Black swans & the ‘10 best days’ myth: Can investors prepare for market outliers?

Black swans & the ‘10 best days’ myth: Can investors prepare for market outliers?

by | Jan 4, 2017 | UpClose |

How much effect do market outliers have on long-term performance? Can the investor prepare for these anomalies, or are they truly ‘black swans’ that cannot be managed?

Editor’s note: Many thanks to Meb Faber and his associate, Prabhat Dalmia, for permission to publish an abbreviated version of this paper, “Where the Black Swans Hide & The 10 Best Days Myth,” which was first published in August 2011. Thanks also to the Market Technician’s Association (MTA), which published this paper in July 2016. A full version of the paper can be downloaded here.

Mr. Faber’s analysis addresses several assumptions behind the “missing the 10-best-days” argument, which, as he says, is “often proffered by advocates of buy-and-hold investing.” He also examines the issues of how market “outliers tend to cluster and the majority of both good and bad outliers occur once markets have already been declining.” Mr. Faber advocates “that investors attempt to avoid declining markets where most of the volatility lies” and concludes that “market timing and risk management is indeed possible, and beneficial, to the investor.”

Nassim Taleb, author of “Fooled by Randomness” and “The Black Swan,” popularized the concept of the black swan theory—namely, the occurrence of utterly unforeseeable events that are thought of as not being possible based on previous experiences.Taleb defines a black swan as an outlier outside the realm of regular expectations because nothing in the past can convincingly point to its occurrence. The event carries an extreme impact and is often “explained” after the fact, giving the impression that it is explainable and could have been predicted.

Many market commentators have latched on to this term to describe all financial market events. However, the existence of large outlier events known as “fat-tailed distributions” in financial market returns has been well-documented for more than 40 years (see Benoit Mandelbrot’s “The Variation of Certain Speculative Prices” and Eugene Fama’s “The Behavior of Stock-Market Prices”). While the financial media have only recently revisited the fat-tail concept (due largely to the occurrence of the Internet bust in 2000–2003, as well as the global financial meltdown in 2008 and 2009), it has been a thoroughly studied field in finance over the past several decades.

Investors should realize that normal market returns are extreme. Individuals that continue to believe in the Gaussian (bell-shaped) distribution, or ignore empirical results, will continue to be surprised by future events. Roughly 40% of all yearly returns in U.S. stocks are greater than 10% or less than -10%. Bear markets are common, and markets can and do decline from 50% to 100%.

Financial market return distributions are similar to fractal systems that follow a power-law distribution (which is useful in describing events such as earthquakes and volcanic eruptions). Below is a chart from the book “The Failure of Risk Management” by Douglas Hubbard, which illustrates the inability of the Gaussian models to account for large outlier moves in financial markets. In a normal-distribution world, a 5% decline in the Dow in a single trading day should not have happened in the past 100 years. In reality, it has happened nearly 100 times.


Unfortunately, many investors have come to the conclusion that rare events are impossible to predict, and therefore, there is nothing to do other than buy and hold their investments and wait out any negative outliers. However, this explanation simply rids the investor (advisor) of any responsibility. The fatalistic attitude becomes “it was a black swan; it’s not my fault!”

In this article, we examine market outliers, their effects, and, more importantly, when they occur and if the investor can do anything to protect against them.

Market outliers: The ‘10 best days’ myth

We begin our examination by taking a look at market outliers in the U.S. stock market back to 1928.

One of the most common rhetorical bulwarks in the defense of buy-and-hold investing is to demonstrate the effects of missing the best 10 days in the market and how that would affect the compounded return to investors. This is perhaps one of the most misleading statistics in our profession (another being the Brinson asset-allocation study misquote). A number of academic papers have examined the effects of missing both the 10 best and the 10 worst days (two good ones are Paul Gire’s “Missing the Ten Best,” published in the Journal of Financial Planning, and Richard Ahrens’ “Missing the 10 Best Days”).

In Table 1, we examine the S&P 500 (and the broad market predecessor) from 1928 to 2010. We use price history only, as dividends will not have a meaningful impact on the daily return data.


What about the outlier returns? Table 2 shows the best and worst 1% of all days, which equates to only about two or three days per year.


One can expect these days to occur a handful of times every year since 1928. Much to the displeasure of the fear-mongering media, -4% and +4% days are fairly regular.

To help us really examine the blackest of swans, Table 3 shows the best and worst 0.1% of all days. They occur, on average, only once every few years.


