Investor Analysis of Index Annuities

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Investor Analysis of Index Annuities

Postby ThePrune » Sat May 18, 2013 9:40 pm

SUMMARY OF THE POSTING: I've taken a first stab at creating a general purpose Monte Carlo modeler for comparing Fixed Index Annuities to combinations of stock and bond mutual funds.

WHAT I'M SEEKING:
A few folks willing to Beta test the program. Must be knowledgeable with Excel programming.
A few folks willing to improve the approach I've taken to to generate random monthly returns on the S&P 500 and the Dow Jones Industrials price indices.
A few folks willing to check to see if there are Fixed Index Annuity schemes that I haven't yet incorporated in the modeler.

IF THESE DON'T DESCRIBE YOU? Nothing more to read here. Move along to the next posting!
________________________________________________________________________________________

As Bogleheads we take great pride in being "data driven" in our analysis of financial investments. Reading this forum over the last several years I have been exposed to numerous excellent studies substantiating the long term superiority of low-cost index mutual funds. This has supplied me with great "ammunition" for discussions with brokerage sales agents.

As many of you are aware, the primary financial product being sold today by Insurance Producers is the Fixed Index Annuity (aka Equity Indexed Annuity). It has always struck me, though, that whenever posting streams on Fixed Index Annuities appear here, the argument comes down to something like, "smart people have analyzed them, they're complicated, and they're a bad investment."

But can't we do something more :confused What if we could produce a program that would allow a Boglehead with reasonable financial and Excel skills to quickly analyse an arbitrary Fixed Index Annuity, quantitatively compare it to a combination of stock and bond index mutual funds, and allow them to show friends the financial drawbacks of the index annuity?
We should have done this years ago :oops: (And maybe someone has! Please let me know, if so!)

So I've taken a stab at this problem. After my most recent request to consider purchasing a fixed index annuity (the Bonus Gold from American Equity Investment Life Insurance Company), I created a general purpose Monte Carlo modeling program (in Excel) for index annuites. It has these features:
- Handles the S&P 500 and the Dow Jones Industrial price indices
-Contract terms from 5 to 20 years
-Can incorporate "premium bonuses"
-Can simulate "Annual Monthly Average", "Anual Point to Point" and "Monthly Point to Point" crediting schemes
-Can handle either cap rate or participation rate limits on the price index increases
-Can apply additional Asset Rate Fees either before or after the cap/participation rate limits

For investment comparisons, it allows a combination of stock and bond mutual funds:
-Percentages of funds in stocks from 100% to 0%
-Set your preferred dividend yield and expense ratio for the stock fund
-Set your preferred bond yield and expense ratio for the bond fund
-Or model a single fund investment with both stocks and bonds
-Annual rebalancing is allowed, but can be turned off

For comparison in taxable brokerage account, you can enter your marginal tax rate, qualified dividend rate, and long term capital gains rate. Or you can ignore taxes.

If you've read this far, you already know what I want: VOLUNTEERS! :D (But not too many.) You can either PM me to get a copy of the program (Excel 2003 with VBA macros), or add to this posting stream with questions, comments or suggestions.
Last edited by ThePrune on Fri May 30, 2014 9:02 pm, edited 1 time in total.
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Re: Investor Analysis of Index Annuities

Postby MN Finance » Sun May 19, 2013 12:07 am

Just a comment, not a volunteer. But I will find this very helpful. Obviously we rail against annuity products, but in today's interest environment, it could very easily be the case that fixed index annuities could provide a better total return than other fixed income options, with similar or lower risk (one being surrender fees). If we can get a CD or bond at 2% and an indexed annuity without riders (as pure an investment as possible) the over/under for the product to come out ahead is very low (2%).
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Re: Investor Analysis of Index Annuities

Postby kpoole » Tue May 21, 2013 9:50 pm

I wouldn't be much help on the programming side, but I analyze over a hundred annuities per year (from various companies), so I might be abble to identify schemes that are not included in your model. Please let me know if I can help.
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Re: Investor Analysis of Index Annuities

Postby bberris » Wed May 22, 2013 7:48 am

MN Finance wrote:Just a comment, not a volunteer. But I will find this very helpful. Obviously we rail against annuity products, but in today's interest environment, it could very easily be the case that fixed index annuities could provide a better total return than other fixed income options, with similar or lower risk (one being surrender fees). If we can get a CD or bond at 2% and an indexed annuity without riders (as pure an investment as possible) the over/under for the product to come out ahead is very low (2%).


