SPIA Return - Am I calculating this correctly?

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corn18
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SPIA Return - Am I calculating this correctly?

Post by corn18 » Tue Apr 10, 2018 2:46 pm

Was thinking about retiring at 55 and taking SS at 70. SS + COLA Pension covers all my base expenses. So, why not try a 15 year certain annuity to cover me from 55 to 70? Went to immediate annuity and got the following info:

Period 15
Cost of Annuity 587,518
Monthly/Annual/Total Payout 4,000 48,000 720,000
Total Gain 132,482
Annual Gain 8,832.13
Annual Return 1.50%

Wouldn't I be in the same spot if I put $587,518 into a high yield savings account with 1.5% interest? If so, it seems the annuity is not the best approach to bridge me to SS.

Appreciate your thoughts.

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dwickenh
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Re: SPIA Return - Am I calculating this correctly?

Post by dwickenh » Tue Apr 10, 2018 3:56 pm

This method is not covering a longevity risk so there are no mortality credits to boost the return over time. I would take 650,000 and put it into a lifestrategy fund with 40 stocks/60 bonds and draw the 4000 per month from that. You would very likely end up with money left over when you started SS at 70. 15 years is a long enough horizon to take some risk.
The market is the most efficient mechanism anywhere in the world for transferring wealth from impatient people to patient people.” | — Warren Buffett

bsteiner
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Re: SPIA Return - Am I calculating this correctly?

Post by bsteiner » Tue Apr 10, 2018 4:31 pm

The annuity protects against the risk that you would earn a lower rate of return.

The cost of the annuity would be less (in other words, you would get the "mortality credits") if the annuity payments were to end at your death if you were to die before the end of the 15 years.

adam1712
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Re: SPIA Return - Am I calculating this correctly?

Post by adam1712 » Tue Apr 10, 2018 5:05 pm

corn18 wrote:
Tue Apr 10, 2018 2:46 pm
Was thinking about retiring at 55 and taking SS at 70. SS + COLA Pension covers all my base expenses. So, why not try a 15 year certain annuity to cover me from 55 to 70? Went to immediate annuity and got the following info:

Period 15
Cost of Annuity 587,518
Monthly/Annual/Total Payout 4,000 48,000 720,000
Total Gain 132,482
Annual Gain 8,832.13
Annual Return 1.50%

Wouldn't I be in the same spot if I put $587,518 into a high yield savings account with 1.5% interest? If so, it seems the annuity is not the best approach to bridge me to SS.

Appreciate your thoughts.
I don't think you are calculating this correctly. You are calculating like the $587,518 is being invested the whole time. But the invested balance will be declining as the payments are being made. Towards the end, there'd be a much smaller amount left in the account earning interest.

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FiveK
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Re: SPIA Return - Am I calculating this correctly?

Post by FiveK » Tue Apr 10, 2018 5:20 pm

corn18 wrote:
Tue Apr 10, 2018 2:46 pm
Period 15
Cost of Annuity 587,518
Monthly Payout 4,000
This is ~2.8% return over the 15 years.

The calculation is similar to "at what mortgage interest would the monthly payment on a 15 year, $587,518 loan be $4000/mo?"

One can use the Excel "Rate" function. E.g., see cells 'Misc. calcs'!G17:G23 in the personal finance toolbox spreadsheet.

longinvest
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Re: SPIA Return - Am I calculating this correctly?

Post by longinvest » Tue Apr 10, 2018 5:34 pm

corn18 wrote:
Tue Apr 10, 2018 2:46 pm
Period 15
Cost of Annuity 587,518
Monthly/Annual/Total Payout 4,000 48,000 720,000
15 years represents 180 months. So, using my financial calculator:

n = 180, PV = -587518, FV = 0, PMT = 4000 => i = 0.233030566

i is a monthly yield. Annualized, it becomes: (1+ 0.233030566%)^12 - 1 = 2.8%.

This stream of payment has an average 7.5 years duration. The 2.8% yield could be compared with the yield on a nominal bond of similar duration (duration is shorter than maturity).

Edited: I see that FiveK provided the answer just above my post.
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corn18
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Re: SPIA Return - Am I calculating this correctly?

Post by corn18 » Tue Apr 10, 2018 5:47 pm

Coolio. Thanks for the formula. That will help me fish.

longinvest
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Re: SPIA Return - Am I calculating this correctly?

Post by longinvest » Tue Apr 10, 2018 5:58 pm

I think that 15 years is a long-enough time to consider the impact of inflation on the payment stream. At an average 2% inflation rate, the fixed payment will have lost near 25% of its value in the 15th year. In other words, the inflation-adjusted value of the $4,000 payment will be $3,000 when expressed in 2018 dollars.

Assuming the same nominal yield as in my previous post, the cost of a term-certain 15-year SPIA with a monthly $4,000 payment that increases by 2% each year should be approximately $677,607. This is 15% more expensive, but it eliminate the 25% real reduction in payments in a 2% inflation environment.

Inflation could turn out higher or lower than 2%, but the inflation risk of a 2%-indexed stream of payment is minimal over a 15-year period.

This is why I selected a 2% annual increment: FRB: What is an acceptable level of inflation?
Last edited by longinvest on Tue Apr 10, 2018 9:38 pm, edited 1 time in total.
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Thesaints
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Re: SPIA Return - Am I calculating this correctly?

Post by Thesaints » Tue Apr 10, 2018 6:07 pm

A 15 year bond with a 2.8% coupon has a duration a little above 12 years. Where do those 7.5 years come from ?

Also, to get a 2.8% interest today you have to buy a 10-year treasury, or something else with more risk, or later maturity.
None of those would be good for you, since you need a stream of payments larger than the interest payout starting on day 1 of your pre-retirement.

longinvest
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Re: SPIA Return - Am I calculating this correctly?

