Budgeting skills are as important as what your portfolio is doing—probably, more important really, because budgeting is an everyday issue. If a person can scale back appropriately so that they can actually survive on a 4 percent withdrawal rate, they’re good. Any reasonably designed retirement portfolio will last with a 4 percent withdrawal rate. Eight percent? You’re going to have to get really lucky in your investments.

We love reading his work and he’s a very sharp, knowledgeable finance maven. But his claim about the 4 percent withdrawal rate seems a tad glib–there are many assumptions built-in to this claim that need explanation. Would you really like to bet on such a simple number for your retirement? We think not.

Intuitively, at 4% withdrawal rate,  if your return is 4%/YR and inflation is nil, then in fact you can simply withdraw the gain each year and never deplete the principal. But if, for example, inflation is 2%/YR and your return is 4%/YR, then we can show 4% withdrawal rate would last you 34 years. Not bad. But if your return is 3%/YR and inflation is 4%/YR, then this account will deplete after 22 years if withdrawals are at 4%/YR.  That’s probably a big difference. We show you how to handle all these “What Ifs”.

This post introduces the idea of the Safe Withdrawal Rate (SWR), a concept that has recently captured the attention of many investment advisors and publications. We introduce our own focus on this topic now. We announce two initiatives. First, we published a descriptive piece in Advisor Perspectives, a highly respected and popular website for investment professionals. This piece explains SWR ideas without math for the average investor. Second, we published our full research results in detail here, in our permanent pages (see Investing Tools drop-menu above, or click this link):

Investing Tools> Safe Withdrawal Rate

This page introduces our technical analysis and methodology to determinine your own, personal SWR. Our innovation: we capture each individual’s beliefs about his own future returns and inflation to find the expected value of his SWR, irrespective of market history. Ultimately, your personal beliefs about how future returns and inflation evolve is all that matters for your planning purposes.

The new assumptions present a far different picture of risk. Consider the 60% stock, 40% bond portfolio that fell about 20% last year. Under the fat-tailed distribution now used in Ibbotson’s tool, that should occur once every 40 years, not once every 111 years as assumed under a bell-curve-type distribution. (The last year as bad as 2008 was 1931.)

Insulation from extreme market events doesn’t come cheap. Allianz SE’s Pacific Investment Management Co., or Pimco, which systematically hedges against extreme market events in several mutual funds launched last year, says the hedges may cost investors 0.5% to 1% of fund assets a year. Pimco uses a variety of derivatives and other strategies to hedge the funds.

You can read the whole article here: ( “Some Funds Stop Grading on the Curve”, 8 SEPT 09 ).

In many ways, this new approach to portfolio optimization incorporates the barkings of Nassim Taleb, of Black Swan fame, who has been incessantly warning of the dangers of designing portfolios assuming the “thin” tails of the Gaussian probability density, rather than using a more realistic “fat tail” model. Fat tails more accurately, and usefully, account for extreme bad outcomes, such as we recently experienced in the credit and real estate markets.

We expect in one to two years the large investment and broker-dealer firms will routinely offer Fat Tail-based portfolio design as well as special mutual funds incorporating these ideas.

Finally,  as we noted in our post of 15 JULY 09, this knowledge has been available for 20 years. So it is quite stunning that the financial industry, which usually is amazingly fast to adopt good ideas, has avoided the fat tail approach until now.

Scenario Planning is an important component of strategic planning for any corporate or government organization that intends to prosper and succeed over time. It applies to individuals, too. Of course, it applies to investing as well.

Wired magazine published a clear, concise description of how to do Scenario Planning for yourself. The author, Peter Schwartz, is one of the pioneers in the field. He uses an example of an aerospace engineer planning for his career in quite uncertain times.

Read the Wired Magazine Article

In the first, The Economist lead editorial sets the stage:

What went wrong with economics

It says:

“In the wake of the biggest economic calamity in 80 years that reputation has taken a beating. In the public mind an arrogant profession has been humbled. Though economists are still at the centre of the policy debate—think of Ben Bernanke or Larry Summers in America or Mervyn King in Britain—their pronouncements are viewed with more scepticism than before. The profession itself is suffering from guilt and rancour. In a recent lecture, Paul Krugman, winner of the Nobel prize in economics in 2008, argued that much of the past 30 years of macroeconomics was “spectacularly useless at best, and positively harmful at worst.” Barry Eichengreen, a prominent American economic historian, says the crisis has “cast into doubt much of what we thought we knew about economics.” “

We almost always find Krugman’s assessment of anything remotely political off-base or wacky, but he definitely gets it right, here!

Two other articles analyze the failures of economists to detect or clearly recover from the calamity. These two focus on various aspects of economic theory itself.

The other-worldly philosophers

Efficiency and beyond

The latter article has a nice discussion of the famous Efficient Markets Hypothesis, which is obviously bogus. I love the EMH! It says. all information that could affect the price of a stock is already incorporated into the price, so over time, no one can profit from investing. Don’t you love it?

