Constant Proportion Portfolio Insurance: Discrete-time Trading and Gap Risk Coverage

Portfolio insurance, as practiced in 1987, consisted of trading between an underlying stock portfolio and cash, using option theory to place a floor on the value of the position, as if it included a protective put. Constant Proportion Portfolio Insurance (CPPI) is an option-free variation on the theme, originally proposed by Fischer Black. In CPPI, a financial institution guarantees a floor value for the “insured” portfolio and adjusts the stock/bond mix to produce a leveraged exposure to the risky assets, which depends on how far the portfolio value is above the floor. Plain-vanilla portfolio insurance largely died with the crash of 1987, but CPPI is still going strong. In the frictionless markets of finance theory, the issuer’s strategy to hedge its liability under the contract is clear, but in the real world with transactions costs and stochastic jump risk, the optimal strategy is less obvious. Frequent rebalancing limits how badly the position can go off track, but costs more than infrequent rebalancing. Gap risk resulting from a down jump that penetrates the floor adds another hard-to-manage risk. In this article, Jessen comparescommon hedging strategies for CPPI and explores how well each does in managing the risks.