Post by longinvest » Tue Apr 10, 2018 6:15 pm

If anyone is curious, here's how I got the $677,607 estimate.

In a fixed 2% inflation environment, a 2.8% nominal yield is equivalent to a (1 + 2.8%) / (1 + 2%) - 1 = .78% real yield.

I did the exact calculation using the monthly yield (instead of the rounded annual yield), which gave me:

((1+ 0.233030566%)^12 / 1.02)^(1 / 12) - 1 = 0.067760515%

n = 180, i = 0.067760515, FV = 0, PMT = 4000 => PV = -677607
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longinvest
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Re: SPIA Return - Am I calculating this correctly?

Post by longinvest » Tue Apr 10, 2018 6:21 pm

Thesaints wrote:
Tue Apr 10, 2018 6:07 pm
A 15 year bond with a 2.8% coupon has a duration a little above 12 years. Where do those 7.5 years come from ?

Also, to get a 2.8% interest today you have to buy a 10-year treasury, or something else with more risk, or later maturity.
None of those would be good for you, since you need a stream of payments larger than the interest payout starting on day 1 of your pre-retirement.
It's a stream of 180 equal payments.

The first payment has a duration of 1 month.
The second payment has a duration of 2 months.
The third payment has a duration of 3 months.
...
The 180th payment has a duration of 180 months.

The average duration of this stream of payment is equal to the sum of the durations of the 180 payments divided by 180.

This is: ((1 + 2 + 3 + ... + 180) / 180)

1 + ... + 180 is called an Arithmetic Series (Wikipedia).

1 + ... + 180 = (180 X 181) / 2 = 16,290

The average duration is thus: 16,290 / 180 = 90.5 months

Translated in years: 90.5 / 12 = 7.5 years
Last edited by longinvest on Tue Apr 10, 2018 6:53 pm, edited 1 time in total.
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Thesaints
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Re: SPIA Return - Am I calculating this correctly?

Post by Thesaints » Tue Apr 10, 2018 6:24 pm

Alternatively, the total payout is 720k. Let's say you receive half now and half after 15 years.
The 588k investment becomes a 588-360=228k investment which nets 360k after 15 years, i.e. 3.09% compounded yearly, which is quite close to the "exact" value of 2.84% calculated with monthly returns.
Last edited by Thesaints on Tue Apr 10, 2018 6:25 pm, edited 1 time in total.

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Re: SPIA Return - Am I calculating this correctly?

Post by Thesaints » Tue Apr 10, 2018 6:25 pm

longinvest wrote:
Tue Apr 10, 2018 6:21 pm
It's a stream of 180 equal payments.

The first payment has a duration of 1 month.
Certainly you mean "maturity". "Duration" is another thing entirely.

GibsonL6s
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Re: SPIA Return - Am I calculating this correctly?

Post by GibsonL6s » Tue Apr 10, 2018 6:36 pm

corn18 wrote:
Tue Apr 10, 2018 2:46 pm
Was thinking about retiring at 55 and taking SS at 70. SS + COLA Pension covers all my base expenses. So, why not try a 15 year certain annuity to cover me from 55 to 70? Went to immediate annuity and got the following info:

Period 15
Cost of Annuity 587,518
Monthly/Annual/Total Payout 4,000 48,000 720,000
Total Gain 132,482
Annual Gain 8,832.13
Annual Return 1.50%

Wouldn't I be in the same spot if I put $587,518 into a high yield savings account with 1.5% interest? If so, it seems the annuity is not the best approach to bridge me to SS.

Appreciate your thoughts.
If this is a 15 year certain annuity the return is 2.8%. This is done using a financial calculator and is not taking into account the tax consequences.

longinvest
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Re: SPIA Return - Am I calculating this correctly?

Post by longinvest » Tue Apr 10, 2018 6:38 pm

Thesaints wrote:
Tue Apr 10, 2018 6:25 pm
longinvest wrote:
Tue Apr 10, 2018 6:21 pm
It's a stream of 180 equal payments.

The first payment has a duration of 1 month.
Certainly you mean "maturity". "Duration" is another thing entirely.
Each payment has no coupon. Duration and maturity are thus equal (for each payment).

Edited to add:

Here's what our Wiki says about it:

Zero-coupon bond
...
Zeros have the unique property of having a duration equal to their maturity. ...
Last edited by longinvest on Tue Apr 10, 2018 6:43 pm, edited 1 time in total.
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Thesaints
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Re: SPIA Return - Am I calculating this correctly?

Post by Thesaints » Tue Apr 10, 2018 6:39 pm

GibsonL6s wrote:
Tue Apr 10, 2018 6:36 pm
If this is a 15 year certain annuity the return is 2.8%. This is done using a financial calculator and is not taking into account the tax consequences.
Yep. And the conclusion is that the OP has no way to get that kind of return on his whole capital, without incurring risks which he may find not suited to his situation.

Thesaints
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Re: SPIA Return - Am I calculating this correctly?

Post by Thesaints » Tue Apr 10, 2018 6:40 pm

longinvest wrote:
Tue Apr 10, 2018 6:38 pm
Each payment has no coupon. Duration and maturity are thus equal (for each payment).
So who gives the OP the 132k he is missing ?

GibsonL6s
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Re: SPIA Return - Am I calculating this correctly?

Post by GibsonL6s » Tue Apr 10, 2018 7:29 pm

Thesaints wrote:
Tue Apr 10, 2018 6:40 pm
longinvest wrote:
Tue Apr 10, 2018 6:38 pm
Each payment has no coupon. Duration and maturity are thus equal (for each payment).
So who gives the OP the 132k he is missing ?
The insurance company gives him a total of $720K, $132k is the return on his money, the difference is the return of his money. So again he is yielding 2.8%. I am not sure how taxes work, but maybe someone else can explain it, thanks

Thesaints
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Re: SPIA Return - Am I calculating this correctly?

