Find the Math Mistake
 12-22-2009, 09:46 AM #1 Thinks s/he gets paid by the post   Join Date: Sep 2008 Posts: 2,171 Find the Math Mistake I have been trying for a long time to figure out the "Magic Number", the balance I need in my retirement accounts in order to be able to retire. I think I have it now, but this most recent calculation gives me a retirement date a year ahead of almost all my previous estimates. The only thing I have added in is an adjustment for Social Security, and since I didn't use my whole projected benefit I didn't think it would make much of a difference. Here are the numbers: Magic Number calculation Projected Pension benefit at age 56 (2012)...........................\$3,488.21/mo .................................................. .............x12=\$41,858.52/yr ..............................................x 0.65=COLA'd portion=\$27,208.03/yr .................................................. ......(rounded off)=\$27,205/yr Adjustment for Social Security*.......................................+\$ 3,000/yr Projected Income............................................ ..........\$30,205/yr Desired budget (2009 dollars).........................................\$ 36,000/yr Desired budget (in 2012, 4.05% infl)...................................\$40,553.54 (rounded up)............................................... ...........\$40,555/yr Shortfall......................................... ....................\$10,350/yr x 25=Required portfolio amount=\$258,750.00 add part of proceeds from sale of house to portfolio (\$100,000)---> MAGIC NUMBER=\$158,750 Current retirement account balance+/-\$115,000 Annual contributions (in 26 paym'ts)=\$22,000 Projected growth (30% equity, 70% fixed)=7% Projected balance by Jan 2012=\$179,544.48 This is based on a pension benefit estimate from the system's online calculator, which is only a projection, but I have requested an official benefit statement from the pension department to verify that I have used the correct benefit. (Unfortunately it takes them 6 weeks to do it.) The only thing I have changed since previous projections is the \$3000 a year for Social Security. My statement says I'm eligible for about \$2000 a month at full retirement age (66+4 mo's) but I only use a quarter of that to give me a cushion, in case I have underestimated expenses elsewhere or there is a reduction in benefits, and I've reduced the one-quarter still further to make up for the fact that I can't start to draw it immediately when I retire. I would not have thought that \$3000 a year would make such a difference in the Magic Number. Where is my math mistake? The financial planner I hired last year told me I wouldn't have enough money even by age 59, even counting all of Social Security. Can I really retire in only two years when I had previously thought at least three and more likely four, or am indulging in wishful thinking? __________________
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12-22-2009, 09:53 AM   #2
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Quote:
 Originally Posted by kyounge1956 Projected growth (30% equity, 70% fixed)=7%
If that 7% figure is an annual return as it appears to be, I think you are being overly optimistic.

Quote:
 Originally Posted by kyounge1956 I would not have thought that \$3000 a year would make such a difference in the Magic Number.
Doesn't seem out of line to me. That \$3k annual income represents more than 8% of your annual budget (in 09 dollars) and that has a significant impact over time.
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 12-22-2009, 01:41 PM #4 Thinks s/he gets paid by the post   Join Date: Sep 2008 Posts: 2,171 Darn! When I previewed my post everything was lined up in columns and now it's all messed up. Might as well not have bothered trying to get it to look pretty.
12-22-2009, 01:47 PM   #5
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Quote:
 Originally Posted by REWahoo On my first quick read of your post this seems questionable: If that 7% figure is an annual return as it appears to be, I think you are being overly optimistic. (snip)
Yes, that is 7% annual. It's the result of a long stint with the spreadsheets and loads of historic return/std deviation/correlation data from SBBI. It's entirely possible I made a mistake in my spreadsheet formula, but looking at the comment I made at the time in the Asset Allocation tutorial, the historic return for that mix was even higher than I have assumed here.

Guess I better stop by the library on the way home and have a look at SBBI. They have historic return/risk data on various blends of stocks and bonds, and I believe 70/30 is one of them. I know, I know, past performance is no guarantee of the future, but what else is there to base an estimated portfolio performance on?

12-22-2009, 01:54 PM   #6
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Quote:
 Originally Posted by kyounge1956 Guess I better stop by the library on the way home and have a look at SBBI. They have historic return/risk data on various blends of stocks and bonds, and I believe 70/30 is one of them. I know, I know, past performance is no guarantee of the future, but what else is there to base an estimated portfolio performance on?
I'd buy 7% for a 70/30 stock/bond mix but you stated the opposite, 30% equity/70% fixed, thus the reason for my comment.

