Jumat, 18 Oktober 2013

This Song Would Totally Be a Hit Today

If only Blake Shelton performed it on "The Voice":

Except that only CeeLo Green would have the guts to do it. Still, that would be interesting, and likely better than many of the battle rounds....

As David Tufte described it:

Odd. A whole song video, sung by Italians, of nonsense words chosen to sound like English.

Made in 1972 by Adriano Celantano, it's a parody of Italian rockers who sang in English even though they didn't speak the language.

The scary thing is that it's not bad at all (if you go in for early 70's bubblegum funk). And you’ve got to love the "harp-syncing".

And who *doesn't* go for "harp-synching" or early '70's bubblegum funk? It's got platinum written all over it!

Kamis, 17 Oktober 2013

The Odds of Going to the Hospital

What are the odds that you will need serious medical care?

By "serious medical care", most people will automatically think of a situation where they might need to be admitted to a hospital to receive care for an unforeseen condition, so that's the standard we'll use to answer that question.

Beyond that, we'll break the information down by age and sex, simply because we can see these being major factors that might affect how likely a person will need hospital care.

It turns out to be a really difficult question to answer, because in the U.S., which is where we first sought to get hospital utilization data, tracks hospital discharges - not admissions. The problem with that is that the number of admissions won't necessarily track with the number of discharges, as patients die or perhaps otherwise leave the hospital before being officially discharged.

So we turned elsewhere to answer the question, and specifically to the island nation of Singapore, whose Ministry of Health makes the data not only easy to find, but presents it in a way that helps us answer our specific questions. Our first chart below illustrates the 2011 hospital admission rates by age group and sex per each 1,000 members of Singapore's resident population:

Singapore: 2011 Number of Hospital Admissions per 1,000 Population, (Excludes Normal Deliveries and Legalized Abortions)

One interesting aspect of the data is that we see such high numbers for the 0-4 age group, which drops off dramatically for the 5-9 age group, which really didn't make a whole lot of sense to us at first. Why would a 4-year old have such a dramatically higher probability of being admitted to a hospital over a 5-year old?

We started thinking about it, and realized that the MOH's statisticians gave us a valuable clue - the number of hospital admissions for each 1,000 members of Singapore's resident population doesn't include hospitalizations associated with either normal deliveries for pregnancy or legalized abortions.

While both of these categories would count as foreseeable conditions, we suspect that the reason in the case of normal deliveries was in part to avoid double-counting. Here, where normal deliveries are concerned, we suspect that infants born in Singapore's hospitals are subsequently "admitted" to the hospital after being born, which is how the hospital admissions associated with normal deliveries are tracked.

Beyond that, we can see that the rate of hospital admissions for women of child-bearing age is over twice that of men of the same age, which likely corresponds to pregnancies that involved complicating factors requiring more intensive care, which would not count as a foreseeable condition.

Having worked out why that apparent anomaly exists, we used that knowledge to determine the probability of being admitted to a hospital for both men and women by age, reverse engineering Singapore's age-group based data to approximate the odds by single year of age from Age 0 through Age 84:

Probability of Hospital Admission for Men by Age (Singapore 2011)

Note how nearly 100% of those 0-year olds are admitted to the hospital! Next, let's look at the same data for women from Age 0 to Age 84:

Probability of Hospital Admission for Women by Age (Singapore 2011)

In looking at the differences in the data between men and women, we see that boys are more likely to be admitted to a hospital before Age 4, after which we see that both boys and girls have similar odds up until child-bearing becomes a factor. At that point, women are much more likely to require hospital admission than men (likely for the reasons we noted earlier), up until their mid-forties, after which, men become much more likely to require hospital admission.

The longer lifespan of women with respect to men likely explains that discrepancy, although we were surprised to see how wide that gap was by Age 84, with women having a 50% probability of being admitted to a hospital and men having almost a 90% probability.


Singapore Ministry of Health. Hospital Admission Rates* by Age and Sex 2011. [Online Report]. 10 November 2012. Accessed 8 October 2013.

Rabu, 16 Oktober 2013

Estimates of Nominal and Real GDP in the U.S. for 2013-Q3

Screen shot of BEA.gov web site, 15 October 2013

Oh no! The government isn't reporting any economic data!

That's something that might stymie a lesser economist, but we're not going to let a lame government shut down stop us!

