Friday, October 31, 2014

Webinar on Sequence of Returns Risk, November 5, 2014

I will be hosting a webinar on Sequence of Returns Risk on November 5 for the Retirement Income Industry Association (RIIA). Although the primary audience is financial advisers, the content will be accessible to most do-it-yourselfers and I hope you will join me.

You do need to register in advance, which you can do by clicking here.

Please post any questions you might have in the comments section below.

I previously wrote a series of blog posts on this topic beginning with Clarifying Sequence of Returns Risk, but I hope you will join me for the webinar, too, where I will cover some new ground.

Hope to see you on November 5!

Monday, October 27, 2014

Spherical Cows

Physicists are known for sometimes oversimplifying assumptions in order to simplify the math required to solve a problem. Physicists refer to these assumptions as "Spherical Cows".

The term comes from a story about a farmer who talks to a physicist about his farm's underproduction of milk and asks if the physicist might be able to offer some advice. The physicist goes away to perform some calculations, but soon returns with an answer.

"I have a solution for your problem," he explains to the farmer, "but it only works for spherical cows in a vacuum."

We encounter a lot of Spherical Cows in retirement finance, huge oversimplifications that make the math easier.

For one, we generally assume that market returns are "normally distributed" even though we have tons of evidence that they are not. If they were normally distributed, we wouldn't see nearly as many market crashes as we do. Often we assume they are log-normally distributed, meaning the logarithms of the returns are normally distributed, but they aren't really that, either.

According to Professors Fama and French, "Distributions of daily and monthly stock returns are rather symmetric about their means, but the tails are fatter (i.e., there are more outliers) than would be expected with normal distributions."

They go on to say that longer periods, like years, conform more to a normal distribution. The 23% drop in the Dow of October 19th, 1987 was something that probably never could have happened in a single day under a normal distribution of returns, but the 37% year-long drop in 2008 was a 2.5 sigma event that might happen once every 80 years.

Their advice to investors is to expect more extreme good and bad returns than a normal distribution would seem to indicate.

So, assuming annual returns are normally distributed works fairly well, but not so with daily or monthly returns.

One of my favorite Spherical Cows is the one used to calculate sustainable withdrawal rates. SWR models assume that a mythical investor will continue to spend the same amount of money each year from savings, even after it becomes obvious that he or she is about to deplete their retirement savings. The models take a percentage, say 4%, of initial portfolio value and subtract that fixed dollar amount ($4,000 from a $100,000 portfolio in this case) from the portfolio balance every year, counting the number of years before the portfolio is depleted.

This assumption makes it far easier to build a spreadsheet than would modeling how a real investor might behave with their spending as their savings grow or dwindle.

I don't think most retirees would behave that way. Would you keep spending the same amount if you saw your savings vaporizing before your eyes? I would expect them to spend a little more when their portfolio grows and a little less when it shrinks. Spending 4% of remaining savings each year instead of a flat $4,000 a year might accomplish that, for example.

In an extreme case, say retirement savings shrink by 50% in the first decade after retiring (or, conversely, grow 50%), I suspect a lot of retirees would not only reduce their spending, but abandon the SWR strategy and look for a new adviser. Of course, by then, the retiree has locked in a lower standard of living for the remainder of her life. The life annuity she took a pass on ten years earlier would start to look pretty sweet in retrospect. Despite what you may have read, a shrunken $50,000 portfolio is not assured of doubling in size because the retiree used to have $100,000.

Every retiree will behave differently, of course, and that would be really hard to implement in a spreadsheet or any other software, so we go with the constant dollar spending models because the oversimplified model makes the math a whole lot easier.

Many financial writers argue that no one really "does it that way", meaning everyone adjusts spending based on their remaining portfolio balance instead of spending a flat amount, but I have two responses to that. If no one does it that way, then everyone in the financial press should stop saying that you can do it that way.

And second, the SWR models predict outcomes for you only if you do "do it that way". (Operations Research guys say that a model is predictive only to the extent that its policies are followed.) The SWR results aren't predictive if you do something else, like adjust spending to portfolio value changes – which apparently is what everyone is actually doing.

