Monday, March 22, 2010

Why Now Is Not the Time for Buy and Hold

The most common question I get from clients is, 'Is now a good time to invest in stocks?' What clients are really asking is, 'If I invest now, will stocks take me where I want to go, on my timeline?' Most advisors answer this question by referring to long-term average returns. Some reference the last 20 years, others the last 30 years, and a small few know average returns over the last 100 years or more. Advisors quote these average returns as though investors are actually likely to achieve this growth regardless of when they invest.

It Matters When You Invest

In reality, the timing of your decision to put your money to work in the stock market has an enormous impact on your likely future returns. For example, if you chose to invest your money in stocks in September of 1929, your portfolio would have achieved growth of -2.34% per year over the next decade. In contrast, if you invested in July of 1932, your portfolio would have grown at over 8% per year over the next 10 years. Investing in August 1972 would have shown investors -3% a year over the next decade, but putting your money to work exactly 10 years later would have netted an investor 10.6% per year after inflation!

Given that timing matters, one is left to wonder if there is something about those dates that would have given investors a clue about what to expect from stocks over the following 10 year period. It turns out that by analyzing Yale Professor Robert Shiller's publicly available database of stock market information going back to 1870, clear patterns emerge that can help investors set expectations about future returns. That's the good news. The bad news is that future returns from here are likely to leave buy and hold investors in the dust.

Are Markets Cheap or Expensive

Most investors are familiar with the commonly cited Price to Earnings Ratio, or PE ratio. This is simply the current price of a stock divided by its last year's earnings, and it is used frequently to describe , very loosely, whether a stock is cheap or expensive. Interestingly, though the PE ratio is the most commonly cited statistic in finance, it provides very little useful information when picking stocks. A stock with a high PE may be growing very quickly in a market with little competition, high margins and high barriers to entry, so that the price is justified. Alternatively, a low PE stock may be lagging its competitors in terms of growth or profitability, and so the low price is justified.

The same ratio can be used to describe the stock market in aggregate. The market's PE ratio is just the current level of the index divided by the combined earnings of all its constituent companies. However, when analyzing the stock market in aggregate it makes sense to adjust the ratio by using average stock market earnings over the past 10 years, adjusted for inflation, rather than just the previous year's earnings. This method was first proposed by Warren Buffet's mentor and value investment guru Benjamin Graham. He wanted a ratio that reflected the long-term trend of corporate earning potential in the economy, adjusted over one full business cycle. The Cyclically Adjusted PE, or CAPE, helps investors avoid the the misconception that markets are cheap just because the economy is at the peak in the current business cycle.

It turns out that, at the aggregate market level, the PE ratio does provide information that is useful to investors. Over time, investors are likely to receive above average returns by investing when markets are cheap (low PE), and below average returns by investing when markets are expensive (high PE). One can see from Chart 1. below that over the last 140 years, markets have traded in a PE range of about 5%(1921, 1932, 1982) through 45% (2000).

Chart 1.

Source: Robert Shiller

Do Cheap Markets Deliver Better Future Returns?

In Chart 2. below, one can clearly see the relationship between the PE of the market and future returns. Starting PE and future returns are inversely related, so low PE = high future returns and high PE = low future returns. In order to illustrate this relationship, I have inverted the PE ratio to show the market's earnings yield (10-year average earnings divided by current price), so the blue line on the following chart is the inverse of the blue line in Chart 1. When the market is expensive, the blue line in Chart 2. is closer to the bottom, not the top. The red line shows the returns to an investor who invested on each date over the subsequent 10-year period, after inflation and including dividends.

Chart 2.

Source: Robert Shiller, Butler|Philbrick & Associates

It is plain to the eye that the 10-year forward returns (red line) very closely track the market's long-term earnings yield ratio (red line). A cheap market (low PE, high earnings yield) usually results in high long-term returns, while an expensive market (high PE, low earnings yield), usually results in low long-term returns.

It is worth noting at this point that the predictive value of the CAPE ratio is less robust when markets are neither very cheap nor very expensive. For the purpose of the analysis below, we assume the market is cheap when it trades in the 1st quartile of all CAPE ratios over the 140 year time period; it is expensive when it trades in the 4th quartile. When the market is priced in the 2nd or 3rd quartiles, it is neither cheap nor expensive.

