Originally Posted by scagnt83
Here you go.
As I said earlier, 5.5% is 100%.
I've got some serious reservations here. The first thing that makes me nervous about these quoted probabilities is the 285 periods bit. I'm taking this to mean 285 is the sample space, that's pretty small to make an inverence like this.
If I run a quick Monte-Carlo on the S&P looking for probability of return over a 20 years period (and focusing on Geomtric mean) I find the following when using two samples spaces, one of 100 and one of 1000.
100 trials give me a probability of 93% for at least 5% over 20 years. certainly not bad, but no 100%
1000 trials gives me a probability of 87.4% for at least 5% return over 20 years.
As my sampel size increases, I get closer to a more realistic probability.
On top of this, my assumptions about the S&P account for total return, not index percentage change (diviends included).
There's a lot more methodology wise that it missing from this piece that would be nice to see.
Please do not take this as a move to tear down this product or advocate against it. This is certainly not my intention. It's simply pointing out that I'd be really uncomfortable using this to suggest the probabilities of certain returns.
To extend this a little further. What's the IRR on the guaranteed column of this IUL? If it isn't 5%, then the 100% probability for 5.5% claim is in contradiction with the illustration.
Of course, one my then question how Lincoln could have this sort of piece and use it. There probably is a methodology somewhere that would support this claim (it might still put them in hotwater, time will tell on that one). Proof that in marketing you don't have to be right, you just can't flat out lie.
This isn't magic, and illustrates well the point that small sample spaces can over or under predict results.
I'll also say that it would be interesting to analyse this based on the IUL crediting method. This would probably smooth things out quite a bit. For those who looked at the Monte-Carlo sim I did for the Insurance Pro Blog, you'll note that 5% came out at about a 93% probability. That simulation used a 30 year period. This highlights the randomness of the index.