(In simpler terms, you can't predict the average height of American men by measuring the height of players in the NBA. That's called the unrepresentative sample fallacy. Likewise, you can't predict portfolio failure rates for people who care about their savings balance from the failure rates of mythical retirees who ignore pending ruin.)

SWR predictions work, but only for spherical cows in a vacuum, or retirees who are oblivious to their current savings balance.

Perhaps the biggest assumption we make to simplify the math is that future stock market returns will look like historical returns.

The argument that they will look similar is an inductive argument that is not strong. Inductive arguments can't prove something is true, they can only argue that something is probably true. They are also defeasible, meaning that future information can prove the conclusion wrong. As Nassem Taleb would say, it was accepted as fact that all swans were white until someone found a black one. Future market returns will mirror past market returns until they don't.

It is interesting that some authors choose various periods of U.S. historical market data upon which to base their studies instead of using it all. They say things like, "We used historical data for the post-World War II era, because market data prior to that period is not representative of the current era." If one past period of history was not representative of this one, how do we know that the author's chosen data is representative of the future era, which is, after all, the one we need to know about?

It does make the math easier, though, when we toss in that little assumption.

On the other hand, there are many strong arguments that the future won't look like the past. Wade Pfau showed that 4% sustainable withdrawals only worked in 4 of 17 developed market nations (Canada, Sweden, Denmark and the U.S., in that order), lending credence to the argument that high equity returns in the 20th Century may be an anomaly of American history not to be repeated. Wade also recently argued effectively that future safe spending rates will be closer to 3% than 4% because the current risk-free rate in the U.S. is so low. That means that both stock and bond returns will be lower in the future than they have been.

Is it safe to assume that the worst thirty-year period of stock returns in our limited history is the worst that will ever happen? Well, no, because a black swan could reset the bottom. The bottom was reset in October 1929, for example.

The 30-year period beginning in 1966 was rough on retirees, but 2007 through 2009 were bad years and their returns are currently showing up only at the end of 30-year periods, like 1979 through 2008. With sequence of returns risk, however, we know that the real damage from these years will show up in studies that begin, not end, around 2008. That will be in 2037 and, again, that's the period recent retirees should wonder about.

But it certainly makes the math easier when we assume that we have already seen the worst.

I'm not saying that the work based on these Spherical Cows is without value, because sometimes having a questionable forecast is better than having none. Sometimes, it's the best we can do, given the shortage of reliable fortune tellers. As a friend of mine is fond of saying, "Bad breath is better than no breath at all."

But I also think it's important to understand the strength of the arguments and the assumptions upon which our plans are based. Assuming you're safe because your portfolio would have survived the worst bear market in the past 50 years is a big assumption.

Friday, October 24, 2014

RIAA – Think Like a Pig

I spoke at the Retirement Income Industry Association Fall Conference in Charlotte yesterday. The title of my presentation was "Think Like a Pig" and the topic was how both the math and the mindset of retirees change after we leave the workforce.

I promised to provide a link to my PowerPoint slides on my blog today and here it is. The floor is always open for questions, whether you attended or not.

I thank RIIA for inviting me. I love public speaking. (And private speaking. And I sometimes talk in my sleep because there isn't enough time in a day to say everything I want to say.)

A few of the advisers at the conference admitted they were there because, given the title, they thought I would talk about barbecue.  I hate to disappoint, so here you go. My wife and I had dinner at Woodmill Smokehouse in Charlotte. It was outstanding.

Monday, October 20, 2014

A Geek in Manhattan

I joined Joe Tomlinson and Wade Pfau in Manhattan this past week for a panel discussion about turning assets into income after retirement. The panel was hosted by MarketWatch's Bob Powell. The video will appear on the MarketWatch website in due course.

If you are not reading these three, then you need to start. I’ve linked their names to their websites.

Heck, Nobel Laureate, William Sharpe mentioned in Advisor Perspectives that he reads Wade’s blog. I think that's a big deal. They don’t call it the “Sharpe” ratio because its pointed, you know, and then there's the Capital Asset Pricing Model. Bill has a blog, too. (And, yes, Wade reads it.)

