Redefining risk

Discuss all general (i.e. non-personal) investing questions and issues, investing news, and theory.

Postby jln » Thu Sep 01, 2011 10:18 am

bobcat2 wrote:No one is forced to annutize in the DC Managed Plan, although it is encouraged. It is, however, apparently used by the professionals managing the plan to price your retirement income goal prior to retirement. I believe pricing a deferred life annuity before retirement is how they determine whether you are on target to meet your retirement income goal whle you are working.


First, thanks for the link to the Merton/DFA plan. I've bookmarked it to enjoy later.

Pricing an annuity to set a target for retirement savings is a common practice. I believe that Bill Sharpe and Financial Engines do this too, and I see it in lots of papers.

However, it occurs to me that for someone who doesn't want to annuitize fully at retirement, the target has to be higher. It's more expensive to try to fund your retirement with portfolio withdrawals at a reasonable "SWR". This is the price you pay for not diversifying your personal longevity risk with other retirees via an insurance pool.

I think that for most people annuities should play a role. There are interesting studies that try to explore the issues of how much of your portfolio you should annuitize and at what age or ages.

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Postby bobcat2 » Thu Sep 01, 2011 10:32 am

Pricing an annuity to set a target for retirement savings is a common practice.
I am not sure it is that common in practice, since such a deferred real life annuity does not exist. The DC Managed estimates the price of what it would cost, if it existed.

However, it occurs to me that for someone who doesn't want to annuitize fully at retirement, the target has to be higher.
I am pretty sure those in the DC Managed retirement plan that are strongly opposed to annuitization are made aware of this fact by those running the plan.

The idea is to get them a safe level of income thru SS, DB pension, and annuitization. If they don't want to meet their retirement income goal solely thru the above, I assume an effort is made to at least annuitize enough to get them a satisfactory minimum level of safe retirement income and only take investment risk in retirement with reaching retirement income levels above that minimum.

Also somewhat who does not want to annuitize can get much of the same effect by setting up a TIPS ladder in retirement. But as you point out John, the TIPS route is more expensive than the annuity route, because of the loss of the mortality credit.

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Postby Dick Purcell » Thu Sep 01, 2011 11:26 am

John --

1. YES!

2. My bug is emphasis or priorities. I want more emphasis on inform-the-investor. See my next post, addressed to Wade -- especially the bottom of it.

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Postby jln » Thu Sep 01, 2011 11:28 am

bobcat2 wrote:The idea is to get them a safe level of income thru SS, DB pension, and annuitization.


Excellent. This idea has always appealed to me too. At least enough to meet basic living expenses. Let the portfolio support fancy vacations and other non-essentials.

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Postby Dick Purcell » Thu Sep 01, 2011 11:34 am

Wade –

Thanks for asking my reaction to the UnifiedTrust retirement plan.

There’s a lot I like about it, but there’s one thing about it I don’t like at all – at least from what I was able to find.

They say the goal for each participant is retirement income = 70% of pre-retirement, and they keep track of how well each participant is on track to that goal, and most of those below track go into aggressive investing which improves these participants’ probabilities of meeting the goal.

What they don’t say is that for below-track participants, going into aggressive also increases chances of disaster. BobK would jump on that, and rightly so.

Maybe they inform the participant of this danger, but I couldn’t find any evidence that they do. In their report to us, they didn’t report on how many participants suffer such disaster – or at least I couldn’t find any report on that.

This leads me directly to the very core of what bugs me about prevailing work in this field – what I think is woeful under-emphasis on inform the investor.

Say that in the UnifiedTrust plan I am below track:

>> If I go conservative I can be durn sure I’ll have just about enough for a rented shack, electricity for computer, and dog food – as long as I live.

>> If I go aggressive, I have 50% chance of meeting the “goal,” renting a house instead of a shack and living on tunaburgers instead of dogfood – but also 20% chance of pennilessness and a home under the 6th Street bridge.

I want the choice on this to be made by me, based on my being informed on this particular fork in my road – not somebody else thinking he determined my “risk aversion” some time ago.

Wade, going from this to broader discussion in this thread, I can see the value of the utility function approach for what you called “default” choices – but I think priority #1 should be to inform the investor in people-ese, with utility-function approaches only priority #2 for as-needed backup. I ‘m very skeptical of claims to measure a person’s A = coefficient of “risk” aversion – and doubt that a person’s A is constant, suspect it varies a lot from decision to decision.

It seems to me that in this field of people’s investment, these priorities are terribly out of balance. Our first and foremost mission, I think, should be informing the investor as best we can.

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Postby jln » Thu Sep 01, 2011 12:01 pm

jln (that's me) wrote:But I doubt if we'd see very many changes like, for example, a sudden 10% change in the allocation to stocks from one year to the next.


Well, I don't have time to do full simulations and graphs right now, but I was able to do a single simple calculation as an example.

Look at the curve for A=3 at year 25. At this point the lock box is 30% of the meta-portfolio, the investment portfolio is 70% of the meta-portfolio, and the stock percentage in the investment portfolio is 77%.

The stock percentage drops from 77% to 74% after one year if we get the expected return. That's the gentle glide down the curve from this year to next year as we make the portfolio slightly more conservative.

If instead we get a different return, the stock percentages are:

-2 SD: 80% - 6% more (port return = -22%)
-1 SD: 77% - 3% more (port return = -7%)
0 SD: 74% - expected (port return = 8%)
+1 SD: 71% - 3% less (port return = 23%)
+2 SD: 69% - 5% less (port return = 39%)

So the jags would be visible, but not super-dramatic except in really extreme cases, e.g., if the portfolio lost half its value in a single year (a return of -50%, about 4 SDs below the mean).

Note that the glide path curves always start at the same place at year 0 and they always end at the same place at year 40. The deviations are only in-between.

The whole experiment assumes that the investor doesn't change his level of risk aversion or his savings rate. This should be noted, because in real life there's always these options as time goes on and the markets go up and down and situations change. The experiment could be modified to play around with these possibilities to see what happens, and I think that would be interesting.

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Postby Dick Purcell » Thu Sep 01, 2011 1:01 pm

John --

I think what you just did is vary return rate for one year out in the middle of the glide curve.

What about effect on the current allocation from deviations in the return rates of all the prior years?

AND -- If I'm the investor, I'm more concerned with the cumulative effect of return rates of all the prior years having made my current balance far below that with the smooth median-every-year curve.

Are you saying that you have determined that I am a CRRA (aka purity), and that my being CRRA means that in determining my allocation I'm indifferent to my current balance?

Indifferent to what my current balance means as to various allocations' future-result probabilities relative to my future needs and goals?

I may ask for a recount in the scoring applied to determine (a) my A and (b) the possibility I am a CRRI or CRRD.

(I was going to add that perhaps I'm not an equation at all, but decided not to say that.)

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Postby jln » Thu Sep 01, 2011 3:15 pm

Dick Purcell wrote:I think what you just did is vary return rate for one year out in the middle of the glide curve.


Yes, as a quick example of possible "jags" from one year to the next.

What about effect on the current allocation from deviations in the return rates of all the prior years?


That would change the overall shape of the jaggy curve as a whole, but not increase the size of the individual year-to-year jags.

AND -- If I'm the investor, I'm more concerned with the cumulative effect of return rates of all the prior years having made my current balance far below that with the smooth median-every-year curve.


The little glide path experiment doesn't even attempt to deal with any of these issues, and it wasn't designed to. Are we even talking about the experiment at this point, or have you changed the topic? It's not clear to me.

But of course you're absolutely right. And at that point you have options - lower the goal, increase the savings rate, or change the allocation (jump to a different value of A, in other words). Or delay your retirement. Have I missed anything big here? Or some combination of these. We've already talked about all of this earlier.

Are you saying that you have determined that I am a CRRA (aka purity), and that my being CRRA means that in determining my allocation I'm indifferent to my current balance?

Indifferent to what my current balance means as to various allocations' future-result probabilities relative to my future needs and goals?


No, not at all. I can't imagine how in the world you might have formed such an impression - I must have said something confusing at some point that should have been clearer. You're really talking about an entirely separate topic. Worrying about your balance relative to your goals and being CRRA have absolutely nothing to do with each other.

Why do you call CRRA "purity"? I don't get the joke. As I've said, IRRA and DRRA are just as valid as preferences - none of these attitudes are any more "pure" than the other ones. Wade and I haven't done it, but it would be possible to do glide path style experiments for those preferences too. And researchers have definitely explored the portfolio optimization math for those kinds of investors - you get different kinds of equations than the ones we've talked about. There's actually some really interesting things that happen, some of them very counter-intuitive. But that's getting way, way beyond the scope of anything we've been talking about up to now.

I may ask for a recount in the scoring applied to determine (a) my A and (b) the possibility I am a CRRI or CRRD.


I'm not sure what this means, but I think it's the same thing - you want to see a different experiment that explores parameters like savings rate and changes in risk preferences as time goes by. As I said, that would be very interesting, but the glide path stuff Wade and I have done doesn't even attempt to address any of this. Like I said, it's a different topic altogether.

You don't need any kind of "scoring" to determine if you're CRRA, IRRA, or DRRA. Just answer this question: If I won the lottery tomorrow, increasing my net worth by an order of magnitude, and decided to add the proceeds to my investment portfolio, would I change my portfolio's asset allocation, and if so, how?

1. Make portfolio more conservative. IRRA.
2. Leave asset allocation the same. CRRA.
3. Make portfolio more aggressive. DRRA.

Are you under the impression that this experiment represents some kind of grand unified retirement planning tool? It's not that at all. It's just an attempt to begin to explore a very specific issue: the impact of human capital on asset allocation decisions in retirement. There's millions of other issues it doesn't address, on purpose. Indeed, this isn't a retirement planning tool at all. It's more of a research and learning tool to investigate one very specific but important issue that is indeed of important to individual investors. Whatever is learned ultimately from the experiment might possibly some day be incorporated in a useful way in some form into such a planning tool for end-users that has much broader goals and addresses a much broader set of concerns, but that's not at all what we're up to at this point. Is that what you're asking for?

I'm kind of confused. Sorry if I have misunderstood whatever point you're trying to make.

