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The St. Petersburg Paradox

This note was originally published at 8am this morning, September 28, 2010. INVESTOR and RISK MANAGER SUBSCRIBERS have access to the EARLY LOOK (published by 8am every trading day) and PORTFOLIO IDEAS in real-time.

“The mathematical expectation of the speculator is zero.”

-Louis Bachelier

 

Louis Bachelier was a French mathematician who was, well after the fact, credited with founding the Efficient Market Thesis.  In 1900 Bachelier published his Ph.D thesis titled “The Theory of Speculation.”  In his paper, Bachelier discussed the use of Brownian motion to evaluate stock prices.  Unfortunately, his thesis was “not appropriately received”, which resulted in academic black-balling and the concept being buried for more than sixty years.

 

Almost sixty-five years later Professor Eugene Fama from the University of Chicago was officially credited with developing the Efficient Market Thesis after publishing his Ph.D thesis.  His paper was titled “The Behavior of Stock Market Prices.”  The core tenet of his paper and the Efficient Market Thesis is that an investor “cannot consistently achieve returns in excess of average of market returns on a risk-adjusted basis, given the information that is publicly available at the time the investment is made.”

 

Is it not somewhat ironic that the determination of who founded the Efficient Market Thesis was not efficient?

 

Despite not having a Ph.D on staff at Hedgeye Risk Management, we have been performing our own experiment to test the Efficient Market Thesis over the past two years.  We call this experiment the Hedgeye Virtual Portfolio, and it is a culmination of our stock picks since inception.

 

In that time, we have closed 510 long positions and closed 490 short positions. 85.9% of the closed long positions have been winners and 83.5% of the closed short positions have been winners.  Obviously, these results are far from a “random walk”.  So, either we are good at our jobs, or the market is not quite as efficient as Efficient Market Theorists believe.  I would submit that it is a combination of both.   

 

Clearly, though, many stock market participants work hard, have processes, and are intelligent.  So, why do many stock market operators underperform even the basic broad market returns? Simply put, because of this little critter called Behavioral Economics that leads many market participants to act against their best interests. 

 

By way of example, let’s consider the St. Petersburg Paradox, which is as follows:

 

“Consider the following game of chance: you pay a fixed fee to enter and then a fair coin is tossed repeatedly until a tail appears, ending the game. The pot starts at 1 dollar and is doubled every time a head appears. You win whatever is in the pot after the game ends. Thus you win 1 dollar if a tail appears on the first toss, 2 dollars if a head appears on the first toss and a tail on the second, 4 dollars if a head appears on the first two tosses and a tail on the third, 8 dollars if a head appears on the first three tosses and a tail on the fourth, etc. In short, you win 2^k−1 dollars if the coin is tossed k times until the first tail appears.”

 

So, what would be a fair price to pay for entering the game?

 

I posed this question to our Research Team at Hedgeye yesterday and they came back with myriad of answers, which ranged from $1 to infinity.  This simple mathematical answer is that you should be willing to pay infinity (or your entire net worth) to play this game as your expected value is infinity.

 

 As one of our astute Analysts responded to me yesterday:

 

“Well, the series doesn’t converge …EV = (1/2)*($1) + (1/4)*($2) + (1/8)*($4) + …EV = ½ + ½ + ½ + …… the sum of which is infinite.  So, is the fair entering price infinite? Strictly speaking, I think the answer is yes – but no one on earth would take that deal (even if we cap the number of rounds such that EV = all your money, since no one has infinite money).”

 

Therein is another paradox, the paradox of the Efficient Market Thesis.  Specifically, most market operators do not make rational decision based on math.  They make emotional decisions based on arbitrary evaluations of risk. This, of course, leaves opportunities for the sneaky mathematicians to make profit.

 

So then, how do we account for valuation when considering an investment?  Surely, valuation is rational?

 

In my view, valuation is an indicator of sentiment around a security.  For instance, when a stock trades with a single digit P/E, its business is either declining, or the collection of market operators believe it is.  There are many studies that support the idea that value based strategies (i.e. buying cheap stocks) outperform over time, but I would submit that this is not because of the valuation, but rather because of the behavioral finance indicator embedded therein.

 

As we consider the stock market today, the first question many strategists try to answer is whether the stock market is “cheap”.  The simple way to make this determination is to pull up a long term price / earnings chart and look at it going back fifty years.  Today, at 15x current earnings and 13.7x forward earnings, the SP500 looks cheap versus history. 

