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Subject:  Re: Strategy comparison S&P500 vs. IUL [rev 1] Date:  4/4/2013  7:40 PM
Author:  Rayvt Number:  71714 of 78166

On a simple annual point-to-point the opening day and anniversaries are the market data points. If the ultimate year's returns were 12%, then any principal balance in place from the initial anniversary gets a credit of the full 12%,
Yes. That't the way I did it.

and any subsequent mid-year contribution gets a pro-rated credit according to the portion of time in.
I didn't do that. I just credited the entire year's worth of additional contributions all at once.
[Let me check... be right back....]
[I'm back.]
Yes. No prorated credit.
New value = (gain_factor * (old_value - expenses)) + all intra-year deposits.
I can change it to a better approximation. Assuming level additions, on average, full gain on the average annual additon balance is Close Enough. Adds to the complexity, though, so CC will scream. ;-)

Yup, it makes things a bit better. For $10,000 & $100/mo, ends with $351,300 instead of $343,700

At the anniversary, all original principal, plus any accumulated growth to date, is considered principal going forward. The straight PTP IUL equity curve is more of an annualize upward zig-zag stair case, climbing to match the naked S&P to the cap, & sitting flat the entire year when the S&P drops.

Yes. What "rolling 12-month" means is this:
Some people have a Jan anniversary. Some have Feb, some Mar, etc. With a large enough universe, 1/12 of the accounts will have their anniversary in each month.

Now, due to sheer happenstance and randomness in the market, sometimes a Jan account will pull ahead of a Feb account, and sometimes a Feb will pull ahead of a Jan. The amount an account ends up with is just a matter of the randomness of the way returns came. For example, the 12 accounts that began in each month of 1975 all started with $10,000. With no additions and no fees, here are their ending balances on the 2012 anniversary:


So Fred who started in Apr-1975 ends up with $126K and Sam who started in Oct-1975 ends up with $177K. That's a difference just due to randomness. If 9/11/01 had happened a month later, all the results would be shifted around.
Neither $126K nor $177K is the "true" final value. Rather, the "true" final value is somewhere in the range of those 12 numbers. The standard way to reduce a set of numbers to one number that represents the range is by taking the average.
The average of these is $145,546. And we can see that indeed that's a more representative number than 122 or 177, because most of the numbers are right around 146.

Whew!! That's what is meant by "rolling 12-month" figures. There are 12 threads through the calendar, one on each anniversary month. The representative value of each and every month is the average of the last value of each thread. IOW, the average of the last 12 months. Perhaps median would be better, but *nobody* understands median - except geeks.

Either that, or you draw the curve with a paintbrush instead of a pen. And then try to explain to a client that his account will be somewhere in that smear. ;-)

The straight PTP IUL equity curve is more of an annualize upward zig-zag stair case, climbing to match the naked S&P to the cap, & sitting flat the entire year when the S&P drops.
Yes. And that's just what the chart looks like. Except that I plotted just the datapoints without the lines between them, and all the same color. That would be be a big smear, since there'd be 12 plots that all lie very close to one another, and overlap one another.

Ehhhh... what I want to solve for is the total income distribution over a 10 year drawdown in full. The naked position will do a straight liquidation, and the IUL will continue the 0/12 principal growth with a 5.3% interest loan distribution.
Darn hard to do! Especially when there is such a big difference in value at the start of the distribution