Any way to "translate" a fixed pension/annuity to an inflation adjusted one?

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rgs92
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Any way to "translate" a fixed pension/annuity to an inflation adjusted one?

Post by rgs92 » Sat Sep 02, 2017 11:26 am

If one has a lifetime (taxable) fixed income stream from pensions or fixed annuities, is there any way approximate the value of each payment (yearly or monthly) as an inflation-adjusted version (a lower one of course)?

As an actionable thing, if a piece of each payment were set aside into, say, a simple 60/40 balanced index portfolio (or something else?), would that theoretically be the equivalent of turning the fixed income stream into a COLA'd one?

And if so, how would this be calculated or estimated? Would this set-aside amount be variable and what would it be based on?

Here's a short version of my question:

Let's say I had $100,000 a year for life as a fixed amount (paid monthly). How much could I spend to mimic an inflation adjusted portfolio and where would I invest the amount set aside?

[Please let's ignore the viability of the payments and assume they were 100% safe for the sake of simplicity, as this is complicated enough I think.]

Thank you.

ThrustVectoring
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Re: Any way to "translate" a fixed pension/annuity to an inflation adjusted one?

Post by ThrustVectoring » Sat Sep 02, 2017 12:56 pm

Easiest way I can think of:

1. Get a quote for how much it'd cost to buy an annuity with your current fixed annuity payments
2. Get a quote for how an inflation-adjusted annuity with the results from part 1 as the principle
3. Spend the result of 2, saving the difference in something. Probably TIPS.

You don't have to value things yourself if there's a fair market value you can use instead.
Current portfolio: 60% VTI / 40% VXUS

heyyou
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Re: Any way to "translate" a fixed pension/annuity to an inflation adjusted one?

Post by heyyou » Sat Sep 02, 2017 1:21 pm

1. Get a quote for how much it'd cost to buy an annuity with your current fixed annuity payments
2. Get a quote for how an inflation-adjusted annuity with the results from part 1 as the principle
3. Spend the result of 2, saving the difference in something. Probably TIPS.
Very well said.
The immediateannuity.com website is one source of those quotes.

www.analyzenow.com/
Has articles by Henry K. "Bud" Hebeler who suggested near the same, steadily saving some portion of the no-COLA pension to compensate for inflation.

Also consider delaying SS to age 70, as a way to boost your inflation protected income.

longinvest
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Re: Any way to "translate" a fixed pension/annuity to an inflation adjusted one?

Post by longinvest » Sat Sep 02, 2017 2:48 pm

rgs92 wrote:
Sat Sep 02, 2017 11:26 am
Let's say I had $100,000 a year for life as a fixed amount (paid monthly). How much could I spend to mimic an inflation adjusted portfolio and where would I invest the amount set aside?
There is no perfect way to do this. But, if we make a few assumptions (unlikely to hold in real life), we can set up a mathematical equation and get an approximate answer.

Assumptions:
  • Do calculations on an annual basis.
  • The annuity pays a nominal $10,000 each year, at the beginning of the year.
  • Constant 2% inflation.
  • Constant 3.5% annual real return on a 50/50 stocks/bonds portfolio (that's a (1.035 X 1.02 - 1) = 5.57% nominal return).
  • Perpetual life (no death).
Here's how we set up the mathematical equation. We know that if we set x% of the payment aside, we'll be left with $y = ($10,000 X (1 - x%)) to spend. We want to spend $y this year, ($y X 1.02) next year, ($y X 1.02^2) the year after, and so on.

But, it's easier to calculate all this in inflation-adjusted terms. In other words, our goal is to spend an inflation-adjusted $y each year.

At the beginning of each year, we will be setting (nominal $10,000 X x%) aside into a 50/50 portfolio. At the end of the year, we will withdraw the 3.5% real growth of the portfolio, leaving the inflation-adjusted constant "principal" untouched.

So, at the beginning of year 1, we get $10,000 from the annuity. We invest ($10,000 X x%) into a 50/50 portfolio. We spend (during the year) the remaining $y.

At the end of year 1, the portfolio has grown (in inflation-adjusted terms) to ($10,000 X x%) X 1.035. We withdraw $z = (0.035 / 1.035) = 3.38% of the end-of-year portfolio, which represents the excess growth of the portfolio over inflation.

At the beginning of year 2, we get an inflation-adjusted payment of (nominal $10,000 / 1.02) = real $9,803.92. We will set aside x% of this. So, our goal is for $z to be equal to ($y - ($9,803.92 X (1 - x%))), where all amounts are inflation-adjusted.

If we solve this, we'll have our perpetual solution, as each year we will set enough aside into the portfolio to cover the future loss of purchase power to inflation (all this assuming utopic constant returns and inflation, of course).

OK. We have all the pieces. Time to do some maths.

