Research On Conditional Risk Multiplier Selection Of CPPI Strategy Based On Johnson Distribution

The portfolio insurance strategy,developed in 1976,is a replication option trading strategy that uses no-arbitrage equilibrium techniques to transfer or hedge the risk of securities market.At present,the most commonly used portfolio insurance strategy in domestic financial market is the CPPI strategy.Traditional CPPI strategies assume a constant risk multiplier.However,the fixed risk multiplier causes the portfolio value to suffer from the falling loss when the market goes down,while it cannot effectively obtain the value-added income of the portfolio when the market goes up.Therefore,scholars proposed dynamic risk multiplier.In addition,the studies of the above scholars assume that risk asset returns follow logarithmic normal distribution,and they estimate the mean value and volatility of risk asset returns on this basis.At present,all the studies assume that the return on risky assets obeys the lognormal distribution,but in practical application,the income distribution of risky assets has negative skewness and spikes.Therefore,this paper introduces the Johnson distribution system.The non-normality of the return on risky assets is characterized,and the non-normal data are transformed into normal data.The GARCH model can be used to obtain the accurate mean value and volatility estimate of the return on risky assets.According to the internal cause of the price change of risky assets in the market,the quartile and local quantile are introduced to adjust the risk multiplier dynamically.In this paper,through the analysis of the operation mechanism of the traditional CPPI strategy,a dynamic CPPI policy model based on Johnson distribution is constructed.By introducing the quartile and local quantile,selecting the conditional risk multiplier,and setting the cushion amount as a linear function,The cushion amount is greater than the threshold L(the critical value of the cushion limit)to a certain probability level(1-a,a is the tolerance of investors to risk loss),and the probability level(1-a)and threshold L are set according to the degree of investor risk preference.The results show that under the Johnson distribution system,the upper bound of the conditional risk multiplier sequence value is a function of the given probability level a,threshold L,and conditional expected rate of return μtk and volatilityσtk of risk asset.The higher the expected rate of return of risky assets μtk is,the smaller the volatilityσtk is,and the higher the conditional risk multiplier is.The higher the tolerance of investors to investment losses,the more risk preference,that is,the greater the probability level a value,the smaller the threshold level,and the higher the conditional risk multiplier.μtk and σtk are estimated by GARCH(1,1)under the Johnson distribution system.The probability level a and the threshold L are set at the beginning of the investment period according to the degree of investor risk preference.Under the condition of long market,the CPPI strategy based on Johnson distribution has the best effect,which can fully grasp the income brought by the rising market,and at the same time,it can also achieve the purpose of capital preservation under the condition of short and volatile market.No matter what the market is in,the CPPI strategy under Johnson distribution system can reduce the "gap risk",that is,the end-of-term portfolio value can achieve capital preservation and obtain better returns.