Tuesday, November 13, 2018

Mean Reversion of Equity Returns and Retirement Planning

Do stock returns exhibit long-term mean reversion? That's an economist's way of asking if stocks get safer the longer we hold them.

Long-term mean reversion would act like a spring returning prices back to a trend line when they advance above that trend or fall below it. The strength of this spring is referred to as its "half-life", the time it would take to recover half of a loss or — often conveniently overlooked — how long it would take to lose half of a gain.

A Society of Actuaries report[6] from 2014 states:
"In a survey by Ivo Welch (UCLA and Yale) in 2000, only 36 of 102 surveyed financial economists said that they believed in long-term mean reversion for stock returns (17 had no opinion and 49 did not believe). "
Among those economists who believe mean-reversion exists, a common half-life is believed to be about 17 years. The longer the half-life, the weaker the effect.

This is an important question for investors because, if stock returns do mean-revert in the long run then stocks are a little less volatile on an annualized basis than a random walk would imply.

As retirees, we have to ask some follow-up questions beyond whether stock returns mean-revert. Does mean reversion equate to less risk? If we believe they do mean-revert, what impact would that process have on retirement plans? How would its impact compare to other factors of retirement planning? How should a retiree bet on mean reversion?

Let's look at the big question first. Do stock returns exhibit long-term mean reversion? Despite extensive research for decades, there is no consensus among economists.

Daniel Mayost of the Office of the Superintendent of Financial Institutions Canada wrote a nice review[1] of the seminal research on the topic in which he concludes,
"The claim that equity returns revert to the mean over the long term is not completely unfounded, and cannot be dismissed out of hand. However, there is at least as much evidence to refute this claim as there is to support it, and there is certainly no consensus answer within the economics profession."
Well said. So, a definite "maybe."

Despite the lack of consensus, many stock traders have developed strategies to attempt to profit from mean reversion of equity returns. Do the strategies work? They probably do, sometimes, if for no other reason than because nearly all strategies will work sometimes.

James Davis, VP of Research at Dimensional, studied the prospects for trading strategies and found that "Evidence of mean reversion is weak, and 780 simulated trading strategies show very limited evidence of reliably positive abnormal returns [profits]."[2]

If we assume that equity returns do mean-revert, how would that impact a retirement plan?

Many have the impression that the mean-reversion "spring" only pushes below-average returns back up toward the underlying average after a market decline. If you read my explanation above carefully, however, you will note that it would also push higher-than-average returns back down toward the average in the future.

That means that long-term mean-reversion might help or hurt retirement finances depending on initial conditions. When returns have been low for a long time, we would expect mean-reversion to slowly lift returns in the future back toward a growth trend line. But if they have been high for a long time, we should expect it to slowly push them lower toward that trend line. It would help when we're below the line and hurt when we're above it, keeping in mind that we don't really know where the line is or, more importantly, where it will be. (In the example below, the red line was added by the author.)

  Created at MacroTrends
Commenting on the CAPE 10 equity valuation measure's level of 34, Larry Swedroe recently wrote[3],
"The concern about future returns is justified by the fact that, while the academic research shows valuations are an extremely poor forecaster of stock returns in the short term, they are the best predictor of long-term returns. A CAPE 10 of 34 translates into a real-return forecast for U.S. stocks of just less than 3%. Add in 2 percentage points for expected inflation and you get a nominal return of about 5%, half the size of the historical return."
If the market is currently highly valued, as the CAPE 10 seems to suggest, mean-reversion implies that future returns are more likely to trend downward back to the mean. So, presently, mean reversion suggests less annualized uncertainty (risk) about an expected return that is likely to be smaller — less risk but a lower expected return. Mean-reversion isn't always a winner.

The popularity of the concept of stock risk declining with time grew with Jeremy Siegel's Stocks for the Long Run[4]. Siegel noted that over long periods of time, stocks do seem to be safer than a random walk would imply.

Economist, Zvi Bodie argues vehemently that stocks are risky no matter how long we hold them. He demonstrates with the following charts that the annual compound risk measured by variance of returns does, in fact, decline with time, as statistics predicts.

But Bodie argues that annual volatility is less a concern for retirees than the uncertainty of terminal portfolio values, which continues to increase with time.