Code: Select all

y = 10,000 X (1 - x/100)
z = 10,000 X x/100 X 1.035 X 0.035/1.035
z = y - ((10,000/1.02) X (1 - x/100))

Code: Select all

Replacing z:
10,000 X x/100 X 1.035 X 0.035/1.035 = y - ((10,000/1.02) X (1 - x/100))

Code: Select all

Simplifying:
10,000 X x/100 X 0.035 = y - ((10,000/1.02) X (1 - x/100))

Code: Select all

Replacing y:
10,000 X x/100 X 0.035 = 10,000 X (1 - x/100) - ((10,000/1.02) X (1 - x/100))

Code: Select all

Simplifying and rearranging:
3.5x = (10,000 - (10,000/1.02)) X (1 - x/100)
3.5x = (10,000 - 9,803.92) X (1 - x/100)
3.5x = 196.07843 X (1 - x/100)
3.5x = 196.07843 - 1.9607843x
(3.5 + 1.9607843)x = 196.07843
x = 196.07843/5.4607843 = 35.9066
This tells us that we must set aside 35.9% of each annuity payment, or more exactly $3,590.66, and invest it into a 50/50 portfolio, every year. We can spend the remaining $6,409.34 as well as 3.38% of the year-end portfolio.

Let's try this.

First year, we invest $3,590.66. We can spend $6,409.34.

At the end of the first year, the portfolio has grown to $3,716.34 in inflation-adjusted terms. We withdraw 3.38%, or an inflation-adjusted $125.67, which brings back the portfolio to $3,590.66.

At the beginning of year 2, we get an annuity payment of $9,803.92, in inflation-adjusted terms. We add (35.9% of it) $3,520.26 to the portfolio, growing it to $7,110.92. We can thus spend: $9,803.92 (annuity) - $3,520.26 (savings) + $125.67 (withdrawal) = $6,409.34

At the end of the second year, the portfolio has grown to $7,359.81 in inflation-adjusted terms. We withdraw 3.38%, or an inflation-adjusted $248.88, which brings back the portfolio to $7,110.92.

At the beginning of year 3, we get an annuity payment of $9,611.69, in inflation-adjusted terms. We add (35.9% of it) $3,451.23 to the portfolio. We can thus spend: $9,611.69 (annuity) - $3,451.23 (savings) + $248.88 (withdrawal) = $6,409.34

And so on.

WARNING: The constant 2% inflation and 3.5% real returns are unlikely to hold in real life!
Bogleheads investment philosophy | One-ETF global balanced index portfolio | VPW

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rgs92
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Re: Any way to "translate" a fixed pension/annuity to an inflation adjusted one?

Post by rgs92 » Sat Sep 02, 2017 7:30 pm

Awesome response Longinvest! Thank you very much for that incredibly detailed analysis. You are clearly a very smart person.
Seems like a good thing to write in perl.
Again, big thanks and cheers.
[I thought this might have come up before as a natural thing to do, but I could not find it in my search for it in any of the forums here.]

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Re: Any way to "translate" a fixed pension/annuity to an inflation adjusted one?

Post by itstoomuch » Sat Sep 02, 2017 8:21 pm

bookmarked.
I can use this thread
Rev012718; 4 Incm stream buckets: SS+pension; dfr'd GLWB VA & FI anntys, by time & $$ laddered; Discretionary; Rentals. LTCi. Own, not asset. Tax TBT%. Early SS. FundRatio (FR) >1.1 67/70yo

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Re: Any way to "translate" a fixed pension/annuity to an inflation adjusted one?

Post by carolinaman » Sun Sep 03, 2017 7:09 am

I have a non COLA pension which covers about 60% of my living expenses. I took a simpler approach. I just took a higher equity allocation for my investment portfolio. No guarantees, but this should enable my portfolio to keep up with or exceed inflation. When/if my expenses exceed my pension/SS, I will withdraw needed funds from portfolio.

I do like the idea of spending less from your pension income for as long as you can, if possible.

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Re: Any way to "translate" a fixed pension/annuity to an inflation adjusted one?

Post by #Cruncher » Sun Sep 03, 2017 4:20 pm

longinvest wrote:
Sat Sep 02, 2017 2:48 pm
Assumptions: ...
  • Perpetual life (no death).
Assuming a perpetual annuity, longinvest, understates the equivalent constant dollar annuity for any reasonable life expectancy. For example, with your 2% inflation and 3.5% real growth, if one assumes the annuity will run for 50 years, the constant dollar equivalent is $7,288, not the $6,409 your method produces.

But first, here is a table showing how your scenario plays out over time. Amounts are in constant dollars. The portfolio balance continually increases approaching a limit of $183,124 (6409.34 / 0.035). This makes sense because eventually all the spending will need to come from portfolio income since the $10,000 nominal annuity approaches $0 in constant dollars.