Chart 3. is a scatter plot of all monthly CAPE ratios and the corresponding future 10-year returns, for all months where the market is either cheap (1st quartile), or expensive (4th quartile). The chart also shows the best fit line for the plot, as well as the least-squares linear approximation formula and R-square value. I then calculated the model's expected future returns from the formula using the current market CAPE ratio (20.63). An R-square value above 0.5 suggests a very strong relationship, so the market's current CAPE ratio does an excellent job of explaining future returns.

Chart 3.

Source: Robert Shiller, Butler|Philbrick & Associates

Chart 4. attempts to illustrate the relationship between the market's CAPE ratio and future returns by showing the distributions of future returns for both cheap (1st quartile CAPE) and expensive (4th quartile CAPE) markets. You can see that the median 10-year real return to stocks when markets are cheap is 10.62% per year, while the return to stocks when markets are expensive is 3.77% per year. Chart 3. shows that the modeled return to stocks when markets are priced at a CAPE of 20.63 is approximately 4.64% per year.

Chart 4.

Source: Robert Shiller, Butler|Philbrick & Associates

Lower Expectations or Pursue Alternatives to Buy and Hold

Many advisors will argue that a 4.6% expected return may be poor, but it is much better than what an investor can expect from bonds or cash. On this basis, an investor should allocate a larger portion of his or her portfolio to stocks. While this logic may be sound if several other conditions are met, it is peripheral to the main conclusion of this analysis. It is helpful to think of the market in the same way that an insurance company thinks of a life insurance policy. Based on a large body of evidence, an insurance company computes the most probable lifespan of a smoker to be less than a non-smoker. All other things equal, a non-smoker has a very high likelihood of out-living a smoker, though any one smoker may live a long, healthy life. In the same way, an expensive market may deliver strong future returns, but the odds are stacked against it.

The primary take-away is that investors should set lower expectations for future returns from here, and build these lower returns into financial and retirement planning models. While most planning software uses future nominal returns of 8% per year (every year!), investors are unlikely to see these returns in practice, especially after fees.

Alternatively, accredited investors may wish to pursue alternative strategies that have demonstrated an ability to deliver robust real returns in good markets and bad. I will spend more time on these strategies going forward, but for an excellent example, look no further than last week's post.

Monday, March 15, 2010

A Cure for Investor Depression

The previous post hinted at a future piece on systematic trading. In this author's humble opinion, well tested systematic investment strategies are the antidote to the poison of expert predictions. These strategies embrace the probabilistic nature of investment markets by applying hard and fast rules for investment decisions based on actual empirical evidence. In other words, these systems do not rely on an elegant theory that is not supported by actual data (like Modern Portfolio Theory, CAPM, or the Efficient Markets Hypothesis), or on the confident views of market experts, but instead rely on rigorously tested systems developed from mountains of actual data. 

These systems demonstrate an ability to do well in bad and good markets across securities, asset classes, geographies, and time frames. But don't take it from me. Take it from one of the most experienced and successful systematic trading teams in Canada, Jason Russel and Nicholas Markos at Acorn Global Investments. See their recent paper below.

Acorn Investments - Systematic Trading

For more information about systematic trading or Acorn's systems, go to their home on the Web.

Smash that Crystal Ball

It's that time of year again.

Yep, the time of year when the major Bay Street and Wall Street firms, along with the major mutual fund companies, parade their gaggle of economists and strategists in front of every camera, microphone and scribbling print journalist in order to emboss their firm's logo on the impressionable minds of investors.

Eventually, the thinking goes, your current manager will have a poor year, or a poor twenty years, and you will inevitably start thinking about moving your hard-earned capital to another, more prospective wealth management group. If their firm has caught your attention over the years more often than other firms, the thinking goes, you are more likely to seek them out than their competition. 

This is one of the more common ways in which firms compete for your business.

They know from experience that you won't remember what their so-called 'expert' proclaimed on the news last year, or last month, about the shape of things to come. They know if doesn't matter what they say so much as the fact that they are out there, in the media, saying something.

