SAFETY FIRST Research Articles

How's the performance of the optimized portfolios by safety-first rules: Theory with empirical comparisons

Safety-first (SF) rules have been increasingly useful in particular for construction of optimal portfolios related to pension and other social insurance funds. How's the performance of the optimal portfolios constructed by different SF rules is an interesting practical question but yet less investigated theoretically. In this paper, we therefore analytically investigate the properties of the risky portfolios constructed by the three popular SF rules, denoted by the RSF, TSF and KSF, which are suggested and developed by A. D. Roy, L. G. Telser and S. Kataoka, respectively. Using Sharpe ratio as a measure of portfolio performance, we theoretically derive that the performance of an optimal portfolio constructed by the KSF approach depends on an acceptable level of extreme risk tolerance. The unique solution where the performance of the KSF portfolio is the same as that of the other two SF portfolios is found. By this we interestingly find that except this special case, under the finite optimal portfolios existent, the KSF portfolio always dominates the TSF portfolio in terms of the Sharpe ratio. In addition, in some market scenarios, even when the RSF and TSF portfolios do not exist in finite forms, the KSF rule can still apply to get a finite optimal portfolio. Moreover, in comparison with the RSF rule, a series of finite KSF portfolios can be interestingly constructed with their Sharpe ratios approaching to the maximum Sharpe ratio, which however cannot be reached by any corresponding finite RSF portfolio. Numerical comparisons of these rules by using a set of real data are further empirically demonstrated.

Elicitation of preferences under ambiguity

This paper is about behaviour under ambiguity—that is, a situation in which probabilities either do not exist or are not known. Our objective is to find the most empirically valid of the increasingly large number of theories attempting to explain such behaviour. We use experimentally-generated data to compare and contrast the theories. The incentivised experimental task we employed was that of allocation: in a series of problems we gave the subjects an amount of money and asked them to allocate the money over three accounts, the payoffs to them being contingent on a ‘state of the world’ with the occurrence of the states being ambiguous. We reproduced ambiguity in the laboratory using a Bingo Blower. We fitted the most popular and apparently empirically valid preference functionals [Subjective Expected Utility (SEU), MaxMin Expected Utility (MEU) and α-MEU], as well as Mean-Variance (MV) and a heuristic rule, Safety First (SF). We found that SEU fits better than MV and SF and only slightly worse than MEU and α-MEU.

Safety-first portfolio selection

A. D. Roy's safety-first (SF) approach to financial portfolio optimization is improved. Safety first means the minimization of the probability of negative returns. The improvement concerns a better estimation of the negative return probabilities by means of mean excess return risk functions. The search for the optimal SF-portfolio is similar to Roy's geometric method but the efficient frontier is different. In case of a finite number of scenarios, the SF-portfolio selection problem is reduced to a mixed linear Boolean programming problem.

What are robust strategies in the face of uncertain climate threshold responses?

We use an integrated assessment model of climate change to analyze how alternative decision-making criteria affect preferred investments into greenhouse gas mitigation, the distribution of outcomes, the robustness of the strategies, and the economic value of information. We define robustness as trading a small decrease in a strategy’s expected performance for a significant increase in a strategy’s performance in the worst cases. Specifically, we modify the Dynamic Integrated model of Climate and the Economy (DICE-07) to include a simple representation of a climate threshold response, parametric uncertainty, structural uncertainty, learning, and different decision-making criteria. Economic analyses of climate change strategies typically adopt the expected utility maximization (EUM) framework. We compare EUM with two decision criteria adopted from the finance literature, namely Limited Degree of Confidence (LDC) and Safety First (SF). Both criteria increase the relative weight of the performance under the worst-case scenarios compared to EUM. We show that the LDC and SF criteria provide a computationally feasible foundation for identifying greenhouse gas mitigation strategies that may prove more robust than those identified by the EUM criterion. More robust strategies show higher near-term investments in emissions abatement. Reducing uncertainty has a higher economic value of information for the LDC and SF decision criteria than for EUM.

US-Thailand Bilateral Safety-first Portfolio Optimisation around the 1997 Asian Financial Crisis

We examine bilateral US- and Thailand-based equity portfolios around the 1997 baht crisis using an extreme value framework for safety-first (SF) portfolio optimisation, with comparisons to the Markowitz mean-variance minimum variance portfolio (MVP). The optimal SF portfolio is invested 100 per cent in the US regardless of the periods considered when returns are denominated in USD, but 80 per cent in the US in the post-crisis period when returns are denominated in THB. The MVP for USD denominations is 85 per cent invested in the US regardless of the period, in contrast to 100 per cent for SF, suggesting more investment in the US when USD returns and safety considerations are paramount. In contrast, there are minimal differences between the MVP and SF for THB denominations, particularly post crisis when there are no differences. The baht crisis seems to have shifted investments toward the US for those with an interest in safety first and USD returns, but had minimal effect on the portfolio composition for those with an interest in THB returns.

Generalized Safety First and a New Twist on Portfolio Performance

We propose a Generalization of Roy's (1952) Safety First (SF) principle and relate it to the IID versions of Stutzer's (Stutzer's 2000, 2003) Portfolio Performance Index and underperformance probability Decay-Rate Maximization criteria. Like the original SF, the Generalized Safety First (GSF) rule seeks to minimize an upper bound on the probability of ruin (or shortfall, more generally) in a single drawing from a return distribution. We show that this upper bound coincides with what Stutzer showed will maximize the rate at which the probability of shortfall in the long-run average return shrinks to zero in repeated drawings from the return distribution. Our setup is simple enough that we can illustrate via direct calculation a deep result from Large Deviations theory: in the IID case the GSF probability bound and the decay rate correspond to the Kullback–Leibler (KL) divergence between the one-shot portfolio distribution and the “closest” mean-shortfall distribution. This enables us to produce examples in which minimizing the upper bound on the underperformance probability does not lead to the same decision as minimizing the underperformance probability itself, and thus that the decay-rate maximizing strategy may require the investor to take positions that do not minimize the probability of shortfall in each successive period. It also makes clear that the relationship between the marginal distribution of the one-period portfolio return and the mean-shortfall distribution is the same as that between the source density and the target density in importance sampling. Thus Geweke's (1989) measure of Relative Numerical Efficiency can be used as a measure of the quality of the divergence measure. Our interpretation of the decay rate maximizing criterion in terms of a one-shot problem enables us to use the tools of importance sampling to develop a “performance index” (standard error) for the Portfolio Performance Index (PPI). It turns out that in a simple stock portfolio example, portfolios within one (divergence) standard error of one another can have very different weights on individual securities.