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Postby jln » Thu Sep 01, 2011 4:36 pm

OK, Dick, let's get creative and have some fun.

Imagine a tool that monitors your portfolio over time. You've told it your goal, and it knows your asset allocation, glide path plan, savings rate, and desired retirement date. It alerts you if you go off the path towards your goal.

The tool shows a thermometer calibrated in dollars with your goal marked and your projected portfolio value on your retirement date.

There are several sliders that you can use to play what if games.

Savings rate slider: Adjust your percentage of income savings rate.

Risk aversion/tolerance slider: Adjust your asset allocation to be more or less aggressive.

Goal slider: Adjust your goal, expressed as an income percentage of your last working year's income prior to your retirement, e.g., 70%.

Retirement age slider.

As you move the sliders, the thermometer moves up and down closer to or farther away from the goal.

In addition to the thermometer, you get a little graph of the projected glide path remaining to retirement.

Above all, you also get an interactive histogram of ending portfolio value probabilities, with informative labels ranging from "cat food" to "luxury yacht", with a magnifying glass to zoom in and out on interesting ranges of possibilities. (Sound familiar?)

There would be a "doit" button to lock in any desired new set of parameters. The software would call your broker or mutual fund company and tell them to make the appropriate changes.

Of course, the tool would also keep your portfolio rebalanced via periodic communications with your financial firm's computers. All totally automated.

There would be an icon with an image of Jack Bogle that you could click to show you how much better you could do with low expenses at Vanguard. The "doit" button would take care of transferring all of your assets there for you.

Add enough bells and whistles, professional graphics and animation, and you could turn it into a video game that would be fun for the kids as well as useful for you. We'd definitely need an option to lock the "doit" button though.

In version 2 we could add a slider for preferences ranging from strong IRRA at one end to CRRA in the middle to strong DRRA at the other end.

In version 3 we'd release the version for cell phones and tablets, with instant message alerts for when your attention is required for some crisis.

In version 4 we'd start to run out of ideas but we'd need the income from suckers who upgrade, so we'd add a little chart of an efficient frontier marked with your current location. We'd let you adjust your risk tolerance level by sliding the marker up and down the frontier. Various animated cartoon characters would pop up and cheer and boo as you did this.

In version 5 we'd add a "good job/bad job" slider that lets you adjust your expected labor income growth rate from now to retirement, plus interactive tools that ask you questions and use the answers to determine the volatility of your labor income and its correlation with the assets in your investment portfolio. This would all be done using data obtained the appropriate Federal government databases. All this information would be used to fine-tune your glide path.

In version 6 we'd add a panic button you could click if you get fired. I haven't figured out what this button should do yet, but maybe I can work on this problem when I'm retired.

In version 7 we'd add an icon of Zvi Bodie. Click it to put all of your money into TIPS except for a bit that's invested in whatever his latest scheme is for exotic long-horizon options to get participation in market upside. This would be called the "safety first" button. As a bonus, clicking Zvi would also automatically place an order for "Risk Free Investing" at Amazon. As the authors of the software, we'd have an arrangement with Zvi to get a small cut of his royalties. This would help finance further development work and also buy a bigger computer to host Bogleheads.

If I were to write such a piece of software, I'd make sure to add a little annotation on the risk aversion/tolerance slider to show your value of A, just to annoy you, and those little cartoon characters would wave tiny flags emblazoned with the equations from mathematical finance. :-)

We could call the tool "Portfolio Planner Plus or Minus", or something like that. Or maybe "One Half Sigma Squared".

But the market for this kind of software is pretty efficient, so someone has probably already written this program. You know, like that $20 bill on the sidewalk that's already been picked up. Oh well.

John Norstad
Last edited by jln on Sat Sep 03, 2011 9:35 am, edited 1 time in total.
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Postby Dick Purcell » Thu Sep 01, 2011 5:01 pm

John –

Did you hear me?

Your last post had me laughing all the way through -- until I got to the thing that shows me my A to annoy me, and I roared.

But seriously -- your post before that one helps me pursue this, and I think the pursuit is valuable, toward a next step that can be done now.

I don't want to try to include all factors such as saving rate -- just allocation as I proceed year by year from start to defined end $$ goal.

For this, I am not uniformly CRRA or DRRA or IRRA at all! It depends overwhelmingly on where I am relative to my goal.

It leads me to propose what I’ll call a “goal-focused utility function.”

In this function, my desired asset allocation depends on the return rate required to get me from my current balance to my goal.

Here are examples, assuming I’m many years from my retirement goal, using your question about how I respond to a lottery win:

1. If the lottery win raised my balance to equal my future goal, I can meet my goal with real return rate 0%, so I go all TIPS to lock it in.

2. If the lottery win raises my balance to 5x my future goal, I can meet my goal with loss of 80% of my balance and I am confident small caps value will not do that badly, so I go all small-caps value for max expected result.

3. If the lottery win raises my balance only to the level that I need 15% return rate here to goal to meet my goal, I might go all small caps and hope, or maybe something less aggressive. Not sure.

4. If the lottery win raises my balance so I need 5% return rate here to goal to meet my goal, I think I’d go something with broadest max diversification, maybe 50-50 stocks and bonds.

Basically I want a combination of best probabilities for meeting my goal and smallest magnitude of shortfall, and if sure of this, max expected, and if little chance of meeting my goal I'm not sure. ??

I think that with some looking at return-rate probability distributions of various allocations for various numbers of years, we could develop a goal-focused utility function that defines allocation as a function of return rate required to go from current balance to goal. (The formulation should consider number of years to goal too.)

Dick Purcell

PS -- John, I labeled CRRA as "purity" because it is unaffected by anything as grubby as wealth. CRRA looks down on the others as "crass."
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Postby LadyGeek » Thu Sep 01, 2011 5:27 pm

Dick Purcell wrote:For this, I am not uniformly CRRA or DRRA or IRRA at all! It depends overwhelmingly on where I am relative to my goal.

Can someone please explain the "CRRA", "DRRA", and "IRRA" acronyms? I can't seem to find anything in this thread, or via google.

jln - Your utility function tutorial, An Introduction to Utility Theory is excellent. I can now understand what's being discussed.
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Postby bobcat2 » Thu Sep 01, 2011 6:13 pm

CRRA - constant relative risk aversion
DRRA - decreasing relative risk aversion
IRRA - increasing relative risk aversion

Link:http://en.wikipedia.org/wiki/Risk_aversion#Absolute_risk_aversion

BobK

PS - I don't think this belongs in the Wiki. :lol:
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Postby Dick Purcell » Thu Sep 01, 2011 6:52 pm

John and Wade --

Are you really satisfied with what the utility function(s) in your glide paths do for the investor across the range of likely situations? Or rather, what they can do to the investor in some situations?

For me, after thinking about John's next-to-last post, and then composing my response, the general goal-focused approach is the only acceptable one. I think to serve the investor's interests, it has to be based on (a) current balance, (b) goal, and (c) required return rate to get from (a) to (b). To go from those variables to allocations, we consider various allocations' return-rate probabilities -- and maybe there is where we consider something about the investor's attitude toward goal-meeting probability vs. magnitude of shortfall.

As I think of various real situations, CRRA and IRRA and DRRA each appear to me to in likely situations go a bad direction for the investor's interests.

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Postby LadyGeek » Thu Sep 01, 2011 9:00 pm

bobcat2 wrote:CRRA - constant relative risk aversion
DRRA - decreasing relative risk aversion
IRRA - increasing relative risk aversion

Link:http://en.wikipedia.org/wiki/Risk_aversion#Absolute_risk_aversion

BobK

PS - I don't think this belongs in the Wiki. :lol:

Let's see if I understand. This is not going into the wiki; Google will find it. :wink: From an engineer's perspective:

The utility function is a financial equation that describes how willing (averse) an investor is to utilize an investment opportunity, based on how much wealth (money) she has.

The X-axis is how much wealth she has (low to high). The Y-axis is the Utility, or, how willing (averse) she is to utilize the given investment (how Useful is this to her).

For example, if she has very little money, she will have a certain acceptance threshold to utilize the investment. If she has a lot of money, she will have a different acceptance threshold.

Just like taxes have a marginal tax rate (how much you pay for each additional dollar), there are marginal utility functions (how much risk you are willing to take for each additional dollar of the proposed investment).

The slope of the line (marginal utility) changes as you get more wealth. The curve is concave (usefulness decreases as wealth increases) for a risk-averse person because accepting one dollar of additional income is a lot more important when you only have a few dollars than when you have a million dollars. A risk-loving person does the opposite, the curve is convex. Risk-neutral means that she doesn't care one way or the other.

Constant, Decreasing, and Increasing Risk Aversion describe how the curve changes over it's range based on investor's preferences. Additional discussions are related to matching these curves to what an investor really does - which is very difficult if not impossible to model in reality.

(Don't confuse the concave / convex curve descriptions with the convexity property of bonds. They both describe curves, but are not related in any way. Or, are they related? Convexity is used as a risk management tool.)
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Postby magellan » Thu Sep 01, 2011 9:21 pm

bobcat2 wrote: It seems to me that instead of using target date funds that attempt somehow to account for the personal financial situation of the retirement investor, what should be used is Robert Merton's life-cycle approach which is done by Merton himself at DFA's DC Managed Plan.
.
.
There is a wealth of information about this plan at DFA through the following link.
http://www.dfaus.com/managed_dc/

I really like the direction they're going with this product because they seem to be focusing on optimizing the risk of the retirement income stream rather than the risk of the retirement investment portfolio. That may sound like a subtle difference, but when you're considering combinations of TIPS ladders, life annuities, and a risky investment portfolio to fund your retirement, it'd be really nice to have tools to optimize the risk/reward of various combinations of these vehicles.

Unfortunately, while this idea will hopefully raise the bar overall, I was disappointed when I read this quote from an article on RIABiz.com:
RIABiz Article wrote:The product will cost 45 basis points, according to BethAnn Dranguet, vice president of Dimensional Retirement. At that price, she says, advisors can still charge their own fee on top of the cost of the product and provide added value to clients.

