Constant Proportion Portfolio Insurance Strategy Research Articles

Constant Proportion Portfolio Insurance in Presence of Jumps in Asset Prices

Constant proportion portfolio insurance (CPPI) allows an investor to limit downside risk while retaining some upside potential by maintaining an exposure to risky assets equal to a constant multiple of the cushion, the difference between the current portfolio value and the guaranteed amount. Whereas in diffusion models with continuous trading, this strategy has no downside risk, in real markets this risk is non-negligible and grows with the multiplier value. We study the behavior of CPPI strategies in models where the price of the underlying portfolio may experience downward jumps. Our framework leads to analytically tractable expressions for the probability of hitting the floor, the expected loss and the distribution of losses. This allows to measure the gap risk but also leads to a criterion for adjusting the multiplier based on the investor's risk aversion. Finally, we study the problem of hedging the downside risk of a CPPI strategy using options. The results are applied to a jump-diffusion model with parameters estimated from returns series of various assets and indices.

Piecewise nonlinear goal-directed CPPI strategy

Traditional portfolio insurance (PI) strategy, such as constant proportion portfolio insurance (CPPI), only considers the floor constraint but not the goal aspect. This paper proposes a goal-directed (GD) strategy to express an investor’s goal-directed trading behavior and combines this floor-less GD strategy with the goal-less CPPI strategy to form a piecewise linear goal-directed CPPI (GDCPPI) strategy. The piecewise linear GDCPPI strategy shows that there is a wealth position M at the intersection of the GD and CPPI strategies. This M position guides investors to apply the CPPI strategy or the GD strategy depending on whether current wealth is less than or greater than M, respectively. In addition, we extend the piecewise linear GDCPPI strategy to a piecewise nonlinear GDCPPI strategy. This paper applies genetic algorithm (GA) technique to find better piecewise linear GDCPPI strategy parameters than those under the Brownian motion assumption. This paper also applies forest genetic programming (GP) technique to generate the piecewise nonlinear GDCPPI strategy. The statistical tests show that the GP strategy outperforms the GA strategy which in turn outperforms the Brownian strategy.

Effectiveness of CPPI Strategies under Discrete-Time Trading

The paper analyzes the effectiveness of the constant proportion portfolio insurance (CPPI) method under trading restrictions. If the CPPI method is applied in continuous time, the CPPI strategies provide a value above a floor level unless the price dynamic of the risky asset permits jumps. The risk of violating the floor protection is called gap risk. In practice, it is caused by liquidity constraints and price jumps. Both can be modelled in a setup where the price dynamic of the risky asset is described by a continuous-time stochastic process but trading is restricted to discrete time. We propose a discrete-time version of the continuous-time CPPI strategies which satisfies three conditions. The resulting strategies are self-financing, the asset exposure is non-negative and the value process converges. We determine risk measures such as the shortfall probability and the expected shortfall and discuss criteria which ensure that the gap risk does not increase to a level which contradicts the original intention of portfolio insurance.