Which Commodity is Wrong? Part II

In the previous blog post, Rick Vollaro brought to your attention an important divergence currently happening in the market -- the one between crude oil prices on one side and the CRB RIND (raw industrials) and copper on the other. These three indicators are typically regarded both as important global growth barometers and as highly correlated with the stock market. Figure 1 highlights the relative price action of these three series since 10/3/2011, when the S&P 500 formed a short term bottom. Since then, crude oil prices have risen more than 25% while the CRB RIND stayed flat and copper bounced around to end about 7% higher (though it seems to be in the process of rolling over). Meanwhile, the S&P 500 has been stuck in the middle, looking like it's not sure which commodity to follow.

We performed a historical analysis (weekly data available since 1988) to determine historically which, if any, of the above commodity series was most relevant for the stock market. In addition to coincident correlations (relation between movements in two variables at the same time) we also looked at leading correlations (relation between movements in one variable and movements in another variable at some point in the future) up to 8 weeks. Table 1 reports the results. Thanks to the heat map, we can clearly see that both copper and CRB RIND have historically been much more correlated to the S&P 500 than crude oil prices in coincident terms. Moreover, even when a lead is applied, the correlation of copper and CRB RIND to the S&P 500 remains elevated. Table 2 reports the T-statistics of the correlations in Table 1. In other words we are testing whether the results from Table 1 are statistically significant, using a 99% confidence level. When it comes to the T-stat, the higher the better -- specifically, we want it to be higher than a given threshold (the right-most column in Table 2) in order to achieve the desired level of statistical significance. While the T-stats on copper and the CRB RIND are very large and passed the test by an ample margin, only a few of the T-stats on crude oil passed the test and only by a tight margin. Based on these results, copper and the CRB RIND appear to be more reliable barometers of global growth and to correlate better with the stock market than crude oil prices.

Figure 1: Relative Price Action Since 10/3/2011

Table 1: Leading the S&P 500 weekly returns (correlations since 1988)

Table 2: Leading the S&P 500 weekly returns (T-stats since 1988)

In the Recession Camp

In our blog posts we often mention the ISM Manufacturing Report on Business PMI and the ECRI Weekly Leading Index, which are usually at the front line of the many barometers of economic activity we watch regularly. While the ISM PMI is built so that a reading below 50 signals economic contraction, its historical track record in calling recessions is far from perfect. On the other hand, while the ECRI team has a stellar historical track record in calling recessions, their weekly growth index doesn’t feature an absolute threshold below which a recession signal is triggered, and its interpretation is not as straightforward, at least for outsiders.

John P. Hussman, a Ph.D. in economics and one of our favorite reads, recently suggested a way of combining these two indicators to obtain a single recession signal that is more reliable than the sum of its parts. Following his idea (but doing our own math, as always), we found that over the last 44 years, whenever the ISM PMI was below 54 and simultaneously the ECRI Weekly Leading Index Growth was below -5, the U.S. was already in a recession (as defined by the National Bureau of Economic Research) 86.80% of the time. Moreover, if the U.S. was not already in a recession, there was a 92.59% chance of entering one within three months and a 95.06% chance of doing so within six months. The accuracy of this combination is easily explained: Our research indicates that the ECRI Index leads the ISM PMI by about four months (see chart below). Therefore this set of conditions can be interpreted as economic growth being near stall speed (low ISM PMI) and headed lower (negative ECRI Index). Adding a third condition (negative S&P 500 trailing-six-month return) and lowering the thresholds to 52 for the ISM PMI and to -7 for the ECRI Index worked even better; whenever these three conditions occurred simultaneously, the U.S. was already in a recession 94.19% of the time and was going to be in a recession within the following three months 100% of the time. That means always. Incidentally, this latter combination is the one we observe today (ISM PMI 50.8, ECRI Index -10, S&P 500 trailing six-month return -10.66% as of 10/31/2011).

Just another (heavy) piece to add to the weight of the evidence.