Code: Select all

                              ---- Portfolio ----
Year    Annuity    Invest     Income      Balance     Spend

Code: Select all

   1  10,000.00   3,590.66     125.67    3,590.66   6,409.34
   2   9,803.92   3,520.26     248.88    7,110.92   6,409.34
   3   9,611.69   3,451.23     369.68   10,562.16   6,409.34
   4   9,423.22   3,383.56     488.10   13,945.72   6,409.34
   5   9,238.45   3,317.22     604.20   17,262.94   6,409.34
   6   9,057.31   3,252.18     718.03   20,515.11   6,409.34
   7   8,879.71   3,188.41     829.62   23,703.52   6,409.34
   8   8,705.60   3,125.89     939.03   26,829.41   6,409.34
   9   8,534.90   3,064.60   1,046.29   29,894.01   6,409.34
  10   8,367.55   3,004.51   1,151.45   32,898.52   6,409.34
  11   8,203.48   2,945.60   1,254.54   35,844.11   6,409.34
  12   8,042.63   2,887.84   1,355.62   38,731.95   6,409.34
  13   7,884.93   2,831.21   1,454.71   41,563.16   6,409.34
  14   7,730.33   2,775.70   1,551.86   44,338.86   6,409.34
  15   7,578.75   2,721.27   1,647.10   47,060.14   6,409.34
  16   7,430.15   2,667.92   1,740.48   49,728.06   6,409.34
  17   7,284.46   2,615.60   1,832.03   52,343.66   6,409.34
  18   7,141.63   2,564.32   1,921.78   54,907.98   6,409.34
  19   7,001.59   2,514.04   2,009.77   57,422.02   6,409.34
  20   6,864.31   2,464.74   2,096.04   59,886.76   6,409.34
  21   6,729.71   2,416.41   2,180.61   62,303.17   6,409.34
  22   6,597.76   2,369.03   2,263.53   64,672.21   6,409.34
  23   6,468.39   2,322.58   2,344.82   66,994.79   6,409.34
  24   6,341.56   2,277.04   2,424.51   69,271.83   6,409.34
  25   6,217.21   2,232.39   2,502.65   71,504.22   6,409.34
  26   6,095.31   2,188.62   2,579.25   73,692.84   6,409.34
  27   5,975.79   2,145.71   2,654.35   75,838.55   6,409.34
  28   5,858.62   2,103.63   2,727.98   77,942.18   6,409.34
  29   5,743.75   2,062.39   2,800.16   80,004.57   6,409.34
  30   5,631.12   2,021.95   2,870.93   82,026.52   6,409.34
  31   5,520.71   1,982.30   2,940.31   84,008.82   6,409.34
  32   5,412.46   1,943.43   3,008.33   85,952.25   6,409.34
  33   5,306.33   1,905.33   3,075.02   87,857.58   6,409.34
  34   5,202.29   1,867.97   3,140.39   89,725.54   6,409.34
  35   5,100.28   1,831.34   3,204.49   91,556.88   6,409.34
  36   5,000.28   1,795.43   3,267.33   93,352.31   6,409.34
  37   4,902.23   1,760.23   3,328.94   95,112.54   6,409.34
  38   4,806.11   1,725.71   3,389.34   96,838.25   6,409.34
  39   4,711.87   1,691.88   3,448.55   98,530.13   6,409.34
  40   4,619.48   1,658.70   3,506.61  100,188.83   6,409.34
  41   4,528.90   1,626.18   3,563.53  101,815.01   6,409.34
  42   4,440.10   1,594.29   3,619.33  103,409.30   6,409.34
  43   4,353.04   1,563.03   3,674.03  104,972.33   6,409.34
  44   4,267.69   1,532.38   3,727.66  106,504.71   6,409.34
  45   4,184.01   1,502.34   3,780.25  108,007.05   6,409.34
  46   4,101.97   1,472.88   3,831.80  109,479.93   6,409.34
  47   4,021.54   1,444.00   3,882.34  110,923.93   6,409.34
  48   3,942.68   1,415.69   3,931.89  112,339.61   6,409.34
  49   3,865.38   1,387.93   3,980.46  113,727.54   6,409.34
  50   3,789.58   1,360.71   4,028.09  115,088.25   6,409.34
For example:

Code: Select all

Year  2: 6,409.34 = 9803.92 - 3520.26 +  125.67
Year 50: 6,409.34 = 3789.58 - 1360.71 + 3980.46

I would use a different method.
  • Assume how many years the annuity will run, i.e., how long one will live.
  • Discount the annuity at the assumed nominal rate of return to get its present value.
  • Calculate the annual payment that produces the same present value when discounted at the real rate of return.
Here are the results for 1 to 50 and 390 to 395 years for a constant 2% inflation and three real discount rates: 0%, 2%, and 3.5%. With the latter discount rate, and 391 or more years my method produces the same $6,409.34 constant dollar equivalent as your method.