 

The more important task though is determining what expectations are embedded in that valuation.  What is the correct earnings multiple for an economy that has crossed the Rubicon of Debt at 90% debt / GDP and has budget deficits projected for the next thirty plus years (I would say infinity, but that’s probably not fair)? Additionally, if growth rates are mired in the 1 - 2% range as a result of this fiscal situation, is the stock market “cheap”?

 

In the shorter term, setting those sneaky valuation metrics to the side for a second, what do you think is priced into the S&P500 up 8.8% in September?  Given the cover of Barron’s this weekend and the rapid rise in the S&P in the last few weeks, the catalyst of the Republicans winning more seats than expected in the midterms is likely priced in. (We called this out on our conference call with Karl Rove in early September - Could the Midterm Election Be A Major Stock Market Catalyst?)  So, what is priced in now?

 

Well, perhaps our friend George Soros said it best:

 

“The financial markets generally are unpredictable. So that one has to have different scenarios. The idea that you can actually predict what's going to happen contradicts my way of looking at the market.”

 

Or as we say at Hedgeye, the plan is that the plan will change.

 

Yours in risk management,

 

Daryl G. Jones

Managing Director

 

The St. Petersburg Paradox - PE


Bear/Bull Battle: SP500 Levels, Refreshed

In the last 6 trading days you could as readily have called the intermediate term TREND line of 1144 resistance as you could support – depends on what hour of the day that you need to call it names.

 

Government sponsored volatility like this is not going to end well, but that doesn’t mean the SP500 can’t continue to scale to lower-highs if 1144 holds. We have an immediate term TRADE line of resistance up at 1154 as of 3PM and we currently have no position in SPY.

 

The more I stare at this, the more I want to do nothing. I’m still waiting and watching as we approach month and quarter end.

KM

 

Keith R. McCullough
Chief Executive Officer

 

Bear/Bull Battle: SP500 Levels, Refreshed - 1


Why We are Short Italy (EWI)

Hedgeye Virtual Portfolio: Short Italy (EWI); Long Germany (EWG)

 

Conclusion:  We are seeing continued negative fundamentals in Italy’s economy and political risk heightening under Berlusconi’s fractured leadership.  We shorted Italy via the etf EWI in the Hedgeye Virtual Portfolio on Sept. 24.

 

One of the first areas we focus on when sizing up an economy’s macroeconomic “health” is its debt and deficit levels (as a % of GDP).  Across our research (in particular on the U.S., Greece, and Japan) we’ve noted the seminal work of economists Reinhart and Rogoff who show historically (across 800+ years) that countries reach a crisis zone of fiscal imbalance when their debt ratio is north of 90% and deficit ratio is greater than 10%. 

 

With a debt ratio at 115.2% as of fiscal year 2009, Italy’s debt is of particular concern to us, while its deficit as a percentage of GDP is less worrisome at -5.3%, yet nevertheless above the -3% target rate set by the EU (see chart below).

 

Why We are Short Italy (EWI) - r1

 

This year we’ve been bullish from a top-down perspective on countries that issue austerity measures to clean up their fiscal houses. That said, fiscal trimming will not be a panacea across Europe to cure its ails. We see clear divergence among countries; we are bullish on Germany and continue to warn of further deterioration in the capital markets of countries like Portugal, Ireland, Italy, Greece, and Spain.

 

With regard to Italy we question the country’s ability to materially cut its bloated balance sheet on the backdrop of a much divided political landscape.  Remember that back in July PM Silvio Berlusconi expelled his speaker of the Parliament, Gianfranco Fini, and other dissents from his People of the Liberty party, which left his party with a majority coalition.  What lies now in the balance is the potential decision by Berlusconi to dissolve his government and set up a new administration or call for early elections next spring, three years ahead of schedule. In any case, we’d expect Berlusconi to choose the most politically expedient route for populous support going forward, which may not necessary equate to fiscal prudence.

 

Despite the issuance of €25 Billion in austerity earlier in the year, Berlusconi is up against a lofty €251 Billion of maturing debt next year (across all coupon types), according to Bloomberg data. As a point of reference, Germany, a country with an economy 1.6 times the size of Italy’s, has €210 due in 2011.