ISM Manufacturing Index

The Manufacturing ISM Report On Business, issued monthly by the Institute for Supply Management, compiles a survey of the nation’s supply executives to gauge economic activity in the manufacturing sector. The report is typically considered one of the growth barometers the market watches most closely. The results of the survey are ultimately condensed into a single percentage number, called PMI, which is scaled so that a reading greater than 50% indicates expansion while a reading below 50% indicates contraction. The September 2011 PMI came in at 51.6%, which is 1% higher than the August PMI of 50.6%. Is this enough to conclude that we've avoided a recession (at least, for now)?

To answer the question we looked at the track record of this indicator versus real GDP growth since 1949. Overall, the ISM manufacturing was 'right' (being above 50% when real GDP growth was positive and below 50% when real GDP growth was negative) about 77% of the time, and 'wrong' (being above 50% when real GDP growth was negative and below 50% when real GDP growth was positive) about 23% of time. Moreover, we found that the probability of the indicator being right or wrong was consistent across periods of positive and negative real GDP growth; this means that the ISM Manufacturing was above 50% 23% of the time when real GDP growth was actually negative. In fact, we found that historically the index was as high as 63.5 during periods of negative real GDP growth. This is certainly a less than impressive track record. Especially given that the September 2011 reading cleared the 50% mark by a margin as slim as 1.6%, we do not regard this as sufficient evidence to conclude that the risks of a recession have decreased.

Unemployment Insurance Claims and Challenger Layoffs

One of the indicators that the financial press uses to gauge the U.S. job market is unemployment insurance claims. The data, compiled weekly by the U.S. Department of Labor, tracks how many new people have filed for unemployment benefits in the previous week. Since the weekly data can be quite volatile, the 4-week moving average is typically monitored.

Today’s report showed that jobless claims inched down by 1,000 last week to 404,000, while the 4-week average fell by 7,000 to stand at 408,000, marking the lowest level since mid-August. Initial unemployment claims saw a sharp decline after reaching the 650,000 mark in March 2009; however, since late 2010, they have been stubbornly stuck in the 400,000-450,000 range. Claims usually fall near the 300,000 level in periods of rapid economic growth, while it is commonly said that a level near 375,000 is necessary just to keep up with population growth without increasing the unemployment rate.

Our research indicates that the Challenger layoff survey may be a good leading indicator for unemployment insurance claims. The data, compiled monthly by the consulting firm Challenger, Gray & Christmas, provides information on the number of announced layoffs by U.S. corporations. Commonsensically, once the announced layoffs are executed, the laid-off workers will need to apply for unemployment benefits. Our study indicates that the pass-through time is around 8 weeks. In this context, the recent spike in the Challenger layoff survey is certainly worrisome. According to the survey, the number of planned layoffs in September amounted to 115,730, the highest in more than two years and more than double August’s total of 51,114. If the correlation we estimated between the Challenger survey and unemployment claims since 1999 holds, then we may see a spike in unemployment claims over the next few weeks. Lastly, it is worth noting Challenger’s comment that September’s increase in planned layoffs was not “directly related to recent softness in the economy.”

If they say so…

Valuation Getting Cheaper, Not Yet Compelling

One of the three core tenets of the investment management process at Pinnacle is valuation. More often than not, market valuation will be at or near neutral levels, and our focus will be on the other two tenets, the business cycle and technical conditions. However, every once in a while, valuation levels become compelling and catch our attention.

In order to assess the level of valuation at any point in time, we typically look at a large variety of at times contrasting indicators. Our quantitatively-oriented valuation model uses all these indicators as inputs and returns a single score ranging from 0 to 10, where higher values signal more attractive valuations. This helps remove a certain degree of subjectivity from the analysis. Currently, the model is an equally-weighted average of 14 different indicators grouped into 4 different categories called P/E Measures, Non-Earnings Measures, Yield-Based Measures, and Intrinsic Value Measures. As part of the constant effort to improve on the efficacy of the model, the team is currently evaluating alternative weighting systems based on the specific explanatory power of the individual components of the model. Regardless of what system is used, since 1981 (the beginning of the sample) our valuation model has exhibited an outstanding ability to forecast future S&P 500 returns, having a roughly 50% correlation with 2-year forward S&P 500 returns and a roughly 70% correlation with 5-year forward S&P 500 returns.