EDIT: I want to point out that a difference of a couple percentage points one way or the other over the next two years shouldn't really make any difference to your retirement plans. It's just that you asked us to look for "math mistakes" and this was the only thing I saw I thought could be a little off.
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12-22-2009, 02:07 PM   #7
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Quote:
 Originally Posted by Independent If I understand your approach, the extra \$3,000 per year reduces your required savings by 25 x \$3,000 = \$75,000. You are adding \$22,000 per year in contributions and expecting \$8,000 in annual interest on your retirement account.
Hey, you just found a mistake. That \$22K is only what I can put in my tax deferred account at my j*b, but I forgot to include the \$6K I can put in my Roth.

Quote:
 So, yes, \$3,000 per year could move your retirement date 2 years. It depends on how much your pension changes if you work two more or less years.
I'll find out when I get the official estimate from the Retirement Dep't, but the amount I'm eligible for could increase substantially over the next two years. The pension benefit is based on the highest two years of salary. I used 24 months of next year's salary for the estimate, but depending what sort of COLA we get in 2011, my monthly benefit could be higher than I've assumed here. I have some old estimates here and the benefit amount goes up a little over \$100 a month between age 56 and 57. I would guess it goes up a similar amount between 55 & 56.

Quote:
 From the overall perspective, the issue is inflation. It appears that your pension alone will cover your Desired Budget in the first year you are retired. After that, your savings and SS only need to fill in the inflation losses. I'm uncertain about how you're doing the inflation adjustments on the pension (is your pension based on final salary? are you expecting raises between now and then? what is the .65 all about?)
I am not expecting raises, except COLA. The pension is based on your 24 highest months whether they are your last 24 or not, but in my case the last will also be highest (barring unforeseen events). The 0.65 is because the pension is partially COLA'd; it increases by 1.5% every year but is guaranteed not to go any lower than 65% of its original purchasing power. After nearly beating my brains out trying to determine how to take this feature into account, I've decided to consider that I have a fully COLA'd pension for 65% of the actual starting amount, but use a multiplier of 25 (which is rather skimpy for my expected 40+ years in retirement), in recognition of the fact that for the first part of my retirement my WR will not need to be the full 4%.

12-22-2009, 02:14 PM   #8
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Quote:
 Originally Posted by REWahoo I'd buy 7% for a 70/30 stock/bond mix but you stated the opposite, 30% equity/70% fixed, thus the reason for my comment. EDIT: I want to point out that a difference of a couple percentage points one way or the other over the next two years shouldn't really make any difference to your retirement plans. It's just that you asked us to look for "math mistakes" and this was the only thing I saw I thought could be a little off.
A couple percentage points over the next two years might not make much diff, but a couple percentage points over the rest of my life could matter bigtime, and I'm planning on maintaining that allocation more or less for the duration (unless I become even more of a Nervous Nellie in my later years).

About 70/30 vs 30/70, I can never remember whether equity or fixed comes first. I'm way too chicken for 70% stocks! What I meant was 70% bonds (now including some TIPs) and 30% equity (+/-evenly split between stocks and REITs). The mix is actually still somewhat higher than 30% equity at the moment due to limited fund choices in my 457 plan. What would you say is a realistic expectation for my Coward's Asset Mix?

12-22-2009, 02:33 PM   #9
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Quote:
 Originally Posted by kyounge1956 What I meant was 70% bonds (now including some TIPs) and 30% equity (+/-evenly split between stocks and REITs). The mix is actually still somewhat higher than 30% equity at the moment due to limited fund choices in my 457 plan. What would you say is a realistic expectation for my Coward's Asset Mix?
My crystal ball is in the shop at the moment so I can't give you an exact number.

However, looking at what we might expect interest rates to do over the next couple of years leads me to believe bonds are going to take a hit in the near term*. That's what led me to doubt an AA comprised of 70% bonds might be expected to return 7% in the short run. Over the next 10 years a 7% return may be more realistic - at least I hope so as I'm sitting on an AA of 40/60 myself.

