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How to replicate an equity-indexed annuity (EIA)
Old 04-07-2008, 01:56 PM   #1
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How to replicate an equity-indexed annuity (EIA)

A word of caution:

This is not intended to be investment advice. Everything described herein has significant risks, including, but not limited to market risk, default risk, tax risk, the possibility that you will screw up the trades, etc. Please consult your advisor and/or due your own due diligence before making any investment whatsoever. YMMV, E Pluribus Unum, Ramen.

What is an EIA?

An EIA is an insurance contract that theoretically offers the buyer the opportunity to participate (to some extent) in equity market performance while guaranteeing a minimum payout at the end of the policy guarantee period. The extent to which the buyer participates in equity market performance typically varies year to year as does the minimum guaranteed crediting rate (AKA interest rate paid on the policy). This has proven to be a tantalizing pitch for many conservative investors. The problems with these policies are that you have little control over how much you participate in the equity market; the policies typically have high early surrender fees and very lengthy surrender periods (10+ years is not uncommon); the internal expenses of these policies are quite high; you are exposed to insolvency of the issuer; the participation is typically limited to price changes in an equity index, with no compensation for dividends on the index; the participation in the index is capped at a predetermined level so that really big gains are truncated within the annuity structure; and the tax treatment of eventual distributions may be less than optimal.

How you can “roll your own” EIA, part 1:

By far, the simplest way to set up an EIA is to do it in an uncapped version. The simplest uncapped replication portfolio consists of a 1 year fixed income investment (such as a CD) and a call option on whatever equity index ETF you want exposure to. So let us assume you can buy a 1 year CD that yields (APY) 4%, you want exposure to the S&P 500, you have $100,000 to invest, and you want a minimum yield of 1%. To replicate an EIA, you would buy the following:

CD: You want $101k in a year, so you invest $101,000/1.04 = $97,115 in a 1 year 4% yield CD. In a year, the CD matures and you get $101,000, which is your desired minimum payout.

Options: Your CD purchase leaves you with $100,000 - $97,115 = $2,885. You take this amount and buy at the money 1 year call options on the S&P 500 index ETF (ETF symbol SPY). At the money means that the option exercise price is about equal to whatever the ETF sells for today. So with SPY trading at $137.93 as I write this in April 2008, we wish to buy April 2009 calls with a strike of $138. Such a thing doesn’t exist, so we will settle for the closest month we can get, which is March 2009. March 2009 calls (Symbol SFBCH) sell for $12 each and must be bought in contracts on 100 shares each, so you want to buy $2885/$1200 = 2.4 contracts, but must buy 2 contracts for $2400.

So you end up with a CD that will pay $101,000 in a year, $485 in cash, and options on 200 shares of SPY struck at 138. The options cover a notional amount of $138 X 200 = $27,600, so your “participation rate” in the index is 27,600/100,000 = 27.6%, meaning that you catch 27.6% of the appreciation of the S&P 500 through next March while bearing none of the downside. When the options are about to mature, you can sell them for cash, assuming the market has gone up and they are worth anything. Otherwise, you collect your $101,000 from the CD, have your $485 plus whatever interest it generated, and decide if you want to play this game again for another year.


Rolling your own, part 2:

Instead of having a small, uncapped participation in the index, you could have a larger participation but cap it at a given level. This is essentially what is done inside the EIA contract sold by most insurers. To replicate the EIA, you would buy the same CD as in the above example. However, the options portion would include:

1) Buy the at the money options on the index as in the above example
2) Sell out of the money options for the same expiration date and underlying ETF.

An example will be helpful:

Lets assume that you would be willing to cap your upside in return for a higher participation rate. That means you want to buy call options at the money ($138 strike) and sell call options at a strike that is about 10% higher ($152 strike). The $152 strike options currently trade for about $5.50 a share. So we buy:

4 contracts of the at the money options (SFBCH) for 400X12 = $4800

And we sell:

4 contracts of the 10% higher strike $152 (symbol SYHCV) and receive cash of $400X5.50 = $2,200.

Total out of pocket for the options is $4,800 - $2,200 = $2,600.

So you end up with a portfolio that consists of a CD that will pay you $101,000 in a year, $285 in leftover cash, and a package of options that gives you up to 10% of the upside on 400 X $138 = $55,200 worth of the S&P 500 index. Note that by capping your potential upside you have increased your participation rate to $55.2% of your $100,000, or double the uncapped version.


About taxes:

If this is done in a taxable account, the CD interest will be taxable and so will the gains or losses on the options. In this case, you would want to set up the portfolio for at least 1 year and 1 day to qualify for long term cap gains on the options. So instead of buying a 1 year CD, perhaps you would buy an 18 month CD and options that expired in 18 months. Inside an IRA or other tax sheltered account this would be of no concern, but your broker may not allow you to set up the capped EIA replication inside an IRA.