Following the turmoil experienced by the stock market in the last few weeks (at the time of writing the S&P 500 is 13.5% off its April 29th high on a closing basis), we would expect valuation to have improved some. The important question is, by how much? Updating our valuation model as of the end of last week returns a score between 6.07 and 6.8, depending on what weighting system is used. This constitutes a great improvement from the score of around 5 seen at the end of July, before the worst of the latest market sell-off. Since the model’s inception, valuation scores in the 6-7 range have been associated with median 5-year forward S&P 500 returns of around 11% (standard deviation of 2%). However, the forecasting power over shorter time frames was less impressive, with 1-year forward S&P 500 returns coming in still at around 11% but with a standard deviation of 12%.

All considered, a score in the lower 6-7 range is not yet overly compelling in our view, especially given the high level of uncertainty that is pervading global financial markets as of late. In addition, the other two tenets of our investment management process suggest that the market may become cheaper before it gets expensive. As a result, we will keep an eye on the model and give it increasing consideration if valuation keeps improving.

The Hathaway Effect

When over 70% of daily stock trades are being executed by robotraders - supercomputers using complex algorithms, often unintelligible even for the very same whiz who programmed them - strange things can happen. Some can be painful, like the May 6, 2010 flash crash, when the DJIA lost and recovered roughly 9% of its value in a matter of minutes. Some, however, are just odd.

With headquarters in Omaha, Nebraska, Berkshire Hathaway is an American conglomerate holding company whose CEO and chairman is the well known value investor Warren Buffet. Anne Hathaway is a talented 1982-born American actress who has been on the rise in the past few years, starring in hit movies such as The Devil Wears Prada (2006) and Alice in Wonderland (2010). Other than name and nationality, the two seem to have nothing in common, except that Berkshire Hathaway shares (BRK.A and BRK.B) seem to post significant gains on days when the homonymous actress is populating the news. Blogger Dan Mirvish was the first to spot this pattern, pointing out a few occasions since 2008 where the correlation was striking:

• September 26, 2008 - Passengers opens:  BRK.A up 1.43%
• October 3, 2008 - Rachel Getting Married Opens:  BRK.A up 0.44%
• January 5, 2009 - Bride Wars opens:  BRK.A up 2.61%
• February 8, 2010 - Valentine's Day opens:  BRK.A up 1.01%
• March 5, 2010 - Alice in Wonderland opens:  BRK.A up 0.74%
• November 24, 2010 - Love and Other Drugs opens:  BRK.A up 1.62%
• November 29, 2010 - Anne announced as co-host of the 83rd Academy Awards:  BRK.A up 0.25%
• February 28, 2011 - Anne co-hosts the 83rd Academy Awards:  BRK.A up 2.94%

The idea is not outrageous. In fact, with today’s technology it is very easy to program softwares to pick up on key words, and more sophisticated ones can read for sentiment too. We actually crunched the numbers (see table below) and found that the average daily return during major Anne Hathaway news appearances since January 2008 was 1.38%, while it was -0.02% on all other days. A simple statistical test based on sample size and standard deviations indicates that the two average daily returns are statistically distinguishable from each other with 98% confidence.

	2008 to Date
	Anne Hathaway Event	No Anne Hathaway Event
Number of Days	8	879
Average Daily Return	1.38%	-0.02%
Standard Deviation	0.98%	2.04%

The fact that Anne’s news appearances correlated with positive returns in Berkshire Hathaway shares, instead of generating simple trading volume increases, makes us wonder whether these robotraders could actually read for sentiment (news regarding Anne Hathaway are seldom negative). Just in case, you may want to think twice before naming your company Lohan or Sheen.

