## CCPI parameter settings

In the first analysis of the CCPI strategy we set the floor at 0.8, we used a multiplicator of 3 and we did monthly rebalancing. In this section we will test how returns, volatility and maximum breakdown change when we change these parameter settings.

**Rebalancing periods**

Instead of rebalancing monthly, we can choose to rebalance the CPPI portfolio more or less frequently. We will evaluate daily, weekly, monthly, quarterly and yearly rebalancing. Definitely, there will be times when daily rebalancing results in frequent transactions. This is impractical and increases transaction costs. But still we want to take daily rebalancing into account because it might teach us something about the effects of adapting even longer rebalancing periods.

Besides the length of the rebalancing periods, we’ll use the same settings as we used in the previous section:

- Strategy: CPPI
- Risky Asset: S&P 500 (starting from 1993)
- Fixed yearly return of the safe asset: 0.5%
- Floor: 80% of the previous peak
- Multiplicator: 3

The results show that for the CPPI strategy applied to S&P500, returns are highest and volatility is lowest with monthly rebalancing periods. Maximum drawdown is a little bit lower with quarterly rebalancing periods compared to monthly rebalancing, but the difference is small (17.8% vs 18.2%).

Conclusion: monthly rebalancing is optimal.

**Changing the floor**

In the previous section, we set the floor at 80% of the previous peak. In figures 4,5 and 6 we show the results with different floorsettings. We ‘ll set floors to 70,80 and 90% of the previous peak.

Besides the floor, we’ll use the same settings as we used in the previous section:

- Strategy: CPPI
- Risky Asset: S&P 500 (starting from 1993)
- Fixed yearly return of the safe asset: 0.5%
- Multiplicator: 3
- Rebalancing: Monthly

As we could expect, with lowering the floor, the maximum drawdown and the volatility increases, but the Annualized Return increases as well. This is logical, since, with lowering the floor most of the time we are more invested in the risky asset (S&P500); so results will be more similar to the results for the risky asset itself.

Since higher volatility and higher maximum breakdowns are negative, while higher returns are obviously positive, the best value of the floor depends on the preferences of the individual investor.

**Changing the multiplicator**

In the previous section, we set the multiplicatorvalue at 3. In figures 7,8 and 9 we show the results with different multiplicators. We ‘ll set multiplicatorvalues from 3 to 10.

Besides the multiplicator, we’ll use the same settings as we used in the previous section:

- Strategy: CPPI
- Risky Asset: S&P 500 (starting from 1993)
- Fixed yearly return of the safe asset: 0.5%
- Floor: 80% of the previous peak
- Rebalancing: Monthly

We see, with increasing the multiplicator, the annualized return increases. In this example the floor is not broken as long as the multiplicator is smaller than 7. With a multiplicator of 7 the maximum drawdown is 20.22%, while with a floor of 80%, we try to avoid a maximum drawdown higher than 20%. Of course the difference is small. We ‘ll investigate the relationship between the floor and the multiplicator in the subsection below.

**Relationship between floor and multiplicator**

With a floor value of 80% of the previous peak, the maximum cushion (difference beween account value and the floor) is 20%. We’ll allocate a fraction of our accountvalue to the risky asset, which is equal to the cushion multiplied with the multiplicator. With a floor of 80% and a multiplicator set at 3, we can never be more than 60% invested in the risky asset. With a floor of 80%, we can be invested up to 100% in the risky asset if we use a multiplicator of 5 or higher; with a floor of 90%, the multiplicator has to be 10 or higher in order to have the opportunity to be fully invested in the risky asset. But what is the effect of these different combinations on return, volatility and maximum breakdown? We ‘ll show it in the tables below.

Annualized Return | Floor 0.7 | Floor 0.8 | Floor 0.9 |
---|---|---|---|

m=3 | 7,59% | 5,32% | 3,02% |

m=4 | 8,30% | 6,19% | 3,58% |

m=5 | 8,19% | 6,78% | 4,03% |

m=6 | 8,07% | 7,15% | 4,33% |

m=7 | 7,67% | 7,13% | 4,49% |

m=8 | 7,56% | 7,03% | 4,68% |

m=9 | 6,19% | 7,37% | 4,49% |

m=10 | 3,75% | 7,78% | 4,72% |

Annualized Volatility | Floor 0.7 | Floor 0.8 | Floor 0.9 |
---|---|---|---|

m=3 | 9,7% | 6,4% | 3,2% |

m=4 | 11,1% | 7,9% | 4,0% |

m=5 | 11,3% | 9,2% | 4,7% |

m=6 | 11,3% | 9,8% | 5,3% |

m=7 | 11,3% | 10,0% | 5,5% |

m=8 | 11,4% | 10,1% | 5,9% |

m=9 | 10,9% | 10,3% | 6,3% |

m=10 | 9,2% | 10,5% | 6,5% |

Maximum drawdown | Floor 0.7 | Floor 0.8 | Floor 0.9 |
---|---|---|---|

m=3 | 27,3% | 18,2% | 9,0% |

m=4 | 29,1% | 19,4% | 9,6% |

m=5 | 29,7% | 19,8% | 9,9% |

m=6 | 29,9% | 19,9% | 10,0% |

m=7 | 30,5% | 20,2% | 10,1% |

m=8 | 30,8% | 20,3% | 11,1% |

m=9 | 31,6% | 20,2% | 12,4% |

m=10 | 33,0% | 20,1% | 13,6% |

The tables show that with a floor of 0.7 return decreases with multiplicators higher than 4; with floor values 0.8 and 0.9, returns improve with increasing multiplicators up to 10. For all floors we see breaking of the floor with multiplicators above 6. With multiplicators 6 or lower, returns are higher with decreasing floors.

Conclusions:

- Investors can choose the level of the floor dependent on their risk aversion: with lower floors we get higher returns but maximum drawdown is higher as well.
- Multiplicators should not exceed 6, since in those cases the floor will be broken (maximum drawdown exceeds the level of the floor). For a floor of 0.7 the multiplicator should not exceed 4 since above 4 returns start to decrease. For floor values of 0.8 and 0.9 multiplicatorvalues of 6 are optimal since they give the best returns.

**Next?**

In the next section we will analyse the distribution of returns, volatility and maximum drawdown for timeperiods of different lengths.