That's why today, we're going to do the job that the furloughed employees of the Bureau of Economic Analysis won't be doing this month, unless the partial government shutdown ends really soon and they crank out a rush job. We're going to estimate what the United States' Gross Domestic Product will be for the just completed third quarter of 2013.

After all, we've previously found that it takes maybe as many as 2.5 economists in the private sector to do the same job that it takes 16 government economists to do, so just how hard could it be?

Technically, we're going to forecast it, but then, since it takes the BEA three attempts before they finally get close to a good number, forecast values for GDP are probably just as good as an official government estimated one.

Let's do this visually, so you can get a sense of where we came up with our estimate of GDP for 2013-Q3. Our first chart is one based on math that we have been developing to quantify and visualize the impact of changes in government spending, taxes and the Fed's quantitative easing programs upon the U.S. economy, but which we'll now use to project what nominal GDP will be reported to be for the third quarter of 2013:

Nominal U.S. GDP, With and Without QE 3.0/4.0, 2012-Q1 through 2013-Q3

Using 2012-Q3's GDP as our base point, our forecasting method has come within 0.02% of the actual figure for nominal GDP that was reported in 2012-Q4, 2013-Q1 and 2013-Q2, or rather, the three quarters preceding the third quarter of 2013. We are projecting a nominal GDP of $16,764.5 billion for the U.S. in 2013-Q3, with the following assumptions that apply since the end of 2012-Q3, which marks our base reference point:

  • Net Change in total assets held by Federal Reserve (QE): $927.8 billion

  • Net Change in government taxes: $168.9 billion

  • Net Change in government spending since 2012-Q3: -$21.0 billion

The first two quantities are pretty locked in at this point and won't likely be subject to future adjustment. The wild card in our forecast is the amount of government spending in the U.S., which consists of spending at the federal government level, as well as at the state and local level, for which we won't likely have a good estimate until late December 2013. Assuming that the BEA's data jocks get back on the job before then.

To get around that limitation, we went over data recorded from 1960 through 2012 to determine that average change in spending for both Federal and State & Local governments from the second quarter of each year to the third quarter to determine our estimate for this year. And you want to know the crazy thing about that? Even though the BEA shut down the computer system that reports historic data as part of their effort to completely flummox lesser economists, we didn't need to use their stinking site to get the historic GDP data on government spending at all.

Speaking of which, that value isn't something that would be impacted at all by the partial U.S. federal government shut down, which didn't begin until 1 October 2013, which is part of the fourth quarter of 2013.

Another factor we need to consider from better, private sector sources of information about the relative health of the U.S. economy is the possible return of organic economic growth, following the year-long microrecession experienced by the private sector of the U.S. economy from July 2012 through July 2013, which may have added a positive contribution to the GDP number. Since those conditions would appear to have resumed somewhat in September 2013 however, we think that contribution will be small, with the actual value likely to be reported to be very close to our forecast nominal GDP number.

As for real GDP, our inertial forecasting methods aren't quite as precise as they would seem to be for nominal GDP. Here, outside of periods where the U.S. economy has turned the corner from expansion to contraction, or vice versa, historical back-testing puts us within 2% of the value the BEA reports about 95% of the time, and within 1% of it almost 75% of the time.

Our second chart shows our projected value for real GDP in 2013-Q3:

Real GDP vs Climbing Limo Forecast vs Modified Limo Forecast, 2004Q1 through 2013-Q3

Here we anticipate that real, inflation-adjusted GDP in the U.S. will most likely fall in a range between $15,590.7 and $15,910.4 billion in terms of constant 2009 U.S. dollars, with a 95% probability of falling in a range between $15,430.9 and $16,070.2 billion.

By definition, it has a 50% probability of being above the midpoint of our forecast range, $15,709 billion. We think that given the relative increase in government spending from 2013-Q2 to 2013-Q3, combined with the positive contribution of organic economic growth, that real GDP in the third quarter of 2013 will indeed be reported to be above that level.

And there you have it - a simple blog just replaced the topline work of the Bureau of Economic Analysis for the third quarter of 2013 using just a handful of data points. We'd actually rather they be able to doing the job themselves, since the full extent of the data collection and reporting that they do is something that does have real world value, but we can't help but think that there ought to be a private sector alternative available to fully pick up the slack during times like these.

Selasa, 15 Oktober 2013

A New View of Future Expectations for the S&P 500

Now that Eugene Fama, Lars Peter Hansen and Robert Shiller have collectively been awarded the Economics Nobel prize for their insights into how asset prices work, insights that we both routinely apply and have extended in our own work, we'll take this opportunity to open up a new window for how all that applies to the S&P 500.

