There is a problem with modeling dissimilar things. Permanent
insurance does not act like a T+I strategy. And there are only
seven people in the whole world who know the full details about how my
policy acts. I am not one of those seven. So how do I compare
when there are so many unknowns? One way is formalization of
ignorance. Ignore what you don't know, compare what you do.
Black
Box
Annual
Gain is one answer:
All that needs to be known to calculate BBAG concerning virtually
any sort of investment is the value at the beginning of year (value_boy), the
value at the end of the year (value_eoy), any out-of-pocket cash
during the year (deposits), and any in-to-pocket cash during the year
(withdrawals). Here is the formula:
value_eoy - value_boy - deposits + withdrawals
-----------------------------------------------
value_boy + deposits - withdrawals
I do not model any withdrawals; it is
stated simply for completeness.
Taxes are not BAGG'd as a withdrawal --
they do not yield in-to-pocket cash.
(... not your pocket, anyway ;)
For monthly payments, the denominator would be:
value_boy + (deposits - withdrawals)/2
Something amazing is revealed. Even though you may know very
little about what is "inside the box", following the BBOX curve gives you
an almost psychic view of certain details.
Why are there so many bumps in all the curves? In mathematical
terms, BBAG results in a "differentiated" function. Hmmm, let's try that
again. BBAG is like a sneeze.
"AAH!" {head tilts back}
"AAAHH!!" {neck and shoulders thrown back}
"CHOOOOO!!!" {head, neck, and torso plunge forward}
Or, I could just say, "1.2 liters of air was expelled strongly from your
lungs." Both are accurate ways of describing the same event; the
"differentiated" description supplies a lot more drama. What drama do
the curves reveal? Here, let's see some secrets.
- The solid purple and turquoise lines in the middle are the T+I cases.
up to age 48 -- very bumpy!
The total return on the underlying bond fund
(
VBIIX)
from 1996 to 2001 (beginning when I was 42) varies. It's return is
affected by both bond income and the underlying relative value of the bonds
themselves. In the long run gain is steady, but year-to-year there are
significant changes in Net Asset Value of the fund. Bumps.
up to age 71 -- smooth ascension
Those years haven't happened yet. I assume an annualized yield of
6.75% for every year, so no bumps. The curves slowly strive to reach
that point, being held back by the $485/year term insurance premium.
The "min T+I" curve is held back more because $485 is a higher percentage of
it — less total money invested than "max T+I", so $485 has a greater
effect on "min". Still, both ascend because total value in both is
increasing, and the term cost is remaining constant.
up to age 73 and 74 -- essentially flat
Term premiums stop; earnings match the 6.75% assumed annualized yield.
Well, kind of. At about age 71, the law requires that money begins
coming out of IRA's. So, a 20-year period begins of the investment
moving from VBIIX into an unspecified tax-free municipal bond fund.
I assume an annualized yield of 6.25% on it.
up to age 91 -- slow minor downward drift
Two things are happening. First, the total yield is slowly dropping from
6.75% to 6.25% as funds are transferred out of the IRA. Second, the
money transferred out of the IRA is subject to a one-time tax. (I assume
a tax bracket of 15%. Only the funds actually transferred each year are
taxed. Funds still within the IRA still accrue tax-deferred. Once
funds are within the tax-free fund, they are not subject to income tax again
— not even when passed to heirs! Thus this money can act just like
a death benefit on life insurance.
up to age 99 -- constant
You see the 6.25% yield assumed on the tax-free municipal bond fund.
No more taxes; no more transfers.
All the other earnings curves conspired to hide the taxation.
Fortunately, there is very little that can be hidden from a BBAG curve.
You won't necessarily know what happened, but it will be obvious if
something did.
Ok, these are not secrets. All details are known ahead of time --
the T+I models are my creation, after all. How about the real
black box, a "Whole Life" insurance policy?
- The other three lines (brown, orange, and green) are Total Cash Value.
My model tracks three insurance strategies, "base policy",
"base policy with extra payments past year 12" (XP), and "front-loaded OPP".