*I'm much better at predicting the past than the future.
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12-22-2009, 05:35 PM   #10
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Quote:
 Originally Posted by REWahoo My crystal ball is in the shop at the moment so I can't give you an exact number. However, looking at what we might expect interest rates to do over the next couple of years leads me to believe bonds are going to take a hit in the near term*. That's what led me to doubt an AA comprised of 70% bonds might be expected to return 7% in the short run. Over the next 10 years a 7% return may be more realistic - at least I hope so as I'm sitting on an AA of 40/60 myself. *I'm much better at predicting the past than the future.
I think what we have here is differing frames of reference. I was looking at long-term historical data and you were looking at short term expectations. But maybe this is not a problem, because when I include the Roth contributions I forgot in my original post, in 2 years I should have more than the Magic Number, even if the market is completely flat starting tomorrow. I am not terribly worried about the near term because I will only need to withdraw small amounts in the first few years, and if I keep some of my house proceeds in cash, as I plan to, I won't have to dip into anything that has decreased in value. I think averaging 7% growth over the next ten (and 20 and 40) years should work out just fine. And if not, there's a significant fudge factor included in those numbers.

12-22-2009, 06:43 PM   #11
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Quote:
 Originally Posted by kyounge1956 I think averaging 7% growth over the next ten (and 20 and 40) years should work out just fine. And if not, there's a significant fudge factor included in those numbers.
Be sure to include some investigation into the order of data that leads to that "average" 7% growth. High returns followed by lower returns averaging 7% obviously yields much different results than low returns followed by higher returns averaging 7%.

Working with averages is convenient but a poor estimator of how the future will look based on past data.
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12-23-2009, 12:34 AM   #12
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Quote:
 Originally Posted by youbet Be sure to include some investigation into the order of data that leads to that "average" 7% growth. High returns followed by lower returns averaging 7% obviously yields much different results than low returns followed by higher returns averaging 7%. Working with averages is convenient but a poor estimator of how the future will look based on past data.
Sounds like a job for.........FIRECalc!!!

I put in my numbers (\$10,350/year, 4.05% inflation, \$275K portfolio) and the failure rates were really scary (about 50% using a randomized 7.5% return/7.1% std deviation which is the target I was aiming at with my asset allocation) and less than 10% success using historic data for 70% 5-year treasuries and 30% equities. I didn't take into account that at 4.05% inflation it would take 23 years for the pension to shrink to 65% of its original purchasing power and so in the early years of retirement I'd be withdrawing less than the full \$10,350, but I don't know how to model that in FIRECalc. To get the success rate above 90% would require somewhere around \$350K (using the random data) and IIRC \$450K using historic. I had the numbers all written out but when I tried to submit my comment it disappeared and I don't have time to do them again.

I think my mistake must be that the 4% WR and hence the 25x multiplier assumes a higher allocation to stocks than I am planning on.

>sigh<

I knew there must be a fly in the ointment somewhere.

12-23-2009, 09:44 AM   #13
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Quote:
 Originally Posted by kyounge1956 Hey, you just found a mistake. That \$22K is only what I can put in my tax deferred account at my j*b, but I forgot to include the \$6K I can put in my Roth. I'll find out when I get the official estimate from the Retirement Dep't, but the amount I'm eligible for could increase substantially over the next two years. The pension benefit is based on the highest two years of salary. I used 24 months of next year's salary for the estimate, but depending what sort of COLA we get in 2011, my monthly benefit could be higher than I've assumed here. I have some old estimates here and the benefit amount goes up a little over \$100 a month between age 56 and 57. I would guess it goes up a similar amount between 55 & 56. I am not expecting raises, except COLA. The pension is based on your 24 highest months whether they are your last 24 or not, but in my case the last will also be highest (barring unforeseen events). The 0.65 is because the pension is partially COLA'd; it increases by 1.5% every year but is guaranteed not to go any lower than 65% of its original purchasing power. After nearly beating my brains out trying to determine how to take this feature into account, I've decided to consider that I have a fully COLA'd pension for 65% of the actual starting amount, but use a multiplier of 25 (which is rather skimpy for my expected 40+ years in retirement), in recognition of the fact that for the first part of my retirement my WR will not need to be the full 4%.
Thanks. It looks to me like you've got your pension and your cost of living lined up appropriately.