Code: Select all

          0.00%      2.00%      3.50% <-- real discount rate
          2.00%      4.04%      5.57% <-- nominal discount rate
          
Years  - - Equiv Constant $ Annuity --

Code: Select all

    1  10,000.00  10,000.00  10,000.00
    2   9,901.96   9,902.93   9,903.65
    3   9,805.20   9,807.77   9,809.66
    4   9,709.71   9,714.47   9,717.97
    5   9,615.46   9,623.00   9,628.55
    6   9,522.43   9,533.32   9,541.34
    7   9,430.62   9,445.40   9,456.29
    8   9,339.99   9,359.21   9,373.36
    9   9,250.53   9,274.70   9,292.49
   10   9,162.24   9,191.86   9,213.65
   11   9,075.08   9,110.64   9,136.78
   12   8,989.04   9,031.01   9,061.85
   13   8,904.11   8,952.94   8,988.81
   14   8,820.27   8,876.40   8,917.62
   15   8,737.50   8,801.36   8,848.23
   16   8,655.79   8,727.80   8,780.61
   17   8,575.12   8,655.67   8,714.71
   18   8,495.48   8,584.96   8,650.51
   19   8,416.86   8,515.64   8,587.95
   20   8,339.23   8,447.68   8,527.00
   21   8,262.59   8,381.05   8,467.62
   22   8,186.91   8,315.72   8,409.78
   23   8,112.19   8,251.68   8,353.44
   24   8,038.42   8,188.89   8,298.57
   25   7,965.57   8,127.33   8,245.14
   26   7,893.64   8,066.98   8,193.10
   27   7,822.61   8,007.82   8,142.43
   28   7,752.46   7,949.81   8,093.09
   29   7,683.20   7,892.94   8,045.06
   30   7,614.79   7,837.19   7,998.30
   31   7,547.24   7,782.53   7,952.78
   32   7,480.53   7,728.94   7,908.47
   33   7,414.65   7,676.40   7,865.35
   34   7,349.58   7,624.89   7,823.38
   35   7,285.31   7,574.40   7,782.54
   36   7,221.84   7,524.89   7,742.80
   37   7,159.15   7,476.35   7,704.13
   38   7,097.22   7,428.77   7,666.50
   39   7,036.06   7,382.11   7,629.90
   40   6,975.65   7,336.38   7,594.30
   41   6,915.97   7,291.54   7,559.66
   42   6,857.02   7,247.58   7,525.98
   43   6,798.79   7,204.48   7,493.22
   44   6,741.26   7,162.22   7,461.36
   45   6,684.44   7,120.80   7,430.37
   46   6,628.30   7,080.18   7,400.25
   47   6,572.83   7,040.36   7,370.96
   48   6,518.04   7,001.33   7,342.48
   49   6,463.90   6,963.06   7,314.80
   50   6,410.42   6,925.54   7,287.89
  ...
  390   1,307.11   5,051.74   6,409.35
  391   1,303.78   5,051.70   6,409.34
  392   1,300.47   5,051.65   6,409.34
  393   1,297.17   5,051.61   6,409.34
  394   1,293.89   5,051.57   6,409.34
  395   1,290.62   5,051.53   6,409.34
Examples for 3.5% real discount rate using the Excel PMT and PV functions:

Code: Select all

 50 years: 7,287.89 = PMT(3.5%,  50, PV(5.57%,  50, 10000, 0, 1), 0, 1)
395 years: 6,409.34 = PMT(3.5%, 395, PV(5.57%, 395, 10000, 0, 1), 0, 1)

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Re: Any way to "translate" a fixed pension/annuity to an inflation adjusted one?

Post by Grt2bOutdoors » Sun Sep 03, 2017 4:21 pm

Also bookmarked, another interesting thread here on the forum. :beer
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Re: Any way to "translate" a fixed pension/annuity to an inflation adjusted one?

Post by Tyler Aspect » Sun Sep 03, 2017 4:36 pm

My thought would be that an inflation adjusted pension is just a way of distributing pension income. Being inflation adjusted means the income stream would start smaller, and there is no guarantee that high inflation might be persistent in the future. In fact, any time when an insurance company is removing a risk from the table, there is a cost to that service.

An inflation adjusted pension might be worse than a constant term pension, but it is hard to tell ahead of time.
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Re: Any way to "translate" a fixed pension/annuity to an inflation adjusted one?

Post by longinvest » Sun Sep 03, 2017 4:58 pm

Tyler Aspect wrote:
Sun Sep 03, 2017 4:36 pm
My thought would be that an inflation adjusted pension is just a way of distributing pension income. Being inflation adjusted means the income stream would start smaller, and there is no guarantee that high inflation might be persistent in the future. In fact, any time when an insurance company is removing a risk from the table, there is a cost to that service.

An inflation adjusted pension might be worse than a constant term pension, but it is hard to tell ahead of time.
If I ever need to buy a Single Premium Immediate Annuity (SPIA) as part of my retirement plan (at age 80, for example), it will be a inflation-indexed one. A SPIA is an insurance product, not an investment product. The goal of buying it is to insure sufficient income in case of long survival (think after age 100), regardless of what future inflation happens to be.

Unfortunately, some of us are burdened with a fixed work pension, without an "inflation rider" option. This is a big problem, because the primary benefit of a lifelong pension is to provide income in case of long life. Yet, a non-indexed pension loses most of its purchase power exactly in the case of long life.

The calculations presented in this thread might mitigate, somewhat, this unsolvable issue. The ultra-conservative assumption of perpetual life keeps calculations simpler and could help a little in case inflation proves higher than 2% or returns happen to be less than 3.5% real.