Days of -8% and +8% are fairly rare, as are the -20% and +16% days. Exactly how big of an impact do these outliers have on performance? Massive. Table 4 shows the annualized returns if the investor missed some of the best and worst days. If you missed the best 1% of all days, your return gets crushed from 4.86% down to -7.08% per annum. However, the converse is also true: if you miss the worst 1% of returns, your returns explode to 19.09% a year. And take special note that if you miss both the best and worst 1% of days, your return is higher than buy and hold.


Most analysts, unfortunately, stop here and throw up their hands. They proclaim buy-and-hold investing to be the only way to ensure being in the market for these best days. Because these events are so rare, and because they have such as massive impact, there is an infinitesimally small chance of predicting when they will occur, and therefore the effort is useless. They take the ball all the way down to the five-yard line but stop there.

What are they missing?

The human element

Markets are a collection of humans, and, therefore, a collection of human emotions. Greed, fear, jealousy, pride, and envy all manifest themselves to the fullest in capital markets.

When you are making money, you are thinking about the new car you are going to buy, how smart you are (and how much smarter you are than your neighbor), the vacation you are going to take, and the (second, third, fourth) house you are going to buy. The part of the brain that is firing nonstop here is the same region that gets stimulated by cocaine or morphine.

However, when you are losing money, you are probably not opening your account statements. Instead, you are thinking about how dumb you are (and how stupid you were to listen to your neighbor) and how you are going to pay for that second house. Even thinking about investing is likely to elicit feelings of revulsion. The brain processes portfolio losses in the same region that is stimulated by the flight response. (For more in-depth discussions on behavioral biases, please consult some of the work of the great MIT professor, Andrew Lo.)

Table 5 examines the returns (and, more importantly, the volatility) when the market is appreciating versus declining (defined as above or below the 200-day simple moving average, or SMA). Based on this data, and that of Table 6, it is little wonder that the volatility found in declining markets can have such a profound impact on investors’ emotional responses.


(To be read: 69.59% of 1% “worst days” occur in a declining market, 78.34% of 1% “best days” also occur in declining markets.)

What about the outliers—where do they occur? As Table 5 shows, the vast majority (roughly 60%–80%) of the best and worst days occur after the market has already started declining. The simple reason is that markets are more volatile when they are declining, and when the really volatile events and days occur, they tend to cluster together.

Our central argument is that returns improve and volatility is reduced when an investor is invested in uptrending markets, thus avoiding the volatility and clustering of best and worst days inherent in declining markets. As you can see in Table 6, in declining markets, returns are much lower and volatility is much higher.


Benoit Mandelbrot provides an insightful passage on volatility clustering and timing in his book “The Misbehavior of Markets”:

“What matters is the particular, not the average. Some of the most successful investors are those who did, in fact, get the timing right.”

This effect also plays out on the monthly time frame as well. For a look at other markets, including real estate, bonds, and foreign stocks, on the monthly time frame back to 1972, you can view a blog post here titled “Your Irrational Brain.”


For those investors pondering how they can attempt to avoid these highly volatile periods in markets, we invite you to download a few of our other white papers : “A Quantitative Approach To Tactical Asset Allocation” and “Relative Strength Strategies for Investing.”

Astute market analysts must also realize the drawbacks and downsides of any indicator or investment approach. In the case of a trend-following approach, there are two main drawbacks. First, in trendless markets, whipsaws can occur that have negative effects on the portfolio. Second, and perhaps more important, a trend-following approach does not guarantee the investor will miss a black swan event in an uptrend. A very sharp move against the trend will not allow the investor or model time to react and protect against such a move. Investors looking for protection against this sort of event can use derivatives such as options to protect the portfolio when fully invested (so-called tail-risk insurance), or consequently, to gain long exposure when mostly in cash and bonds (risk of missing out). This process could be a net cost (insurance) to the portfolio.

That is the point of risk management: understanding and trying to account for as many risks as you can.

Our broad summary points from this analysis?

  1. The stock market historically has gone up about two-thirds of the time.
  2. All of the stock market return occurs when the market is already uptrending.
  3. The volatility is much higher when the market is declining.
  4. Most of the best and worst days occur when the market is already declining. Reason: see #3. Markets are much riskier than models that assume normal distributions can be used to predict.
  5. The reason markets are more volatile when declining is because investors use a different part of their brain when making money than when losing money.