Bodie further argues that if stocks become safer with longer holding times, then the cost of insuring against a loss should also decline. We can insure against stock losses by purchasing a put option but puts become more expensive as their expiration date extends into the future, not cheaper.

Bodie and Siegel are brilliant economists and each score a point or two, but like the broader population of economists, they ultimately disagree. (Here is a transcript of a fun debate between Bodie and Siegel on the topic.[5])

You can also find papers that argue that one or the other's argument is flawed. These aren't arguments about the existence of mean reversion, however. They're arguments about the quality of the arguments about the existence of mean reversion in equity returns. You can chase the issue all over the Internet and you will always end up with "there is some evidence it exists." The problem is that we have too little historical data to argue with any certainty.

There is also a behavioral aspect that could affect retirement plans. Retirees who choose to believe that stocks get safer with holding time might choose a higher equity allocation with little actual evidence to support that decision.

Mean reversion and retirement plans — don't be so sure.
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Next, let's consider how mean reversion of equity prices might impact retirement plans compared to other factors of retirement planning.

Retirement plans entail massive uncertainty. The greatest risk is longevity, in that nearly everyone could fund a one-year retirement but far fewer of us could fund one of thirty-five years. I'd rank expense risk second, as a catastrophic expense would destroy most plans. Market returns are extremely unpredictable, as are interest rates but, of course, that's only important to retirees heavily dependent upon stock investments for retirement income.

The amount of retirement risk explained by long-term mean reversion would likely be quite small compared to these. I've read postings from other researchers who played around with mean reversion in their retirement models until they realized that any risk-reducing effects were swamped by the huge remaining retirement risks. That's one of the reasons I don't bother modeling long-term mean reversion — along with the fact that I don't know if it exists or how powerful it might be, so I'm not sure what I would model. (Regardless of what you've read, Monte Carlo models can be built with mean-reverting processes.)

My final question is "how should a retiree bet on mean reversion of equity prices?"

Mayost addresses this point for the bank when he states,
"Given the large reduction in segregated fund guarantee reserve and capital requirements that would result from assuming mean reversion in equity returns, it would not be prudent for OSFI to approve equity return models that are based on the assumption of mean reversion without strong evidence that mean reversion actually occurs in the market and is likely to continue in the future. The current state of research does not provide such evidence to a sufficiently high degree of certainty.
That's a long way of saying, "No one seems to know but it would be imprudent to bet that equity returns mean-revert without stronger evidence."

I believe retirement planners have little to gain by betting that mean reversion exists unless and until research resolves the issue. (The issue has been around for a long time and it could be a thousand years before we have enough data.) There is significantly more downside to incorrectly guessing there is less risk than there is to incorrectly guessing there is more risk.

To summarize for those of you planning retirement who aren't interested in reading dozens of papers on long-term mean reversion of equity prices that come to significantly different conclusions with no consensus, I suggest the following.

As DeNiro said in Donnie Brasco, "Fuggedaboutit."

Do stocks get safer the longer you own them? There is some evidence that they might and some evidence that they don't. Do you want to bet your retirement on that?

As a retirement planner, I care far less about whether or not equity returns may mean-revert over a couple of decades than I care about how mean reversion, whether or not it exists, might affect my retirement plan. In other words, is it something I need to worry about?

There is no consensus among economists regarding how powerful mean-reversion of equity returns might be or if it even exists.  The only thing you can know for sure is that whether you believe stocks mean-revert or not, there is a really good argument that you are wrong.

(Note the lack of consensus among economists compared to the number of retirees and advisors who claim to know with certainty that it does exist.)

The evidence supporting mean-reversion of equity prices is somewhat weak, as the mean-reversion force also appears to be.

It is debatable (literally[5]) whether mean-reverting equity prices would actually mean that stocks get safer with holding time. It depends on whether you define "safer" as less annualized portfolio volatility or as a narrower range of possible wealth-generation.

Whether or not stocks get a little safer on an annualized basis the longer you hold them is unlikely to have a large impact on your retirement plan. Your plan contains far more risk than mean-reversion would explain and those risks are where you should spend your planning time.

There are actually two larger issues here. First is how much of our planning efforts we should spend on factors that will probably have little impact on our retirement plans. And second, there is a real risk in feeling "certain" about assumptions that actually have limited supporting evidence.