I remember seeing the earlier thread, but forgot who had posted it.

I think this is another way of looking at your situation:
Long term, the COLA'd portion of your pension is \$13,500 short of covering your expenses. Your SS benefit at NRA is \$24,000. Even assuming that law changes reduce you SS benefit by 45%*, your expenses are covered by pension and SS.

Short term, your pension covers your expenses in the first year. So your savings only have to fill in the inflation losses on your pension between retirement and your SS start age. Even figuring a severe 10% inflation rate, that would only cost \$95,000.

This says you've got a \$150,000 cushion.

* Note that SS taxes are sufficient to pay about 75% of scheduled SS benefits on a pay-as-you-go basis. So a 45% reduction seems very unlikely.

12-24-2009, 02:39 PM   #14
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Quote:
 Originally Posted by Independent Thanks. It looks to me like you've got your pension and your cost of living lined up appropriately. I remember seeing the earlier thread, but forgot who had posted it. I think this is another way of looking at your situation: Long term, the COLA'd portion of your pension is \$13,500 short of covering your expenses. Your SS benefit at NRA is \$24,000. Even assuming that law changes reduce you SS benefit by 45%*, your expenses are covered by pension and SS.
I think another way of looking at it is what I need. FIRE Calc and other retirement calculators just don't seem to want to think along the lines I've tried to, hence my frustration at being unable to determine the Magic Number.

Quote:
 Short term, your pension covers your expenses in the first year. So your savings only have to fill in the inflation losses on your pension between retirement and your SS start age. Even figuring a severe 10% inflation rate, that would only cost \$95,000. This says you've got a \$150,000 cushion. * Note that SS taxes are sufficient to pay about 75% of scheduled SS benefits on a pay-as-you-go basis. So a 45% reduction seems very unlikely.
Where did the \$95K amount come from? I used FIRECalc to simulate a 10.4 year "retirement", from Quit the City until SS retirement age. My inputs were 4.05% inflation, 100% in 1-month Treasuries with 0% expense ratio (to simulate a CD ladder). Starting expenses were \$3350, add an additional \$3333 after 2, 4, and 6 years to simulate the shrinkage of my pension (non COLA'd part), which I think still overstates the amounts I would actually need to withdraw, but I don't mind erring a little on the side of caution. FC says I would have needed \$116,500 to succeed in all available runs—possibly there are some decades in the data when inflation was more than 10%. Or maybe that is due to the difference between a constant rate of inflation and an actual series of values.

So, if I understand you, your take on my situation is:
In Phase 1 of retirement, from Quit the City to SSRA, I can cover basic expenses with COLA'd part of pension + remainder of pension + part of portfolio. To make it plainer to me, I assumed that "part" would be the money I plan to set aside from sale of my house, plus if necessary a small VA (thanks Ameritrade) which will finally lose its surrender charge sometime during Phase 1. To make a cushion for luxuries, underestimates, reduction of benefits etc, I could use some income from my retirement accounts (457 & Roth), or reduce spending (e.g. less expensive replacement house) or get a part time j*b, or grow my own food, or....

In Phase 2, after SSRA, I have enough fully COLA'd income for basic expenses, namely 65% of my pension + about half of my projected SS benefit. For a cushion, I would have the other half of SS (also COLA'd) plus 100% of my retirement accounts, or to look at it another way, SS benefits could be cut or taxed by half, or health care cost could expand to eat up half my SS benefit, without being reduced to a bare-bones existence.

One thing I like about this way of looking at it is that after age 66, the "meat and potatoes" are covered and COLA'd by pension and SS, with my portfolio just providing the gravy. Unless both the pension system and SS go bust, I won't starve. Another good feature is that I can use the "withdraw a fixed percentage of portfolio" method, rather than "withdraw a fixed purchasing power amount", and can base the percentage on a realistic growth rate for my actual asset allocation rather than on the more aggressive investment policy assumed by the 4% SWR. That might result in some years with no luxuries, but if I understand it right, it pretty much guarantees the retirement accounts won't be exhausted no matter how long I live. Another positive feature is that they may potentially sit untouched and grow for another ten years during Phase 1. Maybe I could run into difficulties if the accounts grow hugely and I have to take big RMD's, but if that's my only financial worry I won't have anything to complain about.