On Wednesday evening, Joe, Wade and I sat up until well after midnight in the Algonquin Hotel lobby talking about TIPS bond ladders. (I know, right?) Wade referred to this as our own "Algonquin Roundtable." I knew Dorothy Parker frequented the hotel and that James Thurber lived there for a while, but the Roundtable was a fun piece of history to learn. My wife and I stayed there several years ago, hoping some of the "literary cool" would rub off.

The conversation was so much fun for me that I lost track of time and I swear I wouldn’t have noticed if Derek Jeter had walked into the lobby. I learned three things.

First, as you can see with the Jeter thing, I tend to exaggerate a little to make a point.

Second, I am a total geek. This was one of the most enjoyable things I've done in a while. (I am undoubtedly the only person who knows me that wasn’t already aware of that. Becoming so excited when my son gave me Mathematica should have tipped me off. My high school yearbook holds a lot of hints, as well.)

And third, while the three of us have interesting disagreements, they are largely on the fringe. On the important things, we are in complete agreement.

I mentioned during the panel discussion that I am not a huge fan of annuities, in part to bait Joe and Wade into a livelier discussion (Joe bit, Wade just smiled). And while I am not a huge fan of annuities, I am also not a huge fan of sustainable withdrawal strategies. I think we all agree that there is no single great solution to funding a retirement that could last 30 years after funding a working career that could last 40. Working 40 years to pay for 70 is a challenging problem, to say the least.

Joe is a strong advocate for life annuities. I suggest you visit his website and give them a thorough consideration. I don’t think they are right for me personally, but I believe they are ideal for people in certain situations. They are the only way to guarantee income no matter how long you live and I agree with Joe that you should purchase an inflation rider. There have been good arguments that insurance companies overcharge for this inflation protection and that is probably true. But, I wouldn’t forgo fire insurance because I thought insurance companies overcharged for it. When you need it, you need it, and insurance won’t seem too expensive if your house burns down or a tank of gas costs three hundred dollars.

The panel discussion was a lot of fun. I hope you’ll watch the video when it is available. One of my favorite clients was able to attend in person and that was a real treat for me.

Now, I’m on to Charlotte this week to speak at the RIAA conference.

Before long, I'll be back at Caffe Driade drinking lattes, reading papers and writing blogs, but this is a nice change.

Monday, October 13, 2014

Three Portfolios

After my last post on the sensitivity of retirement finance variables to asset allocation, Asset Allocation in Smidges and Dollops, a reader commented that it can be difficult to know what to include in retirement assets and, therefore, how to calculate asset allocation percentages.

And you know what? He's right. It can get complicated.

For a 40/60 portfolio, for example, do I allocate 40% of my total assets to equity or 40% of my liquid assets? Do I include my home equity? A pension or Social Security benefits? How about a fixed income annuity?

An often-asked variation of this question is whether home equity should be included when calculating "sustainable withdrawals".

I suggest the following to make it more clear. Divide all of your assets into three portfolios.

The first, which I'll call the non-retirement portfolio, will contain any investment assets that you choose not to be used to fund your retirement. Your home equity will probably go into this portfolio. If you plan to keep your house and leave it to the kids or to a charity in your will, it goes here.

The non-retirement portfolio will also include money you set aside for your heirs, antique cars, works of art, college savings and any other investment asset that you do not plan to convert to cash to pay for your retirement. Illiquid assets should go here unless and until you convert them to liquid assets. Liquid assets can go here if you don't plan to spend them to fund retirement.


Notice I say that assets go here that you choose not to use to fund retirement. Unless you put the assets in a trust, you can change your mind, move them to another portfolio and spend them later in retirement. This is little more than a "hands-off" sign for assets you hope you won't have to spend for retirement expenses, but that will be there if you need them.

The second portfolio, which I'll refer to as the "floor" portfolio, will contain any asset that will generate retirement income but is not exposed to either market risk or interest rate volatility. This will include Social Security benefits, pensions and fixed income annuities (and probably TIPS bond ladders, though they need further discussion). These sources will provide the same amount of retirement income whether the market sinks or rises and whether interest rates rise or fall. This portfolio will provide a relatively safe floor of retirement income no matter what happens to the stock and bond markets. (I wrote about floors in Unraveling Retirement Strategies: Floor-and-Upside.)