What magic does an insurance company perform to provide you with superior risk-adjusted returns, give a 10 % comish to the salesman, and a comfortable profit margin to themselves?
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Re: Investor Analysis of Index Annuities

Postby dhodson » Wed May 22, 2013 8:21 am

As im sure you know (at least i guess it based on the wording of your post), there is no magic.

In a simplistic form, what the insurance company does is invest the majority of the money invested like 96% in their typical portfolio which is high in bonds/treasuries. They invest the rest in options. If the stock market goes down then the options are worthless and they likely can meet the minimum guarantee via their bonds/treasuries. If the stock market goes up then they credit your acount based on the crediting method chosen beyond the minimum guarantees. If the stock market isnt behaving as they predicted then they can unilaterally change the caps and/or participation rates. The surrender fees/period also make sure they cant get burned. Frankly if they didnt have methods to make sure they didnt get burned then they might have trouble making their guarantees.

Bottom line for me is that there is no magic in this world and that is why a strategy such as index annuities wont work. Costs matter.
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Re: Investor Analysis of Index Annuities

Postby MN Finance » Wed May 22, 2013 10:33 am

This thread wasn't started to debate the merits or lack thereof of an indexed annuity.

I am no annuity sympathizer - far from it. But first, costs don't matter in an indexed annuity. In fact there are no explicit costs. It's not any different than asking your bank what the costs of their CDs are. The only thing that matters are the terms of the contract. When compared to a traditional portfolio (as they are often sold,) they are totally inadequate (which is prune's thesis). My interest is in their possible use as a replacement for other traditional fixed income investments because of the rate environment we're in. The expectation is that in a normal world they would be inferior to conventional bonds (historically they have mirrored EE bond returns closely, both of which very much underperformed the bond market over time). I can buy a 10 year treasury and get 2% over the next 10 years. Alternatively, I could buy a fixed index annuity and get a return between maybe 0% and 10% per year. This is not an unreasonable tradeoff with similar risks, but one that I don't have a firm grasp on - hence my interest in the work prune is doing. (Of course the downside would be the need to surrender the annuity early and pay a penalty.)

Any "magic" is that my return is not solely based on the performance of the specific asset underlying my investment (like any conventional fund). My return is based on the promise of the insurance company to pay the terms of the contract, thus transferring risk, which only shows up if the company becomes insolvent and isn't bailed out.
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Re: Investor Analysis of Index Annuities

Postby dhodson » Wed May 22, 2013 10:53 am

unfortunately my previous post commending him for doing the work was deleted with the recent forum problems and that is why i was only responding to the other post.

however you are wrong about the cost issue. The costs just arent transparent. This is why the company is legally allowed to change unilaterally the caps/participation rates which at the moment are primarily reducing the upper caps if im not mistaken. As you mentioned the interest rate environment right now is low and the majority of the investments the insurance company is making with their general fund will be impacted by this. To say well currently a cd gets x% but historically an index annuity has gotten up to 10% isnt being realistic bc the underlying investements are still bond/treasuries primarily and thus those factors will still impact the return. They cant produce returns higher than what they are investing in minus costs and their costs are high.
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Re: Investor Analysis of Index Annuities

Postby MN Finance » Wed May 22, 2013 11:55 am

The ONLY thing "costs" impact is the solvency of the insurer. If the contract says I have a monthly cap of 2.5% and an annual floor of 0%, neither the 0% or 2.5% are impacted by any costs (stated or otherwise). How is my return impacted by anything other than the 0% and 2.5% numbers? It's not. I don't care if the general account returns any particular return and if it's return is enough to produce my contractual return or vastly more than my contractual return. In aggregate the insurer isn't going to lose money; and they will adjust new contract terms to ensure that doesn't happen, but there's nothing that says I can't evaluate the stated terms of a contract in comparison to other fixed income alternatives. That's a totally valid comparison. I can take a treasury or CD with a known future return and compare that to a monte carlo of potential index annuity returns and make a judgment. If a known future CD return is 2% and the data shows the indexed annuity has a dispersion of outcomes between 1% and 12% with a 95% confidence interval over the same term with an average return of 5% and a standard deviation of 6%, now an informed decision can be made. (Made up numbers, until there's data to look at).
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Re: Investor Analysis of Index Annuities