The EMH is the source of the old joke about two economist walking together down the street. One sees a $20 bill on the ground and reaches to pick it up. Then the other economist stops him, and says “Hey, don’t bother-if that was a REAL $20 bill, someone would already have picked it up!”

One of themes coursing through these articles is that economists have used some important simplifying assumptions, such as EMH, to build their models. These models have worked fairly well. But just as in engineering, one has to consider the “corner cases” before accepting a model. Clearly, economists failed to consider a variety of corner cases, any one of which would have set off alarms about calamity. (A corner case is a situation in which an assumption takes an extreme value. For example, an economic corner case: credit stops flowing completely.)

OK, here is our addition to the post-mortem about economists: Economists need to learn that just because model building is very hard, it’s not a reason to avoid numerous, dirty details. Engineers build elegant, and sometimes ugly, theories. They strive to be elegant and as simple as feasible. They like to avoid complexity. But the engineering mission is to design and build stuff that works according to spec and costs no more than spec. Thus, they do whatever it takes to handle the details of reality.

We acknowledge up front that in the real world, engineers get real feedback, so they know how well their models work. But they also know how to use computers for some of the most beastly models. Just consider the modeling required to predict tomorrow’s weather (Al Gore pay attention). Major mainframe-level facilities are commonly used. Same thing for understanding airflow over a wing design, and how to connect 2 billion transistors to make a speedy CPU.

So, the message to the economics profession is: Life is tough, deal with it! Make models of really messy reality. Just because some social systems can be much more difficult to understand than various physical systems is not an excuse to choose simplicity when brute force of simulation of ugly factors would give better results.

We have been wondering why this technical issue in portfolio management has seemed so hard to solve. As far we can understand, one only has to change the definition of risk in the standard portfolio optimization algorithms and you can account for the Black Swan Events. Pick any measure that seems reasonable. (It’s been clear that using the variance of returns in Modern Portfolio Theory doesn’t capture the really big bad events.) Then do the numerical math and programming. It takes some very straight forward rocket science (OK, we indulge) to produce a more realistic approach.

So we were amazed to discover this problem was in fact solved for the first time in 1987. Even more amazing, one can buy off the shelf software (see This) to perform all the math computations. This whole approach even has a name: “Post-Modern Portfolio Theory (PMPT).

It turns out the Pension Research Institute at San Francisco State University developed the mathematical algorithms of PMPT that are in use today. These methods provide a risk measure that directly accommodates investors’ preferences for upside uncertainty over downside uncertainty in their returns. Many papers and programs have been developed since. But it is supremely obvious that this approach requires much more work and analysis than the original MPT required. Business schools didn’t teach this either. Thus, generations of advisors had no clue that the high risk events everyone is so sensitive to post-catastrophe could be at least numerically handled in portfolio designs.

There was a Devil’s Pact by investors, whose innumeracy avoided discussing issues of risk definition and who wanted to avoid math explanations, and their enablers, those investment advisors who themselves do not understand the basics of quantified portfolio design, let alone an approach as computationally oriented as PMPT.

But armed with this knowledge, we can progress to now use PMPT.

In his latest work, Ted Wong digs deeper into the drawdowns and shows (again) that MAC beats BAH on a risk-adjusted basis as well.

Being passive will not help you, especially when markets deeply drawdown, as they have in last twelve months.

MAC beats BAH

MAC beats BAH on a Risk-Adjusted Basis

Moving Average vs Buy and Hold

We think this is quite an interesting result from an ambitious study. It adds more weight to Wong’s previous findings that timing matters quite a lot and that Buy and Hold suffers as a result. See his previous work here:

What the “Missing Out” Argument Misses

There are many ways to demonstrate this quantitatively, but some of the most elegant proofs are based on observing how you improve your investment returns if you are out of the market sometimes and in it sometimes–at the right times! The point is that those times must be chosen, and thus you are an active (as opposed to passive) investor. Here’s a really simple example of such research which we first read in Forbes Magazine, 11-24-08. It’s written by Laszlo Birinyi, “Uncharted Waters”. He says:

“Assume you had invested $1 at start of the bull market in 1966 and ignored dividends. If you missed the:

• Five best days of each year, investment now = $1.11.
• Five worst days each year, investment now = $2,696.”

This certainly shows it pays to be out of the market sometimes. Those times must be chosen, so that makes you active.

Now we are ready for a much more powerful version of this approach. Theodore Wong has recently published a study of the market for the last 137 years. We provide the original here:

What_the_missing_out_argument_misses

Wong concludes with this question:

“If you could help your clients avoid most of the bear markets, would they mind missing a few mighty rallies?”

We think both the studies presented here compel us to actively evaluate the market situation and take appropriate action, rather than passively buying and holding.

Remember that old (legalistic) warning “past performance is no guarantee of future results”?  That’s obvious. But the implication is that investors believe the past is somehow useful to predict the future (lawyers aside, please). So here’s the catch: the view of prices looking backward is very different than looking forward. When you look forward, making decisions must account for substantially more risk than you can infer from pure historical statistics.

For example, the notion of “implied volatility” in options pricing is supposed to be the view of investors looking forward. But given the method by which this is computed (using only historical prices), it really is only a backward risk level. The view truly looking forward would give higher risk. Keep that in mind!