Obviously, it wouldn't be a good plan to go and buy a non-indexed SPIA and use this thread's calculations to attempt to provide an inflation increment. One should, instead, buy an inflation-indexed SPIA. The presented calculations are only meant to help people who have no choice (e.g. those with a non-indexed work pension).
Last edited by longinvest on Sun Sep 03, 2017 5:02 pm, edited 2 times in total.
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Re: Any way to "translate" a fixed pension/annuity to an inflation adjusted one?

Post by joppy » Sun Sep 03, 2017 5:01 pm

A few additional considerations:
  • Longevity Insurance: A fixed pension/annuity also provides *longevity* insurance. That is, money from annuitants that die earlier is transferred to annuitants that die later, since the income stream terminates at the death of the annuitant. You have to save an additional amount to compensate for the inflation adjusted longevity insurance component, since you are only receiving the fixed longevity insurance component of the payouts. This makes your payments higher.
  • Tax treatment: The growth inside an annuity is tax deferred. The growth in TIPS is taxable, assuming a taxable account. You would need to save an additional amount in TIPS to compensate for the tax drag, in order to get after-tax spendable dollars in retirement.

A simpler way to frame the discussion in your mind is as follows. Instead of trying to "translate" your annuity by adding money to it, "translate" it into an equivalent real income stream. Then figure out how much real income shortfall you have. That is the amount of real income stream you need to support via your investments.

You can compute the equivalent real income stream as follows: Suppose you will receive a fixed annuity equal to $X per year. Look at the purchase price ($Y) of that fixed annuity. Now, find how much of an inflation adjusted annuity you can buy for the same expenditure of ($Y). Let's say that you will receive $Z inflation adjusted for that expenditure. Then a fixed annuity with payments of $X is equivalent to an inflation adjusted annuity with payments of $Z.

Now, you can figure out your income shortfall for your desired standard of living assuming an annual income of $Z, and then save to accommodate that income shortfall from your portfolio.

Cheers,
Joppy

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Re: Any way to "translate" a fixed pension/annuity to an inflation adjusted one?

Post by joppy » Sun Sep 03, 2017 5:05 pm

Oh, and even my method only accounts for *expected* inflation. To build on longinvest's comments, the risk of *unexpected* inflation is not accounted for by any of these techniques, and can only be accounted for by buying a true inflation adjusted annuity.

Cheers,
Joppy

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Re: Any way to "translate" a fixed pension/annuity to an inflation adjusted one?

Post by ThrustVectoring » Mon Sep 04, 2017 12:46 am

ThrustVectoring wrote:
Sat Sep 02, 2017 12:56 pm
Easiest way I can think of:

1. Get a quote for how much it'd cost to buy an annuity with your current fixed annuity payments
2. Get a quote for how an inflation-adjusted annuity with the results from part 1 as the principle
3. Spend the result of 2, saving the difference in something. Probably TIPS.

You don't have to value things yourself if there's a fair market value you can use instead.
Further thought: there's a shortfall here. Annuities are funded in part through mortality credits - essentially, if you die before expected, you surrender your investment to pay for the case where you die later than expected. This makes it more efficient than living off savings, since you are essentially selling a portion of your inheritance. And if you save the surplus, that's an inheritance.

So the amended strategy is:
1. Multiply your annuity income by the CPI
2. Buy that much additional monthly income through another annuity, essentially rolling your own COL adjustment
3. Fund the increase through spending less than your actual annuity payout

It wouldn't work exactly, since the cost of an annuity goes down each year, so you wouldn't need as much of your income saved to buy a COL-adjustment annuity. Plus there's annoying logistical stuff - there's a fairly hefty minimum investment for annuities, and a maximum age at which you can buy them. Anyhow, thoughts?
Current portfolio: 60% VTI / 40% VXUS

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Re: Any way to "translate" a fixed pension/annuity to an inflation adjusted one?

Post by rgs92 » Mon Sep 04, 2017 11:27 am

Again, thanks to everyone for the varying insights and analysis. Very helpful. I guess I should expand the question to:
How do people with a substantial non-inflation-adjusted (and totally fixed for life) income stream deal with this in their financial planning?

I realize that planning tools like Firecalc and I-orp deal with this, but I thought some subjective real-life experience or perspectives would be valuable.
Thanks again. (Apologies if this has been asked before and I missed it; any references to previous threads on this would be welcome.)

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Re: Any way to "translate" a fixed pension/annuity to an inflation adjusted one?

Post by #Cruncher » Mon Sep 04, 2017 11:43 am

#Cruncher wrote:
Sun Sep 03, 2017 4:20 pm

Code: Select all

 50 years: 7,287.89 = PMT(3.5%,  50, PV(5.57%,  50, 10000, 0, 1), 0, 1)
It may be helpful to see how the result of this formula (from my previous post) works out year-by-year in nominal dollars. To review, the assumptions are:
  • $10,000 nominal pension received at the beginning of each year for 50 years.
  • 2% constant increase in the Consumer Price Index (CPI).
  • 3.5% constant real rate of return and consequent constant 5.57% nominal rate of return (1.02 * 1.035 - 1).
The "Spend" column in the table below shows the pensioner spending $7,287.89 the first year. This is the result of the formula above. Each subsequent year he spends 2% more to reflect the increase in the CPI. If the amount spent is less than $10,000, the difference is saved into an assumed portfolio. If the amount spent is more than $10,000, the difference is withdrawn from the portfolio. The far right column shows the portfolio balance assuming a constant 5.57% nominal return.