Post by Thesaints » Tue Apr 10, 2018 7:31 pm

GibsonL6s wrote:
Tue Apr 10, 2018 7:29 pm
The insurance company gives him a total of $720K, $132k is the return on his money, the difference is the return of his money. So again he is yielding 2.8%. I am not sure how taxes work, but maybe someone else can explain it, thanks
So there is a yield after all! That 7.5 year duration calculated at zero yield still looks mysterious...

Dottie57
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Re: SPIA Return - Am I calculating this correctly?

Post by Dottie57 » Tue Apr 10, 2018 7:38 pm

My understanding is that taxes are paid on the 132k . No taxes on the rest since that is return of OP's money.

longinvest
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Re: SPIA Return - Am I calculating this correctly?

Post by longinvest » Tue Apr 10, 2018 7:44 pm

Thesaints wrote:
Tue Apr 10, 2018 7:31 pm
That 7.5 year duration calculated at zero yield still looks mysterious...
It isn't calculated at zero yield. Each payment is $4,000, which sums up to more than the buying price of the SPIA. The yield is 2.8%.

It isn't mysterious, either. Unlike a bond, a term-certain SPIA doesn't have a principal. The term-certain SPIA's payments are evenly spread across the entire period. The duration, which represents the average maturity of all payments, can be intuitively approximated by simply dividing the term by two.

I've provided, in my previous post, the exact duration calculation, which is 90.5/12 = 7.541666... years. Rounded, we get 7.5 years.
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Ron
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Re: SPIA Return - Am I calculating this correctly?

Post by Ron » Tue Apr 10, 2018 7:48 pm

Dottie57 wrote:
Tue Apr 10, 2018 7:38 pm
My understanding is that taxes are paid on the 132k . No taxes on the rest since that is return of OP's money.
Unless the premium is paid with qualified funds, such as from a TIRA or 401(K). In that case, all payouts will become taxable, in the year they are paid.

A plus for an SPIA funded with qualified funds is that the value of those funds are removed from RMD consideration.

- Ron
Last edited by Ron on Tue Apr 10, 2018 7:49 pm, edited 1 time in total.

Thesaints
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Re: SPIA Return - Am I calculating this correctly?

Post by Thesaints » Tue Apr 10, 2018 7:48 pm

longinvest wrote:
Tue Apr 10, 2018 7:44 pm
Thesaints wrote:
Tue Apr 10, 2018 7:31 pm
That 7.5 year duration calculated at zero yield still looks mysterious...
It isn't. Unlike a bond, a term-certain SPIA doesn't have a principal. The SPIA's payments are evenly spread across the entire period. The duration, which represents the average maturity of all payments, can be approximated by simply dividing the term by two.

I've provided, in my previous post, the exact duration calculation, which is 90.5/12 = 7.541666... years. Rounded, we get 7.5 years.
What's the meaning of this "duration" ?

What I can understand is calculating a bond equivalent to the annuity and its duration. A 15-year bond with a 2.8% YTM has a duration a little above 12 years, for instance.
Although that wouldn't be strictly equivalent to the necessary annuity because the coupon payment does not generate sufficient income. One could buy 15 separate 15-year bonds and sell one each year, but that would expose you to market risk.

longinvest
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Re: SPIA Return - Am I calculating this correctly?

Post by longinvest » Tue Apr 10, 2018 8:06 pm

Thesaints wrote:
Tue Apr 10, 2018 7:48 pm
longinvest wrote:
Tue Apr 10, 2018 7:44 pm
Thesaints wrote:
Tue Apr 10, 2018 7:31 pm
That 7.5 year duration calculated at zero yield still looks mysterious...
It isn't. Unlike a bond, a term-certain SPIA doesn't have a principal. The SPIA's payments are evenly spread across the entire period. The duration, which represents the average maturity of all payments, can be approximated by simply dividing the term by two.

I've provided, in my previous post, the exact duration calculation, which is 90.5/12 = 7.541666... years. Rounded, we get 7.5 years.
What's the meaning of this "duration" ?

What I can understand is calculating a bond equivalent to the annuity and its duration. A 15-year bond with a 2.8% YTM has a duration a little above 12 years, for instance.
Although that wouldn't be strictly equivalent to the necessary annuity because the coupon payment does not generate sufficient income. One could buy 15 separate 15-year bonds and sell one each year, but that would expose you to market risk.
One definition of duration is the weighted-average maturity of all payments.

I would think of it this way. I could self-build a 15-year annual SPIA by buying 15 zero-coupon bonds. One bond of a 1-year maturity, one of a 2-year maturity, and so on. What would be the weighted-average maturity of the 15 bonds? It would be approximately 7.5 years.

Now, of course, we could try to be even more precise and calculate a weighted-average using the present-value of each payment. If we used the same 2.8% yield for all 15 zero-coupon bonds, we would get a somewhat lower duration, because longer bonds would have a smaller present value than shorter bonds. Yet, one could argue that it would be unfair for the yield on a 1-year bond to equal the yield of a 15-year bond, when the market provides higher yields for longer-term bonds. So, maybe the present value of longer-term bonds would get further discounted relative to shorter-term bonds, making the duration even shorter.

In other words, what I am saying is that my 7.5 year duration calculation actually overestimates the duration of the term-certain SPIA.

Note that we know that the overall yield, for all payments, has to equal 2.8%, so if we use a lower yield for short-term bonds, we have to use a higher one for longer ones. Unfortunately, the SPIA doesn't advertise the actual yield of each of its payments; we can only calculate the overall yield using a financial calculator.
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Thesaints
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Re: SPIA Return - Am I calculating this correctly?