OK, we know many of you will be glazed like a donut by now, but in case you want to think deeply about the uncertainties of stock investing a good entry is this interview with the lead author ( the interview is actually quite understandable):

What if stocks are not for the long run?

(Read interview with Prof. Lubos Pastor, Booth School of Business, University of Chicago)

For you quants, here is the abstract of the published paper.

Lubos Pastor
University of Chicago – Booth School of Business; Centre for Economic Policy Research (CEPR); National Bureau of Economic Research (NBER)

Robert F. Stambaugh
University of Pennsylvania – The Wharton School; National Bureau of Economic Research (NBER)
May 22, 2009
Abstract:
Conventional wisdom views stocks as less volatile over long horizons than over short horizons due to mean reversion induced by return predictability. In contrast, we find stocks are substantially more volatile over long horizons from an investor’s perspective. This perspective recognizes that parameters are uncertain, even with two centuries of data, and that observable predictors imperfectly deliver the conditional expected return. Mean reversion contributes strongly to reducing long-horizon variance, but it is more than offset by various uncertainties faced by the investor, so that annualized 30-year variance is nearly 1.5 times the 1-year variance. The same uncertainties also make target-date funds undesirable to a class of investors who would otherwise find them appealing.

Keywords: stock, volatility, target-date funds, Bayesian, predictive system, predictive variance

JEL Classifications: G12

Working Paper Series

“Buy and hold” means it doesn’t much matter when you buy stocks, just pick good firms and hold for a long time and expect a rate of return superior to the bond market, with a bit more risk. For many years this approach seemed to work. But in 2008 this approach started to fail without scrutiny.

This was a valid strategy as long as you entered the market during the long, historical bull phase, and bought mostly firms that would survive, and lived long enough (“blue chips”). The long term (secular) trend clearly was up, if for no other reason than the stocks that get traded must profitably survive to be counted!

This chart offers a dramatic way to make the point that stocks trend up, but that you may suffer deeply as you wait. Consider this graph published by dshort.com:

You can see 138 years of upward trending stock prices (as measured by S&P Composite Index). It also shows several deep bear markets along the way. You could have entered the market and gotten a multi-year bull market or a multi-year bear market, and you couldn’t know. It also shows how you can wait many years, over 20 in some cases, for positive ROI.  So the question is: how long does “buy and hold” require?

Before we deal with the question of “how long to wait”, let’s discuss what we must wait for. We need to wait, after major bear drawdowns, to have prices rise close to the previous peak. So, do the math and plot the results. The graph below plots the ROI (vertical axis) you need after a fractional price drop (horizontal axis) to return to the initial price. The graph says nothing about how long it takes. But to give you an idea, suppose your portfolio dropped 50%. Obviously, it needs to double to return to original value. If you can get ROI of 10%/year, it will take roughly 7 years to double.

ROI Required to Return to Original Asset Value After Loss

The intervals during which the bear claws his way down can last longer than a major chunk of a human lifetime. The idea supporting “buy and hold” was that you really had a lot more than 20 years to wait comfortably for your reward. This detail was unstated.

Take a look at this chart, which plots the S&P500 Index for the 50 years ending 2 JAN 09:

S&P500: Prices for 50 years ending 2 JAN 09

Now ask yourself if you would have been happy to buy and hold over a 20 year investment horizon. It appears that 20 years suffices to wait out the many periods of large price drops, had you entered market since 1950. But what about a 10 year interval: would that be enough to wait passively? It depends on timing. Consider this chart, showing S&P500 Index for the 20 years ending 2 JAN 09:

S&P500 Index 20 years ending 2 JAN 09

Those 10 year intervals don’t look so easy to pick at this scale.

Finally, consider this analysis ( Forbes Magazine, 11-24-08: Laszlo Birinyi, “Uncharted Waters”). A major argument for long-term investing has always been that if you get out of the market you may miss the good days when the gains are made.  Assume you had invested $1 at start of bull market in 1966 and ignored dividends. If you missed the five best days of each year, investment now = $1.11. Yup, that looks like staying in was best.

However, if you missed the five worst days each year, your investment now = $2,696. So you would have been a genius just to be on the sidelines some of the time, especially the right time! By this analysis, choosing when to exit market can be quite prudent. Yes, you still must choose, but (roughly speaking) the only way to be reasonably sure of passively winning in the market is to be able to wait at least 20 years (based on these hindsight ideas).

Underlying all these hindsight statistics is a large economic truth. The history of stock markets in USA since 1870 or so is one of stunning GDP growth, beginning with the Industrial Revolution, through creation of railroad, electric power, shipping, telephone, steel, automobile, airline, electronics and computer industries. After WW2, the Baby Boomers populated the country and consumerism took off, and then the Internet “Changed Everything”. The Boomers are entering retirement now, and their kids are entering a depression, and also have to support the collapse of social security for current retirees. Can we really expect the same level of GDP and market growth to continue as they have historically? Maybe. But paying deep attention to your money seems far more prudent than hoping it all turns out OK in 20 years.