 

Already we’re seeing elevated signs of risk in Italian markets.  In the charts below we show that Italy’s CDS spread, while well short of Greece’s 820 bps spread, has blown out to 206 bps.  Also Italy’s 10YR spread over similarly maturing German bunds is kicking to the upside, as its equity market (Titan30) is broken across its TRADE (3 weeks or less) line of resistance and hovering near its TREND (3 months or more) resistance line—all bearish points.  [YTD the Titan30 is down -11%.]

 

Today and tomorrow the Italian government will attempt to sell €9.5 Billion ($12.8 Billion) of bonds. As we’ve affectionately said numerous times: countries cannot continue to kick the can of debt down the road in perpetuity. Italy should be no exception.

 

Matthew Hedrick

Analyst

 

Why We are Short Italy (EWI) - r2

 

Why We are Short Italy (EWI) - r3


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WEN – INDUSTRY OUTLOOK CONFIRMS LACK OF CONFIDENCE

Lower consumer confidence numbers create more bad news for restaurant companies.

 

WEN’s CFO Steve Hare started his presentation at an investor conference earlier this afternoon by saying that in light of the disappointing consumer confidence numbers released this morning that today marked the 24th consecutive time he has started off a presentation with bad news.  He went on to say that the “best” thing he can about the restaurant industry today is that things seem fairly stable.  That being said, he is not pleased with the consumer confidence numbers, which he recognizes as one of the key statistics to measure restaurant trends going forward, “so that’s a step back.”

 

Today's headline Conference Board consumer confidence index number declined to 48.5 from 53.2 last month.  The median estimate from Bloomberg was for a decline to 52.1.  This now puts the confidence index down 14% year-to-date.  The real story lies in the present situations Index which is only up 14% from the low set back in December 2009.  Confidence is critical for the U.S. economy and it is clear that the government stimulus has been lackluster, at best, in boosting the outlook of consumers in America.

 

In fact, there is considerable evidence to suggest that the spending could be worsening people’s confidence.  A pool released by Public Notice today suggests that 71% of people say government spending is too high and, more importantly, 68% say government spending is a factor in their own financial situation.  Consumption accounts for roughly 70% of GDP; restoring some semblance of confidence will be necessary to encourage real economic growth.

 

Mr. Hare also outlined the continued elevated level of unemployment, particularly among its key 18-24 year old demographic, and the rising cost of some key commodities, specifically beef and bacon, as risks to both WEN’s and the QSR industry’s top and bottom lines.

 

WEN – INDUSTRY OUTLOOK CONFIRMS LACK OF CONFIDENCE - conference board present situations

 

Howard Penney

Managing Director

 


Contemplating Turnout In The Midterms

We are on record already saying that we believe that Republicans will do much better than expected in the midterms.  The implication of much better than expected is that the Republicans could take the Senate back and will take the House by a much larger than expected margin.  In fact, we are more bullish on the chances for the Republicans than our friend and former White House Chief of Staff, Karl Rove.  Our bullishness isn’t partisan mind you, but merely based on the math.

 

As it stands today, our view is creeping more and more into consensus, and is certainly getting priced into the stock market.  The current Real Clear Politics poll averages for the Senate have the Democrats at 48 seats, the Republicans at 46 seats, and 6 seats currently “too close to call”.  In the House, the Republicans are currently at 208 seats, the Democrats are at 191 seats, and 37 seats are currently “too close to call”. 

 

If you didn’t know the Senate is in play, now you know. 

 

Currently, the “too close to call” races in the Senate are in CO, CT, IL, NV, WA, and WV.  Our view is that IL and WA will likely go Democratic, while NV, WV, and CO have a real shot at going Republican.  If this occurred, we would be at 50 – 49 for the Democrats, with CT to be decided.  Given the fact that Republican nominee Linda McMahon is willing to spend up to $50MM in advertising, this race is far from a foregone conclusion and in our estimation it is the key race to watch in the coming weeks to gauge whether the Republicans can really take the Senate.

 

The real wild card in the midterms will be voter turnout.  Our stance that Republicans could do much better than expected is based on the fact that the numbers are telling us that Republican turn out could be much, much higher than the Democrats. 