Postby ndchamp » Wed May 22, 2013 11:59 am

First see what you're REALLY getting in a fixed income option.
Probably no need to go any further.
Moshe A Milevsky offers a way to do that.
http://www.advisorone.com/2009/08/01/annuity-analytics-what-is-a-guaranteed-rate-really
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Re: Investor Analysis of Index Annuities

Postby dhodson » Wed May 22, 2013 12:06 pm

MN Finance wrote:The ONLY thing "costs" impact is the solvency of the insurer. If the contract says I have a monthly cap of 2.5% and an annual floor of 0%, neither the 0% or 2.5% are impacted by any costs (stated or otherwise). How is my return impacted by anything other than the 0% and 2.5% numbers? It's not. I don't care if the general account returns any particular return and if it's return is enough to produce my contractual return or vastly more than my contractual return. In aggregate the insurer isn't going to lose money; and they will adjust new contract terms to ensure that doesn't happen, but there's nothing that says I can't evaluate the stated terms of a contract in comparison to other fixed income alternatives. That's a totally valid comparison. I can take a treasury or CD with a known future return and compare that to a monte carlo of potential index annuity returns and make a judgment. If a known future CD return is 2% and the data shows the indexed annuity has a dispersion of outcomes between 1% and 12% with a 95% confidence interval over the same term with an average return of 5% and a standard deviation of 6%, now an informed decision can be made. (Made up numbers, until there's data to look at).



Very easily the contract says they can reduce the 2.5. They will if there is no profit/losing money. That's part of the problem that the 2.5 isn't guaranteed.

Additionally we dont have data with these types of products in a long period of low interest rate as far as i know. That is another reason why the underlying investments and costs are important. You would be making a determination based on data that sounds scientific but isnt practical.

If you look at other insurance products, the companies do make these sort of changes. For instance with LTCi, they have raised rates bc rates arent guaranteed. Recently there was a thread that some states are concerned about the investments that some companies are now looking to make since they are having a hard time meeting their guarantees. This of course is more in line with your concern about just insolvency. They cant just change new contracts to make up the losses since nobody would buy them.
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Re: Investor Analysis of Index Annuities

Postby MN Finance » Wed May 22, 2013 1:14 pm

ndchamp wrote:First see what you're REALLY getting in a fixed income option.
Probably no need to go any further.
Moshe A Milevsky offers a way to do that.
http://www.advisorone.com/2009/08/01/annuity-analytics-what-is-a-guaranteed-rate-really


This is not the product being discussed.

dhodson wrote:Very easily the contract says they can reduce the 2.5. They will if there is no profit/losing money. That's part of the problem that the 2.5 isn't guaranteed.


They can't change the terms of a contract. If the contracts states the terms accurately, then a judgment can be made.

I'm not trying to make a case for myself or anyone else to by an indexed annuity, but any knowledgeable investor should be interested in understanding what options exist. There is very little data on the performance of indexed annuities, which is exactly why this is a valid exercise. That's my only point in commenting at all.
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Re: Investor Analysis of Index Annuities

Postby dhodson » Wed May 22, 2013 1:24 pm

MN Finance wrote:
ndchamp wrote:First see what you're REALLY getting in a fixed income option.
Probably no need to go any further.
Moshe A Milevsky offers a way to do that.
http://www.advisorone.com/2009/08/01/annuity-analytics-what-is-a-guaranteed-rate-really


This is not the product being discussed.

dhodson wrote:Very easily the contract says they can reduce the 2.5. They will if there is no profit/losing money. That's part of the problem that the 2.5 isn't guaranteed.


They can't change the terms of a contract. If the contracts states the terms accurately, then a judgment can be made.

I'm not trying to make a case for myself or anyone else to by an indexed annuity, but any knowledgeable investor should be interested in understanding what options exist. There is very little data on the performance of indexed annuities, which is exactly why this is a valid exercise. That's my only point in commenting at all.


The terms of all these contracts say they CAN change those things. Is that something that you are unaware of? Ive already mentioned that i commended him for the work. I think doing work on this or other investment strategies is always beneficial but one needs to understand the limits of the study being performed. I can only hope that the additional posts will draw more people in to consider working with the OP (since he wasnt getting any traction earlier).
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Re: Investor Analysis of Index Annuities

Postby ThePrune » Wed May 22, 2013 1:43 pm

dhodson wrote:Very easily the contract says they can reduce the 2.5. They will if there is no profit/losing money. That's part of the problem that the 2.5 isn't guaranteed.
This is indeed correct.