I'm just not sure how a typical 401k investor will end up ahead with this product, compared to a simple "age in bonds" or target-date default strategy from Vanguard, once you consider that it's layered onto DFA's already costly model of selling only through advisors. The total costs of 50-100bp will easily eat 25-50% of an investors expected real return.

IMO, this is a great lesson in how even the best intentions of academics and researchers can get badly mucked up by the time they get to retail investors.

Jim
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Postby bobcat2 » Thu Sep 01, 2011 9:37 pm

Hi LadyGeek,

The following is a relatively minor point about utility functions, but it sometimes confuses people.

Sometimes its useful to talk about the utility an individual receives from real wealth - utility=U(W). However, unless the person is some sort of miser, wealth in its own right has no direct utility. It is only when wealth is spent on the consumption of goods and services that any utility results from wealth.

It is more common to define a utility function as the utility an individual receives from real consumption - utility=U(C). This is why everything at Wikipedia about risk aversion is in terms of U(C) and not of U(W).

As Adam Smith, the father of economics, noted over two centuries ago.
Consumption is the sole end and purpose of all production


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Postby bobcat2 » Thu Sep 01, 2011 9:55 pm

Hi Jim,

You wrote about the expenses associated with the Dimensional DC Managed plan. I wish they were lower too, but the fact of the matter is these costs are very much in line with what DFA charges for accessing their stock mutual funds.

For instance, according to M*, the expense ratio for the very popular DFA US small value fund is 0.52%, slightly higher than the expense ratio for the DC Managed plan. And of course the advisors charge their own fees on top of this for individuals to access the funds.

The popularity of DFA mutual funds does not seem to have been diminished by a very similar expense structure to that of the managed plan. People seem more than willing to pay these fees to access the funds, apparently because they believe they are receiving a high quality product. That could very well work much the same way with the managed plan.

The alternative of having most people mucking around with combinations of TIPS ladders, life annuities, and risky investment portfolios to fund retirement is definitely not a pretty sight to contemplate. :lol:

BobK
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Postby wade » Fri Sep 02, 2011 12:37 am

Dick Purcell wrote:John and Wade --

Are you really satisfied with what the utility function(s) in your glide paths do for the investor across the range of likely situations? Or rather, what they can do to the investor in some situations?

Dick Purcell


Dick, honestly I'm starting to fall behind in this discussion and I need to read the recent posts much more carefully. But about this fixed glide path issue, I'm still satisfied that it is a "second best" solution that will be about the best we can do for someone not willing to put in the extra efforts. Your approach is superior for someone willing to make the effort though. This will help avoid cases where the default option would do something inadvisable if we could more clearly understand the individual's circumstances.

Target date funds are now one of the default options for DC pensions after the Pension Protection Act of 2006. They are growing rapidly in use. There is still argument over the best default guide paths
for them. My conclusion is that the range of glide paths offered by companies currently seem to get it right, but that the problem is it is still random whether any given company offers an aggressive target date fund or a conservative target date fund. I think that companies should offer 3 target date funds: aggressive, moderate, and conservative. Then people who don't want to make the extra effort can set it and forget it. I did learn that Mel advocated a similar position in his Forbes column. I don't think this is a perfect solution by any means, but I think it would be good enough. Those 3 glide paths can be defined with utility analysis like what is used in John or my figures.


----

About this other really interesting issue and John's post above about the "dream software" to guide you toward your goal, I just wrote up a blog entry about it which follows here:

Trying to Reach a Wealth Target in a Volatile World

A rather interesting discussion is taking place in the "Redefining Risk" thread at Bogleheads. Many different aspects are being considered now, and here I'm interested in the issue really gaining momentum on page 5 about what sort of issues to build into the analysis when trying to guide people toward their wealth accumulation goals. John Norstad wrote an especially interesting and funny comment here. In moving through your career, you have all kinds of options to make adjustments to your strategy as you compare where you stand and where you want to be at retirement, such as making changes to your savings rate, your asset allocation, your retirement age, your wealth accumulation goals.

In my recent paper, “Getting on Track for a Sustainable Retirement: A Reality Check on Savings and Work”, which will be included in the upcoming October 2010 Journal of Financial Planning, one of my major points was to emphasize just how difficult it is to know whether you are on tracking to meeting a particular wealth accumulation goal at your retirement date. That is why I encouraged a different approach toward knowing whether you are on track, which is explained in that paper.

Since then, I have been playing around with some simulations that sort of anticipated John's comments. These matters are only half finished, but I thought I could share a few figures now.

This analysis is based on someone with a constant real salary saving for their retirement. I use Monte Carlo simulations based on Ibbotson Associates's SBBI data for 1926-2010, for the S&P 500 and intermediate-term government bonds. For 5 different asset allocations, the portfolio arithmetic returns and standard deviations are as follows:

Code: Select all
% stocks   expected real return   standard deviation
  0          2.52                  6.84
  20         3.75                  7.09
  40         4.99                  9.43
  60         6.23                  12.76
  80         7.46                  16.49
  100        8.70                  20.39




Again, my purpose for working on these simulations was to demonstrate how hard it is to know if you are on track for reaching a wealth accumulation goal. In this case, the goal is to be able to replace 50% of your final salary using fixed real withdrawals from your portfolio and using the 4% "safe withdrawal rate". This means you need 12.5x your final wealth.

Now, this first figure shows the case for someone who plans to work for 30 years. Assuming they will contribute to their savings at the end of the year for 30 years, based on the expected fixed geometric returns they use an excel spreadsheet to calculate the savings rate they need to use that would provide them with 12.5x final salary at their retirement date. What this figure figure shows is, for each different asset allocation, the distribution for the number of years it takes to actually reach their wealth accumulation goal. Because stocks have higher returns and higher volatility, a lower savings rate is required on average, but you can also see that the distribution for the career length is also wider. For something that you "expect" to take 30 years to happen, it could actually take anywhere from 15 to 60+ years. Planning to reach a goal is harder than it looks!

<img src="http://4.bp.blogspot.com/-98JWlxLN8FM/TmBTvkpWB-I/AAAAAAAAAR8/LPrWdhvowso/s1600/F1.jpg" width="700">

That is assuming that the person doesn't make any adjustments during their career. So far, I've gotten around to considering two other adjustments. The first is to adjust the savings rate depending on your progress toward your goals, and the second is to adjust your asset allocation depending on your progress toward your goals. This work is still unfinished and there is more I want to do, but the following is what I have so far. It's not complete, but what this is meant to show is how easy it is to be "tricked" into thinking you are or are not on track, compared to what actually ends up happening. As well, it shows how someone who is trying to carefully target in on their goal, just how hard it can be even with a willingness to make large annual adjustments to their savings rates and asset allocation.

Let's consider someone working over a 30-year career and trying to aim in on the 12.5x wealth accumulation goal at their retirement date. They are going to make an earnest effort at doing this. Let's just consider the case for now of someone starting with a 60/40 asset allocation. Here is what he does:

1. For the first five years of his career, he does save more than required to help get him off to a good start (this "more" is the 75% percentile of savings rates needed to get to the goal from some separate simulations I haven't specifically discussed).

2. After that, the savings rate he uses is what he gets from using the expected returns for his portfolio and comparing his current wealth accumulation to the final goal. If he is ahead of schedule (the blue line is above the red line in the top part of these figures - though that red line is specifically for 60/40 and his asset allocation may diverge from that), he can save less. If he is behind schedule, he saves more. His savings rate is allowed to vary between 0 and 40%.

3. Regarding asset allocation, I have built in a way for him to lower his stock allocation from the starting level, but not to increase it. The rule is, if he finds that his required savings rate is below zero, he starts checking the savings rate needed with lower stock allocations until he finds another positive savings rate. Then he uses new asset allocation. This can happen down to 0% stocks. Again, I have not yet built in a way for him to increase the allocation after that, but I need to do that too. Also, about locking in a goal with all bonds, he really should buy some bonds that will precisely get him to his goal. But so far I still only have him investing in a bond mutual fund that still has some volatility. This can cause him to potentially fall behind schedule again from a point where he should be able to lock in a goal.

The point again, of showing this, is to show how difficult it still is to reach the goal, despite allowing for very volatile savings rates. While the volatility of final wealth is not so much now, just consider, still, how difficult in would be to use these different savings rates each year that you really cannot plan for in advance.

Despite doing all this extra work, the distribution of wealth outcomes is still rather wide, compared to the goal of a 12.5x wealth accumulation. Here is about this distribution from 1,000 simulations:

Code: Select all
Summary Statistics for Terminal Wealth
 
Mean:              12.438
Minimum             6.695
5th Percentile      9.039
1st Quartile       11.463
Median             12.498
3rd Quartile       13.512
95th Percentile    15.656
Maximum             21.61
Std. Deviation      1.902


Here are a few sample illustrations of this from the Monte Carlo simulations.

This first one shows perhaps about as good as one can possibly expect to do. This person was fortunate to spend most of his career ahead of schedule. He was able to lower his stock allocation to make it easier to lock in his goal. He did still have somewhat volatile savings rates, as he could start lowering them between years 5 and 15, but then got some bad luck that pushed him off track compared to where he needed to be (the red line is the expected wealth path for 60/40, and after switching to 0/100 he needs to be higher at any given moment. In the end though, he did make it and achieve his goal. Not everyone is so lucky.

<img src="http://4.bp.blogspot.com/-u3NUwzXLKvQ/TmBTv1rw_8I/AAAAAAAAASA/xZN0kP6qn_s/s1600/F2.jpg" width="700">

Consider this guy. He was slightly ahead of schedule for more than 20 years. Never enough to lower his stock allocation, but his savings rates could drop quite a bit and were close to zero for a while. Then, sometime after year 20 some bad market returns arrived which pushed him off track, forced him to increase his savings rate to 40%, and still left him quite far below his goal of 12.5 after 30 years. He seems to be at about 7x his salary.

<img src="http://4.bp.blogspot.com/-LpoYvnqmaTQ/TmBTwdj074I/AAAAAAAAASE/qrPWTFr8ebg/s1600/F3.jpg" width="700">

Here is another case in which the goal was reached, but savings rates were pretty volatile in the mean time.