Other odds & ends:

- I have ignored transaction costs here. The CD should cost you nothing. Most discount brokers will charge less that $20 for an option trade.
- Brokers generally require customers to apply for approval before they can trade options.
- Note that you can buy options on any index you like that has an ETF with options traded.
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Old 04-07-2008, 02:12 PM   #2
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Nicely done. First question: How many CD buyers are also willing to buy options? Not many folks I know........

I agree it is not as hard as folks think...........
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Old 04-07-2008, 02:15 PM   #3
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Nicely done. First question: How many CD buyers are also willing to buy options? Not many folks I know........
That is up to them. I think its kind of a dumb strategy to begin with, but for 5 minutes' work you can skip Gawd knows how many thousands of dollars of expenses if you decide you really like the whole return of principal thing.
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Old 04-07-2008, 02:41 PM   #4
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That is up to them. I think its kind of a dumb strategy to begin with, but for 5 minutes' work you can skip Gawd knows how many thousands of dollars of expenses if you decide you really like the whole return of principal thing.
I suppose there's also a way to duplicate a hedge fund with ETFs and ETNs but most folks might not attempt that.........
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Old 04-07-2008, 02:42 PM   #5
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I suppose there's also a way to duplicate a hedge fund with ETFs and ETNs but most folks might not attempt that.........
Depends on the type of fund, I suppose. You can get merger arb at the retail level via MERFX at almost any broker. Some of the more esoteric strategies, not so much. But for the vast majority of investors, such things are a waste of time anyway.
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Old 04-07-2008, 03:36 PM   #6
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Good write up Brewer.

A couple of things worth noting. The upside you get doesn't include the 2+% dividends that you'd collect by owning an S&P index fund/ETF.

Finally, with market volitality having increased dramatically over the last year, (To be fair 2003-2006 time frame was uncharacteristically stable) the cost of the option you are purchasing has gone up considerably. Meanwhile the interest rate on your CD has dropped dramatically. Adding these two together, and it is easy to see why, EIAs never a good investment, to begin with are particularly bad now days.
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Old 04-07-2008, 04:54 PM   #7
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Thanks Brewer. Good explanation.
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Old 04-07-2008, 05:30 PM   #8
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For Scenario 2

The total results over the last 96 rolling 12 month periods:1/1/2000 - 1/1/2008:

34 times you would have maxed out with a 10 percent or greater return +99,280
(2920 X 34)
33 times you would have had a total washout with a negative return -86,460
(2620 x33)
5 times a partial loss (gain of less than 4.7% 6.5pts/138) -11,622.51

24 times a partial gain (greater than 4.7 percent less than 10 percent) +35,332.64

Total net over 96 occurences: positive $36,530.13 or a net positive on average of $380.52 per occurence with at risk money of $2,620 for a net average return per transaction of 14.5 percent over each of the last 96 12 month periods assuming present costs of options.

In that time frame the S&P500 went from 1248 to 1379 a 10 percent gain in the index over 8 years.
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Old 04-07-2008, 05:38 PM   #9
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Originally Posted by brewer12345 View Post
A word of caution:

This is not intended to be investment advice. Everything described herein has significant risks, including, but not limited to market risk, default risk, tax risk, the possibility that you will screw up the trades, etc. Please consult your advisor and/or due your own due diligence before making any investment whatsoever. YMMV, E Pluribus Unum, Ramen.

What is an EIA?

An EIA is an insurance contract that theoretically offers the buyer the opportunity to participate (to some extent) in equity market performance while guaranteeing a minimum payout at the end of the policy guarantee period. The extent to which the buyer participates in equity market performance typically varies year to year as does the minimum guaranteed crediting rate (AKA interest rate paid on the policy). This has proven to be a tantalizing pitch for many conservative investors. The problems with these policies are that you have little control over how much you participate in the equity market; the policies typically have high early surrender fees and very lengthy surrender periods (10+ years is not uncommon); the internal expenses of these policies are quite high; you are exposed to insolvency of the issuer; the participation is typically limited to price changes in an equity index, with no compensation for dividends on the index; the participation in the index is capped at a predetermined level so that really big gains are truncated within the annuity structure; and the tax treatment of eventual distributions may be less than optimal.

How you can “roll your own” EIA, part 1:

By far, the simplest way to set up an EIA is to do it in an uncapped version. The simplest uncapped replication portfolio consists of a 1 year fixed income investment (such as a CD) and a call option on whatever equity index ETF you want exposure to. So let us assume you can buy a 1 year CD that yields (APY) 4%, you want exposure to the S&P 500, you have $100,000 to invest, and you want a minimum yield of 1%. To replicate an EIA, you would buy the following:

CD: You want $101k in a year, so you invest $101,000/1.04 = $97,115 in a 1 year 4% yield CD. In a year, the CD matures and you get $101,000, which is your desired minimum payout.