I will know my portfolio has hit the Magic Number when its likely income + half of SS is a cushion over and above basic expenses that passes the "sleep at night" test. Maybe I really can retire in 2 years after all.

 12-24-2009, 06:06 PM #15 Thinks s/he gets paid by the post   Join Date: Jun 2006 Location: Boise Posts: 2,673 I alluded to this in another thread, but I assume 25% of my actual SS benefit as an NPV, and it makes a difference of about a year if I take it out. So at first blush your question about a math mistake makes me think, "Yeah, that's reasonable." I'm also assuming about a 7% rate of return and am looking at FIRE in about 4 years. It will be longer before I am able to collect SS, though - about 18 years or so. 2Cor521 __________________ "At times the world can seem an unfriendly and sinister place, but believe us when we say there is much more good in it than bad. All you have to do is look hard enough, and what might seem to be a series of unfortunate events, may in fact be the first steps of a journey." Violet Baudelaire.
 12-24-2009, 06:34 PM #16 Thinks s/he gets paid by the post   Join Date: Sep 2008 Posts: 2,171 what does NPV stand for?
 12-24-2009, 06:37 PM #17 Give me a museum and I'll fill it. (Picasso) Give me a forum ...   Join Date: Jun 2002 Location: Texas Hill Country Posts: 43,360 __________________ Numbers is hard Although rare, it is possible to read something on this forum you don't agree with and simply move on with your life Retired in 2005 at age 58, no pension
12-26-2009, 09:19 AM   #18
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Quote:

Now I'm the one with the math mistake. Trying to reproduce my math today, I get \$121,400 instead of \$95,000. I threw away the earlier work, so I can't check it.

I did an extremely simple spreadsheet. The key is that I assumed an investment return exactly equal to the inflation rate - assume both are 10%.

I figured the first year of retirement you have a surplus of \$41,858 - \$40,533 = \$1,325. I added that to the \$121,400, accumulated at 10%, and ended the year at \$134,998.
The second year there is a shortfall of \$41,858 - \$44,586 = -\$2,728. I reduced my fund by that, accumulated at 10%, and ended the year at \$145,496.
The third year shortfall was \$41,858 - \$49,045 = \$7,187 and the end of year fund was \$152,140.

With 10% inflation, the sixth year is the first time that 65% of the initial pension, accumulated at the inflation rate, exceeds \$41,858. The number I got was \$43,818. So I used that as the pension, and ended the sixth year at \$141,639.
Continuing thru the 10th year, I end with a fund of \$0, so the beginning \$121,400 was exactly sufficient.

So the key here is that I'm assuming you can find some 1-10 year investments that will reliably match inflation. I'm not assuming any return in excess of inflation, just equal to inflation. It seems to me that TIPS fit this bill, (I haven't checked pricing today) but you might prefer to take a little more risk on something that might exceed inflation. Note that the early year shortfalls are small and the investment return isn't very important over short periods, so a mixture of CDs and TIPs would probably work.

This was the approach I used when I retired. Stocks may be the right investment over 30 years, but I was looking at a way to fill the SS gap from 59 to 66, so I focused on carving out dedicated assets that I figured would at least stay even with inflation, without a lot of market price risk. Your situation is more complex than mine, but I think that approach still deserves consideration.

Technically, even if TIPS perfectly matched inflation, you haven't completely eliminated the inflation risk. If you set aside \$121,400 and inflation is only 5%, you finish the 10 years \$52k ahead. But, if inflation turns out to be 15%, you are \$53k in the hole. Presumably, you'll give this another look before you actually walk out the door.

 12-26-2009, 11:53 AM #19 Thinks s/he gets paid by the post   Join Date: Jul 2006 Posts: 1,901 TIPS exceed inflation by the issue or the current trading rate. __________________ “I guess I should warn you, if I turn out to be particularly clear, you've probably misunderstood what I've said” Alan Greenspan
 12-27-2009, 10:40 AM #20 Thinks s/he gets paid by the post   Join Date: Oct 2006 Posts: 3,955 I know, but I also noticed that within the past year prices implied yields that were barely above inflation, maybe 1%. I didn't go out and check prices today. Given the other approximations, and the difficulty of buying exactly what you need, I thought I'd ignore the excess. __________________

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