<img src="http://3.bp.blogspot.com/-0UrXlD94m0c/TmBTwk3sYoI/AAAAAAAAASI/dWwWld47Thg/s1600/F4.jpg" width="700">

And just for fun, here is the case of the person with the lowest final wealth accumulation of anyone:

<img src="http://2.bp.blogspot.com/-logUMAVD61I/TmBTw4wwgVI/AAAAAAAAASM/PyLneJn6Sqs/s1600/F5.jpg" width="700">


And the person with the highest final wealth accumulation of anyone:

<img src="http://2.bp.blogspot.com/-wkIzG75Wt2Q/TmBTxSJzeaI/AAAAAAAAASQ/twAmwvk4b68/s1600/F6.jpg" width="700">
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Postby Dick Purcell » Fri Sep 02, 2011 1:33 am

Wade --

I may have created a bit of misunderstanding with that post from which you quoted the excerpt. I intended that post as an "add-on" to a post I put in shortly earlier, including examples of my answers to John's test questions of reaction to a lottery windfall.

In those two posts, I was not trying to attack the utility function approach again, but to offer an idea about it that I hoped might be constructive.

Specifically, I was suggesting trying to make a utility function that is goal-focused, in very much the same way as your "Volatile World" approach and examples. I think the only difference between what I was suggesting and your Volatile World examples is that while you adjust savings rate and maybe allocation, I was not addressing savings rate but instead making allocation the thing the investor adjusts.

Is this idea, sggested in my prior message with examples and illustrated in your Volatile World, incompatible with the utility function idea? If it can be incorporated, i think it can make the utility function approach much better.

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Postby wade » Fri Sep 02, 2011 3:17 am

Dick:

I see (I think).

Each year, as you progress through your career, you look at your current wealth and compare it to your target wealth. Then you calculate your required return based on how many years are left before the target date.

Now, you are ready to pick an asset allocation for that year. Utility analysis can help to choose this asset allocation by helping to evaluate the tradeoff between the higher expected returns and the higher volatility of increased stocks. For someone falling behind on reaching their goal, the required return will be higher, but that doesn't necessarily push them to a higher stock allocation because with enough risk aversion they also want to avoid very bad outcomes. A risk tolerant person, on the other hand, will have an easier time moving toward 100% stocks when falling behind on their goals.

Does this sound right? I can probably program in something to look at this.

I'm guessing it might lead to very volatile shifts in asset allocation from year to year. Should we limit how much you can change it from year to year?

Should I add in something like TIPS guaranteeing a real yield when held to maturity that risk-averse (or any) people have an option to buy when they are able to lock-in to their target?

I'll keep thinking about this.

Just on a personal note, my wife and I are expecting our second baby to arrive any day now, and so at any given moment I might disappear for a while :D
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Re: I wish the rest of us were more like cjking

Postby cjking » Fri Sep 02, 2011 6:21 am

peter71 wrote:
bobcat2 wrote:cjking you are the best poster on this thread. Hardly anyone ever changes their mind on these threads when presented with contrary evidence, it takes a big person to do that. You have done just that. My hat's off to you :!:
:sharebeer

Best,
BobK


CJ is a good man for changing his mind, but as soon as I saw you'd defied anyone to not agree with your chart I figured it was probably some implausible deductivist BS sequence cooked up to overstate a point . . . and so it is!!!!

9 years of 10% losses followed by 9 years of 10% gains!!!!!!!

CJ, I think your instincts were right the first time . . . volatility drag and compounding matter, but they matter a lot less in the world as we've known it than in a fantasy world in which returns are that relentlessly sequential.

Best,
Pete


I did an exercise in the spirit of the linked article, but with a 30 year savings period followed by a 30 year withdrawal and looked at 4 scenarios where there were ten bad (0% return) years followed or preceeded by 10 good (12% return) ones, at the time of peak wealth. One scenario had the variation all in accumulation, one all in withdrawal, and two straddled the switch-over. I set the contribution and withdrawal figures to fixed amounts that would deliver exactly a $0 final balance if there was a constant return of 6% across the 60 years. One alternative scenario (good years at end of accumulation, bad years at start of withdrawal) was actually better than the baseline, the other three went broke roughly ten years early.

I don't think I can complain about the extra artificiality of the scenarios, as for me the idea of taking a constant SWR from a volatile portfolio for a fixed number of years is a pretty crazy way to approach things in the first place.

But it is the context that is usually used.

When, in this excercise, the investor makes no adjustment to his target income when his retirement balance is well below target, that is utterly nuts, but it is essentially the same thing as assuming in withdrawal-only experiments that withdrawals remain constant no matter what happens to prices.

My thoughts are a bit fuzzy on this whole issue now, and I need to do some more work to clarify them. I think there are interesting conclusions (such as the difference dividend policy can make) that still do apply in more subtle scenarios, but not in these crude ones.
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Postby Dick Purcell » Fri Sep 02, 2011 9:01 am

Wade --

First and foremost -- HAPPY BABY !

From your reply, it sounds as if what I was proposing is a non-utility system with a utility supplement. That could certainly be valuable, but was not my purpose.

I am trying to create a system that is itself a utility function system, but does better than any of the Big Three (CRRA, DRRA, IRRA) in doing what an investor would have wanted it to do. In considering various situations, I concluded that each of the Big Three would do quite differently from what an investor would want in some common situations.

I'm trying to propose something that is no more complicated to automate than CRRA, DRRA, or IRRA -- or maybe just a hair more complicated. But not a fancy non-utility system with a utility supplement.

How about this simpler approach:

At the very start, the investor enters a dollar goal, and says he is IRRA up to that wealth and DRRA above it.

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Postby wade » Fri Sep 02, 2011 9:48 am

cjking: Just to clarify, you are finding that the best performing scenario was with 10 good years at the end of accumulation and 10 bad years at the start of retirement?

I wonder if it could be because the bad years were not so bad (just 0% returns) and the sequence of returns for the accumulation phase did matter: those 10 years of good returns really helped boost the total portfolio value at retirement so it could withstand those withdrawals more easily.

Dick: Thanks, and I still may be a bit slow on this. I have to review some past posts more carefully.

Maybe I'm still way off, but are you suggesting something like:

start with 100% stocks but decrease stocks as you get closer to your goal (but are still under). At the goal, you should be at a very low stock allocation. But then, as a little bit of stocks helps the portfolio to creep upward, start increasing your stock allocation again?

But, if you just lock in your goal with bonds, you won't be going above it. So, would risk averse people ever get a chance to show their DRRA above the goal?

Just to generalize, John is the elegant, closed-form, analytical, mathematical solutions guy, and I am the brute-force, mostly atheoretical, simulations guy. I am mostly interested in the utility aspects because I think it very importantly picks up the aspect of diminishing marginal returns from income/wealth, which is something missing, to the great detriment, of a lot of the analysis on these retirement topics.

So this might be something that we need John's mathematical solutions for, rather than my approach. This seemingly depends on what savings rate is used, there there doesn't seem to be any way for me to apply my mechanical glide paths without CRRA. I'm still having trouble picturing how I could do it except with some sort of utility add-on for a non-utility approach as I was describing earlier.

I apologize if I'm still completely misunderstanding your point though.
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Postby jln » Fri Sep 02, 2011 9:58 am

This is a personal story.

So we've being doing all this talking about glide paths, and at the same time I'm at the very end of my own glide into retirement (one month left). This prompted me to think about all the decisions I've made over my years of saving for this glorious day.

I started saving for retirement in 1979, when I turned 30. That was the age at which my employer automatically enrolled people in our retirement plan at TIAA-CREF. At the time, as with most young people, I figured I was going to live forever, and I paid no attention. The default asset allocation at the time was 50% in TIAA Traditional, a very conservative fixed income fund, and (I believe) 50% in some kind of US stock fund. I was ignorant, so that's what I accepted.

It wasn't until the late 1990s that I took an interest in Finance, when I was about 50. That was when I switched to my current 60/40 portfolio and improved my diversification in various ways, including bond funds and foreign stock funds at both TIAA-CREF and Vanguard, and switching to low-cost index funds.

So what did my personal glide path look like? 20 years of pretty conservative (while the stock market was booming), followed by 12 years of more aggressive (while the stock market was tanking).

So my glide path sloped up instead of down, and I was unlucky to boot.

Plus, the job I've had for 35 years is considerably more secure than most. I work at a university, and while I'm not a professor (much less tenured), it's always been a very safe job. I've never had to worry about being laid off or demoted. My future always looked very safe and sound. So if anything, my glide path should have been more aggressive than average, especially during those first 20 years when I was so conservative.

Fortunately, mostly due to an above-average savings rate thanks mostly to an incredibly generous matching contribution from my employer, I did OK, and I'm able to retire now well above the "cat food" level but also well below the "luxury yacht" level.

So I guess this is one of those "Do as I say, not as I do" stories.

Young people who hang out here on Bogleheads and listen to the good advice they get don't know how lucky they are.

Regretfully yours,

John Norstad
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Postby Dick Purcell » Fri Sep 02, 2011 10:41 am

Wade --

For this investing, I don't think what the utility function should be based on is the basic idea that the more you have the less another dollar is worth, because more aggressive has more downside as well as more upside.

I think the way to fit most people's real values is to base it on closeness to goal. The closer, the more risk averse. The further away from goal, below or above, the less risk averse.

Example: I was right at my goal and my choice was all TIPS -- but then John just gave me a lottery winning that made me 5x goal, so now I can risk suffering big losses and still be above goal so I'm going all small caps value for highest expected.

So IRRA below goal and DRRA above goal fits people's values and interests. The further below or above, the more he is willing to take risk. Below because he needs to take risk for hopes of meeting goal. Above, because he has so much more that goal that he can suffer losses and still be above goal so he goes for higher expected.

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Postby DRiP Guy » Fri Sep 02, 2011 12:27 pm

Dick Purcell wrote:Wade --

For this investing, I don't think what the utility function should be based on is the basic idea that the more you have the less another dollar is worth, because more aggressive has more downside as well as more upside.

I think the way to fit most people's real values is to base it on closeness to goal. The closer, the more risk averse. The further away from goal, below or above, the less risk averse.

Example: I was right at my goal and my choice was all TIPS -- but then John just gave me a lottery winning that made me 5x goal, so now I can risk suffering big losses and still be above goal so I'm going all small caps value for highest expected.