Post by Thesaints » Tue Apr 10, 2018 8:15 pm

longinvest wrote:
Tue Apr 10, 2018 8:06 pm
I would think of it this way. I could self-build a 15-year annual SPIA by buying 15 zero-coupon bonds. One bond of a 1-year maturity, one of a 2-year maturity, and so on. What would be the weighted-average maturity of the 15 bonds? It would be approximately 7.5 years.
What does it tell you ? You are not selling those bonds. How they respond to interest rates changes does not matter.
Now, of course, we could try to be even more precise and calculate a weighted-average using the present-value of each payment. If we used the same 2.8% yield for all 15 zero-coupon bonds, we would get a somewhat lower duration, because longer bonds would have a smaller present value than shorter bonds. Yet, one could argue that it would be unfair for the yield on a 1-year bond to equal the yield of a 15-year bond, when the market provides higher yields for longer-term bonds. So, maybe the present value of longer-term bonds would get further discounted relative to shorter-term bonds, making the duration even shorter.
All those zeroes have a face value of 48k. Naturally the 15-year ZC will be valued differently (likely less) than the 1-year ZC, that much is obvious.
Then again, the correctly weighted duration might be 4 years, or 10 years. So what ? You are still carrying all 15 of them to maturity.

longinvest
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Re: SPIA Return - Am I calculating this correctly?

Post by longinvest » Tue Apr 10, 2018 8:17 pm

Thesaints wrote:
Tue Apr 10, 2018 8:15 pm
All those zeroes have a face value of 48k. Naturally the 15-year ZC will be valued differently (likely less) than the 1-year ZC, that much is obvious.
Then again, the correctly weighted duration might be 4 years, or 10 years. So what ? You are still carrying all 15 of them to maturity.
The weighted-average maturity of 15 equal-value zero-coupon bonds* with respective maturities of 1, 2, 3, ..., 15 years is:
(1 year + 2 years + 3 years + ... + 15 years) / 15 = 8 years.

* As I wrote earlier, if instead of being equal value, they are discounted to provide equal payments, longer-term bonds will have smaller values and their longer maturity will have less weight in the weighted average, leading to a smaller length than 8 years.

This tells me that I'll get my payments in 8 years, on average. This makes sense, because I'll get my first payment is 1 year and the last payment in 15 years. The average is (1 + 15) / 2 = 8 years. That's what "duration" is about.
Last edited by longinvest on Tue Apr 10, 2018 8:28 pm, edited 1 time in total.
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Oicuryy
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Re: SPIA Return - Am I calculating this correctly?

Post by Oicuryy » Tue Apr 10, 2018 8:27 pm

Money is fungible | Abbreviations and Acronyms

longinvest
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Re: SPIA Return - Am I calculating this correctly?

Post by longinvest » Tue Apr 10, 2018 8:43 pm

Oicuryy wrote:
Tue Apr 10, 2018 8:27 pm
FWIW, I get a duration of 84 months.
http://www.wolframalpha.com/input/?i=(4 ... )%5E(-i-1)

Or maybe 84.2 months.
http://www.wolframalpha.com/input/?i=(4 ... +1)%5E(-i)

Ron
Here's a detailed calculation, using the 2.8% annual yield (or 0.23% monthly yield) for all 180 payments in a spreadsheet:

Code: Select all

   SPIA monthly yield   0.2330305702%
                                     
            Payment #   Present value   Weighted maturity
                    1       $3 990,70        0.0067924735
                    2       $3 981,42        0.0135533635
                    3       $3 972,17        0.0202827802
                    4       $3 962,93        0.0269808334
                    5       $3 953,72        0.0336476324
                    6       $3 944,53        0.0402832865
                    7       $3 935,36        0.0468879045
                    8       $3 926,21        0.0534615947
                    9       $3 917,08        0.0600044653
                   10       $3 907,97        0.0665166240
                   11       $3 898,89        0.0729981784
                   12       $3 889,82        0.0794492354
                   13       $3 880,78        0.0858699019
                   14       $3 871,76        0.0922602843
                   15       $3 862,75        0.0986204887
                   16       $3 853,77        0.1049506209
                   17       $3 844,81        0.1112507864
                   18       $3 835,88        0.1175210902
                   19       $3 826,96        0.1237616372
                   20       $3 818,06        0.1299725319
                   21       $3 809,18        0.1361538783
                   22       $3 800,33        0.1423057803
                   23       $3 791,49        0.1484283415
                   24       $3 782,68        0.1545216649
                   25       $3 773,88        0.1605858535
                   26       $3 765,11        0.1666210098
                   27       $3 756,36        0.1726272359
                   28       $3 747,62        0.1786046338
                   29       $3 738,91        0.1845533051
                   30       $3 730,22        0.1904733511
                   31       $3 721,55        0.1963648726
                   32       $3 712,89        0.2022279703
                   33       $3 704,26        0.2080627446
                   34       $3 695,65        0.2138692954
                   35       $3 687,06        0.2196477225
                   36       $3 678,48        0.2253981252
                   37       $3 669,93        0.2311206025
                   38       $3 661,40        0.2368152534
                   39       $3 652,89        0.2424821761
                   40       $3 644,40        0.2481214689
                   41       $3 635,92        0.2537332297
                   42       $3 627,47        0.2593175558
                   43       $3 619,04        0.2648745447
                   44       $3 610,62        0.2704042932
                   45       $3 602,23        0.2759068979
                   46       $3 593,85        0.2813824551
                   47       $3 585,50        0.2868310610
                   48       $3 577,16        0.2922528111
                   49       $3 568,85        0.2976478010
                   50       $3 560,55        0.3030161257
                   51       $3 552,27        0.3083578801
                   52       $3 544,01        0.3136731587
                   53       $3 535,77        0.3189620557
                   54       $3 527,55        0.3242246651
                   55       $3 519,35        0.3294610805
                   56       $3 511,17        0.3346713953
                   57       $3 503,01        0.3398557026
                   58       $3 494,86        0.3450140950
                   59       $3 486,74        0.3501466651
                   60       $3 478,63        0.3552535051
                   61       $3 470,54        0.3603347068
                   62       $3 462,47        0.3653903619
                   63       $3 454,42        0.3704205617
                   64       $3 446,39        0.3754253972
                   65       $3 438,38        0.3804049592
                   66       $3 430,39        0.3853593381
                   67       $3 422,41        0.3902886242
                   68       $3 414,46        0.3951929072
                   69       $3 406,52        0.4000722769
                   70       $3 398,60        0.4049268226
                   71       $3 390,70        0.4097566332
                   72       $3 382,81        0.4145617977
                   73       $3 374,95        0.4193424045
                   74       $3 367,10        0.4240985417
                   75       $3 359,27        0.4288302974
                   76       $3 351,46        0.4335377592
                   77       $3 343,67        0.4382210145
                   78       $3 335,90        0.4428801503
                   79       $3 328,14        0.4475152536
                   80       $3 320,41        0.4521264109
                   81       $3 312,69        0.4567137085
                   82       $3 304,98        0.4612772324
                   83       $3 297,30        0.4658170683
                   84       $3 289,63        0.4703333018
                   85       $3 281,99        0.4748260180
                   86       $3 274,36        0.4792953018
                   87       $3 266,74        0.4837412380
                   88       $3 259,15        0.4881639110
                   89       $3 251,57        0.4925634049
                   90       $3 244,01        0.4969398035
                   91       $3 236,47        0.5012931905
                   92       $3 228,95        0.5056236492
                   93       $3 221,44        0.5099312627
                   94       $3 213,95        0.5142161138
                   95       $3 206,48        0.5184782851
                   96       $3 199,02        0.5227178588
                   97       $3 191,59        0.5269349171
                   98       $3 184,16        0.5311295416
                   99       $3 176,76        0.5353018140
                  100       $3 169,38        0.5394518154
                  101       $3 162,01        0.5435796268
                  102       $3 154,66        0.5476853291
                  103       $3 147,32        0.5517690026
                  104       $3 140,01        0.5558307277
                  105       $3 132,71        0.5598705843
                  106       $3 125,42        0.5638886522
                  107       $3 118,16        0.5678850108
                  108       $3 110,91        0.5718597393
                  109       $3 103,67        0.5758129168
                  110       $3 096,46        0.5797446219
                  111       $3 089,26        0.5836549331
                  112       $3 082,08        0.5875439287
                  113       $3 074,91        0.5914116866
                  114       $3 067,76        0.5952582846
                  115       $3 060,63        0.5990838001
                  116       $3 053,51        0.6028883104
                  117       $3 046,42        0.6066718924
                  118       $3 039,33        0.6104346230
                  119       $3 032,27        0.6141765786
                  120       $3 025,22        0.6178978354
                  121       $3 018,18        0.6215984696
                  122       $3 011,17        0.6252785569
                  123       $3 004,17        0.6289381727
                  124       $2 997,18        0.6325773925
                  125       $2 990,21        0.6361962912
                  126       $2 983,26        0.6397949438
                  127       $2 976,33        0.6433734247
                  128       $2 969,41        0.6469318082
                  129       $2 962,50        0.6504701687
                  130       $2 955,62        0.6539885797
                  131       $2 948,74        0.6574871152
                  132       $2 941,89        0.6609658483
                  133       $2 935,05        0.6644248523
                  134       $2 928,23        0.6678642001
                  135       $2 921,42        0.6712839645
                  136       $2 914,63        0.6746842178
                  137       $2 907,85        0.6780650324
                  138       $2 901,09        0.6814264801
                  139       $2 894,34        0.6847686329
                  140       $2 887,62        0.6880915623
                  141       $2 880,90        0.6913953395
                  142       $2 874,20        0.6946800357
                  143       $2 867,52        0.6979457217
                  144       $2 860,86        0.7011924682
                  145       $2 854,20        0.7044203456
                  146       $2 847,57        0.7076294241
                  147       $2 840,95        0.7108197736
                  148       $2 834,34        0.7139914639
                  149       $2 827,75        0.7171445645
                  150       $2 821,18        0.7202791446
                  151       $2 814,62        0.7233952735
                  152       $2 808,08        0.7264930198
                  153       $2 801,55        0.7295724523
                  154       $2 795,04        0.7326336394
                  155       $2 788,54        0.7356766492
                  156       $2 782,05        0.7387015497
                  157       $2 775,59        0.7417084087
                  158       $2 769,13        0.7446972938
                  159       $2 762,70        0.7476682721
                  160       $2 756,27        0.7506214110
                  161       $2 749,86        0.7535567771
                  162       $2 743,47        0.7564744373
                  163       $2 737,09        0.7593744580
                  164       $2 730,73        0.7622569054
                  165       $2 724,38        0.7651218455
                  166       $2 718,05        0.7679693443
                  167       $2 711,73        0.7707994672
                  168       $2 705,42        0.7736122798
                  169       $2 699,13        0.7764078472
                  170       $2 692,86        0.7791862343
                  171       $2 686,60        0.7819475060
                  172       $2 680,35        0.7846917268
                  173       $2 674,12        0.7874189611
                  174       $2 667,90        0.7901292731
                  175       $2 661,70        0.7928227266
                  176       $2 655,51        0.7954993854
                  177       $2 649,34        0.7981593131
                  178       $2 643,18        0.8008025729
                  179       $2 637,03        0.8034292281
                  180       $2 630,90        0.8060393415
                                     
                Total     $587 518,00       84.2339973123
It results, effectively, into a 84.23 months duration, which is 7 years.
Last edited by longinvest on Tue Apr 10, 2018 10:10 pm, edited 2 times in total.
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longinvest
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Re: SPIA Return - Am I calculating this correctly?