For example, the contract terms of the Bonus Gold index annuity that I modeled with my program stated that American Equity had the right each year on the anniversary of the contract date to change the index cap or the participation rate, but that those rates could never be less that rates stated in the contract. For May 2013 here are actual numbers for this 16 year :shock: contract index annuity:

Monthly Index Average or Annual Point-to-Point with cap.
Current cap = 2.75%
Minimum cap = 1.00%

Monthly Index Average or Annual Point-to-Point with participation rate.
Current participation rate = 20.0%
Minimum particiaption rate = 10.0%

Monthly Point-to-Point with cap.
Current cap = 1.70%
Minimum cap = 1.00%

One of the difficutlies with modeling an index annuity is deciding how to deal with the freedom the issuing insurance company has to annually change (OK, drop!) the caps and partitipation rates. In my initial comparisons I took a "Best Case" approach and left the caps / participation rates at their starting levels. Even here the combination of index mutual funds can out as a superior investment.

I have also incorporated into the program the ability to make annual adjusments to the caps and participation rates. I'm trying to get my head wrapped around the rules that the insurance company would follow in dropping these caps / rates.
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Re: Investor Analysis of Index Annuities

Postby ThePrune » Wed May 22, 2013 1:59 pm

MN Finance wrote:Just a comment, not a volunteer. But I will find this very helpful. Obviously we rail against annuity products, but in today's interest environment, it could very easily be the case that fixed index annuities could provide a better total return than other fixed income options, with similar or lower risk (one being surrender fees). If we can get a CD or bond at 2% and an indexed annuity without riders (as pure an investment as possible) the over/under for the product to come out ahead is very low (2%).

I don't know about "easily", but it could happen.

It's like the old joke about an economics professor and one of his students who are walking along a sidewalk. The student spots a $20 bill and stoops to pick it up. The professor tells him not to bother: if it really were a $20 bill, someone would have already picked it up!

Bogleheads know that, in general, they aren't going to find numerous index annuities having competitive value as they walk along the investment world's sidewalk. But if they had a handy tool, they could be in a position to quickly decide if they had run across one of those rare "$20 bills".

The above points are interesting, but my main motivation for this program is to be able to produce real numbers to back up my recommendations not to invest in a specific index annuity. Because I teach retirement planning and investing classes in my community, I get asked such things. I'd like to get beyond, "They're just bad" to being able to say, "Here's how much worse this particular index annuity is in dollars."
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Re: Investor Analysis of Index Annuities

Postby Frugal Al » Wed May 22, 2013 3:29 pm

I understand some people just love to crunch numbers to quantitatively prove a point, but this product becomes a non starter when it combines illiquidity along with the insurance company's controlling the expenses (via the cap/participation rates) at their own discretion. If we then throw in the fact that they don't include dividends in the "returns" they use, and the gains are all taxable as ordinary income, this proves to be a product only an insurance marketing team could endorse. Once again, beware the high cost of guarantees.
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Re: Investor Analysis of Index Annuities

Postby dhodson » Wed May 22, 2013 5:51 pm

I hear you OP but as you can probably guess from my posts, im not sure you can really do what you want to do and have serious validity since you dont have enough data points to really know what they will do with the caps/part. These products havent existed in a longer low interest rate environment to produce data.

There really arent any rules about when they change caps/part rates besides what you mentioned which is typically they can do it yearly. It is at their leisure and for any reason they want. Lets take the product you mentioned with a 16 year contract/surrender period. Those 16 years given them a huge advantage since if it isnt working out as desired for them then they can really hit you on the caps/surrender until you have a product that is definitely below inflation and it gets pretty unlikely that they lose money. Now dont get me wrong, i dont think their intent is to definitely screw people down to the bare minimum. If for some reason we are in an environment where the bonds/treasuries from their general funds are doing great and the options are doing great then i think they will pass some of that along. In the end if you arent willing to live with a mainly bond/treasury investment with a small play on options including an additional fairly high commission then it isnt likely that this is the ticket for you.