So IRRA below goal and DRRA above goal fits people's values and interests. The further below or above, the more he is willing to take risk. Below because he needs to take risk for hopes of meeting goal. Above, because he has so much more that goal that he can suffer losses and still be above goal so he goes for higher expected.

Dick Purcell


I'm not saying anything you've stated is wrong. I am, however going to give you *one* person's different perspective, but it's one based on a world where I often hear tales, such as when a past 26 million dollar lotto winner plays the lotto subsequently, and is in the news for winning again, because they threw a lot of that prior money at gambling to win again. I *know* I am at least a minority, if not a rarity... or even singularity:

1. I agree that the further under your goal you are, the more willing you are to take a risk, especially as a youngster. We are wired that way from an evolutionary perspective, and it also seems to also make logical sense as an individual -- if you are going to have reversals of fortune, best to have them early where there is time to recover.

2. And I agree that as you get nearer and nearer to your goal, the more risk adverse you are both likely to become and also ought ot become. No issue there.

3. But this idea that the more overshoot there is in your nest egg, the more willing you are and ought to be to gamble it on trying to get FURTHER funds... well, it not only does not make sense to me, I can't imagine myself acting in that way. Change standard of living, and willingness to spend? Sure, to some degree. But re-enter the market and take more market risk on my equity the more of it I have over my goal? The very idea of that is POISON to me. I call anything over my 'goal' "Gravy" -- I consider it a fortuitous 'gift'. And I'll be darned if I am going to go out and risk 'extra' gravy on the chances of getting.... more gravy! I already had more than I either needed or expected!

I can, however, clearly and often see via the media that there are some people for whom NO amount of money is 'enough'. But for me, once my financial future as already envisioned, and not some Hollywood dream, is fully realized, then anything extra that might come in does NOT become gambling money. It may become money I use to buy bigger, better or more 'stuff' than I otherwise would have, but trying to 'parley' that into more... and then more... and then more... that behavior seems to me personally to be pathological at it's root. And yet, I do agree that it also seems to be current human nature, for the most part.

So am I somehow 'broken' to not see the proposition as everyone else does? I'm not saying I would not be more 'relaxed' and willing to take on more *spending* (consumption rate increases), I'm saying my need/willingness/inclination to take market risk, once it hits zero, STAYS at zero, and does not inflect back up.
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Postby Dick Purcell » Fri Sep 02, 2011 1:03 pm

DRiPGuy --

I was thinking of purposes more constructive than just gambling to pile up sickening wealth. Maybe venture capital to spur clean-energy innovation and job growth. Accumulate more to donate to worthy causes, which I will refrain from naming out of respect for Bogleheads Forum Rules.

But your viewpoint is certainly valid and should be accomodated. Maybe for the high side, John will let you set your A for DRRA so your tolerance of risk holds at zero from your goal all the way up to infinite wealth.

John, can you do that for DRiPGuy?

Will this do it? --

A = E(r) / (1/2 * [sigma]^2)

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Postby jln » Fri Sep 02, 2011 1:14 pm

Dick Purcell wrote:I don't want to try to include all factors such as saving rate -- just allocation as I proceed year by year from start to defined end $$ goal.


But why exclude all other factors? If you're short of your goal, making your allocation more aggressive is only one of several things you can do. Shouldn't investors be permitted and encourage to explore all the options?

Making your allocation more aggressive to meet your goal is going to seriously increase cat food probabilities, for one thing, compared to the option of increasing your savings rate. Delaying your retirement by another year or two is also a perfectly reasonable option. Why deny the investor the opportunity to explore this option?

Why not have a tool that lets you explore allocation changes, as you wish, which is great, but also lets you just as easily explore all the alternatives?

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Postby Dick Purcell » Fri Sep 02, 2011 1:28 pm

John --

I agree completely, and mis-stated.

What I meant was for this single step in the long progression toward your ultimate analysis, I wanted to consider just the allocation response.

I was just trying to avoid overloading the complications all at once, out of consideration for the math types.

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Postby jln » Fri Sep 02, 2011 1:30 pm

Dick Purcell wrote:So IRRA below goal and DRRA above goal fits people's values and interests.


DRiP Guy wrote:But this idea that the more overshoot there is in your nest egg, the more willing you are and ought to be to gamble it on trying to get FURTHER funds... well, it not only does not make sense to me, I can't imagine myself acting in that way.


Big argument! I know the right answer! You're both wrong! There's only one true path!

No, this all just personal preferences. There's no right or wrong here. Dick like apples. DRiP Guy like oranges. I like bananas. Nothing to see here - move along.

By the way, IRRA at lower levels of wealth and DRRA at higher ones would also be a valid kind of utility function that might be the one that best describes Dick's preferences. Good for Dick! It works for him. But he shouldn't try to impose his preference on others. DRiP Guy's preference is just as valid, if it works for DRiP Guy.

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Postby jln » Fri Sep 02, 2011 2:52 pm

First, Wade - congratulations and best of luck! I remember when my own kids were born. It's a really, really big day. I've got two of them, but they're 25 and 30 years old now.

This post is kind of a combined reply to lots of other ones and wanders around talking about several topics. I'm not going to quote everyone. I'll just start with one quote from my good friend and sparring partner Dick Purcell. (By the way, if we got together and wrote that program I proposed, we'd definitely have to put Dick in charge of making sure that we always stayed focused on helping real people achieve their goals - he'd be our chief quality control guy. And for sure Wade would be lead engineer for our simulations team).

Dick Purcell wrote:But your viewpoint is certainly valid and should be accomodated. Maybe for the high side, John will let you set your A for DRRA so your tolerance of risk holds at zero from your goal all the way up to infinite wealth.

John, can you do that for DRiPGuy?


DRiP Guy seems to be a classic IRRA kind of Guy. (Sorry about the pun). As I've mentioned before, yes, there are ways to model this.

By the way, why all this fixation on fixed dollar goals? I don't know anyone who actually thinks that way, except maybe Dick, and I'm not even sure of that. "I need $1,236,512 to retire, not a penny more, not a penny less." Like those guys carrying around their "goal" signs in that financial commercial on TV, which I found hilariously stupid at first and then incredibly annoying as they ran it over and over and over again, until I started wishing that the neighbor clipping his hedge (the one who just "threw money at the problem") would use his nice sharp clippers to do something unpleasant to the idiot and/or his sign.

Really? Really? You wouldn't take $10 less or $10 more? How about $1,000 less or more? How about $10,000 less or more, or $100,000? Now maybe we're talking real money. Falling short by $100K would hurt. Overshooting by $100K would be nice, but it's not critical. I'd be hurt more by $100K short than I'd be pleased by $100K over, that's for sure.

And markets are fickle, you know. The chances that we end up exactly at our goal are about as close to zero as you can get (Liebnitz' infinitesimals come into play here, with hairy greek letters like Epsilon, but that's not important right now). We're going to fall short or go over no matter what strategy we take (except maybe for Bodie's TIPS, but pretend we're not following his strategy). So it would probably make sense for us to at least pay a little bit of attention to those possibilities, right?

Hey, I have an idea. Maybe we should assign a "pleasure/pain index" to these outcomes. We could make our goal have an index of exactly 1. $10 short might have index 0.999, and $100K short might have index 0.612, with $10 over at 1.0008 and $100K over at 1.163. Or something like that - you get the idea - we'd have to work on it some more, I guess. Then we could get Wade to write an optimizer that would maximize the average pleasure index of all the possible outcomes over all of our available strategies to reach our goal. That would tell us which strategy is best for us in order to reach our goal! Dick would be thrilled! Especially with charts and graphs!

Oh, wait .... that's just what utility theory does. Sorry I brought it up. It's obviously a horrible idea that has nothing to do with reaching goals. Sorry, Dick, I though I was on to something there for a minute.

OK, enough of that fantasy. Let's get back to talking about dollar goals again, and I'll talk about myself for a bit (my favorite topic).

I've never focused on dollar goals in my own retirement planning. A specific dollar amount was simply never the goal for me.

My goal was always to retire with the same standard of living that I had before retirement, and as soon as possible. Retiring earlier takes more money than retiring later (especially if you retire before you take Social Security, and double especially if you retire before Medicare kicks in). When you run the numbers in a spreadsheet it's amazing what a big difference even one year makes. So I never had a dollar goal.

In addition, I never obsessed over that standard of living goal either. Plus or minus 5% would have been fine with me.

I monitored my progress toward this goal as time went on. After periods of below-average market returns, my projected retirement date would go up. After periods of above-average market returns, my projected retirement date would go down. I did also try to do a bit of adjusting of my savings rate, but that's hard to do for most middle class families like mine, especially those with only one income like mine.

I never changed my asset allocation. I have the kind of personality that is comfortable at 60/40. Being more aggressive than 60/40 would make me nervous. This is what "risk tolerance" is all about.

So of the four major ways to make adjustments along the way in order to reach my goal, I had the following priorities, in order from most important to least important:

1. Adjust retirement age.
2. Adjust savings rate.
3. Adjust desired standard of living in retirement.
4. Adjust asset allocation.

That was my path, but not a path I recommend to others or one that I think is better than others. I know people, for example, who want to be rich in retirement, and are willing to work much longer than I am to achieve their own personal goal.

To repeat myself for about the 10th time (at least), goal monitoring is of course important, for whatever your own "goal" might be (dollar amount or otherwise). If you start falling short of your goal, you have a number of options and tradeoffs to consider. Making your portfolio more aggressive is only one of them.

I want to note that if you hold a reasonably "efficient" portfolio (on that "efficient frontier"), say something that's based on broad index funds, then the only way to reach your goal by becoming more aggressive is to simultaneously increase the probability of those bad cat food outcomes. That's what "efficient" means (by definition). There's no free lunch in this strategy - there's a big downside.

Finally, and this is VERY IMPORTANT, I left out a huge major feature in my proposed new software tool. As Richard has repeatedly pointed out, all of these kinds of formulas and simulations require that we know the various input parameters with way too much precision, and for that reason we should never take the exact numbers that come out the other end very seriously.