We'll do that by remaking our favorite chart - the one that shows how changes in the year-over-year growth rate of today's stock prices keep pace with changes in the year-over-year growth rates of the dividends per share that are expected at specific points of time in the future - replacing the dividend futures data we obtain from IndexArb with dividend futures data from the Chicago Board of Exchange, which are really different from one another. The chart below shows all that data for each future quarter's dividends going all the way from 3 January 2013 through 10 October 2013:

Change in Growth Rates of Expected Future Trailing Year Dividends per Share with Daily and 20-Day Moving Average of S&P 500 Stock Prices, through 10 October 2013

Each of the data series that apply for a future quarter's dividends per share represent the expectations that investors have for the amount of dividends they will earn in that quarter. In the absence of large sources of noise, or variance, changes in the growth rate of stock prices will closely track with the trajectories associated with a specific future quarter where investors collectively focus their forward-looking attention.

In the chart above, we see that's the case at the very beginning of 2013, where investors focused their attention on the expected future defined by the second quarter of 2013 in setting stock prices. The focus of investors remained on that quarter, which ended in June 2013, well into April 2013.

At that point, investors began shifting their forward-looking attention to the more distant future defined by the expectations for dividends associated with the first quarter of 2014. We observe this shift in focus in the transition of daily stock prices (the dotted blue line) from the data series for 2013-Q2 to 2014-Q1.

That attention stayed there until 19 July 2013, when stock prices suddenly deviated from where investors were focused in response to what we've called the Bernanke Noise Event. Here, investors reacted to the new information that Fed Chairman Ben Bernanke communicated at a press conference that the Fed was seriously considering tapering off its purchases of government-issued securities once certain economic targets were hit by sending stock prices considerably lower than they would otherwise have been set if only the expectations of future dividends to be paid in 2014-Q1 were driving them.

That reaction was more than the Fed was ready to handle at that time. It took a month of effort, but the Federal Reserve finally succeeded in restoring the expectation that investors previously had that there would be no tapering of its QE programs until 2014, which we observe in stock prices resuming to closely track the expectations for 2014-Q1's dividends. But then, positive economic data combined with statements by lesser Fed officials led investors to believe that the Fed could begin tapering its QE program before the end of the third quarter of 2013.

That set off a larger negative reaction in stock prices. Only here, investors shifted their focus away from the more distant future quarter of 2014-Q1 in setting stock prices to instead fully focus on the critical quarter of 2013-Q3. We observe that shift taking place from the end of the Bernanke Noise Event through the end of August 2013, which marked the high point for the expectation of investors that the Fed would being tapering its QE programs in September 2013.

And then, the real-time economic outlook for the U.S. economy began to take a turn back to the worse, leading investors to increasingly bet that the Fed would not act to cut back its QE programs at the end of 2013-Q3, which led to rising stock prices as investors refocused their attention toward 2014-Q1. The Fed then surprised many, including us, that it would not act in 2013-Q3 to trim its QE bond-buying spree, but in retrospect, the evidence from stock prices and the expectations for future dividends supports that interpretation of events.

Unfortunately, before they could make it back to the level that would be fully consistent with the expectations associated with 2014-Q1, a new negative noise event centered around the potential for a government shut down and partial default on the nation's debt reared its ugly head, causing stock prices to once again deviate away from the level they would otherwise be. And that brings us nearly up to the present.

If all this makes the stock market sound like a chaotic place, that's because it frequently is - but that doesn't mean there isn't a predictable order underlying it all. That's what lies beyond the work of newly-minted Nobel-prize winning economists Fama, Larsen and Shiller, whose work has made what we do possible.

Speaking of which, if you want to find out more about our work, it all begins here. You only have to review several years of worth of what we've worked out live, in real time, without the benefit of any sort of safety net to catch up to us!...

Notes: we've modified the chart in this post from previous versions by eliminating an additional scale factor of 12 that we were applying to both the changes in the growth rates of dividends and the change in the growth rate of stock prices, which was an artifact our annualizing the monthly data we were using when we first discovered the relationship between the two. Since this additional scale factor is applied to both dividends and stock prices, it effectively cancels out of our math describing how changes in the growth rates between the two are related, so we're taking this opportunity to dispense with it altogether.

