## utility theory question

Financial Independence/Retire Early -- Learn How!
ataloss
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### utility theory question

Here at NFB, I have demonstrated, to my own satisfaction at least, that personal utility theory influences financial planning and (do I dare say it?) SWR analysis.

TRC, I don't quite understand this.
Have fun.

Ataloss

therealchips
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### Clarification (?)

ataloss asked for clarification of my comment; "Here at NFB, I have demonstrated, to my own satisfaction at least, that personal utility theory influences financial planning and (do I dare say it?) SWR analysis." Here it is, in three parts.

Part the First: Being modest or cautious or something, I put in that qualifier about the demonstration satisfying me, even if it satisfied no one else. That way, I avoided claiming that I have answered the question completely, forever, and for everyone, with mathematical certitude, etc., etc. :wink:

Part the Second: Here is my purported proof that someone's personal utility function influences his financial planning. I started a thread on the subject at http://nofeeboards.com/boards/viewtopic.php?t=956 This is a summary of my first post of May 31, 2003, on that thread. Suppose, for example, that you know exactly ahead of time what the real return on your investments will be for the next twenty years and that your stash is one million dollars invested at 4%. Does that tell you everything you need to know to plan your withdrawals? No, because the withdrawal plan depends also on your purposes and values.

If your intent is to maximize the sum of your withdrawals and end up broke, you let everything ride until the end of the 20 years and then make one massive withdrawal. (It will be \$2,191,123.14)

If your intent is to take the same amount each year and end up broke, your annual withdrawal will be \$73,581.75 for twenty years. Here the implicit utility function for a withdrawal is simply the number of dollars in it.

If your goal is to maximize the total utility of your withdrawals, and you use logarithmic utility, you will start with a withdrawal of \$51,998.29 in the first year and increase your withdrawals gradually to \$106,364.14 in the twentieth year and again end broke.

Q. E. D., which is mathematiker talk for "Quite Easily Done", meaning the proof is complete. (Isn't it?)

Part the Third: How does all this influence SWR analysis? We frequently agree around here that a retired person may not be willing to continue fixed real annual withdrawals in the face of market declines. If we admit that sort of psychological consideration into SWR analysis, then it seems reasonable also to include an explicit recognition of the planner's utility function and see where that leads us.
He who has lived obscurely and quietly has lived well. [Latin: Bene qui latuit, bene vixit.]

Chips

karma
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I've always thought that though utility theory is interesting, it is very hard to work with in a logical sense, mainly because everyone's personal utility is unique.

Perhaps it would help to view the "father"￾ of utility theory, Jeremy Bentham, who, and I'm trying to stay within ES's guidelines, was a very odd duck indeed. If you think present day economists are strange...

http://www.ucl.ac.uk/Bentham-Project/Faqs/auto_icon.htm

It could be assumed that all financial decisions, once made, are fixed over time. But that doesn't take into account changes in all the variables over time. Tax rates? Inflation? Improvements in medicine (therefore changes in longevity)? Even very local occurrences, such as changes in zoning (changing land from being sold in quarter-acre lots to 5 acre lots) could have profound effect on what you think you're going to get when you FIRE. Suppose they change the law on mineral rights? You just can't think of everything.

There is a real reason why Gummy keeps yakking about canasta.

Chips:
As I see it, calculating personal withdrawal rates would, ideally, consider life expectancy, income tax liabilities, attitudes about continuing withdrawals in the face of declining markets, as well as a utility function and the usual features of market return and inflation and their variability. Also, ideally, the analysis computes the withdrawal amounts for a thirty year period, say, as a thirty-dimensional optimization problem, without necessarily assuming a constant real standard of living throughout the plan. I haven't yet figured out a way to include all those factors at once.

I'm sure Chips will correct me if I'm wrong, but his 30-dimensional optimization problem would occur even without including utility theory. You just can't tell, year to year, what is going to happen in the future. You can model all you want about the past, as long as you have enough data, and all it will tell you is about the past. You can even model trends. But there is no telling when some brilliant idea is going to hit and change every thing.

Personal utilities - your feeling about risk, whether or not the "official"￾ inflation rate pertains to you, your personal family health history, and so on just confuses things more.