Code: Select all

                     Save or    Portfolio
Year      Spend    (Withdraw)     Balance

Code: Select all

   1    7,287.89    2,712.11     2,863.18
   2    7,433.64    2,566.36     5,731.96
   3    7,582.32    2,417.68     8,603.58
   4    7,733.96    2,266.04    11,475.05
   5    7,888.64    2,111.36    14,343.17
   6    8,046.42    1,953.58    17,204.49
   7    8,207.34    1,792.66    20,055.29
   8    8,371.49    1,628.51    22,891.58
   9    8,538.92    1,461.08    25,709.11
  10    8,709.70    1,290.30    28,503.28
  11    8,883.89    1,116.11    31,269.18
  12    9,061.57      938.43    34,001.58
  13    9,242.80      757.20    36,694.84
  14    9,427.66      572.34    39,342.96
  15    9,616.21      383.79    41,939.53
  16    9,808.54      191.46    44,477.69
  17   10,004.71       (4.71)   46,950.13
  18   10,204.80     (204.80)   49,349.05
  19   10,408.90     (408.90)   51,666.12
  20   10,617.07     (617.07)   53,892.48
  21   10,829.42     (829.42)   56,018.67
  22   11,046.00   (1,046.00)   58,034.65
  23   11,266.92   (1,266.92)   59,929.69
  24   11,492.26   (1,492.26)   61,692.39
  25   11,722.11   (1,722.11)   63,310.63
  26   11,956.55   (1,956.55)   64,771.50
  27   12,195.68   (2,195.68)   66,061.29
  28   12,439.59   (2,439.59)   67,165.43
  29   12,688.39   (2,688.39)   68,068.41
  30   12,942.15   (2,942.15)   68,753.79
  31   13,201.00   (3,201.00)   69,204.09
  32   13,465.02   (3,465.02)   69,400.74
  33   13,734.32   (3,734.32)   69,324.04
  34   14,009.00   (4,009.00)   68,953.08
  35   14,289.18   (4,289.18)   68,265.68
  36   14,574.97   (4,574.97)   67,238.28
  37   14,866.47   (4,866.47)   65,845.93
  38   15,163.80   (5,163.80)   64,062.13
  39   15,467.07   (5,467.07)   61,858.80
  40   15,776.41   (5,776.41)   59,206.17
  41   16,091.94   (6,091.94)   56,072.70
  42   16,413.78   (6,413.78)   52,424.92
  43   16,742.06   (6,742.06)   48,227.40
  44   17,076.90   (7,076.90)   43,442.58
  45   17,418.43   (7,418.43)   38,030.69
  46   17,766.80   (7,766.80)   31,949.59
  47   18,122.14   (8,122.14)   25,154.64
  48   18,484.58   (8,484.58)   17,598.58
  49   18,854.27   (8,854.27)    9,231.36
  50   19,231.36   (9,231.36)        0.00
For the first 16 years less than $10,000 is spent and the surplus is added to the portfolio. Starting in year 17, to keep up with inflation, more than $10,000 is spent each year. Money is taken from the portfolio to make up the shortfall. But because of the 5.57% investment return, the portfolio balance continues to grow through year 32. By then the annual withdrawals are so large that they exceed the investment growth. The portfolio balance therefore begins to drop each year so that after 50 years it has fallen to exactly $0.

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Re: Any way to "translate" a fixed pension/annuity to an inflation adjusted one?

Post by alex_686 » Mon Sep 04, 2017 12:04 pm

If you want to add a little complexity you don't have to assume a perpetual life. For each year one could multiple the Spending / Income / Payment amount by a survival rate. i.e., in year 1 when you are 65 you would have a 100% survival rate. In year 30 when your are 95 you would have a 10% rate - number pulled out of thin air. You can go to the SS website and pull the actuarial tables for your calculations. This should get your numbers closer to a immediate annuity quote.

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Re: Any way to "translate" a fixed pension/annuity to an inflation adjusted one?

Post by longinvest » Mon Sep 04, 2017 12:10 pm

You may want to compare that to the simplicity, in nominal dollars, of the approach I've proposed. My approach can be summarized as:
  • At the beginning of each year, receive a nominal $10,000 pension payment, and:
    • Add $3,600 of it to a dedicated portfolio.
    • Set aside the remaining $6,400 into a savings account for spending during the year.
  • At the end of each year, withdraw 3.4% of the dedicated portfolio balance and set it aside into a savings account for spending during the upcoming year.
The dedicated portfolio starts with a balance of $0.

The advantage of my method is that it works without having to do any calculation other than multiplying the dedicated portfolio balance by 3.4%, once a year. It even works with a real-life dedicated portfolio with varying annual returns. Of course, in that later case, it won't generate perfect inflation increments, but that's something I've warned about all along. I've rounded the numbers, because precision, here, is illusive.