The third portfolio, which I'll refer to as the retirement income portfolio, will contain all assets that you intend to use to fund retirement and that are exposed to market risk and/or interest rate risk. The stream of spending created by the retirement income portfolio (due to the unfortunate acronym, I won't refer to it as the RIP) depends on stock and bond market returns and is risky. Diversifying among multiple stock and bond asset classes helps manage this risk.


I'll make one last point about portfolio contents regarding our homes because it is often a subject of confusion. I initially put the home in the non-retirement portfolio under the assumption that the retiree would keep the house throughout her lifetime. (Surveys show that's what most older American hope to do.)

But, as I mentioned above, these non-retirement assets can usually be accessed for retirement income if you need them.  The equity in a home can be transferred to the retirement income portfolio as cash if you sell the home. Also, the equity can be transferred to the floor portfolio if you take out a reverse mortgage. So, there are ways for your home to provide retirement funds that you can spend, but you have to sell your home or use it as collateral before that can happen.


If you have no plans to downsize or take a reverse mortgage, your home won't be a source of retirement income and should not be used in the sustainable withdrawal rate (SWR) or retirement income asset allocation calculations.

Back to our three portfolios, let's consider their very different natures.

The non-retirement portfolio has no retirement spending rate because you have chosen not to spend from it. The investment horizon may vary for each asset. A grandchild's college costs may need to be covered in three years while investments for heirs may not be spent for decades. Depending on its contents, the non-retirement portfolio may be exposed to market and interest rate risk. Unless the assets are in a trust, you can probably transfer their value to the retirement income or floor portfolios later in retirement. Asset diversification may be beneficial in the non-retirement portfolio, but it isn't linked directly to your retirement income portfolio allocation.

(The non-retirement portfolio isn't completely irrelevant to the retirement income plan. If you have a lot of non-retirement assets, you can take a little more risk with your retirement income strategy, knowing you have these other assets available as a backup in a crisis. If your non-retirement portfolio is empty, you need to be even more careful with your retirement income portfolio asset allocation.)

The floor portfolio, in contrast, provides income that is critical to our standard of living. The assets in this portfolio are not exposed to interest rate risk or market risk. (The exception to this is a bond ladder which I will discuss in a separate post.) Though diversifying among Social Security benefits, pensions and fixed annuities might be beneficial, it is rarely practical. The spending rates for these assets are fixed by the Federal government for Social Security benefits, our pension provider, or the insurance company that sold the fixed income annuity.

Lastly, the retirement income portfolio will have a spending rate, assuming the floor portfolio doesn't cover all of our expenses. It will typically be in the 3% to 4% range of remaining portfolio assets. The assets in this portfolio are exposed to interest rate risk and market risk. The investment horizon is laddered: we will have short term needs, long term needs until the end of our life, and everything in between.

The following chart summarizes the differences between the three portfolios.


So, back to our original questions, which assets are included in the percentages for calculating sustainable spending amounts and asset allocations? The answer is the total assets in the retirement income portfolio. If we move assets from one of the other portfolios (our home equity, for example) into the retirement-income portfolio in the future, we recalculate then.

Which portfolio assets can we move in the future? We can move non-retirement assets or retirement income assets into either of the other two portfolios, though we may have to convert the asset to a liquid form (usually meaning cash) before we do.

Moving out of the floor portfolio is more difficult. We can't move Social Security benefits. Moving a pension or an annuity would mean selling it for what is typically pennies on the dollar and is usually cost-prohibitive. Bonds can be moved to either of the other two portfolios, subject to interest rate risk.

These are important things to know when we are developing a plan. Some parts of the plan can be changed to adapt to changing circumstances over time, like our asset allocation, our spending rate and which assets we hope to bequeath to our heirs and which will we use to pay our own bills.

Other parts of the plan are very difficult to move once executed, typically prohibitive to undo, like changing a Social Security benefits claim or converting a pension or fixed income annuity into cash.

