CPPI has become a well-known investment concept that combines downside risk protection with participation on the upside in a risky asset. This strategy is typically implemented by investing an amount into the money market that accrues interest over time and ensures a certain capital protection level at a future point in time. To ensure upside participation, the remaining investment amount that is not needed to ensure the capital protection level is invested in the risky asset, typically allowing for a leveraged investment with the leverage multiple M. The use of a multiple greater than 1 implies the risk that the investment in the risky assets is wiped out completely and only the risk-free money market investment survives till maturity.
The derivation of the optimal leverage factor within a Black-Scholes model framework goes back to the seminal article of Merton (1971) and shows that (taking equities as a risky asset) the expected return maximizing multiple M (see formula (1)) is given by the premium of the expected equity-drift rate over the risk-free rate divided by the variance of the returns of the equity market. The optimal leverage factor ensures the optimal balance between leveraging the upside potential of the risky asset on one hand and the well-known adverse “buy high/sell low” effect due to the frequent rebalancing of the leveraged investment scheme on the other hand (for details, see Giese 2010).
Furthermore, Estep and Kritzmann (1988) have extended the basic concept of the CPPI to investment strategies that are not limited to a fixed maturity date. Instead, they consider a so-called time invariant proportional portfolio (TIPP) strategy with value It, where, analogous to the CPPI, the portfolio value exceeding the protection level Ft is invested in the risky asset (using a leverage multiplier M), whereas the amount Ft is invested in the risk-free money market. The crucial part of the methodology is the definition of a maximum drawdown limit 1-f, which the strategy can never exceed, where f denotes the protection level on the current portfolio value It. We assume that the floor is ratcheted using a fixed capital protection floor f<1, i.e., Ft is assumed to grow with the risk-free rate in time unless the investment scheme grows such that f times It reaches or surpasses the current floor Ft, in which case the floor is ratcheted to Ft = f It.
Consequently, (1-f) is the maximal drawdown that can occur at any given point in time, and therefore the factor f can also be interpreted as the minimum capital protection level at any given point in time.
It is interesting to note that Grossman and Zhou (1993) show that the expected return maximizing leverage factor M on the risky asset portion It -Ft for the TIPP strategy is (analogous to the CPPI strategy) given by the expected equity-drift rate over the risk-free rate divided by the variance of the returns of the equity market.
Both CCPI and TIPP models have led to a broad stream of academic research that we briefly summarize in the following without claiming completeness. To start with, the properties of continuous-time CPPI models are studied in Black and Perold (1992), Perold and Sharpe (1995), and Bookstaber and Langsam (2000). The development path from a standard CPPI to so-called optimized PPI and a comparison of the models involved can be found in Bertrand and Prigent (2002a). A theoretical extension related to models involving stochastic volatility and extreme value approaches is developed in Bertrand and Prigent (2002b, 2003), with more advanced downside-risk measures developed in Bertrand and Prigent (2011). Within the broad stream of research analyzing the risk and return profile of optimized PPI models (OPPI), we would like to mention the works of Cox and Huang (1989), Brennan and Schwartz (1989), Grossman and Villa (1989), Black and Perold (1992), Grossman and Zhou (1993, 1996), Basak (1995, 2002), Browne (1999), Tepla (2000, 2001) and El Karoui et al. (2005). Furthermore, more empirical simulation-based studies can be found in Cesari and Cremonini (2003) and Do and Faff (2004).
Although CPPI and TIPP strategies have become the catalyst of extensive academic research due to the fact that they allow for closed-form solutions as well as the application of optimization techniques, their practical importance is quite limited.
To be precise, apart from the CPPI—which has become a well-known model in the insurance industry—these models have had little success in the wider asset management community, particularly in the market for funds, ETFs and financial products in general.
At a first glance, this is quite surprising, since risk-reduction methodologies such as target-volatility strategies, low-beta strategies or minimum-variance strategies have become standard investment schemes in the asset management space, and are even available in the form of certificates or exchange-traded funds.
In fact, the TIPP strategy offers a more attractive risk-reduction mechanism in the form of an absolute drawdown protection level, whereas target-volatility, low-beta or minimum-variance strategies simply limit or reduce the volatility of the investment portfolio without necessarily limiting the drawdown in a serious market crash. In principle, this makes the TIPP strategy more appealing to investors in related financial products than volatility-reducing investment strategies.
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