Cppi Strategy Gap Risk Research

Constant Proportion Portfolio Insurance (CPPI hereinafter), put forward by Black, Jones and Perold in 1987, is one of the portfolio insurance strategies. The strategy is well known for its downside protection as well as the upside potential through the dynamic asset allocation. As a result, a large number of financial institutions have adopted CPPI to take advantage of its "principal guarantee" characteristics. Derivatives on CPPI emerge as well. Six principal guaranteed mutual funds in China employs CPPI as their main investment strategy and lots of retail bank products are also based on CPPI or use CPPI notes as the underlying asset.This paper focuses on the risk that CPPI cannot protect the principal at maturity, which is defined as "gap risk". The paper discusses the measurement and management of gap risk through theoretic analysis and empirical study. Optimization problem is also explored after taking CPPI's expected return into account. .First of all, source and measurement of gap risk is analyzed. In continuous model, CPPI can realize 100% principal guarantee, which means gap risk doesn't exist at all. However, when trade is discrete, substantial drop of risky asset price will trigger the gap risk. This paper defined two indicators to measure the gap risk, namely shortfall probability and expected shortfall. By theoretical and empirical analysis, factors that impact the gap risk are found, including the drift and volatility of risky asset price, multiplier and rebalancing rule, etc.Secondly, management of CPPI's gap risk is discussed. The approaches usually focus on one or two variables in CPPI, such as reducing exposure of risky asset, increase floor of CPPI based on the portfolio value, migrate from calendar rebalancing to volatility rebalancing. The paper analyzes the applicability, effect and drawback of all the approaches.Finally, optimization problem of CPPI is explored. Although gap risk could be reduced by lowering multiplier, return of CPPI will decline as well. To find out the optimal tradeoff between risk and return, this paper defines the expected return/utility as the objective of investor and sets an upper limit on shortfall probability/expected shortfall. The optimal multiplier could be obtained in this way. In addition, this paper extends the traditional CPPI based on the above findings by changing the fixed multiplier to variable one so that investor could seek optimal asset allocation in every sub-period. Historical simulation proves that dynamic proportion portfolio insurance (DPPI hereinafter) could realize higher return than traditional CPPI. This paper contributes to the current research on CPPI in the following respects. Previous researches usually focus on the return of CPPI and overlook its risk features. This paper targets at the key risk of CPPI and put forward the appropriate measurement methods. In the meanwhile, fewer attempts were made on the discussion of multiplier. This paper tries to provide some theoretical foundations of the multiplier selection, and extends these findings to Dynamic Proportion Portfolio Insurance (DPPI).