Fortunately, this is really easy to fix. We just apply an image blurring filter to the entire screen so that you can only read the numbers if you squint real hard. This forces the user to focus on the forest of patterns displayed, not on the trees of actual numbers. Brilliant!

My apologies to Richard and everyone else for not including this CRITICAL feature in my original design.

John Norstad
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Postby Dick Purcell » Fri Sep 02, 2011 3:53 pm

John –

I’m warning my friends that if they, like I, have constructive suggestions to expose to you, they better get them in right now.

Unless they rush, they will really get surrounded by volumes of verbiage coming at them from all sides -- once you retire and have time for writing.

Then I had a better – scratch that, safer – idea. To retain a modicum of focus in the exchanges, and in self-defense, communicate with you only by Twitter. Ha!

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Postby jln » Fri Sep 02, 2011 4:45 pm

Dick Purcell wrote:I think to serve the investor's interests, it has to be based on (a) current balance, (b) goal, and (c) required return rate to get from (a) to (b). To go from those variables to allocations, we consider various allocations' return-rate probabilities -- and maybe there is where we consider something about the investor's attitude toward goal-meeting probability vs. magnitude of shortfall.


Well, if it helps think about this, the calculations are pretty trivial. Given your goal, your current balance, the number of years you have left, and your savings rate, there's a single simple equation that will tell you what rate of return you need to have a 50/50 chance of reaching your goal. Given that rate of return, it's another simple equation to tell you what stock/bond allocation has that rate of return (or allocation among some finer-grained set of assets).

But assuming you already hold a reasonably efficient portfolio, the only way to increase your return is to increase your risk, increasing the probability of those very scary large shortfalls. In terms of utility theory, you have to jump to a lower value of A - you have to change your personal risk preferences so that you are more risk tolerant.

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Postby jln » Fri Sep 02, 2011 4:52 pm

Dick Purcell wrote:Then I had a better – scratch that, safer – idea. To retain a modicum of focus in the exchanges, and in self-defense, communicate with you only by Twitter. Ha!


LOL. But best to use short words of just one syl like Paul S did. Would slow me down. Said this with 178 chars and only 1-syl words BTW. Ha! back to U! Ta-ta 4 now.

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Postby Dick Purcell » Fri Sep 02, 2011 6:28 pm

John –

Are you mocking my friend John Norstad??

You present me this choice? –

A. Maintain my U = E(r) – ½ * A * (Little Greek thing)^2

OR

B. Improve my prospects for dollars

Gee, I dunno. That’s a toughie.

+++++

I’m very averse to that Little Greek thing.

Still, I think I’ll opt for the better prospects for dollars.

The very reason I ran when they tried to yoke me in a U is that I want to be free to go for the better prospects for dollars, without having to undergo the psychological stresses of changing my A. The psych person never got to hand me a questionnaire, so he couldn’t affix me to an A. I don’t have one. I’m free to pursue prospects for dollars.

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Postby wade » Sat Sep 03, 2011 1:18 am

Dick Purcell wrote:Wade --

For this investing, I don't think what the utility function should be based on is the basic idea that the more you have the less another dollar is worth, because more aggressive has more downside as well as more upside.

I think the way to fit most people's real values is to base it on closeness to goal. The closer, the more risk averse. The further away from goal, below or above, the less risk averse.

Example: I was right at my goal and my choice was all TIPS -- but then John just gave me a lottery winning that made me 5x goal, so now I can risk suffering big losses and still be above goal so I'm going all small caps value for highest expected.

So IRRA below goal and DRRA above goal fits people's values and interests. The further below or above, the more he is willing to take risk. Below because he needs to take risk for hopes of meeting goal. Above, because he has so much more that goal that he can suffer losses and still be above goal so he goes for higher expected.

Dick Purcell


No baby yet!

This issue about what to do when you are above the goal is perhaps an unnecessary distraction. Either you lock-in your wealth and be happy with what you have ala DRiP Guy, or you lock in the goal part of your wealth and use the surplus to seek greater riches ala Dick. It doesn't matter, and people who are above their goal don't need the help anyway.

So let's focus on people who are under their goal. When you said,

For this investing, I don't think what the utility function should be based on is the basic idea that the more you have the less another dollar is worth, because more aggressive has more downside as well as more upside.


That seems to be exactly why utility is helpful. You don't feel a need to take risk getting more upside, because the gains from that upside will be overwhelmed by the losses that the risky strategy exposes you to. And the more risk averse you are, the more you focus on avoiding the losses. If I'm not explaining this well, please take a look at Larry Swedroe's explanation:

http://moneywatch.bnet.com/investing/bl ... ntent;col1

Dick, I am understanding better a valid point I think you are making, which is concern that the utility function doesn't incorporate a specific money goal. Though I agree with what I think John is saying, which is that specific monetary goals are rather overrated, it is possible using "prospect theory" to build in the goal and then experience disutility when you fall below it.

But I am also thinking that this fits in with what John and I already did with our glide paths. Then, you just calibrate your savings rate accordingly so that it will get you to your goal in the average case, and the more risk averse you are, the closer to your goal you will end up on either side (but also you will need to be using a higher savings rate).

This thread is incredibly interesting, and there is so much going in it. I'm just providing some half-formed thoughts. I'm enjoying the exchanges between Dick and John very much.
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Postby jln » Sat Sep 03, 2011 7:44 am

Dick Purcell wrote:You present me this choice? –

A. Maintain my U = E(r) – ½ * A * (Little Greek thing)^2

OR

B. Improve my prospects for dollars


I present you with this equivalent choice:

A. Keep the probabilities of the bad cat food outcomes low.

OR

B. Improve my prospects for dollars by going more aggressive.

That's how all the equations translate into plain English. Or, more properly speaking, that's how the plain English translates into equations.

It's a tradeoff. You can have A OR B, but not both.

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Postby jln » Sat Sep 03, 2011 8:53 am

To get serious for a moment, that fantasy tool I outlined is actually doable. I've spent a professional lifetime designing and developing this kind of software in other disciplines, and the technology is up to the task.

Some parts are harder than others. The parts that talk to the outside world (investment firm computers, government databases) would be tough and the fantasy is a bit futuristic. But I've done work like this for my own personal use automating queries and transactions with both Vanguard and TIAA-CREF, so it is indeed possible. The big problem is a lack of standards, so you'd need to write one piece of code that knows how to talk to Vanguard's computers, another piece that knows how to talk to Fidelity's computers, and so on. A plug-in architecture would probably be best. This would be boring work and would require continuous maintenance. No fun at all, and unavoidably fragile given the current state of the technology.

Acquiring all the data that would be needed is another big part of the job. There's no simple central data warehouse that can be consulted to get the return, volatility, and correlation data we'd need for every imaginable investment. But a good deal of this would be doable with enough work.

Making the goal thermometer go up and down as you adjust the sliders would be fairly easy, and would use equations that are well-known. The interactive histogram of ending value probabilities would have to be done with Monte-Carlo.

Showing how much better you could do with low fees at Vanguard would be easy.

Even showing what the picture would look like with Bodie's worry-free strategy would be fairly easy, and interesting because he uses TIPS and options to essentially cut off the bottom end of the probability distribution - no "cat food" outcomes to worry about! The downside to his strategy is that it's expensive - you have to have a high savings rate. I think it would be interesting to turn on his strategy in the tool and use the savings rate slider to see just how much more expensive it would be to reach your goal.

Another thing that could be easily done would be to save different collections of slider settings (strategies or "profiles") and give them names, then call them up by name to produce various graphs and charts that compare them side-by-side.

Another possible feature would be performance monitoring. The tool could show you your alpha and beta in the CAPM model, and your alpha, beta, and small and value risk factor weights in the Fama-French model. The personal tools I use for my own portfolio monitoring do this sort of thing.

The human interface design would be critical. Out of the box the tool would behave and present it's results in a completely non-technical way designed for real non-technical people to use. No equations or greek letters or formal finance terms would be used. Advanced data visualization tools would be key. This would be a challenge but it's critical that it be the central goal of the tool.

Preference settings or modes or progressive disclosure techniques could be used to give people access to some of the more technical information. Examples might be efficient frontier charts and the kind of CAPM and FF performance monitoring I mentioned above. But this would all be optional, and it would all be hidden by default.

We'd also need facilities to help people figure out their goal. They should work for both individuals and couples. Goals would not have be specific target dollar amounts. They could be defined and expressed in a variety of ways.

Ideally the tool could also help retirees, not just working people saving for retirement. Similar kinds of what-if games could be implemented with things like withdrawal rate strategies, annuities, social security, pensions, and post-retirement glide paths, for example. This should all be integrated with the pre-retirement tools we've already discussed.

So to summarize, despite all the jokes, I was also being serious, and I'm trying to take Dick's vision seriously of tools that help real people reach their goals. Even a preliminary stripped-down version of such a tool would require at least several man-years of development work, but it is indeed possible, not totally a fantasy.

There are many tools out there already that do some of this kind of thing, but I don't think any of them do all of this stuff in an integrated way that is goal-oriented and consumer-friendly. But maybe I'm wrong. Much of the existing stuff is fairly expensive commercial software intended for use by financial professionals (advisors, etc.) I've never bought any of it to check it out, so I'm not familiar with it.

Finally, I should stress that I'm not volunteering. I'm retiring precisely because I've spent a lifetime doing this kind of thing, and now I want the chance to spend time with my many other interests. I'll do a little bit of this sort of thing here and there from time to time, but no more big stressful major development projects like this one.

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Postby jln » Sat Sep 03, 2011 10:10 am

LadyGeek wrote:Can someone please explain the "CRRA", "DRRA", and "IRRA" acronyms?

jln - Your utility function tutorial, An Introduction to Utility Theory is excellent. I can now understand what's being discussed.


LadyGeek:

I'm very sorry to be so late in my reply. I somehow missed your question and only saw it today.

CRRA = constant relative risk aversion. The investor prefers to hold the same percentage asset allocation (has the same "relative" attitude towards risk) at any level of wealth. Based on evidence from historical data, this is usually considered to be roughly a "representative" or "average" or "neutral" attitude.

IRRA = increasing relative risk aversion. The investor prefers to make his portfolio more conservative as his wealth increases.

DRRA = decreasing relative risk aversion. The investor prefers to make his portfolio more aggressive as his wealth increases.