Note that the dedicated "inflation increment" portfolio must be kept separate from the retiree's normal portfolio from which retirement withdrawals are taken (using a method such as VPW).
Last edited by longinvest on Mon Sep 04, 2017 12:47 pm, edited 5 times in total.
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Re: Any way to "translate" a fixed pension/annuity to an inflation adjusted one?

Post by itstoomuch » Mon Sep 04, 2017 12:21 pm

^ sure. LoL
Annuitant receives into checking account $10,000 annual lump sum or $833/mn. I'm spending mine on junk food and toys. I've saved for too long to not enjoy some of the benefits. :sharebeer
Rev012718; 4 Incm stream buckets: SS+pension; dfr'd GLWB VA & FI anntys, by time & $$ laddered; Discretionary; Rentals. LTCi. Own, not asset. Tax TBT%. Early SS. FundRatio (FR) >1.1 67/70yo

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Re: Any way to "translate" a fixed pension/annuity to an inflation adjusted one?

Post by longinvest » Mon Sep 04, 2017 12:29 pm

itstoomuch wrote:
Mon Sep 04, 2017 12:21 pm
^ sure. LoL
Annuitant receives into checking account $10,000 annual lump sum or $833/mn. I'm spending mine on junk food and toys. I've saved for too long to not enjoy some of the benefits. :sharebeer
The fixed (non-COLA*) pension payment of someone retiring early at age 55, in a 2% inflation world, will have lost almost 40% of its purchase power by age 80. In a 3% inflation world, it will have lost more than 50% of its purchase power.

* COLA = Cost of living adjustment.
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Re: Any way to "translate" a fixed pension/annuity to an inflation adjusted one?

Post by itstoomuch » Mon Sep 04, 2017 1:50 pm

That's good know, so for 55 yo, the alternatives are what?
My signature line say we are 67/70.
Sometime this week I'm turning on my wife's deferred annuity. RMD year. 34% set aside for taxes. :mrgreen:
Rev012718; 4 Incm stream buckets: SS+pension; dfr'd GLWB VA & FI anntys, by time & $$ laddered; Discretionary; Rentals. LTCi. Own, not asset. Tax TBT%. Early SS. FundRatio (FR) >1.1 67/70yo

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Re: Any way to "translate" a fixed pension/annuity to an inflation adjusted one?

Post by longinvest » Mon Sep 04, 2017 2:35 pm

Itstoomuch,

I forgot to tell you about his wife, age 50, who will happen to survive to age 105...
itstoomuch wrote:
Mon Sep 04, 2017 1:50 pm
That's good know, so for 55 yo, the alternatives are what?
Of course, there's the imperfect scenario presented above, trying to self-construct inflation increments for the fixed pension. It might work or fail, based on actual inflation and market returns.

Another possibility is to quit the job and the pension plan for another job with a COLA pension, as soon as possible. There are risks, here too, as finding such a job might be difficult, the job might not be as satisfying, and the new employer could even drop the cost of living adjustments after the transition to the new job.

A better possibility might be to reduce one's cost of living, such that Social Security, delayed to age 70, will be sufficient to cover basic expenses (and taxes) in old age. If necessary, a supplemental inflation-indexed SPIA could be bought, as late as possible in life*, to cover any projected deficit from the fixed pension (when combined with delayed Social Security), in case of long survival.

* There's at least two advantages to this:
  1. It won't need to be bought if one is already dead.
  2. The cost of an inflation-indexed SPIA declines the older one gets. (But, insurance companies stop selling them when one gets too old).
itstoomuch wrote:
Mon Sep 04, 2017 1:50 pm
My signature line say we are 67/70.
Sometime this week I'm turning on my wife's deferred annuity. RMD year. 34% set aside for taxes. :mrgreen:
:thumbsup
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Re: Any way to "translate" a fixed pension/annuity to an inflation adjusted one?

Post by #Cruncher » Mon Sep 04, 2017 3:44 pm

alex_686 wrote:
Mon Sep 04, 2017 12:04 pm
If you want to add a little complexity ... For each year one could multipl[y] the ... amount by a survival rate. i.e., in year 1 when you are 65 you would have a 100% survival rate. In year 30 when your are 95 you would have a 10% rate - number pulled out of thin air.
My longevity estimator does the survival weighting you're suggesting, Alex. This makes the nominal to inflation-indexed translation easy. For example, assuming the 3.5% real and 5.57% nominal returns longinvest did in his original post, for a 65-year old male and the SSA 1950 Cohort Life Table:
  • Present value of survival-weighted $1,000 per month annuity discounted at 5.57% is $126,030.
  • Present value of survival-weighted $1,000 per month annuity discounted at 3.50% is $149,656.
  • Equivalent inflation-indexed pension is 84.2% of nominal pension (126030 / 149656).

longinvest wrote:
Mon Sep 04, 2017 12:10 pm
You may want to compare that to the simplicity, in nominal dollars, of the approach I've proposed.
I assume by "that", longinvest, you mean my post two before yours. I wasn't intending that someone actually go through the computation each year. I was just trying to demonstrate that, if the assumptions of longevity, inflation, and real return actually did pan out, a $7,288 constant dollar pension is equivalent to a $10,000 nominal one. I think the only purpose of translating a nominal pension to a constant dollar equivalent is for retirement planning purposes when one is working in constant dollars.