So, I do mostly what I want. Strive to keep my wants small. And keep canasta in the reserve.

karma

wanderer
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great summary for the incredibly lazy, chips.

karma - legend has it that the UCL bowling team used Bentham's noggin' for a ball, using either the eye sockets and mouth or mouth and nostrils as the 'holes'... (that's a joke. )
regards,

wanderer

The field has eyes / the wood has ears / I will see / be silent and hear

ataloss
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How does all this influence SWR analysis? We frequently agree around here that a retired person may not be willing to continue fixed real annual withdrawals in the face of market declines.

I have this feeling that my utility curve might be somewhat aberrant. I think I might have difficulty withdrawing an inflation increased amount from a declining portfolio.

REHP shows that a March 2000 retiree would be taking a 7.2% withdrawal as of May 03. Although it is by no means certain that this would fail, I would not be comfortable with 7.2%.
http://www.retireearlyhomepage.com/worstre.html
Have fun.

Ataloss

bpp
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Q. E. D., which is mathematiker talk for "Quite Easily Done"

Cheers,
Bpp
Last edited by bpp on Thu Oct 30, 2003 11:27 pm, edited 1 time in total.

karma
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wanderer:
legend has it that the UCL bowling team used Bentham's noggin' for a ball, using either the eye sockets and mouth or mouth and nostrils as the 'holes'... (that's a joke. )

Well, I'm very happy I had nothing liquid around me when I read that. Actually, I wish I had put that on my History of Economics exam. Instead I did a limerick about the Physiocrats, which isn't easy in French, especially if you are deficient in the language. Bentham was a weirdo, wasn't he!

ataloss:
I have this feeling that my utility curve might be somewhat aberrant. I think I might have difficulty withdrawing an inflation increased amount from a declining portfolio.

Well, that's why I keep the "playing canasta" ticket in my back pocket. Nothing in life is certain, blah, blah, blah... Sometimes, you just have to go for it.

karma

[KenM]
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I've read all of chip's posts and I think understood them at the time but an understanding of that sort of stuff never seems to stay in my mind long enough for me to use it - so this may not be relevant - but I found long ago that if I regularly calculated my net worth I became obsessive about trying to get maximum return on each type of asset - which led to trading - which damaged my financial health. So, odd as it might appear (stupid if you like - but it worked for me), although for many years I've obviously known we're very comfortably off and had a very rough idea of net worth, I'm not sure how utility theory would work in circumstances where basic information is that vague.

I'm also not sure whether this is again relevant to utility of money, but an issue I think I'm going to have to overcome next year when I retire is my wife's natural instinct for LBYM. For many years we've not had a formal savings pattern but expenditure has always been below salary income and savings have resulted. After retirement, regular monthly income will be just about right for our usual expenditure - but I could easily add substantially to the monthly income from financial assets if needed. Problem is, after all these years, I think my wife may feel uncomfortable spending all the regular income and will subsconciously adjust her spending downwards so that there is some left over every month - so I may have to transfer money from financial assets into the monthly account so it looks like "savings" and then transfer it back again if we're to maintain expenditure at a level to achieve our usual comfortable standard of living.

That may seem extremely odd behaviour to many - I get the impression that most members at NFB lead very well ordered, logical financial lives with spreadsheets etc - am I the only one who has to play psychological tricks on themselves to keep their financial affairs in order????
KenM
Never try to teach a pig to sing. It wastes your time and annoys the pig.

wanderer
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am I the only one who has to play psychological tricks on themselves to keep their financial affairs in order????

I think the trick is to play tricks on yourself.

e.g. Sweep (and invest) all but living expenses from your bank accounts on a monthly basis. Increase sweep with raises and tax refunds. Unseen is unspent.

e.g. Make mental note when earnings/growth/additions of investments equals or exceeds a) bi-weekly pay stub, b) monthly pay stub, c) yearly pay stub, d) yearly pay stub for you and spouse (from a few years ago), e) all of the above from more recent years, f) half of cost of living in a low cost paradise, g) all of cost of living in a low cost paradise, etc.

Wellness psychology emphasizes 'flow' - being so immersed in a task that you don't think about other stuff (you look up and notice it is 10 hours later), sense of control while being tested at the limits...