The most important thing I have learned from two decades of studying retirement finance is how little I know for certain. Unfortunately, overconfidence extends to many retirement planning assumptions beyond the nature of mean reversion of equity returns.

I once had a conversation with a healthy 60-year old client about claiming Social Security benefits and he assured me with great confidence that he would never see age 80.


[1] Evidence for Mean Reversion in Equity Prices, Mayost, D., 2012.

[2] Mean Reversion in the Dimensions of Expected Stock Returns, James Davis, Dimensional.

[3] Seeing Valuations Clearly, Larry Swedroe.

[4] Stocks for the Long Run, Jeremy Siegel.

[5] The Great Debate, Siegel and Bodie.

[6] Simulation of Long-Term Stock Returns: Fat-Tails and Mean Reversion, Rowland Davis.

Friday, October 19, 2018

HITBLITS: Charles Barkley and Saving for Retirement

"I'm a HITBLIT", Charles Barkley, in the waning days of his NBA career, told his interviewer.

"A HITBLIT?" the reporter asked.

"Yes, that stands for had it. . . but lost it", the aging Round Mound of Rebound explained with a laugh.

Having it and losing it seems to be heavy on the minds of many near-retirees who see record equity prices and who have lived long enough to know that bull markets don't last forever. They can end very badly. Severe bear markets near a retirement date can delay retirement plans and even permanently lower a standard of living in retirement.

Robert Powell recently wrote at The Street[1] regarding a subscriber who asked, "What is the best thing to do with a 401(k) if the market keeps crashing or we go into another recession when I only have a few more years to go before retiring? I need to minimize losses at this point."

Two things we can be relatively sure about are that the market will keep crashing and that there will be another recession. Bear markets often overlap with recessions but not always, as the following chart from Capital Economics[4] shows.

Powell responded to the question with answers from a number of retirement advisers (including yours truly). It's a nice piece and you can read it at the link below but I can distill the essence of the advice.

Don't gamble more than you can afford to lose.

"Once you win the game, stop playing", William Bernstein advised about saving for retirement. I don't believe, as some have suggested, that he means that you should stop investing in stocks once you've funded retirement. I think he's making a more subtle point about utility, a measure of the satisfaction we receive from consuming goods and services.

If you have an income of $1,000 and you receive an additional $100, the additional consumption that a hundred bucks enables would probably make you happy. It would probably make you much happier than if you had an income of $100,000 and received an extra $100. The "utility" of an extra $100 becomes less as income grows.

There is a similar utility issue when we consider how much to invest in the stock market as we approach retirement because investing more means we might earn more but also that we might lose precious capital. For most of us, losing capital after we have "won the game" would generate a lot more pain than increasing our savings by that same amount would generate happiness.

Earlier in our careers, the scenario is reversed. We don't have much financial capital to lose and we have decades to make up for any losses. We have lots of "human capital", the ability to earn money from our labor. The losses are less painful because we expect to win in the long run and we don't need the money for decades. We can better afford losses because we have lots of two key ingredients: time and the ability to work. Both diminish with age.

The solution is to gradually shift the game away from growth of capital and toward preservation of capital, though not entirely. We'll probably still need some growth. After decades of saving for retirement, many of us have difficulty making that shift from accumulation to spending. It's a different game.

Sadly, I have much more experience with HITBLITS than most. During the Tech Crash, I personally knew dozens of 20- and 30-somethings who had amassed 5 or 10 millions dollars or more in tech stock options but refused to sell them and rode them all the way back to zero. It happened quickly. From zero to millions to HITBLIT in about ten years. The crash was over in months.

A close friend in his early 60s sat atop $4M of vested MCI stock options only to see his boss, Bernie Ebbers, convicted of the largest accounting fraud in U.S. history, at least until a different Bernie stole that record. At least the 30-somethings had a few decades to recover, though they were very unlikely to see such wealth again as they once had. My friend had a handful of working years left and a bankrupt employer.

Just after the Great Recession, the national press was replete with stories of near-retirees who were looking at postponing retirement for years in hopes of getting back to where they were in early 2007 with no certainty of ever reattaining that level of wealth. They had simply had too much equity exposure.