Post by longinvest » Tue Apr 10, 2018 9:00 pm

Thesaints,
Thesaints wrote:
Tue Apr 10, 2018 8:15 pm
You are not selling those bonds. How they respond to interest rates changes does not matter.
[...]
Then again, the correctly weighted duration might be 4 years, or 10 years. So what ? You are still carrying all 15 of them to maturity.
The reason I mentioned duration, in my initial calculation post, was for comparing the 2.8% yield with market yields. One should only compare an average 2.8% yield on a 7-year duration stream of payments with the yield on a bond (or average yield on a collection of bonds) of similar duration.
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longinvest
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Re: SPIA Return - Am I calculating this correctly?

Post by longinvest » Tue Apr 10, 2018 9:19 pm

It would be a mistake, for example, to compare the 2.8% SPIA yield with the yield on a 15-year Treasury because its duration would be much higher than 7 years.

Looking at FRED's constant-maturity rates, I get:
7-Year Treasury Constant Maturity Rate | FRED | St. Louis Fed: 2.72% (2018-04-09)
10-Year Treasury Constant Maturity Rate | FRED | St. Louis Fed: 2.78% (2018-04-09)

A 7-year Treasury has a lower duration than 7 years. A 10-year duration Treasury has a longer duration than 7 years. This tells me that the SPIA's yield is a few basis points higher than the yield on a similar-duration Treasury.

In other words, the 15-year term-certain SPIA's pricing seems fair, in the current market.
Last edited by longinvest on Tue Apr 10, 2018 9:50 pm, edited 1 time in total.
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longinvest
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Re: SPIA Return - Am I calculating this correctly?

Post by longinvest » Tue Apr 10, 2018 9:35 pm

Corn,
corn18 wrote:
Tue Apr 10, 2018 2:46 pm
Appreciate your thoughts.
First, I apologize for all the complex details about duration; you don't need to worry about them. It is sufficient to know that the 2.8% yield goes along a 7-year duration, and that this seems like a fair yield, in the current market.

Second, just in case you missed it, please read this post, where I discuss the use of a 2%-indexed 15-year term-certain SPIA, instead of a flat-payment one.
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Thesaints
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Re: SPIA Return - Am I calculating this correctly?

Post by Thesaints » Tue Apr 10, 2018 9:58 pm

longinvest wrote:
Tue Apr 10, 2018 9:19 pm
It would be a mistake, for example, to compare the 2.8% SPIA yield with the yield on a 15-year Treasury because its duration would be much higher than 7 years.

Looking at FRED's constant-maturity rates, I get:
7-Year Treasury Constant Maturity Rate | FRED | St. Louis Fed: 2.72% (2018-04-09)
10-Year Treasury Constant Maturity Rate | FRED | St. Louis Fed: 2.78% (2018-04-09)

A 7-year Treasury has a lower duration than 7 years. A 10-year duration Treasury has a longer duration than 7 years. This tells me that the SPIA's yield is a few basis points higher than the yield on a similar-duration Treasury.

In other words, the 15-year term-certain SPIA's pricing seems fair, in the current market.
Thank you for the patient explanation. Now I understand and, yes, I think you are absolutely right,

heyyou
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Re: SPIA Return - Am I calculating this correctly?

Post by heyyou » Wed Apr 11, 2018 12:59 am

At the OP:
With all that distant certainty, why do you need so much certainty for the first 15 years of retirement? For most of us, the distant years are when the uncertainty occurs. Have you looked at just spending from bonds first (for your first 15 years) as suggested by Michael H. McClung, to let the equity portion grow longer? That bypasses sequence risk that some mention to scare retirees into asking them to manage their assets.

Another option is to first use a lower or a variable withdrawal(WD) rate on the portfolio, than the historical optimal one. The variable WD is a fixed % of each, most recent annual portfolio balance for the first 15 years, so that portion of your retirement income changes some each year. That may sound bad, but inflation does the same, first to your annuity, then to your pension. The nominal payments stay the same, but the value of each payment is slowly shrinking by inflation.

Yes, there is risk in every method, but you have less long term risk than most others here.

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corn18
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Re: SPIA Return - Am I calculating this correctly?

Post by corn18 » Wed Apr 11, 2018 6:09 am

heyyou wrote:
Wed Apr 11, 2018 12:59 am
At the OP:
With all that distant certainty, why do you need so much certainty for the first 15 years of retirement? For most of us, the distant years are when the uncertainty occurs. Have you looked at just spending from bonds first (for your first 15 years) as suggested by Michael H. McClung, to let the equity portion grow longer? That bypasses sequence risk that some mention to scare retirees into asking them to manage their assets.

Another option is to first use a lower or a variable withdrawal(WD) rate on the portfolio, than the historical optimal one. The variable WD is a fixed % of each, most recent annual portfolio balance for the first 15 years, so that portion of your retirement income changes some each year. That may sound bad, but inflation does the same, first to your annuity, then to your pension. The nominal payments stay the same, but the value of each payment is slowly shrinking by inflation.

Yes, there is risk in every method, but you have less long term risk than most others here.
Thanks for addressing how to get to 70. That's the part I am exploring right now and just looking at different options. My pension and SS are both COLAd, so I am covered for longevity vs. inflation. Just need to make it to SS.

longinvest
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Re: SPIA Return - Am I calculating this correctly?

Post by longinvest » Wed Apr 11, 2018 7:14 am

Corn,
corn18 wrote:
Wed Apr 11, 2018 6:09 am
Thanks for addressing how to get to 70. That's the part I am exploring right now and just looking at different options. My pension and SS are both COLAd, so I am covered for longevity vs. inflation. Just need to make it to SS.
Personally, I would never adopt McClung's approach. I've provided a few comments about it across multiple posts in another topic.