The opinions expressed in this article are those of the author and do not necessarily represent the views of Hilbert Financial Group. These opinions are presented for educational purposes only.

Source: Black swan events and the ‘10 best days’ myth

Buy and Fold

Buy and fold

by | Mar 10, 2016 | UpClose |

The only investment approach investors should consider is one they will actually follow.

Millions of Americans follow what has become traditional advice to “buy and hold.” This approach might be best summarized by John Bogle, founder of The Vanguard Group: “Get out of the casino, own corporate America, and hold it forever.”The basic idea of buy and hold is that you can’t time the market. Investing is a zero-sum game, so if you try to time the market, the only party that wins is the one collecting the commissions (the casino dealer/croupier in Bogle’s analogy).The most commonly cited evidence about investor inability to time the market is the DALBAR Quantitative Study of Investor Behavior (QSIB). The key statistic from the 2014 QSIB was quite remarkable, though not a surprise to advisors who have witnessed investor behavior firsthand:

The 20-year annualized S&P return was 9.85%, while the 20-year annualized return for the average equity mutual fund investor was only 5.19%—a gap of 4.66 percentage points.

Put more plainly, the average equity mutual fund investor underperformed the broad equity index by 4.66 percentage points annually over the last 20 years. 4.66! Over that lengthy period of time, and especially when compounding is factored in, that represents a tremendous difference in the ending value of a portfolio. These investors are giving up (compared to the “market return”) close to $380,000 in gains for each $100,000 of principal (see chart).

The buy-and-holders cite this as evidence that misguided attempts at timing the market (buying those funds high and selling them low) is the main explanation for poor returns. In theory, it is difficult, maybe even impossible, to argue with buy and hold. The problem comes when we all wake up and realize investors/clients do not live in a theoretical world and they do not retire on theoretical money.

To summarize, the buy-and-holders believe that large-scale underperformance comes from investors not using buy and hold. I have a slightly different hypothesis: Investors “buy in” to buy and hold when the case looks the best—market tops—and they “fold” (give up) on buy and hold when it looks worst—market bottoms.

How low would you go?

What if a client found out that their current portfolio was 300% riskier than he or she was prepared to tolerate? At our firm, we see it every day when analyzing the holdings of a new client or prospect. Besides questions of knowledge, experience, time horizon, liquidity needs, and so on, the most important risk-tolerance question we ask is this: “You are investing $XXX dollars with us today. What is the lowest balance you could handle before you would fire us or go to cash?”Clients often answer that a 15% decline in portfolio value would be a tipping point, but the answers can fall anywhere from 0% to 50%. This is not unexpected, given our relatively large sample of clients with unique goals, experience, sophistication, and life situations.

When we show an equity investor with a theoretical maximum loss tolerance of 15% that the maximum drawdown of the S&P 500 is well over 50%, and can exceed 20% on a fairly regular cyclical basis, they’re often shocked. No wonder they have difficulty being disciplined investors—they were never mentally prepared to withstand a 50% loss. They aren’t trying to “time” the markets, per se, when they sell at the bottom—they’re panicking! They’re throwing in the towel on the entire idea of buy and hold.

If you know ahead of time that you will panic when the market enters bear territory, why would you commit to a strategy that historically has lost twice your tolerance (or more) every five to seven years?

Don’t blame Bogle

Mr. Bogle is, of course, 100% aware of the past. In a recent CNBC interview, he said an investor should be prepared for two 50% drawdowns in the next ten years. Many people mistook this for a “call” or prediction. It wasn’t. It was Mr. Bogle stating historic fact, that markets go up and markets go down, and if you are going to buy and hold, you should fully expect the future to at least resemble the past.To reiterate, I believe when investors buy at the top, they are “buying” buy and hold as a concept or strategy. Conversely, when investors sell at the bottom, they are throwing in the towel on an idea they were never emotionally prepared to follow in the first place.

When investors buy and hold, they often don’t consider things like drawdown, or they don’t anticipate how they may respond during a bear market and premeditate their actions. Most important, their expectations do not match historical results.How do you reduce that drawdown to something in line with a level of risk they can actually handle? In my experience there are only two ways to do it:

  1. True diversification.
  2. Dynamic management.

For the sake of brevity, we define true diversification across three levels:

  1. Multiple assets. (For example, don’t hold just one company, hold many. This is what many people think of when discussing “traditional” diversification.)
  2. Multiple asset classes. (For example, equities, fixed income, commodities, currencies, private equity, and real estate.)
  3. Multiple strategies. (Ideally, managers or strategies with varying approaches/strategies.)