Again i wish you the best with your research and i look forward to seeing what answers you feel you find.
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Re: Investor Analysis of Index Annuities

Postby ThePrune » Thu May 23, 2013 10:27 am

I've done some more Internet research using Google and have discovered that EIA sales and marketing groups are WAY ahead us us. They have already developed Monte Carlo based "sales demonstration tools" to help Insurance Producers "close the sale" for index annuity products.

An example: MCP Suite Basic: EIA Software.
As an agent or financial advisor, your job is to present products you believe will improve or protect your client's financial situation. Put away that yellow notepad and instead impress them with simple historical charts that
demonstrate how an EIA might have performed versus the stock market or their CD over any time period you choose. Then, drive the point home by illustrating their possible future earnings with a concise, colorful Monte Carlo simulation. With minimal effort on your part you successfully gain their respect, earn their trust, and close the sale. As we like to say, "Work smarter, not Harder!"

By using Monte Carlo software, the sales agent brings the "aura of quantitative objectivity". Of course these programs focus on the risks of loss when investing in 100% equities, and then compare that to the guarantee of no loss with an EIA product. I doubt there is any effort to compare the EIA to the best combination of low-cost stock and bond index funds.

It's one thing to simply state, "Index anuities are a bad investment." It's an entirely different situation when the person seeking our advice comes with a fancy printout from a Monte Carlo sales tool and says, "This advanced mathematical analysis shows that the EIA is a better investment. Why should I believe what you're saying?"
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Re: Investor Analysis of Index Annuities

Postby ThePrune » Thu May 23, 2013 11:12 am

kpoole wrote:I wouldn't be much help on the programming side, but I analyze over a hundred annuities per year (from various companies), so I might be abble to identify schemes that are not included in your model. Please let me know if I can help.

kpoole, thanks for your offer, and my apologies for being slow to respond.

Here are the cediting schemes I thought were most common and therefore incorporated first into the MC program:
    Annual Monthly Average with cap
    Annual Monthly Average with participation rate
    Annual Point to Point with cap
    Annual Point to Point with participation rate
    Monthly Point to Point with cap
Here are some crediting schemes I've since read about but haven't incorporated yet:
    Monthly Point to Point with participation rate
    Annual Point to Point with monthly Look Back and cap
    Annual Point to point with monthly Look Back and participation rate
    Contract Term Point to Point with cap
    Contract Term Point to Point with participation rate
    Contract Term Point to Point with annual Look Back and cap
    Contract Term Point to Point with annual Look Back and participation rate
    Contract Term Point to Point with monthy Look Back and cap
    Contract Term Point to Point with monthly Look Back and participation rate
Can you suggest which of these additional types of crediting schemes would be most important to add? In fact, I could add all of them without too much trouble. (Note: I don't want to get into modeling daily lookbacks!)

Another feature that FIA contract have is variously refered to as a "Spread" or a "Asset Fee Rate". My program can incorporate these either before or after the caps/participation rates are applied. (But I think these are typically applied afterwards.)

Currently I have only incorporated the S&P 500 and the Dow Jones Industrial Average for index crediting. I am aware that some companies offer other indexes: NASDAQ 100, EuroStox 600, etc. Are any of these alternatives really chosen very often by individual purchasers?

Any other features you'd suggest adding?
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Re: Investor Analysis of Index Annuities

Postby Oicuryy » Thu May 23, 2013 1:40 pm

How would your software analyze this index-linked CD?
http://PROSPECTUS.BONDTRADERPRO.COM/$48124JZU5.PDF

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Re: Investor Analysis of Index Annuities

Postby gerrym51 » Thu May 23, 2013 1:46 pm

Oicuryy wrote:How would your software analyze this index-linked CD?
http://PROSPECTUS.BONDTRADERPRO.COM/$48124JZU5.PDF

Ron



i have looked at these(fidelity also sells them). the efficiente index is relatively complicated although i've read its brochure. the problem i have with it is say the index keeps going up for 5 years then on the day before you figure out its final interest and it crashes back to original price you get nothing. its the price on day 1 subtracted from price on last day.

the efficiente index has a big GOLD component. in the fine print of efficiente index it cautions on gold.
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Re: Investor Analysis of Index Annuities

Postby ThePrune » Thu May 23, 2013 2:23 pm

Oicuryy wrote:How would your software analyze this index-linked CD?
http://PROSPECTUS.BONDTRADERPRO.COM/$48124JZU5.PDF
Ron

Ron, thanks for writing with the challange. I had always wondered how these Index linked CD's sold by JPMorganChase were structured.