10-Year Normalized P/E Ratio (Part 3 of 3)

Even though picking and choosing which data points to consider and which to ignore may be considered borderline to manufacturing data, it is often common practice to assume an equal percentile of data points at the top and bottom of a sample to be outliers, i.e. anomalies, not representative of the true distribution of the variable. Consistent with this assumption, such data points are thrown out of the sample. In Figure 3 (shown below) we experiment with the 5th and 95th percentiles of the sample. This definition of outliers causes the range to be bounded between 9.57 (5th percentile) and 30.23 (95th percentile). Consequently, the whole 2000 tech bubble, as well as some of the lowest values recorded during the depressions of the 1920s and 1930s, are ignored.

This approach implicitly assumes that all the relevant information that can be extrapolated from the P/E 10 has to do with its relative position within the 5th-95th percentile range, and that any values outside of this range do not provide any additional information. For instance, if the P/E 10 decreases from 15 to 10, this may be considered a move from undervaluation to extreme undervaluation. However, if the P/E 10 decreases further from 10 to 5, the market will simply remain extremely undervalued.

Perhaps the most important effect of capping a distribution at given percentiles and eliminating outliers is the one of bringing the average, median and mid-range of the capped distribution closer to each other. In our example, the median of the capped P/E 10 distribution remained the same at 15.85, and so did the percentile of the most recent reading of 25.90. However, the average decreased from 18.06 to 17.69 and the mid-range decreased from 26.70 to 19.90. In this framework, the most recent P/E 10 of 25.90 is still 63.45% above its historical median of 15.85 and still ranks at about the 90th percentile of the historical sample. However, the same P/E 10 now appears slightly more overvalued when compared to the average (from 43.40% overvalued to 46.38% overvalued) and 30.17% overvalued when compared to its mid-range (from 2.99% undervalued).

We can therefore conclude that, when we contemplate the presence of a certain degree of outliers in the historical distribution, the current level of the P/E 10 indicates a consistent high level of overvaluation regardless of whether it is compared to its long-term average, median, ranking, or mid-range.

10-Year Normalized P/E Ratio (Part 2 of 3)

At any given point in time, figuring out how to interpret the P/E 10 may not be as straightforward as it seems. Figure 2 (below) plots the P/E 10 for the S&P 500 since 1880 to date. If we consider the historical average equal to 18.06 to be a normal or fair value for the P/E 10, then the most recent reading of 25.90 would indicate a 43.40% overvaluation. If instead we were to use the historical median, currently equal to 15.85, the S&P 500 would appear to be 63.45% overvalued. Alternatively, if we wanted to consider how the most recent reading of 25.90 ranked within the historical sample, we would find that it corresponds approximately to the 90th percentile, where anything above the 50th percentile would be considered overvalued territory. Therefore, depending on whether we use the average, the median, or the percentile ranking, currently the S&P 500 would appear to be between 40% and 63.45% overvalued.

Notwithstanding a sizeable difference between these two numbers, certainly neither of them bode well for buy and hold investors entering the market at this point. However, this is only one way of looking at the problem. If we instead focused on the historical range of the P/E 10, we would notice that historically the P/E 10 was as low as 4.46 and as high as 48.94. The implied mid-range is 26.70, which is approximately 3% greater than 25.90, the most recent reading. Therefore, using this approach, currently the market would appear to be slightly undervalued.

The cause of the large discrepancy in the conclusions reached by the different methodologies is not a mystery: Figure 2 clearly shows that during the 2000 tech bubble the P/E 10 inflated to never-before-seen levels. If this once-in-a-century event is ignored, then the upper bound of the historical range would have been below 35, implying a mid-range of approximately 20 and consequently some degree of overvaluation in the most recent reading of 25.90.