Beyond that, we've also changed our amplification scale factor, which is the scale factor that matters in our math. This change was driven by our change in data sources, where there can be considerable differences between the dividend futures data reported by IndexArb and that reported by the CBOE. Using IndexArb's data, we had settled on a typical amplification scale factor of 9.0, while the factor we're opting to use for the present with the CBOE's data is 5.0.

Senin, 14 Oktober 2013

The Differences Between the Expected Futures for Dividends

We've previously discussed our sources for where we obtain the dividend futures data we use to track what investors expect at different points in time of the future, but we haven't shown how they compare with respect to one another, much less to how actual dividends per share play out!

We going to do that today using data for the just-ended third quarter of 2013. Our chart below shows how the data for 2013-Q3's expected cash dividends per share tracked from 3 January 2013 through the end of the calendar quarter on 30 September 2013:

Comparison of Expected Future for 2013-Q3 Cash Dividends per Share and Actual Final Value Reported by S&P, 3 Jan 2013 to 30 Sept 2013

As we noted before, the main difference between our primary sources of dividend futures data is how they determine how much the cash dividends per share will be at the end of the quarter they track. The Chicago Board of Exchange (CBOE) dividend futures contract uses a "top-down" approach, where the price of the contract is set by futures trading activity (if you access their data, the reported value is ten times the expected cash dividends per share for the quarter, so be prepared to shift the decimal point accordingly).

Meanwhile, IndexArb uses a "bottom-up" approach, which takes expected dividend per share data from each of the S&P 500's component companies and weights them according to their market capitalization within the index to create its expected cash dividend per share value. IndexArb also complicates its reporting for future quarters as the information it provides really indicates the total amount of estimated dividends per share for the index that will be paid out between the present (today) and the end of the dividends futures contracts upon which they're based.

That means that to find the expected amount of dividends per share that will be paid out in a given quarter, you have to take the total amount of dividends per share that will be paid out by the end of that quarter and subtract the total amount of dividends per share that will be paid out by the end of the preceding quarter. So, if we want to do find the value for 2013-Q3, we have to subtract the dividends per share that would be paid out by 2013-Q2 from it!

That creates some problems, which you can see in the chart above. Here, the data for 2013-Q3 from IndexArb effectively flatlines at the expiration of the dividend futures contract for 2013-Q2 on the third Friday of June 2013 (21 June 2013), because the futures data for the preceding quarter is no longer available for us to do that subtraction operation.

Market Volatility - Source: Schweitz Finance

We can also see differences in how the values start and change over time. Here, the CBOE's dividend futures data starts and a higher value than IndexArb's, but is subject to greater volatility, which you would expect given how its value is set.

The IndexArb data is less volatile, and although it begins at a lower value, we can see that it converges toward the values that the CBOE projects, at least through the end of the preceding quarter's data. Based on the trend we observe in the data before that time, we think that the two would converge very close to each other by the actual expiration of the dividend futures contracts on 20 September 2013.

Meanwhile, both of the expected dividend values for both sources fell short of the actual level of cash dividends per share of $8.909 that S&P reported for 2013-Q3 after the end of the calendar quarter on 30 September 2013.

We think the primary source of the discrepancy between the dividend futures and the actual value for cash dividends per share can be traced to the estimate of each S&P 500 component company's weighting within the index. S&P is the final arbiter of those values, while estimates used by others are just that - estimates. We should also note that there is also a bit of mismatch between the terms of the dividend futures contracts and the dividends that are paid out by the ends of the calendar quarters that S&P reports, which may also account for a good portion of the discrepancy between the futures and the actual data once it is reported.

Given our experience in tracking the data, what we find to be really remarkable that the dividend futures data is typically within a 3% margin of S&P's officially recorded value (that's true even of the three-month earlier cutoff for IndexArb in the absence of a real market-shaking event), and often, is within a much closer margin of error than that.

Speaking of which, since the CBOE data stays "live" longer than the IndexArb data, our next update of our favorite chart will be based solely on the CBOE's data, which we're going to unveil tomorrow. We were going to wait to do that development until our annual end of year hiatus, but it turned out to be a snap to do, and there's some really interesting insights that come out of it!

Image Credit: Schweitz Finance.

Data Sources

EODData. Implied Forward Dividends September (DVST). [Online Database]. Accessed 7 October 2013.

IndexArb. Dividend Analysis. [Online Data Report]. Accessed daily from 3 January 2013 through 21 June 2013.