Executive Summary: JPMorganChase will give you the original invested principle back at the end of 5 years. If you are really nice to them, they might give you a little bit more back.

Details: to use the Monte Carlo model, it is necessary to be able to describe the crediting index with a stationary statisitcal distribution. But when you look at the crediting index being used by JPMorganChase, the JPMorgan ETF Efficiente 5 Index, the index is not stationary. Rather, JPMorgan has the right to change the percentages of each ETF in the index monthly according to their internal opinion about what Modern Portfolio Theory would predict to be the most efficient mix of stocks, bonds, alternative investments and cash over the next month. Basically, there is no way of knowing how they will adjust the mix in advance. Just modeling their index alone would be tougher than modeling an entire FIA which uses a more traditionally defined index.

I really like this JPMorganChase statement
POTENTIAL CONFLICTS wrote:We and our affiliates play a variety of roles in connection with the issuance of the CDs, including acting as CD calculation agent and index calculation agent and hedging our obligations under the CDs. In performing these duties, the economic interests of the CD calculation agent and other affiliates of ours are potentially adverse to your interests as an investor in the CDs. It is possible that such hedging or trading activities could result in substantial returns for us or our affiliates while the value of the CDs declines.

They should just drop the word "potentially" out of the sentence I highlighted in red :annoyed
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Re: Investor Analysis of Index Annuities

Postby gerrym51 » Thu May 23, 2013 3:12 pm

i wonder why your moniker is ThePrune as opposed to Prune. just wondering :mrgreen:
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Re: Investor Analysis of Index Annuities

Postby ThePrune » Thu May 23, 2013 3:25 pm

gerrym51 wrote:i wonder why your moniker is ThePrune as opposed to Prune. just wondering :mrgreen:

Gee, no particular reason. When I had to create a username, that's what came to mind. It's a play on words of sorts, since my last name is French and means plum tree. But I'm well past 50, and no longer a young plum :mrgreen:
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Re: Investor Analysis of Index Annuities

Postby gerrym51 » Thu May 23, 2013 3:28 pm

ThePrune wrote:
gerrym51 wrote:i wonder why your moniker is ThePrune as opposed to Prune. just wondering :mrgreen:

Gee, no particular reason. When I had to create a username, that's what came to mind. It's a play on words of sorts, since my last name is French and means plum tree. But I'm well past 50, and no longer a young plum :mrgreen:



my grandparents were from canada and mine is a grain :mrgreen:
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Re: Investor Analysis of Index Annuities

Postby ThePrune » Mon May 27, 2013 4:31 pm

I've finished updating the Excel modeler for Fixed Index Annuities (aka Equity Indexed Annuities). I decided to use the terminology from and to include all the contract options explained in the NAIC Buyer's Guide to Fixed Deferred Annuities, which has an Appendix devoted to Equity Indexed Annuities. Final result: 10 index crediting schemes, each of which can be combined with caps, participation rates, floors and margins/spreads.

I found it very useful to review the NAIC Buyer's Guide. I had forgotten that FIA's sometimes use a Simple Interest approach for crediting, rather than the Compound Interest approach. One more variable to add into the modeler! But the consumer warnings seemed too weak :annoyed Consider this statement:
As with any other insurance product, you must carefully consider your own personal situation and how you feel about the choices available. No single annuity design may have all the features you want. It is important to understand the features and trade-offs available so you can choose the annuity that is right for you.
Can't really understand those features and trade-offs without a modeler!

On the Monte Carlo side, I've added Historical Returns Sequence and Historical Returns Distribution as new approaches to generating the simulated monthly index returns:
    Historical Returns Sequence: randomly pick a starting month in the range 1927-2012. Simulate monthly returns in the model as following the observed historical sequence of returns starting from that point. Repeat 1000's of times. If the sequence gets to March 2013 before the end of the contract term, loop back to the beginning and follow the historical returns from there.

    Historical Returns Distribution: this is the classic "Bootstrap" approach to mimicing an empirical distribution. Each monthly return in the simulation is derived by randomly selecting an observed monthly return from historical period 1927-2012, with replacement. This approach leads to a larger variance in contract term outcomes, since it lacks the "reversion to the mean" inherent in Historical Returns Sequence approach.

I'm still interested in getting some others to check over the modeler for Excel coding errors.
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