If my objective was to replace missing delayed Social Security payments between age 55 and 70, I would seriously consider a fairly-priced 2%-indexed 15-year term-certain SPIA with payments equal to future Social Security payments.
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GibsonL6s
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Re: SPIA Return - Am I calculating this correctly?

Post by GibsonL6s » Wed Apr 11, 2018 10:14 am

The other option which may make sense is to draw SS at 62 and buy a life annuity for the difference between SS at 70 and SS at 62. A quick review of the annuity sites shows the premium about the same as a 8 year bridge to full SS. It may give some peace of mind to collect SS now as protection against future changes, which is of course speculative.

Dottie57
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Re: SPIA Return - Am I calculating this correctly?

Post by Dottie57 » Wed Apr 11, 2018 10:49 am

Ron wrote:
Tue Apr 10, 2018 7:48 pm
Dottie57 wrote:
Tue Apr 10, 2018 7:38 pm
My understanding is that taxes are paid on the 132k . No taxes on the rest since that is return of OP's money.
Unless the premium is paid with qualified funds, such as from a TIRA or 401(K). In that case, all payouts will become taxable, in the year they are paid.

A plus for an SPIA funded with qualified funds is that the value of those funds are removed from RMD consideration.

- Ron
Take a look here https://annuities.blueprintincome.com/l ... /#taxation

"The taxation of annuities depends first and foremost on whether the annuity was purchased with pre-tax or post-tax money. If the premium was paid with post-tax money, as with a non-qualified annuity, the portion of any income payments that constitutes a return of that premium will not be taxable. On the other hand, qualified annuities are purchased with pre-tax retirement savings. Because the money used to fund the annuity has never been taxed, all distributions from the annuity will be fully taxable. In either case, ordinary income tax rates will apply."

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Re: SPIA Return - Am I calculating this correctly?

Post by Dottie57 » Wed Apr 11, 2018 10:58 am

corn18 wrote:
Tue Apr 10, 2018 2:46 pm
Was thinking about retiring at 55 and taking SS at 70. SS + COLA Pension covers all my base expenses. So, why not try a 15 year certain annuity to cover me from 55 to 70? Went to immediate annuity and got the following info:

Period 15
Cost of Annuity 587,518
Monthly/Annual/Total Payout 4,000 48,000 720,000
Total Gain 132,482
Annual Gain 8,832.13
Annual Return 1.50%

Wouldn't I be in the same spot if I put $587,518 into a high yield savings account with 1.5% interest? If so, it seems the annuity is not the best approach to bridge me to SS.

Appreciate your thoughts.
I've gone through same analysis. I would rather keep control of my money since there isn't a real financial benefi.

I wish I had been smart enough to put money into a deferred annuity 5 years ago. The payout would be better.

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Re: SPIA Return - Am I calculating this correctly?

Post by The Wizard » Wed Apr 11, 2018 11:21 am

Now that the OP's question has been explained properly, the issue of whether to go through with it can be addressed.
If the OP has sufficient investment assets, it might work better over the 15 years just to withdraw $4000 per month from a 50/50 (or thereabouts) portfolio.
I'd recommend at least a 25X portfolio for confidence, meaning at least $1.2M for this case.
This is the approach I'm taking for a shorter 7-year bridge to age 70...
Attempted new signature...

longinvest
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Re: SPIA Return - Am I calculating this correctly?

Post by longinvest » Wed Apr 11, 2018 11:53 am

The Wizard wrote:
Wed Apr 11, 2018 11:21 am
If the OP has sufficient investment assets, it might work better over the 15 years just to withdraw $4000 per month from a 50/50 (or thereabouts) portfolio.
This is called a "constant-dollar withdrawal" approach (many call it SWR as in "safe withdrawal rate"). It is one of the worst approaches to taking money out of a portfolio. This has been extensively discussed in this forum. (See the collection of posts I made in the Michael Kitces 4% rule podcast on Madfientist topic).

I think that the original poster (OP) has a good plan, in wanting to provide for a robust replacement for Social Security payments during the age 55 to 70 gap before receiving delayed Social Security payments. This can be achieved in many ways.

Using a 2%-indexed 15-year term-certain SPIA with payments equal to future delayed Social Security payments is a simple approach.

Another approach would be to build a non-rolling TIPS ladder which delivers, each year, coupons and maturing principals equal to 12-months of future delayed Social Security payments. Forum member #Cruncher has developed an awesome tool for this; the link is at the end of the following post: Re: How should I build a TIPS income ladder?.

Yet another, but riskier in face of inflation, approach would be to use a CD ladder or a simple high-interest savings account as has been suggested in Delay Social Security to age 70 and Spend more money at 62.

The idea, here, is to construct a robust lifelong inflation-indexed base income which is not exposed to market risk. This base income consists of Social Security (SS) delayed to age 70 (to maximize it) and of a 15-year payment stream (equal to future SS payments) between retirement at age 55 and age 70 (self-constructed using TIPS, CDs, or a savings account, or bought from an insurance company as a 2%-indexed 15-year term-certain SPIA).

Then, the remaining balanced portfolio would be used for withdrawals taken using a sensible approach, such as our wiki's variable-percentage withdrawal (VPW) method.
Last edited by longinvest on Wed Apr 11, 2018 12:11 pm, edited 9 times in total.
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Re: SPIA Return - Am I calculating this correctly?

Post by smitcat » Wed Apr 11, 2018 11:58 am

Dottie57 wrote:
Wed Apr 11, 2018 10:58 am
corn18 wrote:
Tue Apr 10, 2018 2:46 pm
Was thinking about retiring at 55 and taking SS at 70. SS + COLA Pension covers all my base expenses. So, why not try a 15 year certain annuity to cover me from 55 to 70? Went to immediate annuity and got the following info:

Period 15
Cost of Annuity 587,518
Monthly/Annual/Total Payout 4,000 48,000 720,000
Total Gain 132,482
Annual Gain 8,832.13
Annual Return 1.50%

Wouldn't I be in the same spot if I put $587,518 into a high yield savings account with 1.5% interest? If so, it seems the annuity is not the best approach to bridge me to SS.