10-Year Normalized P/E Ratio (Part 1 of 3)

The 10-Year Normalized Price-to-Earnings ratio, commonly known as P/E 10, was originally introduced by Professor Robert Shiller in his ground-breaking book Irrational Exuberance [Princeton University Press 2000, Broadway Books 2001, 2nd ed., 2005]. The database used in the book is regularly updated and made publicly available on Professor Shiller’s website (www.econ.yale.edu/~shiller/).

In its simplest version, the ratio is calculated dividing the price of a security (usually a market index such as the S&P 500) by the 10-year average of its trailing-four-quarter earnings per share. The rationale behind this metric is twofold: to obtain a valuation measure that is purely historical (i.e. ignoring any analysts’ estimates of future earnings, which could be biased) and to adjust for the cyclicality in earnings. Figure 1 (below) illustrates how the 10-year average smoothes out earnings volatility, portraying a clearer picture of the long-term trend in earnings.

It is fairly easy to illustrate the power of the P/E 10. For example, using Professor Shiller’s database, we calculated the average five-year annualized S&P 500 return following a P/E 10 lower than 11.16 (the historical 10th percentile) as well as following a P/E greater than 25.38 (the historical 90th percentile). The former is equal to 10.54%, while the latter is equal to 1.13%. Moreover, based on the respective standard deviation and number of observations, the two averages are statistically different from each other with a 99% confidence level. These results constitute strong evidence of the P/E 10’s ability to predict future returns based on valuation.

Crude Oil Momentum

Crude oil momentum is commonly defined as the rate of change in the price of oil ($/bbl) of a given quality and over a given time frame. Several independent research providers that we read on a regular basis look at the 252-day (or annual) rate of change in the price of WTI (Western Texas Intermediate or Texas light sweet), which is refined mostly in the Midwest and Gulf Coast regions in the U.S. and is the underlying commodity of the New York Mercantile Exchange’s oil futures contracts. Their research indicates that, historically, excessively steep increases in the price of WTI were often followed by poor stock market performance.

Two commonly-watched critical levels for the 252-day rate of change are 33%, above which the stock market tended to trade sideways without offering significant gains, and 100%, above which the stock market tended to suffer significant slumps. The rationale behind these results is simple: given the pivotal role of oil in both U.S consumption and production, a “too much, too fast” rise in oil price may be difficult for the economy to absorb, knocking an ongoing economic recovery or expansion out of sync.

In an effort to keep a closer look on this indicator, we developed a tool that allows us to track the 252-day rate of change in the price of WTI in real time, based on daily closing prices as well as intra-day prices. What follows is our Crude Oil Momentum report, updated as of yesterday morning, when WTI spiked to $113.33/bbl.

The top chart (blue line) plots the S&P 500 and highlights a few major tops. The second chart (red line) plots the 252-day rate of change in the price of WTI and compares it to the 33% and 100% critical levels (dotted lines). From 1983 to date, the 100% critical level was reached only 5 times, which are highlighted and correspond to the major S&P 500 tops highlighted in the top chart. Grey areas in both charts correspond to official recessions, as determined by the National Bureau of Economic Research. Yesterday’s intra-day price of $113.33/bbl corresponds to a 37% 252-day rate of change, which is above the 33% critical level but still well below the 100% critical level.

Concluding the report is a table indicating how often, historically, this rate of change was within a given range, and what the average S&P 500 return was in the following 12 months. As the table reports, from 1983 to date the 252-day rate of change in the price of WTI was between 33% and 100%, as it is now, 20.6% of the time on a daily basis. Observations in this range were followed by an average 12-month S&P 500 return of -0.52%. From this point forward, it will be critical for our stock market outlook to observe whether crude oil momentum stabilizes at or below 33% or keeps climbing towards 100%.