We've talked more about these kinds of variations in preferences and tastes for risk elsewhere in this thread, but it's easy to miss because the thread is so long and has jumped around among so many topics. I also do discuss this in my Introduction to Utility Theory paper, although most of that paper is devoted to developing the CRRA class of utility functions. Section 10 on pages 22-24 gives an example of one possible class of IRRA utility functions where relative risk aversion increases linearly with wealth. On page 23 there's a graph that shows a somewhat contrived example of an investor who's preferred asset allocation would gradually decrease from 100% in a made-up risky asset at wealth $1 thousand all the way down to less than 10% in the risky asset at wealth $10 million.

I can't believe you actually looked at one of my papers. Very few people do. I sometimes get email from people who have looked at them, but they're usually confused MBA or grad students looking for help with their homework. They used Google and ended up at my web site, got even more confused, and basically wanted me to do their homework for them. Funny. Although I've also had some people who found them actually valuable for their own sake, and have sent me nice corrections to typos. But I'm talking about maybe one email message every couple of weeks or every month tops. This isn't exactly wildly popular stuff.

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Postby LadyGeek » Sat Sep 03, 2011 10:57 am

wade - The forecast date of your new arrival will put an entirely new meaning to the "Labor Day" holiday. Congratulations! :)

===========

jln - If you have a Vanguard account, go to the bottom right corner of the login page and click the "Financial Engines plan" link under the Services menu. That will bring you to the FinancialEngines.com website, which is the one founded by Bill Sharpe.

This software does exactly as you describe. In my opinion, this software has a very well designed GUI and provides me with a range of forecasts that lets me know if I'm on track or not. It even has a slider bars for risk, which ranges from very conservative to very aggressive; and for retirement age (adjust your age until you hit your goals).

There's enough documentation of how it works to satisfy most investors.

What bothers me is that it persistently bugs me to increase my risk level, even though I have a > 90% chance of reaching my goals. The other complaint is that it is very aggressive in terms of recommending international stocks (google the forum for "financialengines.com", you'll find several of threads).

If I just use this tool with it's worst-case forecast, how is this going to be any different than what you are planning? That's the differentiator here. The average investor won't understand, or may not care, about all the details under the hood. Adding sliders for functions other than 1) "how much money do you need" and 2) "when do you want to retire" will totally confuse them.

=========================
As for reading your paper- In truth, I only read the introduction and the first example; the rest was too deep for what I was looking for.

I'm grateful for those stopping to help explain the basic concepts. This thread is currently at 9,903 views. I'm sure there are a lot of "average investors" (in addition to myself) who may not understand the concepts. That's why I ask - to educate.

Let me go a little further about "risk aversion" and interpreting the graphs. The graphs are plots of Utility (Y-axis) versus Wealth (X-axis).

What's clearly stated is that risk aversion is the slope of the line, but it's really "the slope of the slope", i.e. the 2nd derivative. The more risk averse, the steeper the line. It's why the phrase Marginal Utility is used, as it's the slope of the Utility function.

So, a risk-averse person has a very steep line at low wealth (the extra dollar is very important, don't risk it), then the slope gets very shallow at high wealth (the extra dollar is not important, take the risk). This gives the curve its concave shape.

References: An Introduction to Utility Theory and Wikipedia Absolute risk aversion.
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Postby Dick Purcell » Sat Sep 03, 2011 12:23 pm

Wade –

1. Yes, Yes – we should forget what people might do with wealth far above their needs and goals. Where most folks are and help is needed is below. As you say, that should be our focus.

2. In the population of people below goal, there is a preponderance of people hopelessly below. For example, 10 years from rapid decline of capability to work, maybe $100k in savings. I think that here is a terrible moral dilemma: What to advise?

It appears to me that in the “most common” or “default” application of utility theory, the advice that comes out is since you have very little wealth, your allocation should be more aggressive than if you had more. But is that the right advice? I don’t think it’s clear that it is. I don’t think it's clear what to advise, or what to make the presentation suggest is best.

We could advise he can’t risk going even lower. But if he goes conservative – or as John would say, “Big A” – he’s locking himself and family into something so bad it’s retirement on dogfood, and only two tablespoons of that per day, one on weekends.

We could say he has to go aggressive for any chance of growth to a retirement upgraded to tunaburgers. But that would have serious danger of making things so bad that even the dogfood menu is out of reach, he can’t even afford the rent on that rusted Packard as his home. It’s under the 6th Street bridge to sleep, and for food to beg.

What is the responsible advice?

I hope BobK is reading this. BobK, I’d like to learn what answer you suggest to this dilemma. I’d also like to learn whatever you can report about if and how there are answers to this dilemma from the scholars addressing retirement plans whose work you monitor and report to us about.

3. It seems to me that the kind of situation illustrated by the example above – sadly, very common – is the ultimate case of where our obligation is highest to inform the investor as best we can.

I don’t think we have a right answer. It’s his money, life, fate. The right answer is whatever he chooses if he’s fully informed and fully understands.

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Postby wade » Sat Sep 03, 2011 5:23 pm

LadyGeek: Thanks for that link!

Dick Purcell wrote:2. In the population of people below goal, there is a preponderance of people hopelessly below. For example, 10 years from rapid decline of capability to work, maybe $100k in savings. I think that here is a terrible moral dilemma: What to advise?


Yes, this really is the big $64,000 question for those who only have $64,000!

What is the appropriate response if you are falling short: more risk or no? Should you make the Hail Mary pass?

I think the best way we have to try to figure this out in a general way is with utility functions to try to see the role of risk aversion, though of course your software can provide some guidance as well. The amount of Social Security benefits is clearly going to play an important role in the analysis as well.

I'm interested to hear what BobK suggests, as I'm not sure whether there are studies about this. My feeling is that finance people are more focused on the case where people are much closer to reaching their goals, and the economists who are pointing out: wait a minute, most Americans are no where near their goals! Are not getting involved with this type of financial analysis.

If I may venture a guess, though I haven't done the analysis: If you are at a point where your savings are not looking to be able to add much on top of Social Security anyway, then you may want to go ahead and make the Hail Mary pass unless you are very risk averse.
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Postby DRiP Guy » Sat Sep 03, 2011 7:47 pm

wade wrote: If you are at a point where your savings are not looking to be able to add much on top of Social Security anyway, then you may want to go ahead and make the Hail Mary pass unless you are very risk averse, while you plan to continue to work until you *do* amass sufficient funds to retire.


A friendly amendment?
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Postby wade » Sat Sep 03, 2011 8:16 pm

DRiP Guy wrote:
wade wrote: If you are at a point where your savings are not looking to be able to add much on top of Social Security anyway, then you may want to go ahead and make the Hail Mary pass unless you are very risk averse, while you plan to continue to work until you *do* amass sufficient funds to retire.


A friendly amendment?


Thanks DRiP Guy. For these cases, we might want to add some "career survival probabilities" to consider how likely it is from year to year that one's career might be involuntarily terminated. That may affect asset allocation choices too. Not having done the analysis, it does seem to me that having the opportunity extend one's career does reduce the willingness for making the Hail Mary pass.
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Re: Redefining risk

Postby Bongleur » Sun Sep 04, 2011 1:27 am

Don Lawson wrote:Most long-term investors have an incorrect view of risk. They define risk as a loss of principal when the real risk to a long-term investor is the loss of purchasing power over time.


Sorry I missed this thread from the start... I noticed that you have defined your premise in two different ways. A few hours after the OP you said:

"It's about constructing a portfolio that will increase purchasing power over time while still taking distributions."

So which is your premise -- that the investor needs to increase, or only maintain?

Seems like the former requires more risk than the latter.
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Postby jln » Sun Sep 04, 2011 8:03 am

LadyGeek wrote:jln - If you have a Vanguard account, go to the bottom right corner of the login page and click the "Financial Engines plan" link under the Services menu. That will bring you to the FinancialEngines.com website, which is the one founded by Bill Sharpe.

This software does exactly as you describe. In my opinion, this software has a very well designed GUI and provides me with a range of forecasts that lets me know if I'm on track or not. It even has a slider bars for risk, which ranges from very conservative to very aggressive; and for retirement age (adjust your age until you hit your goals).

There's enough documentation of how it works to satisfy most investors.

What bothers me is that it persistently bugs me to increase my risk level, even though I have a > 90% chance of reaching my goals. The other complaint is that it is very aggressive in terms of recommending international stocks (google the forum for "financialengines.com", you'll find several of threads).

If I just use this tool with it's worst-case forecast, how is this going to be any different than what you are planning? That's the differentiator here. The average investor won't understand, or may not care, about all the details under the hood. Adding sliders for functions other than 1) "how much money do you need" and 2) "when do you want to retire" will totally confuse them.


Yes. The Financial Engines software is pretty good - probably the best example of this kind of software that I've seen. (Although I haven't yet looked at the Merton/DFA approach.) It should be, with Bill Sharpe behind it. Sharpe is a very sharp guy. (Sorry). And he has always been very concerned with helping real investors reach their goals.

I think the human interface could be improved, for one thing. Human interface design has always been a passion of mine - the user should always be at the center of the computing experience, no matter how much code the programmer has to write to make this happen. Most programmers do not have this point of view. I also think it could use more features. For example, does it deal with your human capital issues and glide paths? I don't remember, but I don't think it does, or if it does, it's in a very simplistic way. I think this is important. For example, college professors, stock brokers, and plumbers are different in important ways that are relevant for their asset allocation decisions when saving for retirement. And it doesn't have my proposed features to help automate the implementation of the plan by communicating with your investment firm (as I said, a bit of a futuristic dream, so I can't be too critical). And there's too much emphasis on portfolio optimization, which sometimes leads to odd recommendations (like all those foreign stocks). And encouraging people to take on more risk doesn't sound so great to me, although I don't have the full context to really criticize. Finally, a comprehensive tool would be useful for retirees as well as for savers, with the two parts of the tool integrated into a coherent whole. For example, I think that simply pricing an annuity to set the dollar goal isn't enough. For example, attention should be paid to the roles of Social Security, pensions, partial annuitization at different times, and variations on withdrawal strategies, with facilities for exploring the implications and tradeoffs involved in these factors. OK, enough, this is just a quick list of things off the top of my head. My vision is for a tool that is considerably more comprehensive than Financial Engines, I think.