Calculate roughly and act accordingly...
regards,

wanderer

The field has eyes / the wood has ears / I will see / be silent and hear

therealchips
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### Economists Utility Theory is not Bentham's.

I enjoyed all the responses, and will respond further myself in a way that respects your time and my own. First, though, I want to address this from Karma which I think is potentially quite confusing:
Perhaps it would help to view the "father"￾ of utility theory, Jeremy Bentham,

The utility theory that I have been talking about predates Bentham and has a different purpose.
http://www.gober.net/victorian/reports/utilitar.html Bentham's basic premise to his philosophy can be found in An Introduction to the Principles of Morals and Legislation: Nature has placed mankind under the governance of two sovereign masters, pain and pleasure. It is for them alone to point out what we ought to do as well as to determine what we shall do. Along with this idea of pleasure and pain as sovereign masters Bentham introduced what he called the principle of utility. This principle can be summarized as the principle that "every action should be judged right or wrong according to how far it tends to promote or damage the happiness of the community." . . . In Introduction to the Principles he states that it is " the greatest happiness of the greatest number -- that is the measure of right and wrong". These principles were intended by Bentham to be " a precept addressed to the legislators, to those responsible for the management of society" (27)2.. . . Although its premises were first published in the 1790's Bentham's Utilitarianism heavily influenced social reforms in Great Britain during the 1830's and 40's.

It has not been my purpose here to advocate or promote any theory of government or morals, and certainly not Bentham's. His theory involves far too much government meddling in society for me. ('the management of society" by legislators, indeed! harumphhh! snort!) I have not proposed any alternative theory in politics or ethics here lest it lead us too far off the subject of FIRE.

What utility theory has been my subject then? Here I repeat a quotation about work from years prior to Bentham's work:
The expected utility hypothesis stems from Daniel Bernoulli's (1738) solution to the famous St. Petersburg Paradox posed in 1713 by his cousin Nicholas Bernoulli (it is common to note that Gabriel Cramer, another Swiss mathematician, also provided effectively the same solution ten years before Bernoulli). The Paradox challenges the old idea that people value random ventures according to its expected return. The Paradox posed the following situation: a fair coin will be tossed until a head appears; if the first head appears on the nth toss, then the payoff is 2^n ducats. How much should one pay to play this game? The paradox, of course, is that the expected return is infinite. . .Yet while the expected payoff is infinite, one would not suppose, at least intuitively, that real-world people would be willing to pay an infinite amount of money to play this!

Daniel Bernoulli's solution involved two ideas that have since revolutionized economics: firstly, that people's utility from wealth, u(w), is not linearly related to wealth (w) but rather increases at a decreasing rate - the famous idea of diminishing marginal utility, (Chips: here it gives some expressions using the notation of the calculus with the intuitive meaning that each additional dollar contributes something to the owner's utility, but that the increase is less for each subsequent dollar) ; (ii) that a person's valuation of a risky venture is not the expected return of that venture, but rather the expected utility from that venture.

Still, Bentham's skeleton has shown up just in time for Halloween.
He who has lived obscurely and quietly has lived well. [Latin: Bene qui latuit, bene vixit.]

Chips

karma
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Well, in spite of all the yak about Bentham, IIRC economists are really only concerned with the Bernoulli type of utility theory. At least I sort of remember stuff about diminishing marginal utility. This was microeconomics, which doesn't get into any political stuff, at least it didn't way back when.

You can get to the point where the next unit of something, even money, will decrease your utility. It's easy to see that if you kept getting a consumer good like cars or oranges, pretty soon you would have so much that it would be a pain. I think that would be true even with money. If I ever got so much money that I had to spend a lot of time managing it (charitable trusts, etc), fending off people that wanted some, and so on, my utility for money would decrease rather than just diminish.

Not sure how this fits in with what else has been said about utility theory.

karma

therealchips
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TRyan said, and I agree, "the dollar you add today is MORE useful than the dollar you add tomorrow." This is not just because the earlier dollar will work for you longer, but also because you are becoming richer.

Karma said "I bet you're going to tell me I can approximate it with Solver" and I had to laugh at this feedback on my promotional activities. I admit that I advocate use of multidimensional optimization strategies where they are applicable, and I'm sorry that people frequently overlook that usefulness.