 

The supporting evidence is as follows: 

  • Reuters Ispos Poll – September 16th to 19th – 72% of Republicans said they are very likely to vote, 55% of Democrats said they are very likely to vote
  • Gallup Poll – September 20th to 26th – 48% of Republicans said they are very enthusiastic about voting, 28% of Democrats said they are very enthusiastic about voting
  • Fox News Poll – September 14th to 16th – 42% of Republicans said they are very interested in the elections, 22% of Democrats said they are very interested in the elections
  • McClatchy-Marist Poll – September 22nd – 46% of Republicans said they were very enthusiastic about voting, 30% of Democrats said they were very enthusiastic 

The differences in these numbers are outright staggering and suggest a Republican base that is ready and willing to vote, while a Democrat base that is more than likely to stay home. 

 

In midterm elections, voter turnout is typically less than 40%, so these voter enthusiasm numbers will have a significant impact.  Particularly given the context that the registered and likely voters is currently split in the country with 36.5% identifying as Democrats, 35.5% identifying as Republicans, and 24.8% indentifying as Independents (according to pollster.com), which we highlight below.  With the Republicans currently up +4% in the generic Congressional ballot, these turnout numbers may potentially add insult to injury for the Democrats.

 

Daryl G. Jones

Managing Director

 

Contemplating Turnout In The Midterms - 1


CONSUMER CONFIDENCE - WHERE IS THE PULSE OF THE CONSUMER AND THE ECONOMY?

Today's headline Conference Board consumer confidence index number declined to 48.5 from 53.2 last month.  The median estimate from Bloomberg was for a decline to 52.1.  This now puts the confidence index down 14% year-to-date.  The real story lies in the present situations Index which is only up 14% from the low set back in December 2009.  Confidence is critical for the U.S. economy and it is clear that the government stimulus has been lackluster, at best, in boosting the outlook of consumers in America.

 

In fact, there is considerable evidence to suggest that the spending could be worsening people’s confidence.  A pool released by Public Notice today suggests that 71% of people say government spending is too high and, more importantly, 68% say government spending is a factor in their own financial situation.  Consumption accounts for roughly 70% of GDP; restoring some semblance of confidence will be necessary to encourage real economic growth.

 

The Richmond Fed manufacturing survey fell to -2 from expectations of +5.  In total, 7 out of 8 Richmond Fed indicators declined, with just vendor lead-time remaining flat at 0.  The new orders index fell to 0 this month from 10 in September and shipments index fell to -4 from 11. The Richmond Fed’s district accounts for about 9.1% of the nation’s gross domestic product.

 

This morning, Hedgeye Financials sector head Josh Steiner’s read on the Case/Shiller numbers was not good.  His conclusion: “Home prices are just starting to roll, but downside will accelerate in coming months. We expect next month's number to be a wake-up call and the month after that to be a significant negative catalyst for the market generally and Financials specifically.”

 

In response to these data points, the VIX is up 1%, Gold is spiking up 8% and the dollar is down 0.4% (down 5% for the month).  The S&P is basically unchanged. 

 

The consumer is far from a picture of health, home prices are headed lower, the economy is decelerating and the S&P 500 is up 3.7% year-to-date.  The outlooks certainly seems decidedly bearish, but apparently two “big” boys think otherwise.

  • David Tepper said on CNBC yesterday that stocks are in a win-win situation.
  • From Zerohedge - “John Paulson Lecture: Bonds Are Wrong, Stocks Are Right"

The first day of the 4th quarter is setting up to be an ominous day, with the ISM manufacturing index to be reported.  The August reading of 56.3 posted a big upside surprise versus 52.8 expectations and setting off a 9% rally in the S&P 500.  Since then Factory orders, ISM non-manufacturing, Empire Manufacturing, Philadelphia Fed, Chicago Fed and the Dallas Fed have all reported disappointing numbers relative to expectations.  All of the regional FED readings, except the Empire State manufacturing reading, are showing numbers that imply economic contraction, not expansion.


A reading below 50 on the ISM is in play for the first day of October.

 

Howard Penney

Managing Director

 

CONSUMER CONFIDENCE - WHERE IS THE PULSE OF THE CONSUMER AND THE ECONOMY? - conference board present situations

 

CONSUMER CONFIDENCE - WHERE IS THE PULSE OF THE CONSUMER AND THE ECONOMY? - conference board confidence

 

CONSUMER CONFIDENCE - WHERE IS THE PULSE OF THE CONSUMER AND THE ECONOMY? - conference board expectations


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