Minimax: Portfolio Choice Based on Pessimistic Decision Making

[MachineGhost]

In this paper, we propose a trading strategy called Minimax, which is based on pessimistic decision making and which suits a highly risk-averse investor. In particular, Minimax is an appropriate asset allocation optimization for big pension funds or other institutional investors that are due to daily risk reporting, either because of regulatory requirements or because of mark-to-market accounting. Maximizing the worst case payoff of a portfolio, Minimax strategies are practically easy to implement and constitute a proper alternative to common risk-minimizing optimizations such as minimum variance.

We use US data on indexes of stocks, bonds, real estate and commodities from January 1990 to December 2010 in order to calculate daily portfolio returns. We compare the proposed allocation strategy with alternative asset allocation strategies. Therefore, we calculate a minimum variance portfolio, which minimizes volatility within one year of historical daily returns, a mean-variance portfolio with risk aversion parameter equal to 3, an equal weights strategy that invests one fourth of funds into each asset class, and a typical US pension fund portfolio, which imitates an asset allocation that a representative investor could possibly run.

Our main result is that the proposed Minimax strategy outperforms all competitors, in terms of different risk and performance measures. We find the minimum variance portfolio to be the hardest competitor for Minimax, assuming a highly risk-averse agent, and portfolio characteristics of both strategies are comparable. We show that the particular advantage of the Minimax strategy is the avoidance of very large losses. Optimizations based on volatility as a symmetric risk measure such as minimum variance strategies fail to provide optimal portfolios with attractive performance characteristics, because they minimize not only negative, but also positive returns. Minimax, however, only cares about huge portfolio losses, and provides preferable performance characteristics by allowing positive portfolio returns. Naive portfolio allocation rules are not competitive to Minimax in terms of performance and risk. Still, this does not mean that naive portfolio allocation strategies are in general not appropriate for any investor. Studies show that many optimization strategies fail to beat simple rules of thumb, and by diversifying funds across dierent asset classes, one can reduce risk efficiently without imposing strong restrictions ex ante. Another advantage of fixed weight strategies, besides their simplicity and applicability, is low turnover. This feature make them particularly interesting for long-term investors that face high transaction costs. Mean-variance optimization is not competitive to all above mentioned strategies, due to high estimation error.

Considering portfolio characteristics, we find admirable features for portfolio weights that result from all strategies but from mean-variance optimization. Portfolio weights are relatively stable over time for Minimax and minimum variance, resulting in comparable turnover and transaction costs. Transaction costs are particularly high for the mean-variance portfolio, implied by high estimation error and extreme portfolio weights. Minimax and minimum variance portfolios both invest on average about 50-60% of their funds into bonds, while the rest of funds is spead across the remaining asset classes. By doing so, the resulting portfolios are satisfyingly diversified.

In a last analysis, we check our results for robustness. For yearly returns (instead of daily returns), we lose dominance over the minimum variance strategy. This is particularly due to the fact that yearly returns are closer to normality than daily returns. In a scenario with normally distributed returns, portfolios based on Markowitz (1952) are shown to be optimal. We also check whether the chosen rebalancing period of one year has particular influence on our results. We show that using daily rebalancing, we obtain even better results as when using yearly rebalancing. Lastly, we allow for short-selling, which was constrained in all optimizations before. As expected, mean-variance weights fluctuate even more, resulting in high turnover and transaction costs. The dominance of Minimax over minimum variance portfolios remains.

All results suggest that Minimax strategies provide an attractive alternative asset allocation optimization for a highly risk-averse investor that is concerned with daily risk management. Since Minimax prevents portfolios from yielding high extreme losses, institutional investors that are due to daily risk reporting can lower their portfolio risk. Additionally, Minimax strategies are easily implementable due to its simple algorithm and because exchange traded funds provide easy access to all considered asset classes.

https://papers.ssrn.com/sol3/papers.cfm ... id=2078861