Just like the two T+I cases, these three curves seem to have the same
general personality, and track each other. And, boy, do they bounce!
(Note that the XP and Base cases are exactly the same for the
first 12 years; XP simply continues normal premium payments a bit longer.
OPP uses extra money above premium to "overfund" the policy. While
this occurs, BBAG is dragged down due to a larger denominator.
Once premiums and overfunding cease in all three cases, the ratios are on
an equivalent footing.)
Since the tables below comes directly from the spreadsheet, I used the
same style conventions.
- bold column labels are beginning-of-year values.
- non-bold labels are end-of-year, or somewhere in between
- yellow background
is a value which is either historical or guaranteed
To date, I have received statements for the first
five policy years. These numbers are not projections,
guesses, or derived calculations. They are what NYL has
actually reported to me, or guaranteed in the policy contract.
Dark Yellow
represents a mixture of guaranteed and speculative.
I have not yet made the OPP payments for the final
three years shown, so increasing the guaranteed value by this
amount is neither historical nor guaranteed.
- violet background
is a value directly from the policy illustration
- white background
(normal) is a value derived by my model
|
Let's use one of Ricky's dictums to see what's causing the bouncing:
bbag_curve + numbers = intuited_grey_box
-- Ricky's Little Book of Financial Truisms
I suggest you open up the BBAG curve (click on it to get a 2nd,
smaller window of just the image), then scroll back down here.
You may be able to look at the curves, the tables, and my description
at the same time.
Base Policy
|
Yr |
value beg.of year |
premium
(cash_oop) |
delta Guar.Value |
estimated Costs |
value end of year |
bbag |
comments |
1 |
$0 |
$1764 |
$0 |
-$1764 |
$0 |
-100% |
Compare BBAG with dGV (change in Guaranteed Value). Oscillations
in dGV are the primary reason BBAG seems so bouncy. This remains
true for the life of the policy. Other sources of earnings build
rather smoothly, but dGV goes up and down for no obvious reason.
The Estimated costs column involves a lot of
guesswork and supposition. Don't trust it except to get an approximate
idea of what policy fees might be. The model does not use estCost
as input into any other calculation.
|
2 |
$0 |
$1764
{$3528} |
$0 |
-$1604 |
$160 |
-91% |
3 |
$160 |
$1764
{$5292} |
$1300 |
-$304 |
$1,673 |
-13% |
4 |
$1,673 |
$1764
{$7056} |
$1600
{$2900} |
-$304 |
$3,548 |
3.2% |
5 |
$3,548 |
$1764
{$8820} |
$1500
{$4400} |
-$404 |
$5,390 |
1.5% |
6 |
$5,390 |
$1764
{$10,584} |
$1800
{$6200} |
-$304 |
$7,603 |
6.3% |
7 |
$7,603 |
$1764
{$12,348} |
$1800
{$8000} |
-$304 |
$9,892 |
5.6% |
8 |
$9,892 |
$1764
{$14,112} |
$1800
{$9800} |
-$304 |
$12,265 |
5.2% |
9 |
$12,265 |
$1764
{$15,876} |
$1900
{$11,700} |
-$304 |
$14,828 |
5.7% |
- The continued bumpiness is due to oscillations in Guaranteed Cash Value.
I blame a lot of the localized variance on some marketing manager years
ago. Let's call him Manager Mayfield. A conversation like the
following may have taken place in the mid-1950's:
MM: Yes? Oh, it's you. Enter.
[young clerk enters Manager Mayfield's office and stands nervously]
MM: Your Guaranteed Cash Value table is very precise.
clerk: Thank you, sir. [clearly pleased]
MM: I don't want precise.
clerk: Sir?!?
MM: People want hundreds, they don't want dollars.
clerk: I do not understand, sir.
MM: The numbers are too ... busy. Why say $1327? $1300 is better.
clerk: $1327 is the right number, sir. Well, $1326.89 was right, but I rounded.
MM: Round some more. No, don't round. Just make the last two numbers '0'.
clerk: What about the $27?
MM: Add it in the next year. Give me two zeros each year. Hundreds.