Options: Your CD purchase leaves you with $100,000 - $97,115 = $2,885. You take this amount and buy at the money 1 year call options on the S&P 500 index ETF (ETF symbol SPY). At the money means that the option exercise price is about equal to whatever the ETF sells for today. So with SPY trading at $137.93 as I write this in April 2008, we wish to buy April 2009 calls with a strike of $138. Such a thing doesn’t exist, so we will settle for the closest month we can get, which is March 2009. March 2009 calls (Symbol SFBCH) sell for $12 each and must be bought in contracts on 100 shares each, so you want to buy $2885/$1200 = 2.4 contracts, but must buy 2 contracts for $2400.

So you end up with a CD that will pay $101,000 in a year, $485 in cash, and options on 200 shares of SPY struck at 138. The options cover a notional amount of $138 X 200 = $27,600, so your “participation rate” in the index is 27,600/100,000 = 27.6%, meaning that you catch 27.6% of the appreciation of the S&P 500 through next March while bearing none of the downside. When the options are about to mature, you can sell them for cash, assuming the market has gone up and they are worth anything. Otherwise, you collect your $101,000 from the CD, have your $485 plus whatever interest it generated, and decide if you want to play this game again for another year.


Rolling your own, part 2:

Instead of having a small, uncapped participation in the index, you could have a larger participation but cap it at a given level. This is essentially what is done inside the EIA contract sold by most insurers. To replicate the EIA, you would buy the same CD as in the above example. However, the options portion would include:

1) Buy the at the money options on the index as in the above example
2) Sell out of the money options for the same expiration date and underlying ETF.

An example will be helpful:

Lets assume that you would be willing to cap your upside in return for a higher participation rate. That means you want to buy call options at the money ($138 strike) and sell call options at a strike that is about 10% higher ($152 strike). The $152 strike options currently trade for about $5.50 a share. So we buy:

4 contracts of the at the money options (SFBCH) for 400X12 = $4800

And we sell:

4 contracts of the 10% higher strike $152 (symbol SYHCV) and receive cash of $400X5.50 = $2,200.

Total out of pocket for the options is $4,800 - $2,200 = $2,600.

So you end up with a portfolio that consists of a CD that will pay you $101,000 in a year, $285 in leftover cash, and a package of options that gives you up to 10% of the upside on 400 X $138 = $55,200 worth of the S&P 500 index. Note that by capping your potential upside you have increased your participation rate to $55.2% of your $100,000, or double the uncapped version.


About taxes:

If this is done in a taxable account, the CD interest will be taxable and so will the gains or losses on the options. In this case, you would want to set up the portfolio for at least 1 year and 1 day to qualify for long term cap gains on the options. So instead of buying a 1 year CD, perhaps you would buy an 18 month CD and options that expired in 18 months. Inside an IRA or other tax sheltered account this would be of no concern, but your broker may not allow you to set up the capped EIA replication inside an IRA.

Other odds & ends:

- I have ignored transaction costs here. The CD should cost you nothing. Most discount brokers will charge less that $20 for an option trade.
- Brokers generally require customers to apply for approval before they can trade options.
- Note that you can buy options on any index you like that has an ETF with options traded.

thank you very much........
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Old 04-07-2008, 06:04 PM   #10
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Thanks, brewer!
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Old 04-07-2008, 06:07 PM   #11
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Thanks also for the write up. Let's say I'm using the SP 500 and it goes up 8% a year. (That may be optimistic over the next years per Bogle and others.)

Using the uncapped I would expect 1% plus about 27.6% of 8% or 3.21% total. (ignoring the cash left over)

Using the capped I would expect 1% plus about 55.2% of 8% or 5.41% a year with a max cap of about 6.52%.

Frist of all, is that correct? If so, I could likely have done about as well or maybe even better in CD's or a bond fund. I think it says options are very expensive insurance.
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Old 04-07-2008, 06:14 PM   #12
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very good, but to truly replicate an EIA don't you need to withdraw 2-3% each
year and throw it in the fireplace ?
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Old 04-07-2008, 06:36 PM   #13
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Thanks also for the write up. Let's say I'm using the SP 500 and it goes up 8% a year. (That may be optimistic over the next years per Bogle and others.)

Using the uncapped I would expect 1% plus about 27.6% of 8% or 3.21% total. (ignoring the cash left over)

Using the capped I would expect 1% plus about 55.2% of 8% or 5.41% a year with a max cap of about 6.52%.