Question what you read about “active managers”

I can just hear the media’s generalization now, “Managers?! 80% of managers fail to outperform the market!” (Before we get too far, if anyone ever tells you they know how to buy at the exact bottom and sell at the exact top, politely excuse yourself, grab your wallet, and run.) But, back to the “80% of managers” adage—I have several responses to that notion.First, I’ve never found a reputable study that proves that point the way it is commonly understood.

Second, I have found studies that say 80% of active mutual funds underperform their benchmarks, but here’s the problem: Mutual funds are not active (by our definition). Many have an investment mandate that requires them to stay fully invested and not deviate from their stated asset classes and allocations. (How active is a manager when they have to stay invested in one asset class or sector, and stay fully invested, regardless of conditions? When you are required to stay invested in a single asset class, can only diversify within that single class, but yet charge a higher fee than a passive benchmark that does the exact same thing, underperformance is the only logical outcome.)

The final piece to the response is the most important. Our clients are not looking to outperform the market. Rather, they are seeking to outperform on a risk-adjusted basis.

For example, consider two portfolios: Portfolio A has a compound annual return of 8% over the past 10 years, with a maximum loss of 15%. Portfolio B has a compound annual return of 10%, with a maximum loss of 55%. Which one is “better?” (“Better” is a very subjective term, as each person’s situation is unique, but for discussion purposes, I’ll use the word.)

Buy-and-holders would say the second. Annual performance that is 2% greater is enormous over ten years. “Brace yourself to deal with the 55% drawdown and stay patient,” they say.

Our clients would select the first. Getting an 8% return in a portfolio strategy you can handle long term is much more effective than “buying” portfolio B at the top and “folding” on portfolio B at the bottom (which, instead of those 10% returns, might lead to flat performance or even a loss).

If your clients are fine with sustaining a 50% loss every four to seven years to guarantee they never fall far short of long-term “market performance,” they should feel free to go for a buy-and-hold strategy. (This is not tongue in cheek at all.) If they are more focused on minimizing expenses and achieving raw returns rather than risk-adjusted returns, then it might be just fine for them over a very long period of time (assuming that the sequence of returns will not be an issue).

However, if they are anything like the hundreds of clients we’ve worked with over the years, the buy-and-hold strategy may include risk parameters far outside their tolerance. It remains my humble opinion that advisors should discourage clients from buying into a strategy they won’t be able to maintain for the long haul. Buy and hold, unfortunately, too often turns into buy and fold.

Tony Hellenbrand, RICP, is a partner at Fox River Capital, a registered investment advisor in the state of Wisconsin. For more information and full disclosures, please visit

Source: Buy and fold | Proactive Advisor Magazine

10 Reasons Investors Need Active Management in Retirement

Without employment earnings to offset portfolio losses, protecting portfolio value is essential for retirees. Do so with an active management portfolio!

by Linda Ferentchak | Jun 8, 2016


1. The traditional age-adjusted portfolio isn’t working

Traditional asset allocation maintains that as individuals age and approach retirement, their investment portfolios need to reduce exposure to high-risk assets and focus on capital preservation through investments such as more conservative bonds. A typical portfolio recommendation for an investor over the age of 55 might look like this:


Based on the Barclays U.S. Aggregate Bond Index, this pegs the majority of the portfolio at approximately a 2.1% annual yield, just below recent inflation estimates for the Consumer Price Index (CPI) around 2.2%. Add in taxes, and the equity and real estate portions of the portfolio have to provide substantial outperformance to offset both the loss in buying power of a bond-heavy portfolio and to provide real returns.


2. Bond risk is greatly underestimated

There can be no guarantee that a high bond allocation will preserve the value of the portfolio. Bonds face many of the same risks as equity investments, including the financial health of the issuer—default risk—and market risk. But they are particularly vulnerable to interest-rate and inflation risks. Since bonds typically offer a fixed interest rate (TIPs are one exception), increases in market interest rates lower the value of the bond, while increased inflation will whittle away the value of the return.


