portfolio optimization based
on reducing simultaneous asset shocks across a collection of assets. This may
be understood as an alternative approach to risk reduction in a portfolio based
on a new mathematical quantity. First, we apply recently introduced
semi-metrics between finite sets to determine the distance between time series'
structural breaks. Then, we build on the classical portfolio optimization
theory of Markowitz and use this distance between asset structural breaks for
our penalty function, rather than portfolio variance. Our experiments are
promising: on synthetic data, we show that our proposed method does indeed
diversify among time series with highly similar structural breaks and enjoys
advantages over existing metrics between sets. On real data, experiments
illustrate that our proposed optimization method performs well relative to nine
other commonly used options, producing the second-highest returns, the lowest
volatility, and second-lowest drawdown. The main implication for this method in
portfolio management is reducing simultaneous asset shocks and potentially
sharp associated drawdowns during periods of highly similar structural breaks,
such as a market crisis. Our method adds to a considerable literature of
portfolio optimization techniques in econometrics and could complement these
via portfolio averaging.