Standard and Poor. S&P 500 Index Earnings and Estimates. [Excel Spreadsheet]. Accessed 7 October 2013.

Jumat, 11 Oktober 2013

Penguin Slapping

First, a right-thinking penguin describes their motive for slapping others:

Hippies, of course, being the among the groups of people who who are just a little too pleased with themselves. Speaking of which, penguins putting the slapdown on others would appear to be something that actually happens in nature:

Cultural evolution in action!

Kamis, 10 Oktober 2013

How Much Would a Federal Default Affect the U.S. Economy?

Since the single topic of the press conference that President Obama staged with his party's media collaborators on Tuesday, 8 October 2013 revolved around the topic of what could happen if the U.S. government chooses to default on its debt obligations, or as will more likely be the case, doesn't default on those obligations and instead doesn't spend as much as U.S. politicians would like it to spend, we thought we would go straight to the bottom line and find out how much the U.S. economy would be affected.

But first, we'll need some numbers, which CNBC tracked down for us:

Treasury Secretary Jack Lew is about to face the very same choices confronted by any financially struggling American household: Which bills to pay and when to pay them.

If Congress fails to raise the debt ceiling by around Oct. 17, Lew, who has been in the job less than a year, will have to sit at his desk and figure out how to make due on roughly one-third less in the way of government funds for the bills he has to pay. Because he can no longer borrow, according to the Bipartisan Policy Center, government spending will fall by about 32 percent, or $108 billion in the first month.

On a side note, to put that situation in context, this is no different from what could very well happen just 20 years from now when Social Security's trust fund has been fully depleted, as expected. At that time, the federal government will reduce all payments to Social Security beneficiaries by roughly 26%, unless it significantly increases the amount it borrows. And that's if everything goes as U.S. politicians have promised without any spending reform - this is one reason why the political fight over the debt ceiling and government spending levels is taking place now, because waiting will make needed reforms so much more painful. Not to mention, more necessary.

Back now to the question at hand: how much would a government spending cut of that magnitude affect GDP?

The good news is that we can answer that question with just back-of-the-envelope math! And we can do it on a "daily" basis.

The Multiplier Effect - Source: Lion Investing That $108 billion reduction in federal government spending works out to be $3.6 billion per day. We know that the GDP multiplier for all government spending in the U.S. is 0.6, which we know from research published by the U.S. Federal Reserve applies when the nation's official unemployment rate is over 7.5%. Which is the case at present, thanks to the furloughing of federal government employees! If it were under 7.5%, we would need to use a GDP multiplier of 0.5 to account for the shock of a sudden change in government spending, as government spending is considered to deliver even less of an impact to GDP when the economy is in a healthier state.

Taking our potential government spending reduction of $3.6 billion per day, and multiplying it by our GDP multiplier for government spending of 0.6, we find that the U.S. economy will lose out the equivalent of $2.16 billion worth of GDP per each day that Uncle Sam doesn't have his credit limit reset to a higher level.

Now, to measure the impact upon GDP, just multiply that number by the number of days the U.S. federal government operates in that situation!

If played out through the remaining 78 days of 2013, assuming we stick with President Obama's planned schedule for putting the U.S. federal government into default, that would reduce the nation's GDP for the fourth quarter of 2013 by $168.48 billion.

To put that number into perspective, the fiscal drag produced by the $56.3 billion by which U.S. federal taxes will be higher in the fourth quarter of 2013 than they were in the fourth quarter of 2012 thanks to President Obama's tax hikes that took effect back in January 2013, GDP in the U.S. will be nearly $168.92 billion smaller in 2013-Q4 than it would otherwise have been given the GDP multiplier for taxes.

Why, that's almost exactly the same amount! Perhaps that explains why President Obama has been so intent on doubling down on his "no negotiation with the duly elected representatives of American citizens" strategy - he'll produce twice the negative fiscal drag on the U.S. economy in 2013-Q4 if only he and his supporters can stick with it!

And yes, numbers like those mean a recession, as the Federal Reserve's quantitative easing programs won't produce enough juice for the economy to offset that kind of fiscal drag, offsetting only somewhere between $250 billion and $290 billion of the hit if the debt ceiling isn't increased by 31 December 2013.

Of course, if the debt ceiling situation is resolved sooner than than, it is very much possible that the U.S. will have positive economic growth in 2013-Q4 - only seeing slower growth than it would have had instead. Which is pretty much the story for every quarter during President Obama's entire tenure in office.