Abstract
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.
Highlights
Beyond Markowitz’s (1952)[16] mean-variance methodology, the safety-first (SF) criteria, suggested originally by Roy (1952)[21] and developed by Telser (1955)[23] and Kataoka (1963)[11], have been well-known in risky assets allocation
In some market scenarios, even when both the Roy safety-first (RSF) and the Telser safetyfirst (TSF) portfolios do not exist in finite forms, the Kataoka SF (KSF) rule can still apply to get a finite optimal portfolio
(2) By comparing P (R X ≤ Rb) of the portfolios by the three rules in each of Panels 2-4, the RSF portfolio is safest among the three SF portfolios, and the KSF portfolio is safer than the TSF portfolio, in view of the extreme risk prevention with respect to the given referenced rate of return Rb
Summary
Beyond Markowitz’s (1952)[16] mean-variance methodology, the safety-first (SF) criteria, suggested originally by Roy (1952)[21] and developed by Telser (1955)[23] and Kataoka (1963)[11], have been well-known in risky assets allocation. Even in the case where the optimal TSF portfolio exists, it cannot perform better than the KSF portfolio in terms of the Sharpe ratio.
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