As an example of the asset allocation calculation, if we have $100,000 home equity in the non-retirement portfolio and $200,000 in the retirement income portfolio and would like a 40/60 retirement portfolio allocation, we would invest $80,000 in equities and $120,000 in bonds, ignoring the home equity. How would we allocate the $100,000 of non-retirement portfolio assets? That depends on our goals for those assets, but it may be very different than 40/60.



Our Retirement System and Some Odds and Ends

I am un-retiring for the next month or so to attend some conferences. I'll be taking my first "business trip" in ten years this week. I hope they're more fun than I remember. I'll let you know.

On Wednesday, I will be joining MarketWatch Senior Columnist and Retirement Weekly Editor, Robert Powell, who will moderate a panel discussion in New York on retirement income. Wade Pfau, Joe Tomlinson and I will be on the panel. (Wade and Joe are brilliant retirement planners; I'm the token retiree.) For more information or to RSVP, please email MarketWatchevent@wsj.com by Monday, Oct. 13th, i.e., today.

On October 23rd, I will speak at the RIIA Conference in Charlotte on retirement planning from the retiree's perspective. I'll be doing a webinar on sequence of returns risk in November.

My regular stream-of-consciousness posts on retirement planning for the unwealthy may be somewhat disrupted for a few weeks (if it is possible to disrupt stream-of-consciousness), so here are a couple of links you might find interesting.

The New York Times printed a piece this morning on the retirement system in the Netherlands entitled, No Smoke, No Mirrors: The Dutch Pension Plan that I found interesting.

It's interesting to compare and contrast this with an older piece in the Times by Teresa Ghilarducci on the American retirement system entitled, Our Ridiculous Approach to Retirement. These won't help your individual retirement planning except to the extent that they provide global context, but I find them interesting.

Wade Pfau's excellent blog recently mentioned a Journal of Finance paper by Gordon Irlam. Irlam uses dynamic programming to explore dynamic asset allocation. The paper is rather dense, in other words, not targeted to do-it-yourself planners, but he has a Java-based asset allocation tool at https://www.aacalc.com/ that you might want to play with. If you do, please let me know what you think by commenting below. I'll be playing with it more after I wade through the paper sufficiently.

Tuesday, September 23, 2014

Asset Allocation in Smidges and Dollops

How important is it to precisely nail your asset allocation in retirement? You may be spending a lot more time than you need to fretting about investing 35% of your portfolio in equities instead of 40%.

Asset allocation affects a number of retirement plan factors including your portfolio’s exposure to a market crash, your long term expected portfolio return and volatility, and your sustainable withdrawal rate (and sequence of return risk). In this post, I'm primarily referring to your equity and bond allocations, which is the first allocation decision we make.

In his earlier books, The Intelligent Asset Allocator and The Four Pillars of Investing, William Bernstein suggested that the first step in choosing your asset allocation should be answering the question, “What is the biggest annual portfolio loss I am willing to tolerate in order to get the highest returns?"

Bernstein provided a table of asset allocations based on the answer to this question. I have included this table below alongside losses for the 2007 to 2009 market crash according to IFA.com. As you can see, Bernstein's recommendations were reasonable but were more optimistic than actual losses during that crash.

(This is a demonstration of the weakness inherent in using historical data to predict future market risk and returns. The Intelligent Asset Allocator was published in 2001 and a new low-water mark was set in 2009.)


Your individual risk tolerance – at least the risk tolerance you think you have – and your risk capacity are factors that will combine to suggest an appropriate asset allocation, according to Bernstein, and you will note that a 10% change in your portfolio’s equity exposure resulted in about a 6% change in the maximum loss you might have incurred during the 2007-09 crash.

(To clarify, a 5% increase in equity allocation here means increasing stocks from 30% of the portfolio to 35%, and not to 5% more of the original allocation, which would increase equities to 31.5%.)

How precisely you need to nail your asset allocation from the perspective of maximum loss in a market downturn depends, then, on how precisely you feel you need to limit those losses. If a 15% maximum loss versus a 20% loss feels significant to you, then a 10% change in equity exposure is important. If 20% and 30% maximum losses feel about equally acceptable, your equity allocation can vary by as much as 20%.