But there is another, more insidious reason why each major firm has a variety of experts on staff loudly proclaiming their views year after year. The reason is simple: banks, mutual fund companies and investment firms make no money while clients are sitting in cash. Each time the investing public observes an expert loudly proclaiming that gold is going up, or interest rates are going up, or banks are going up, a few of them take heed, call their Advisor or consultant, and make changes to their portfolio. And each time they make a change, the Advisor, investment firm, or mutual fund company makes money.

Unfortunately, on average the investing public doesn't. In fact, by acting on this silliness, the average investor earned 4% per year less than the stock market from 1991 -2011.

Actual results to mutual fund investors vs. stock and bond benchmarks - 1991 to 2011
Source: Dalbar

That's why, at this time of year it is especially important to remind yourself about the abysmal track record these 'experts' have had over the years.

But before presenting the ugly details, I want to emphasize that investors should not feel disheartened by the evidence that financial marketing and media is dominated by loud, overconfident shills and mountebanks. On the contrary, investors should feel liberated to pursue other interests rather than reading or watching business news. For those that enjoy the cognitive 'sport' of investing from the standpoint of strategy and game theory, feel free to explore the latest economic, financial, ideological or philosophical fads with your colleagues and friends as provocative dinner conversation. This type of thinking keeps the mind young, after all.

Just don't orient your portfolio on the basis of your conclusions, or the conclusions of other prognosticators. We are all bound to be wrong far more often than we are right. For that is the nature of complex, dynamic systems like the markets.

The Truly Dismal Science

Now, here is the evidence. The following charts show aggregate forecasts from Wall Street's most famous oracles through time, next to the actual trajectory of the forecast variable. Note that these charts are sourced from James Montier's book Behavioural Investing (2007):

Chart 1. Consensus bond yields forecasts 1 year out vs. actual

Chart 2. Consensus S&P500 level 1 year forecasts vs. actual

Chart 3. Consensus S&P500 aggregate earnings 1 year forecasts vs. actual

In all cases the analysts appear to do a noteworthy job of describing what just happened, but appear to have no vision whatsoever about what is about to happen next. This applies to interest rates, the level of stock indices, and aggregate earnings.


Do any experts get it right? What about the experts at the Federal Reserve who are in charge of setting interest rates? Can they predict the magnitude or direction of interest rates over the next six months?

A working paper entitled "History of the Forecasters: An Assessment of the Semi-Annual U.S. Treasury Bond Yield Forecast Survey" (Brooks & Gray, 2003) studied the ability of Federal Reserve economists, including Alan Greenspan, from 1982 - 2002 to discover whether the group of experts that sets interest rates is able to effectively forecast their trajectory through time. 

Chart 3.
Source: (Brooks & Gray, 2003)

Again we see a strong talent for describing what has just happened, but no talent whatsoever for predicting what will happen next. Just how poor was the forecasting ability of Fed economists, including sitting Fed Chairmen like Alan Greenspan, over the 20 year survey?

Chart 4. 
Source: (Brooks & Gray, 2003)

The scatter plot above shows how Fed forecasts of interest rates six months out are negatively correlated with actual outcomes. The r-squared of the regression is 0.07, which is not statistically significant, but if you were a betting man, your best bet would be in the opposite direction of what is forecast to happen by the people who actually set interest rates for the economy.

Overconfidence - of course

The error rate would not be so worrisome if it weren't for the high level of confidence that investment professionals imbue on their predictions. This effect is perhaps best illustrated using the results of a study by Torngern and Montgomery (2004). The study set laypeople (psychology undergraduates, the perennial guinea pigs) against investment professionals in a competition to select the stock that they thought would outperform over the next month from pairs of stocks. All the stocks were well known companies, but participants were given information such as the industry and prior 12-month performance for each stock as well. Participants were asked to choose the best performer from the pair, and to provide their level of confidence in their choice.

Over many picks, one might hope that when participants were 50% confident that their choice was right, they were accurate about half the time, and when they were 90% confident, they were right almost all the time. In fact, as you can see from the chart below, a person's confidence level was largely irrelevant to their accuracy over time. In other words, having greater confidence in a choice did not lead to higher accuracy levels. In fact, at extreme levels of confidence (>80%), professionals were actually less likely to get it right. At a 90% level of confidence, professional investors actually got it right only 15% of the time, while at a 55% - 75% level of confidence they achieved about 40% accuracy.