MM: ... People like hundreds. I like hundreds.
clerk: Well, ok. ... but ... it will make our job messier.
MM: [stares at clerk]
clerk: Yes, sir. Good day, sir. [exits stage right]
I more or less understand why NYL chooses to list Guaranteed Cash
Value in divisions of hundreds. (I like hundreds, too!) But
since GCV is a primary component of policy earnings, the arbitrary $100
increments do show up in a plot. Hence, continuos bumps are
observed in Black Box Annual Gain.
For comparison, the below table adds in front-loaded extra payments, and
completely messes up Manager Mayfield's marketing simplifications.
Base Policy + OPP Front-Loading
(Option to Purchase Paid-up Additional Insurance)
|
Yr |
value beg.of year |
premium + OPP |
delta Guar.Value |
estimated Costs |
value end of year |
bbag |
comments |
1 |
$0 |
$2064 |
$277
{$286} |
-$1787 |
$286 |
-86% |
With the front-loaded OPP strategy, there is significantly more Cash Value
early on. Guaranteed Value increases the same choppy way, unaffected
by OPP purchases. But with more cash, the BBAG ratio is less
driven by Guar. Cash Value, and more by total Cash Value. A less
wild curve results.
The Guaranteed Value includes both the contracted guaranteed value
as well as the cash value of the purchased Paid-Up Additional insurance.
Estimated costs here include one of the few known costs. There
is a 3% load on OPP purchases, so it is added in.
(In the first year I got fee'd! OPP purchased
later than one month after your policy anniversary gets "adjusted"
-- in essence, a late fee. Instead of $300 at eoy, I only had $286.
The OPP rider does state this will happen.
This is the only extra fee I have had to pay.)
|
2 |
$286 |
$2436
{$4500} |
$652
{$969} |
-$1624 |
$1,138 |
-58% |
3 |
$1,138 |
$2700
{$7200} |
$2208
{$3239} |
-$332 |
$3,647 |
-5.0% |
4 |
$3,647 |
$2400
{$9600} |
$2217
{$5541} |
-$323 |
$6,285 |
3.9% |
5 |
$6,285 |
$2400
{$12,000} |
$2117
{$7763} |
-$423 |
$8,959 |
3.2% |
6 |
$8,959 |
$2400
{$14,400} |
$2417
{$10,280} |
-$323 |
$11,980 |
5.5% |
7 |
$11,980 |
$2400
{$16,800} |
$2417
{$12,843} |
-$323 |
$15,133 |
5.2% |
8 |
$15,133 |
$2400
{$19,200} |
$2417
{$15,426} |
-$320 |
$18,420 |
5.0% |
9 |
$18,420 |
$2400
{$21,600} |
$2417
{$18,126} |
-$317 |
$21,947 |
5.4% |
- OPP tracks higher than XP, which tracks higher than the Base Policy case.
Dividend rates are pretty much the same in all three curves. Guaranteed
Cash Value is the same in all three curves. They vary because of a
third and even fourth source of annual gain, called
LIV (Linear Increase in Value). OPP has
a lot more LIV than XP, which has a little more than the Base Policy case.
- The dip in later years is likely due to cost of insurance.
Remember, Fred the actuary says I'm supposed to be dead at 79. The
cost of insurance gets really expensive as I approach this age, and downright
astronomical once I pass it. So why does the curve flatten out and
go positive again? Remember the earlier curves that shows the
convergence of Total Cash Value and Death Benefit? There was a
reason to cause this convergence. It was not done just because it
"seemed natural" or "looks good". My policy only insures the
difference between Base Death Benefit and Guaranteed Cash Value.
This is all it needs to do. Besides, if it kept paying for a flat $100,000
Death Benefit, the cost of insurance would likely eat up all earnings.
So the lines converge, and the amount that needs to be insured gets less.
Cost of insurance remains manageable, even though expensive.
BBAG is useful if you only care about annual, not total performance.
In fact, no matter how "psychic" the information provided, the above curve
is useless in representing total performance. (Differentiation:
all plot, no theme.)