First of all, is that correct? If so, I could likely have done about as well or maybe even better in CD's or a bond fund. I think it says options are very expensive insurance.
In the first case:
Assuming you were to get a return of 8 percent per year you would first need to deduct the 2 percent dividend so you would have 6 percent price appreciation per year. You would then receive 6 percent of 138*200 or .06 X $27,600 = 1,656 dollars on your original investment of $2,400 plus transaction costs. That is because you need the index to rise 8.7 percent per year merely to break even on the time value of the options. This would make a total of 2.656 percent total return.

The other unknown is since you could average 8 percent per year with some 20 percent down years once the year is down more than zero it has no effect on your return so in actuality you probably would do much better than the calculation above. For instance if the S&P were to rise from 1380 to 1550 in a year and drop to 1280 followed by a rise to 1550 you would make 200 * 17 = 3400 in year one followed by a loss of 2,400 followed by a gain of 200 * 27 = 5400 for total gain of $6,400 on an average price gain of six percent per year. This would be compared to the expected $4,968 on a straight line 6 percent.
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Old 04-07-2008, 06:45 PM   #14
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In the first case:
Assuming you were to get a return of 8 percent per year you would first need to deduct the 2 percent dividend so you would have 6 percent price appreciation per year. You would then receive 6 percent of 138*200 or .06 X $27,600 = 1,656 dollars on your original investment of $2,400 plus transaction costs. That is because you need the index to rise 8.7 percent per year merely to break even on the time value of the options. This would me a total of 2.656 percent total return.

The other unknown is since you could average 8 percent per year with some 20 percent down years once the year is down more than zero it has no effect on your return so in actuality you probably would do much better than the calculation above. For instance if the S&P were to rise from 1380 to 1550 in a year and drop to 1280 followed by a rise to 1550 you would make 200 * 17 = 3400 in year one followed by a loss of 2,400 followed by a gain of 200 * 27 = 5400 for total gain of $8,800 on an average price gain of six percent per year. This would be compared to the expected $4,968 on a straight line 6 percent.
Good points, Thanks. It would help a little if there were to be a crash. Still pretty pathetic overall though.
If I could pay 2% or 3% a year for downside insurance and get 100% of the upside, I'd consider it.
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Old 04-07-2008, 06:47 PM   #15
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Thanks, Brewer, this gives people the numbers they need to ask questions about EIA expenses-- "So, what if I just duplicated your offer with CDs and options trades?"

This sounds a lot like Taleb's "Black Swan" portfolio-- Treasuries & options.

Quote:
Originally Posted by FinanceDude View Post
Nicely done. First question: How many CD buyers are also willing to buy options? Not many folks I know........
The other side of the question is how many options traders are also willing to hedge with CDs.
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Old 04-07-2008, 08:02 PM   #16
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The other side of the question is how many options traders are also willing to hedge with CDs.
None I know of..............
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Old 04-07-2008, 08:26 PM   #17
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I haven't looked at option prices for awhile but just did. If I were to buy a 1 year at-the-money put to fully protect a SP500 position it is costing about 8%. That is very expensive insurance (I know the premiums are somewat high right now but not huge). When I last looked at EIA's, some offer unlimited (100%) of the upside, or close to it, for a few percent a year in extra expenses. How do they do it? Is it all gimmicks? (I suspect it is)

It seems to me that they do offer the insurance cheaper than I can do myself in the options market? What am I missing?
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Old 04-08-2008, 04:06 AM   #18
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brewer i like that plan alot. like i said im looking to bolster my safe bucket of cash by a point or 2. that bucket cant risk principal and this works just the way i would want it to.

like i said as a stock proxy these suck but as a safe way of increasing return on my income/cash bucket these are a nice enhancement to an income bucket

now anyway to do the same using a variable interest rate with a guaranteed min interest rate floor?.

my plan was to use both. when rates are rising the renewable rate annuity would be good and when rates drop the min floor would protect you.

when rates drop eventually the market comes back and the indexed to the s&p should pull ahead. by using both i hope to see a pretty consistant boost to income
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Old 04-08-2008, 08:09 AM   #19
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I was remiss in not including this link to more than you ever wanted to know about EIAs: Library

The author is very knowldegable and more or less impartial, although I think he is a bit of an apologist for the EIA industry. He does have some historical return info amongst the rest of this stuff.
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Old 04-08-2008, 08:15 AM   #20
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brewer i like that plan alot. like i said im looking to bolster my safe bucket of cash by a point or 2. that bucket cant risk principal and this works just the way i would want it to.

like i said as a stock proxy these suck but as a safe way of increasing return on my income/cash bucket these are a nice enhancement to an income bucket

now anyway to do the same using a variable interest rate with a guaranteed min interest rate floor?.
I dn't understand what you are asking. Care to elaborate? The CD in the example varies after just a year. If you really wanted to, you could do the same thing every quarter with a new 90 day CD and a new set of options.
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