Chart 6: Accuracy and confidence on a stock selection task
Source: Torngren and Montgomery (2004)

It is important to remember that over a 1-month time horizon the results of these stock choices are almost random, so we are not out to skewer professionals on the basis of their accuracy in this test. Instead, we are left to wonder why anyone should have expressed such high levels of confidence in their choices. When asked this question, the layperson group admitted that they were mostly guessing, but also placed some emphasis on the previous month's returns (ahh, momentum at work). In contrast, almost no professionals admitted to guessing; instead, they attributed their choices to 'Other knowledge' about the stocks, and 'Intuition'. Incidentally, the only factor with any predictive power in this example, however small, is the previous month's results (momentum).

Chart 7. Average rating of decision input importance
Source: Torngren and Montgomery (2004)

So Now What?

The quantum leap in thinking that we strive to compel with this post is toward an understanding that the world is too complex to enable accurate forecasting. Axiomatically, people should consider expert forecasts as no more than entertaining narratives - brain candy to stimulate the imagination. 

The best we can hope for is an assessment that an existing dynamic or trend is likely to stay on a certain course, or alternatively that the dynamic is reverting to the mean. Forecasting the direction or the magnitude of the change in trend is empirically impossible.

Fortunately, statistics offers a useful toolkit for evaluating the probability of trend continuation or mean reversion, and offers an estimate about the magnitude of the change. Further, statistical models tell us how confident we should be in our estimates given the amount of data we have at our disposal, and the type of problem we are trying to solve.

Quantitative systematic approaches to investing explicitly leverage the power of statistics to make a large number of bets with better than even odds of success. Quantitative risk management techniques and optimizations can further stabilize results by minimizing the impact of being wrong, which in markets will happen a lot. 

Quantitative approaches are no silver bullet - they suffer periods of poor performance too. But they are explicitly built to take advantage of the law of large numbers, and to stay out of trouble when statistical forecast accuracy is poor.

For more information about quantitative approaches, please read the following articles.

Friday, March 12, 2010

Mythbusters: Investor Edition

Myth # 2: You Will Get Rich by Heeding the Forecasts of Experts

Among all forms of mistake, prophecy is the most gratuitous. – GEORGE ELIOT

We have spent a great deal of time offering evidence that we are poor forecasters of the future. Disturbingly, it turns out that experts are no more prescient than the rest of us, even in their area of primary expertise. This post will describe the results of the most comprehensive and compelling study of expert fallibility to date, and offer lessons from the study that we can use to make better use (or not!) of expert opinions in future decisions.

Of course, we – the consumers of expert pronouncements – will continue to be in thrall to experts for the same reasons that our ancestors submitted to shamans and oracles: our uncontrollable need to believe in a controllable world and our flawed understanding of the laws of chance. We generally lack the willpower and good sense to resist the snake oil products on offer. Who wants to believe that, on the big questions, we could do as well tossing a coin as by consulting accredited experts.

Philip Tetlock spent over 20 years asking some of the top experts in their fields to make predictions about the future. The idea for the experiment took shape in the two or three year period prior to 1984 during the early years of the Reagan administration. Many of you will recall that this was a time of great anxiety and tension as the Soviets and the Americans seemed to move closer to nuclear Armageddon each day. Tetlock served on a committee charged with observing and forming opinions on American/Soviet relations. At that time in late 1983 the Bulletin of Nuclear Scientists had moved their Doomsday clock closer to midnight than at any other time since the Cuban Missile Crisis. It was widely believed by liberals that Reagan was leading the country on the road to nuclear apocalypse. Conservatives meanwhile believed that the best realistic outcome was for it to adopt a neo-Stalinist mode and retreat. Generally, the dominant view on both sides of the political aisle was that nothing good was going to happen.

While on this committee, which consisted of many well known political and military strategists at the time, it was widely noted that Gorbachev was rising through the political ranks in the Kremlin. Tetlock observed that no one at the time, however, believed that Gorbachev was likely to assume a leadership role in the Politboro. Further, it was commonly held that Gorbachev was secretly a neo-Stalinist in disguise. No one of any credibility thought that Gorbachev would execute a liberal revolution which would lead to the dissolution of the Soviet Union, and eventually the collapse of the Berlin wall and the reunification of Germany.