3. Traditional age-adjusted portfolios lack an inflation hedge

Inflation has been remarkably mild in recent years, but there is no guarantee it will continue at or below 2%. The U.S. money supply, as measured by M1, has increased since the credit crisis, generally outpacing domestic economic growth. Through the increased money supply, the Federal Reserve has deliberately sought increased inflation. At some point their wish will be more fully granted. The maturity value of a $20,000 bond investment 10 years in the future is still $20,000 regardless of whether or not it will buy an equivalent amount of goods or services.


4. Correlations break down in severe market declines

Traditional market theory maintains that bond values and stock prices are uncorrelated—they move in opposing directions. When stocks decline, bonds should increase in value, maintaining the overall value of a diversified portfolio. Studies have shown that in times of market uncertainty, relationships tend to break down with higher-risk bonds most vulnerable to losses. In the 2007–2009 market decline, asset classes became more correlated, moving down together.



5. Retirees need equities for higher returns, but may not have time to recover from a severe bear market

Buy-and-hold investment approaches rely on the market’s long-term upward bias to recover from a bear market. But the recovery is neither guaranteed nor predictable. It took close to five years for most major market indexes to recover from the 2000–2002 market decline and over three years to recover from 2008–2009’s worst levels. History shows that, on average, a new bear market begins every 5.5 years, with an average duration of 18.1 months. Omitting the distortion of the 1929 crash, the average time lost making up bear markets is 3.6 years. And that calculation merely measures the time spent for indexes to return to breakeven from the lowest point in a bear market—recapturing past market highs can often take even longer.


6. Active management offers more effective risk management than a bond-centric approach

The difficulty with using bonds for risk management is that investors forego the opportunity to participate in equity-market gains while remaining vulnerable to bond-market losses. 2013 was a good example of bond-market risk. The average core bond fund (at least 85% of assets in investment-grade bonds) fell 2% in 2013, including reinvested interest. The S&P 500 Index gained 31.9%, including reinvested dividends. The challenge is to capture equity performance for a retiree’s portfolio, but without the potential for losses such as the 37% loss that the S&P 500 experienced in 2008. Active management, with its focus on minimizing losses and participating in the majority of the market’s trend, is one approach to do so. Active management also has the potential to reduce the risk of bond investments, with the ability to utilize long/short bond funds and other tactics.


7. Active management doesn’t have to be perfect to work

The common criticism of active management is the statement that no one has ever been able to perfectly predict the market. But active management isn’t based on predictions, and doesn’t have to be perfect to work. The reason is the mathematics of gains and losses. It doesn’t take a 37% gain to recover from a 37% loss. It takes a 59% gain. Reduce the loss and an investor increases the leverage on the upside. With its goal of avoiding the majority of the market’s losses and capturing the majority of gains, active management can benefit from the leverage of having more capital to invest when the market cycle turns positive again.


8. There’s more than one way to actively manage a portfolio

Active management encompasses a wide spectrum of investment strategies and approaches. As the availability of data, computing power, investment alternatives, and market intelligence expands, so, too, do the active management capabilities. The right approach is the one that makes sense for the investor and the manager. Often that means a quite diverse blend of strategies and asset classes, all of which can benefit under the active management umbrella.


9. Active management accommodates behavioral finance biases

Faced with market declines or market gains, people tend to approach investing in predictable—although not necessarily logical—ways. These reactions tend to be counterproductive to long-term portfolio growth, and it is well-documented how individual investors have historically underperformed broad market indexes when left to their own emotion-driven decisions. Active management adds discipline, through professional money management, to the equation, resulting in the increased peace of mind so important to retirees. And this can benefit both advisors and their retired clients, with active management’s smoothing of returns over time facilitating the decision by clients to participate in the equity markets.


10. Market bubbles are inevitable

Exploiting their opportunity and limiting their damage requires active management. When it comes to pursuing exceptional portfolio gains, there’s nothing better than a good market bubble. But what goes up inevitably comes down. One of the best quotes on that topic comes from market analyst John Mauldin, credited to one of his mentors: “Mr. Market is a vicious sadist. He will do whatever it takes to create the greatest amount of pain for the largest number of investors.” Active management is a tool for participating in the “bubble” with eyes wide open, while always keeping one eye on the exit door.



It’s hard to calculate how long today’s retirees might live, but the one thing they want to know is that their money will not run out before they do. Answering in the affirmative requires combining capital preservation with the opportunity for capital appreciation. While no investor or investment management style can predict the future, everyone requires the flexibility to respond to opportunity. Active management can offer that opportunity.


Source: 10 reasons for an active management portfolio | Proactive Advisor Magazine