I propose four main sliders that all seem to be important to me:

1. Retirement date.
2. Standard of living in retirement.
3. Asset allocation from conservative to aggressive.
4. Savings rate.

(1) and (2) define the goal. (3) and (4) define the strategy for reaching the goal (along with the glide path).

This thread is currently at 9,903 views.


9,800 of those are just me and Dick making repeated visits to check on the latest salvos, I'll bet. :-)

Let me go a little further about "risk aversion" and interpreting the graphs. The graphs are plots of Utility (Y-axis) versus Wealth (X-axis).

What's clearly stated is that risk aversion is the slope of the line, but it's really "the slope of the slope", i.e. the 2nd derivative. The more risk averse, the steeper the line. It's why the phrase Marginal Utility is used, as it's the slope of the Utility function.

So, a risk-averse person has a very steep line at low wealth (the extra dollar is very important, don't risk it), then the slope gets very shallow at high wealth (the extra dollar is not important, take the risk). This gives the curve its concave shape.


Well-stated.

The Pratt-Arrow relative risk aversion function is what you're trying to get at here, I think. It's defined as -U''/U'*w, where U(w) is the utility function. For the CRRA class of utility functions, this gives the number A that we've been talking about, the single constant number that measure's a CRRA investor's relative attitude towards risk at any level of wealth. You can evaluate the same function for other classes of utility functions. For example, for IRRA investors you get an increasing function, and for DRRA investors you get a decreasing function, instead of a constant. For other investors (like Dick?) this function might increase over one range of wealth and decrease over another range, and so on.

But I think this is all not of much interest to most Bogleheads. The details are all in that paper of mine, in the remote chance that anyone besides you and me really cares about them.

I know that Dick despises this stuff. But here's how I see it, put in the form of some simple questions (a Socratic dialog?):

1. Do you agree with the universally held view that some investors have more tolerance for risk than do others? That we differ from each other in this respect? That this has asset allocation implications for investors?

2. If so, do you think that it would be interesting and useful to try to build formal mathematical models of these attitudes? In the same way, for example, that we build and use the random walk model for asset prices?

3. If the answer to 1 and 2 is yes, have you looked at the standard utility theory model that economists have developed over the last half-century and that they use to do this kind of modeling and use to develop strategies to help individual investors reach their goals? If you don't like it, what's wrong with it, and what alternative models would you propose?

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Postby jln » Sun Sep 04, 2011 9:07 am

Dick Purcell wrote:2. In the population of people below goal, there is a preponderance of people hopelessly below. For example, 10 years from rapid decline of capability to work, maybe $100k in savings. I think that here is a terrible moral dilemma: What to advise?


Start saving more, right now, as much as you can, forget about retiring early, and most likely forget about your dreams for a financially comfortable and secure retirement. Asset allocation concerns are second or third order compared to this. It's a tough, tough problem, with no easy answer or magic wand solution. In brutally honest terms, the only real answer is "sorry, you blew it." Maybe a lottery ticket, but you'd really be better off taking the money you'd spend on it and adding it to your next retirement contribution.

It appears to me that in the “most common” or “default” application of utility theory, the advice that comes out is since you have very little wealth, your allocation should be more aggressive than if you had more.


No, that's not what happens at all.

3. It seems to me that the kind of situation illustrated by the example above – sadly, very common – is the ultimate case of where our obligation is highest to inform the investor as best we can.


Yes, absolutely.

I don’t think we have a right answer. It’s his money, life, fate. The right answer is whatever he chooses if he’s fully informed and fully understands.


Yes, there's no single answer that applies uniformly to all people, as with the answers to most other questions involving risky endeavors. Utility theory is one imperfect tool economists use to model these differences between us as unique individuals.

Short answers for once!

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Postby nisiprius » Sun Sep 04, 2011 9:49 am

jln wrote:
It appears to me that in the “most common” or “default” application of utility theory, the advice that comes out is since you have very little wealth, your allocation should be more aggressive than if you had more.
No, that's not what happens at all.
I don't know what the theory says. I know that the Fidelity Retirement Income Planner began by suggesting that I use age 94 as a planning horizon, which I accepted. Under one detailed entry of my real-world data, it told me that under its default set of assumptions my money would run out at age 93. It then recommended a specific and significantly higher stock allocation. (It wasn't a computed number, it was a round number from a "model portfolio" about two notches more aggressive than my actual allocation). I tried re-running the model with their suggested allocation... and got a substantially identical result!

So, whatever the theory says, the real-world advice from this particular automated tool was to increase my stock allocation, even though the same tool forecast that increasing my stock allocation would not improve the outcome!

I wasn't familiar with the IRRA/CRRA/DRRA distinction. I believe that the common personal mindset of people giving advice is DRRA, and that, furthermore, if you in effect say that you personally are IRRA, the response is not to accept it, but to tell you that IRRA is wrong and that you should be DRRA.
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Postby Dick Purcell » Sun Sep 04, 2011 1:36 pm

John –

Imagine one of us 100 million peasants daring to accept your invitation -- to answer your three Socratic questions of entry into that deep dark Forest of Utility Functions.

He proceeds with trepidation, taking the first three steps you’ve beckoned him toward – but about your questions, asking his questions.

Your Socratic question 1 –

1. Do you agree with the universally held view that some investors have more tolerance for risk than do others? That we differ from each other in this respect? That this has asset allocation implications for investors?


1.a – To us peasants, risk means uncertainty that is consequential, the more consequential the more risk. You would not use another definition of risk that represents uncertainty but omits consequence – would you??

1.b – For us peasants, to judge risk we need to understand it. You wouldn’t measure and express it in some way that most of us do not understand – would you? Say for example some Little Greek thing?

1.c – You say that tolerance for whatever you mean by risk varies from person to person. You do recognize that for one of us peasants, whatever attitude you are talking about also varies from situation to situation and decisision to decision – don’t you? If you somehow “measure” a person’s attitude for one situation-and-decision, that may not be his attitude for the next situation-and-decision. You wouldn’t assume that what you’ve measured for a person for some situations-and-decisions applies to his next situation-and-decision – would you?

(Confidential family example: My Uncle Evel Knievel kept his money in T-bills.)

Your Socratic question 2 –

2. If so, do you think that it would be interesting and useful to try to build formal mathematical models of these attitudes? In the same way, for example, that we build and use the random walk model for asset prices?


2.a – “Interesting and useful”? Well, I’ll give you interesting. That idea strikes me as having a world-record sky-high ratio of interesting / useful. You don’t suppose that after finding it interesting, academics would start to think that we peasants are objects on which to use it, the way a person with a hammer may view and hit everything as if it were a nail – do you?

What an opportunity. 100 million nails!

I remember the story of a friend who was on the way to choose and buy a new car. On the way, she was accosted by a pride of academics!

They told her “we have a better way.” They asked her multiple-choice questions on her "feelings" about trains, motorboats, biplanes, even skateboards. Then they told her the car she should get was an American Motors Pacer.

I’ve always wondered why they didn’t just let her continue on her way to look at various cars and decide for herself. Somebody once suggested to me that maybe some of the academics -- unknown to themselves -- do that stuff to make themselves feel and appear more important.

Your Socratic question 3 --

3. If the answer to 1 and 2 is yes, have you looked at the standard utility theory model that economists have developed over the last half-century and that they use to do this kind of modeling and use to develop strategies to help individual investors reach their goals? If you don't like it, what's wrong with it, and what alternative models would you propose?


3.a -- Answer your Swiss-cheese-packed questions 1 and 2 with a simple “yes”? That’s a stunning suggestion. No.

Yes, I’ve looked at that utility stuff applied “for” individual investors. I don’t dispute that it can have use. But I don’t like its current gross overuse because it (a) fails to focus on the investment purpose and (b) transfers too much of the investor's decisionmaking to others who don't understand him as well as they think they do and are doing things he does not understand. I’ve seen it serve the revenue interests of the financial industry and the conceptual interests of academics better than the financial interest of the investor.

My proposed “alternative model” is to inform the investor of how alternatives compare in probabilities for the purpose he is investing for and understands --net real dollar results for his future needs and goals.

Reasons for this are a pretty good one-two: (1) that’s the investor’s purpose. (2) That he understands.

It’s sorta like letting my friend see the cars and choose for herself, rather than quizzing her on biplanes and then telling her "AMC Pacer."

For some people, I’d show it to them in graphs of net-real-dollar probability distributions with a scrollbar to see probabilities high and low.

For other people, it woud be better to present the same probabilities-for-dollars assessments and comparisons another way. EG – For that guy age 55 with a balance far below what he needs for retirement, we could use five-picture sets to capture alternatives. In the five-pictures set for an alternative, each of the five pictures depicts very roughly 20% probability.

The conservative all-TIPS approach locks him into a retirement living in that rusty Packard eating dogfood. We show that alternative with five pictures of that.

The aggressive small-caps-value approach gives him some chance of retirement upgraded to tunaburgers, but some risk that he can’t afford dogfood or the rented Packard, so he's living under the 6th Street bridge. So to represent that approach we show two pictures with tunaburgers, two in the Packard with Alpo, one under that bridge.

Dick Purcell
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Dick Purcell
 
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SWR via removing excess gains from risk pool

Postby Bongleur » Sun Sep 04, 2011 7:44 pm

I'm still only on pg 4 but I have had a thought.

I think that the way all SWR calculators work is that they depend upon the compounding of excess returns to make up for years with inferior returns.

I would prefer a "plan" that takes any year's excess returns and removes the excess from the risk pool. When there is a year of inferior returns, then the amount would be made up by returning some of the previous excess to the risk pool.

I would prefer a "calculator" that will tell me if my plan is capable of succeeding in that manner. Its a lot more conservative and probably most people won't be able to do it. But for those who have large enough capital at the start of their withdrawal phase, it shows that they can take a lot less risk.
Seeking Iso-Elasticity. | Tax Loss Harvesting is an Asset Class. | A well-planned presentation creates a sense of urgency. If the prospect fails to act now, he will risk a loss of some sort.
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