Of course, that’s just what Gorbachev went on to do. Interestingly, once Gorbachev had executed his coup, strategists of all stripes were eager to claim credit for having predicted just this outcome. Tetlock knew that in fact no one had predicted this outcome. This convinced Tetlock that there really would be great value if someone tried systematically to keep score on political experts. And that is just what he proceeded to do. From 1984 through 2001 Tetlock solicited frequent predictions from 284 experts in international affairs, economics, political strategy, and other complex fields. The experts consisted of a mixture of academics, journalists, intelligence analysts and people in various think-tanks, with an average of roughly 12 years of work experience each. No political view was over or underrepresented. Each expert made approximately 100 predictions, resulting in about 28,000 predictions in total. This allowed Tetlock to put the law of large numbers to good use. Experts were asked to make predictions on such topics as economic growth, inflation, unemployment, policy priorities, defense spending, leadership changes, border conflicts, entry-exit from international agreements, etc.

The results from the study are broad reaching and complex. Generally the results support the view that it is the way one thinks, not the depth of knowledge about a certain topic or theory, which matters most in tests of complex prediction. Tetlock expounds on the spectrum of thinking process bounded by foxes at one end of the spectrum and hedgehogs on the other, but this distinction is beyond the scope of this essay. We are more interested specifically in how well experts delivered accurate predictions over time, especially as it relates to experts’ confidence in their own predictions.
Here is a summary of the important lessons from the study:
  1. Experts are no better at predicting the future than the rest of us. In fact they are less accurate than a large group of dart-throwing monkeys
  2. Experts (like everyone else) are unlikely to admit when they are wrong, or to revise their beliefs in the face of conflicting evidence
  3. Those who know a lot about a subject are more likely to predict extreme outcomes (which rarely happen), and are more overconfident in their forecasts
  4. Specialists are no more reliable than non-specialists in forecasting outcomes in their own domain of study
  5. Experts who hedge their views, are self critical and consider alternative outcomes are more likely to be right
  6. Those experts who are better known and more frequently quoted are less likely to be right. Frightfully, these experts also make entertaining media guests
  7. Experts are no better at forecasting than basic trend-following systems such as ‘no change’ or ‘continue with the same rate of change’
  8. Of the 284 experts who offered predictions over 18 years, not one expert demonstrated a superior forecasting ability
In a review of Tetlock’s book, Louise Menand at The New Yorker magazine tells how Tetlock witnessed a shocking experiment during his student days at Yale. According to Tetlock,
“A rat was placed in a T-shaped maze. Food was placed in either the right or the left transept of the T in a random sequence such that, over the long run, the food was on the left sixty per cent of the time and on the right forty per cent. Neither the students nor (needless to say) the rat was told these frequencies. The students were asked to predict on which side of the T the food would appear each time. The rat eventually figured out that the food was on the left side more often than the right, and it therefore nearly always went to the left, scoring roughly sixty per cent—D, but a passing grade. The students looked for patterns of left-right placement, and ended up scoring only fifty-two per cent, an F. The rat, having no reputation to begin with, was not embarrassed about being wrong two out of every five tries. But Yale students, who do have reputations, searched for a hidden order in the sequence. They couldn’t deal with forty-per-cent error, so they ended up with almost fifty-per-cent error.”
Amos Tversky, the eminent behavioral economist, was fond of saying that human beings can only distinguish between three probabilistic outcomes: something is sure to happen; something is sure not to happen; and maybe. Quantitative economists and other forecasters can likely distinguish probabilities at a much higher level of granularity, but the experts that subscribe to these models are likely susceptible to the same overconfidence, and are thus not particularly reliable. The reality is that we live in a probabilistic world, not a deterministic one. On this basis, a decision making style that is predicated on adaptation rather than forecasting makes the most sense. Endeavour to not mistake a compelling narrative about future events with a strong likelihood of accuracy. In fact, one would do well to ignore loud exponents of fancy theories altogther, especially where those theories are used to make confident forecasts. By making many smaller bets with less confidence rather than few large bets with great confidence, you are likely to meet with greater success over time. 

For more information on Tetlock’s study and his results, I urge you to watch a presentation of his results at this link:

Also, the full New Yorker article is worth reading. You will find it at

Purchase Philip Tetlock’s book at Amazon.