Karma also said:
I'm sure Chips will correct me if I'm wrong, but his 30-dimensional optimization problem would occur even without including utility theory. You just can't tell, year to year, what is going to happen in the future. You can model all you want about the past, as long as you have enough data, and all it will tell you is about the past. You can even model trends. But there is no telling when some brilliant idea is going to hit and change every thing.

No correction is necessary; you have that right. I simplified it to a 20-dimensional optimization problem, just to keep the post brief. You can see it at http://nofeeboards.com/boards/viewtopic.php?t=956 This is a summary of my second post of May 31, 2003, on that thread.
Continuing with the earlier example, and reverting to measuring the utility of money as simply its amount in dollars, the following example includes consideration of life expectancy. Now the planner is concerned only with the withdrawals that he lives to make . . . The data on probability of dying came from Commissioners 1958 Standard Ordinary Mortality Table, for ages 55 to 74, converted from Deaths per 1000.
Solver's solution has the interesting and unanticipated result that is puts the first two year's withdrawals at zero, then starts with a withdrawal of \$84,794.15 in year three, increases gradually to \$92,234.57 in year 9, and then declines gradually to \$63,795.18 in year 20. This resembles the solution someone might come up with to take advantage of the opportunity for the capital to grow. Then it also recognizes that delayed gratification may be lost because of untimely death so that it makes sense (maybe) to plan on a declining standard of living in the years you are least likely to see.

Karma's more important point is that all our modelling, planning and analyses are incomplete and will remain so as long as we lack the ability to see the future. I agree. I think the planning is interesting and useful even so. Further, no one who warns that the past is no guarantee about the future deserves criticism for omitting some relevant factors in the data analysis since no one includes all relevant factors and no one sees the future.
He who has lived obscurely and quietly has lived well. [Latin: Bene qui latuit, bene vixit.]

Chips

therealchips
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### Pretending the house is not an asset.

Kenm:
That may seem extremely odd behaviour to many - I get the impression that most members at NFB lead very well ordered, logical financial lives with spreadsheets etc - am I the only one who has to play psychological tricks on themselves to keep their financial affairs in order????

I'm one of the spread sheet party, so you probably included me in that comment. I played a big psychological trick on my self when I bought this house. The previous one did not bring enough to pay this one off, so I arranged a margin loan with my broker that allowed me to buy the new house outright. Then, I carried part of the house equity on my books as if it were a financial asset in the retirement stash. I gradually paid that off, completely, in two years. I am pretending that the purchase of the house was a consumer expenditure, with no more residual value than a hair cut. The point was to spread the acquisition cost over several years in my books even though I actually paid all of it on one day. Omitting the house from the retirement stash allows me to plan retirement expenses from that stash without including rent.

I have both an investment account and a separate household checking account at Charles Schwab. For the purpose of encouraging myself to spend regularly, I have Schwab transfer a fixed amount from the investment account to the checking account automatically each month. (Payday! First of the Month! Tomorrow!) The transfer doesn't achieve the purpose of getting me to spend all this "income". Sometimes I transfer the month's spending allotment back to the investment account. Does that something like sound like either of you?
He who has lived obscurely and quietly has lived well. [Latin: Bene qui latuit, bene vixit.]

Chips

ataloss
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wrt to certitude:

"Doubt is uncomfortable, certainty is ridiculous."
-- Francois Marie Arouet Voltaire
Have fun.

Ataloss

wanderer
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ataloss wrote: wrt to certitude:

"Doubt is uncomfortable, certainty is ridiculous."
-- Francois Marie Arouet Voltaire

hocus and jwr strike me as two really 'certain' individuals. hocus, for example 'knows' that It is not a true statement that it may not be safe. The 4 percent number is not safe for retirements beginning at the top of the bubble, presuming that stocks perform in the future as they have in the past. He 'knows' this in spite of the fact that he doesn't know waht the sequence of returns will be and in spite of the fact that the remaining 27 years of that 30-year sequence are as yet unaccounted for. Hocus seems particularly 'certain' to me.
regards,

wanderer

The field has eyes / the wood has ears / I will see / be silent and hear