CPPI Returns for different floors

I am new to the topic of Constant Proportion Portfolio Insurance, and have implemented it in R for the first time.

Now if I calculate the cumulative return of the CPPI portfolio corresponding to different floors ($$100$$%, $$95$$%, ..., $$0$$%) i get the following result:

For $$100$$%, I obviously invest everything into a bond all the time, thus my return is the risk-free interest rate $$r=1$$%.

For $$0$$%, I invest everything into the risky market, yielding a return equal to that of the market $$\mu=10$$%.

Now in between both extremes, I do not quite understand the behaviour of the realized returns: They are negative for high floor values ($$90$$% - $$60$$%), but then suddenly become positive for floor $$\le 40$$% finally converging to $$\mu$$.

Why is that? Why doesn´t it interpolate, but drop off first?

• Are you comparing returns on a given history of stock index prices or are you comparing average returns on a set of histories generated by Monte Carlo simulation? Jul 17 '20 at 13:37
• @noob2 Returns on a given history of the MSCI World Jul 17 '20 at 13:46
• Caution: The returns are path dependent so the returns on a single history are not necessarily of great importance, and in particular do not necessarily represent the returns going forward or on a different time frame in history. It is a good way to test the code but not a good way to choose a floor value. Jul 17 '20 at 14:04
• @noob2 I understand, it was more a toy example. But still it left me wondering how it is possible that even with a lower floor value, we achieve less return despite the market performing well overall. To be precise: For floor=$0.9$ we go below the risk-free interest rate. Only as we approach floor=$0$, we achieve a return close to the market return. Why is is this dip in the beginning so prominent? Is this a flaw in the CPPI or in my code? Jul 17 '20 at 14:41
• I will add this, then I will shut up and let others comment: CPPI is good if the goal is to arrive at time T with wealth equal to at least X. It is not helpful as a way to get a good return given risk between now and then. A fixed mix (eg. 60% equities, 40% fixed income) is probably better for the latter objective. "If you don't need insurance don't buy it". Jul 17 '20 at 18:44