Appreciate your thoughts.
I've gone through same analysis. I would rather keep control of my money since there isn't a real financial benefi.

I wish I had been smart enough to put money into a deferred annuity 5 years ago. The payout would be better.
Without knowing your details - I would guess you did just fine with that money over these past 5 years of growth.
FWIW - every time I look back to see whether I did something that could have been done better I find that I have.

Rear veiwing vision is always 20/20.

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Re: SPIA Return - Am I calculating this correctly?

Post by Oicuryy » Wed Apr 11, 2018 12:03 pm

The Wizard wrote:
Wed Apr 11, 2018 11:21 am
If the OP has sufficient investment assets, it might work better over the 15 years just to withdraw $4000 per month from a 50/50 (or thereabouts) portfolio.
I'd recommend at least a 25X portfolio for confidence, meaning at least $1.2M for this case.
That does not look much different from a 44/56 portfolio consisting of $525k in a TSM fund and $675k in a 15-year immediate annuity yielding 2.8%.

Ron
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Chuck
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Re: SPIA Return - Am I calculating this correctly?

Post by Chuck » Wed Apr 11, 2018 2:05 pm

I just went to Vanguard and bashed together a ladder of 15 zero-coupon treasuries between 2019 and 2033. The cost came out to $580,620.96. So you could save ~$7000 and do that. (Incidentally, it reported the average duration of the ladder at 7.32 years.)

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Re: SPIA Return - Am I calculating this correctly?

Post by Chuck » Wed Apr 11, 2018 2:19 pm

And here is a ladder of zero-coupon treasuries with a rough 2% annual increase (rounded to the nearest bond) for expected inflation. It costs about $662K.

Code: Select all

Maturity  Qty   Cost
  2019    48    47,229.60
  2020    49    47,034.61
  2021    50    46,758.00
  2022    51    46,261.59
  2023    52    45,928.48
  2024    53    45,351.57
  2025    54    43,809.66
  2026    55    44,285.45
  2027    56    44,092.72
  2028    57    42,755.70
  2029    59    42,633.40
  2030    60    42,702.00
  2031    61    41,087.16
  2032    62    41,461.26
  2033    63    40,544.91
TOTAL          661,936.11

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corn18
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Re: SPIA Return - Am I calculating this correctly?

Post by corn18 » Wed Apr 11, 2018 2:21 pm

Chuck wrote:
Wed Apr 11, 2018 2:19 pm
And here is a ladder of zero-coupon treasuries with a rough 2% annual increase (rounded to the nearest bond) for expected inflation. It costs about $662K.

Code: Select all

Maturity  Qty   Cost
  2019    48    47,229.60
  2020    49    47,034.61
  2021    50    46,758.00
  2022    51    46,261.59
  2023    52    45,928.48
  2024    53    45,351.57
  2025    54    43,809.66
  2026    55    44,285.45
  2027    56    44,092.72
  2028    57    42,755.70
  2029    59    42,633.40
  2030    60    42,702.00
  2031    61    41,087.16
  2032    62    41,461.26
  2033    63    40,544.91
TOTAL          661,936.11
Coolio, thanks for this. I priced a SPIA with a 2% annual increase and it came out to right at $667,000. Looks like the SPIA is a good value.

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Re: SPIA Return - Am I calculating this correctly?

Post by Chuck » Wed Apr 11, 2018 2:32 pm

corn18 wrote:
Wed Apr 11, 2018 2:21 pm
I priced a SPIA with a 2% annual increase and it came out to right at $667,000. Looks like the SPIA is a good value.
:-?

That wasn't my takeaway at all. The treasury ladder is $5,000 cheaper, and you can change your mind at any time. (If you need cash, you can still sell some of the bonds.) So, I was trying to point out that the SPIA, being more expensive, and limiting your options, is not a good value at all.

Chuck
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Re: SPIA Return - Am I calculating this correctly?

Post by Chuck » Wed Apr 11, 2018 3:17 pm

And since I'm enjoying the exercise...

If you make a ladder of treasuries for years 1-5, and CD's for years 6-15, you can generate $48,000 per year spending only $545,000, so about $40,000 less. I could have done a better job with filtering out callable CD's, but now I'm more sure that I wouldn't want a SPIA in your situation.

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corn18
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Re: SPIA Return - Am I calculating this correctly?

Post by corn18 » Wed Apr 11, 2018 3:23 pm

Complexity plays a role in my decision, too. SPIA=simple. Ladders=more complex.

Chuck
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Re: SPIA Return - Am I calculating this correctly?

Post by Chuck » Wed Apr 11, 2018 4:00 pm

corn18 wrote:
Wed Apr 11, 2018 3:23 pm
Complexity plays a role in my decision, too. SPIA=simple. Ladders=more complex.
Of course. I only make about $100K per year, so a $40K savings is worth it if I spend less than 5 months on it. (It might take 2-3 days to set up the ladder.) But it sounds like you're doing a little better than I am.

longinvest
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Re: SPIA Return - Am I calculating this correctly?

Post by longinvest » Wed Apr 11, 2018 4:09 pm

Chuck wrote:
Wed Apr 11, 2018 3:17 pm
If you make a ladder of treasuries for years 1-5, and CD's for years 6-15, you can generate $48,000 per year spending only $545,000, so about $40,000 less. I could have done a better job with filtering out callable CD's, but now I'm more sure that I wouldn't want a SPIA in your situation.
I guess that "CDs for years 1-5 and treasuries for years 6-15" was meant, instead.

I'd like to see the detailed pricing for the 15 securities. The $40,000 estimate seems to imply a significant difference in yields of the 1-5 year securities.
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