Stochastic dominance of portfolio insurance strategies

Abstract

The purpose of this article is to analyze and compare two standard portfolio insurance methods: Option-based Portfolio Insurance (OBPI) and Constant Proportion Portfolio Insurance (CPPI). Various stochastic dominance criteria up to third order are considered. We derive parameter conditions implying the second-and third-order stochastic dominance of the CPPI strategy. In particular, restrictions on the CPPI multiplier resulting from the spread between the implied volatility and the empirical volatility are analyzed.

On the Stochastic Dominance of Portfolio Insurance Strategies

“…The proof is similar to the proofs of Theorems 2, 3 and 4 of Zagst and Kraus [10] except that we take account of Relation (12) 5 . -The first step consists in proving the following equivalence:…”

“…In what follows, we provide several sufficient conditions to get stochastic dominance results as in Zagst and Kraus [10] but without assuming as them that q is equal to 1 (see previous Relation 12).…”

“…where k S denotes the set of all real functions H, with k changes of sign: ≤ , we can conclude, using theorem of Mosler [12], that, if [10]), this condition is necessary satisfied.…”

“…As mentioned by Zagst and Kraus [10], the third order stochastic dominance (denoted by 3  ) can be deduced under some specific assumptions. …”

“…However, as proved theoretically by Zagst and Kraus [10], stochastic dominance of portfolio insurance strategies can be obtained mainly from the third order. Our main purpose is to extend previous results when taking account of quite general share values and/or of specific constraints such as capped strategies introduced to limit financial risk exposures.…”