Growth Optimal Portfolio Insurance for Long-Term Investors

Volume 13, No. 2, Second Quarter, 2015
Daniel Mantilla-García

We solve the growth-rate optimal multiplier of a portfolio insurance strategy in the general case with a locally risky reserve asset and stochastic state variables. The level of the optimal time-varying multiplier turns out to be lower than the standard constant multiplier of Constant Proportion Portfolio Insurance (CPPI) for common parameter values. As a consequence the outperformance of the growth-optimal portfolio insurance (GOPI) strategy does not come with higher risk. In the presence of mean reverting stock returns the average allocation to stocks increases with horizon and the optimal multiplier introduces a countercyclical “tactical” component to the strategy. Furthermore, we unveil a positive relationship between the value of the strategy and the correlation between the underlying assets.