For example, if one will get $30,000 per year Social Security and a $10,000 nominal pension, how does one combine them in determining the residual constant dollar amount one's portfolio needs to provide? Assuming 2% inflation and a 3.5% real return your conservative method would add $6,400 to the $30,000 SS. A method assuming 50 years of life would add $7,300. A method based on the SSA 1950 Cohort Life Table for a 65-year old male would add $8,400. (See my response to alex_686 above.)

When retirement comes and one begins collecting the $10,000 nominal pension, it makes no sense to try and keep track of a hypothetical side portfolio. Instead, if one's estimate of longevity, inflation, or real return changes dramatically, one should just re-translate the $10,000 nominal pension to a new constant dollar amount and revise one's overall retirement plan.

By the way, for those wishing to use your "perpetual" method with other assumptions for inflation and real return, I've distilled the calculation in your original post down to the following formula:

Code: Select all

constant $ equiv = (1 / nominal rate + 1) / (1 / real rate + 1)
          64.09% = (1 / 0.0557       + 1) / (1 / 0.035     + 1)
This is if payments are received at the start of each period. The following formula is if they are made at the end of each period.

Code: Select all

constant $ equiv = (1 / nominal rate) / (1 / real rate)
          62.84% = (1 / 0.0557)       / (1 / 0.035)

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Re: Any way to "translate" a fixed pension/annuity to an inflation adjusted one?

Post by longinvest » Mon Sep 04, 2017 3:57 pm

#Cruncher,
#Cruncher wrote:
Mon Sep 04, 2017 3:44 pm
When retirement comes and one begins collecting the $10,000 nominal pension, it makes no sense to try and keep track of a hypothetical side portfolio. Instead, if one's estimate of longevity, inflation, or real return changes dramatically, one should just re-translate the $10,000 nominal pension to a new constant dollar amount and revise one's overall retirement plan.
OK. I agree. It's important to consider the entire retirement plan, not its pieces in isolation.
#Cruncher wrote:
Mon Sep 04, 2017 3:44 pm
By the way, for those wishing to use your "perpetual" method with other assumptions for inflation and real return, I've distilled the calculation in your original post down to the following formula:

Code: Select all

constant $ equiv = (1 / nominal rate + 1) / (1 / real rate + 1)
          64.09% = (1 / 0.0557       + 1) / (1 / 0.035     + 1)
This is if payments are received at the start of each period. The following formula is if they are made at the end of each period.

Code: Select all

constant $ equiv = (1 / nominal rate) / (1 / real rate)
          62.84% = (1 / 0.0557)       / (1 / 0.035)
Neat!
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Re: Any way to "translate" a fixed pension/annuity to an inflation adjusted one?

Post by pezblanco » Thu Dec 07, 2017 5:35 pm

I didn't know of the existence of this thread ... but thanks to Longinvest, I do now. The view up till now has been one of a deterministic approach to inflation and investment i.e. a constant year by year 2% or what have you. I took a stochastic approach via simulation from the last 51 years of data from the DFA Matrix .... The results are detailed in this thread:

viewtopic.php?f=10&t=233865#p3650516

The results are a little more pessimistic than those produced by the deterministic viewpoint.

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Re: Any way to "translate" a fixed pension/annuity to an inflation adjusted one?

Post by Thesaints » Thu Dec 07, 2017 5:54 pm

Future inflation is unknown.
The "cost" differential between nominal and inflation-indexed annuities is the cost of insurance against inflation. It can very well turn out to be a very different number from the eventually realized inflation.

cfr. yield difference between standard and their equivalent inflation-indexed treasuries. Really unfortunate it is referred to as "implied inflation", as it suggests that somehow the market knows what the inflation will be in the next 30 years.

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Re: Any way to "translate" a fixed pension/annuity to an inflation adjusted one?

Post by GAAP » Sat Dec 09, 2017 1:43 pm

rgs92 wrote:
Mon Sep 04, 2017 11:27 am
Again, thanks to everyone for the varying insights and analysis. Very helpful. I guess I should expand the question to:
How do people with a substantial non-inflation-adjusted (and totally fixed for life) income stream deal with this in their financial planning?

I realize that planning tools like Firecalc and I-orp deal with this, but I thought some subjective real-life experience or perspectives would be valuable.
Thanks again. (Apologies if this has been asked before and I missed it; any references to previous threads on this would be welcome.)
Mine thankfully isn't "substantial", so I've been calculating NPV with an assumed inflation rate to determine whether or not to take it early or wait until age 65. In my case, the answer is basically take it now (age 57) for any inflation rate over about 2% and any lifetime less than age 87. After 87, the nominal value of even the full pension won't buy much anyway. Since I'm moving to a state with no income tax, I'm waiting until after the move and will take it at age 58. One additional note: I currently don't expect a change in federal tax brackets when I retire -- which drastically simplifies the assumptions.

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