Asset allocation also affects the long term expected return and volatility of your portfolio. During a market crash, most asset classes tend to fall. This is referred to as “systematic risk" in modern portfolio theory (MPT) and it cannot be diversified away. Over the long term, however, asset diversification is a powerful tool.

Based on index portfolios from IFA.com, using data from 1964 to present, we can see the impact of increases in equity allocation at the conservative end (a 30% equity portfolio with the remainder in bonds and cash) and the more aggressive 70%-equity end of the spectrum.


You can see, for example, in the second row of data that increasing the equity allocation from 30% to 40% would increase the expected portfolio return from 8.01% to 8.9% and the risk from 7.13% to 9.2%.

How do you choose between a portfolio with an 11.15% expected return and a standard deviation of 15.67% and a portfolio with an 11.8% expected return and a 17.9% standard deviation? These are the parameters that would change for an investor contemplating an increase in her equity allocation from 70% to 80% (the fourth row of data in the table above). Although the expected return seems to increase significantly, so does the risk and there is actually very little difference between the two portfolios.

Using a tool provided by MD Anderson called Inequality Calculator, I compared probability density functions for the log-normal distributions of both portfolios. As the diagram below shows, even after increasing equity allocation from 70% to 80%, the probability of improving annual returns of your portfolio is only about 51%.


In other words, there isn't a lot of difference between the two portfolios. You haven't turned a low-risk portfolio into a high-risk one by increasing the equity allocation from 70% to 80%.

A small increase in returns can have a significant impact on terminal wealth after 30 years. Following is another graph from IFA.com showing the growth of $1,000 in their various index portfolios from 1984 through 2013, thirty years.


At the conservative end, an increase in equities from 30% to 35% resulted in a portfolio about 12% larger after 30 years. Increasing the asset allocation from 70% to 75%, on the other hand, increased the portfolio 9.7%. Those returns, however, are not guaranteed. The odds that your portfolio will end up larger with an 80% equity allocation than with a 70% allocation is still just a tad over 50/50.

A third factor influenced by your portfolio’s asset allocation, for those implementing a sustainable withdrawal rate (SWR) spending strategy, is the sustainable withdrawal rate itself. For a demonstration of the impact, let’s look at the original studies published in William Bengen’s Conserving Client Portfolios During Retirement


As his charts for both taxable and tax-deferred portfolios show with 30-year life expectancies, the SWR is essentially flat from about 30% to 80% equity allocations. Unless your portfolio has a very low equity allocation or a very high one, changing your equity allocation won’t have much affect on your sustainable withdrawal rate.

Even below 30% equities, the impact on SWR is on the order of a quarter- to a half-percent and it becomes less as retirement progresses. Of the three impacts we are considering, SWR is the least sensitive to asset allocation.

To summarize, you won't change your portfolio's volatility much by changing your equity allocation a 5% or 10% step up or down. You will improve the expected portfolio return, but the probability of improving your actual return or terminal wealth is roughly a coin toss. It won't have an impact on your sustainable withdrawal rate unless you move below about 30% equity or above about 80%.

The factor most sensitive to asset allocation seems to be maximum loss in a bear market. I personally pay the most attention to this dimension of risk because I am just finishing the first decade of retirement and sequence of return risk is front and center of my attention. Bernstein refers to this as "deep risk", a risk from which one might not recover, as opposed to long-term portfolio volatility risk. Antti Ilmanen refers to it as "bad returns in bad times".

Of course, the "best" equity allocation depends on what future market returns turn out to be, which is, of course, unpredictable. If 2007 found you woefully below the equity allocation most experts would recommend, you would've enjoyed the next three years much more than they did. We're trying to find a bet that will work more often than others, not the "best" bet.

Bernstein recommends portfolio allocations in "smidges of natural resources" and "dollops of Treasuries", which tells you what he thinks about our ability to make precise bets. In his words, "Once you’ve arrived at a prudent asset allocation, tweaking it in one direction or the other makes relatively little difference to your long-term results."