These experiences probably left me with a different perspective than most have regarding the need to protect your savings when you have little time left to recover from losing them.

HITBLITS: Charles Barkley and saving for retirement.
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Why not just accept bear market losses with the confidence that a higher equity allocation will help you recover quickly? That works fine in early stages of the accumulation phase but the calculus is quite different as one approaches retirement.

Younger households still have careers that let them buy more equities at bargain prices after a crash. As a result, their portfolios will recover even faster than the market. Near-retirees, on the other hand, have far less time to recover and most of their wealth growth comes from their base of capital and not new savings.

Not long ago, a reader pointed out to me that when dividends are included, the U.S. market recovered from the Great Depression relatively quickly. There are some markets that have never recovered, though, and Japan's recovery has exceeded 20 years and counting.

But, my reply to the reader was "you are not that guy." Someone beginning a career right after the Great Depression would probably have had little to lose in the market crash but years to work and save money to invest in a recovering market. By investing periodically in stocks, his portfolio would have grown even faster than the market.

For someone retiring around the time of the Great Depression, however, the crash would have devastated her savings just when she needed to begin spending them. Instead of adding new investments like the early-career guy, she would be spending from a depleted portfolio. Her portfolio would recover much more slowly than the market and, in fact, would likely never recover. Large market losses in our youth are far less dangerous than losses when we approach retirement.

I often receive comments saying something like, "but the market recovered in just 5 years after the Great Recession!" True, but if you were paying bills for those 5 years by selling investments, your portfolio didn't.

I think anxiety is an excellent metric for asset allocation. Bernstein agrees. In The Intelligent Asset Allocator[2], he recommends first allocating one's portfolio between stocks and bonds based on the greatest bear market loss we believe we could stomach without being tempted to bail out at market-bottom prices.

There are other factors to consider beyond the equity allocation of our portfolio, including total wealth and our floor of safe (not market-based) investments.

Very wealthy households may spend only a small percentage from their portfolios each year. They can afford to take more equity risk with limited risk to their standard of living. They have the luxury of riding out market declines and waiting for the recovery. If you only spend a percent or so of your investment portfolio each year, a bear market shouldn't bring on an anxiety attack.

Households without large savings but with significant safe income from Social Security benefits, annuities and pensions also have a more secure standard of living. I've helped clients whose safe income could completely cover their standard of living. They, too, have the luxury of riding out market declines and waiting for the recovery.

Retirees and near-retirees who lose sleep over the next bear market are likely to be largely dependent upon market returns to fund their desired standard of living. The problem may not be their portfolio's exposure to equity risk but a lack of income from non-market sources.

For these households, purchasing annuities can ensure more of their standard of living and allow them to take more risk — and potentially enjoy more gains — with a smaller equity portfolio.

Sleep loss and anxiety attacks aren't the only symptoms of a retirement plan that might not be right for you. Frequently checking your portfolio balance or regularly checking market levels can also be a red flag.

I check my portfolio balance (or more often my net worth) once or twice a year. I have felt the need to rebalance perhaps three times in thirteen years of retirement. Admittedly, I check more often in a severe bear market (I'm not immune to anxiety) and I suspect most retirees check more frequently than I do. Nonetheless, if you feel the need to check on your stocks more than monthly (or anxiously await your daily dose of Mad Money), it's probably worthwhile asking yourself why.

If your current retirement plan has you on edge like The Street subscriber, then your concern is likely more about losing your standard of living than seeing your savings balance abruptly (and hopefully temporarily) decline. Maybe you have too much equity exposure for your risk tolerance and risk capacity but maybe your plan is too dependent on market returns.

One of my favorite quotes about retirement planning is a comment from Michael Finke to financial advisors:
"Your goal is to make [clients] as happy as they can be in retirement and it may make them happier to have less anxiety about their investment portfolio.[3]
If your retirement plan makes you overly anxious about bear markets, maybe you need a plan that makes you happier.


[1] What to Do With Your Retirement Portfolio in This Volatile Market, The Street.

[2] The Intelligent Asset Allocator, William F. Bernstein, Chapter 8.

[3] What Makes Us Happy, The Retirement Cafe.

[4] Bear Markets and Recessions, Capital Economics via Business Insider.