Life Isn’t Always Linear

Being an Investment Analyst often involves looking at a vast array of indicators that are supposed to be correlated to different degrees with some relevant financial variable. When a given indicator is said to be either positively or negatively correlated to a variable, in most instances this refers to linear correlation. However, two variables may very easily be non-linearly related in which case testing for linear correlation alone will produce misleading results. Responding to this issue, we developed a tool that applies a number of different non-linear transformations to the data in order to test for non-linear relationships between an indicator and a financial variable of interest. In addition, these transformations are applied on different moving averages and percent changes of the raw data, and the correlation is measured not only concurrently but also using different lags from 1 month to 24 months. In the chart below, the black dashed arrow represents a simple linear transformation while the other data points represent the different non-linear transformation that we also consider.

Each time this tool is applied to a single indicator, it produces over 1,500 data series derived from the original one and estimates the correlation of each one of them with the relevant variable. When performing such a massive data mining exercise, we are bound to find some significant correlations simply by chance. If statistical inference doesn’t betray us, for each one hundred correlations that we estimate we would expect, on average, to find at least one of them to be significance at a 99% confidence level. In these instances, it is important to remember that correlation does not necessarily imply causation, and the latter is what we are looking for. A good example is the famous Super Bowl Stock Market Indicator, based on the observation that in 29 out of the 36 years from 1967 to 2003 an NFC victory preceded positive stock market returns while an AFC victory preceded negative stock market returns. Even though it is undisputed that such a correlation existed historically, it would be foolish to expect this phenomenon to repeat itself in the future, unless there is a valid reason to believe that an NFC victory caused the stock market to rise and an AFC victory caused the stock market to fall.

This is where the big brains of Pinnacle’s Investment Team come into play: each time we run into a variable that seems to have a strong predictive power based on empirical tests, it is a team effort to determine whether we believe an underlying causation effect based on sound economic theories actually exists. If the conclusion is negative, then the indicator is discarded as there is no reason to expect the historical correlation to repeat itself in the future. In conclusion, let’s hope that the current NFL lockout gets resolved, otherwise the stock market may not move at all next year.

The New Guy on the Block

A few weeks ago the members of Pinnacle’s Executive Team decided to do their part in lowering the U.S. unemployment rate with a new hire, and they chose me. Needless to say, I feel very fortunate having the opportunity to join this amazing team. My journey with Pinnacle began in the spring of 2010, when our Chief Investment Officer Ken Solow spoke to the Quantitative Equity Investment Strategy class I was taking as a graduate student at the University of Maryland. The class was composed of three students (I guess equities were not so popular back then), which gave me the opportunity to introduce myself. After the presentation I expressed my interest in Pinnacle to Ken, and I guess Pinnacle did not mind having some cheap labor around, because supply and demand met and turned into a part-time summer internship.

For me, the internship was a very positive and instructive experience. Most of my time was spent working on Pinnacle’s quantitative models and observing Pinnacle’s investment process. I guess the investment team members liked my work and were not yet sick of my Italian accent by the end of the summer, because the internship turned into a full time offer. I accepted with much enthusiasm – I could not believe that someone was willing to pay me to do some of the things that I love most, which are investing and playing with numbers. After graduating in December 2010 and enduring the lengthy process of obtaining a work visa, I was finally able to join the firm at the beginning of the New Year. As I am now into my fourth week as a Junior Investment Analyst, I have to say so far my experience has been great – no one has asked me to get them coffee or to make copies.

All jokes aside, everyone at Pinnacle has been very supportive and as enthusiastic for my presence as I am for being here. The past four weeks have been a confirmation of last summer’s experience, which taught me that Pinnacle isn’t just another advisory firm. It is a firm where clients’ needs truly come first, and where the comfortable tenets of Modern Portfolio Theory are questioned every day to the benefit of an investment model that can actually work in the real world. In addition, I discovered that the organizational culture really encourages open dialogue and the sharing of ideas. Although, as the new guy, my policy has generally been to keep my mouth shut and my ears wide open (I believe at this point I have much more to learn from than to teach to my colleagues), I feel like my input is already highly valued. To conclude, I cannot overemphasize how fortunate I feel for being part of this great team, and I am looking forward to paying back the trust that was given me, and to becoming another contributor to this blog.