19 May 2014

Who holds (and has held) Federal Debt?

Via the outstanding FRED Blog, this is a graphic that shows how the composition of Federal debt-holders has evolved over time. The FRED Blog posted this data as a pie chart showing the current composition. I thought it would be more interesting to show the evolution. The left axis shows the percent (totaling 100).

The brown area shows the percentage of outstanding Federal debt held by foreign and international investors. The white area is the percentage held by domestic investors.* The green area is the percentage held by the Federal Reserve.





*The amount of Federal debt held by domestic investors is not calculated directly, so this series is determined by arithmetic.

24 April 2014

Apple Split



I'm trying to wrap my head around the "efficient-markets" meaning of the Apple split. I guess the entire notion of stock splits seems to me to be in violent conflict with EMH. It seems I'm not the only one who's scratched his head over this. 

While the authors of those links are concerned chiefly with the event-study implications (positive signaling and so forth), I am more curious about how to reconcile EMH with the idea that a cheaper share price should make a stock more attractive. Surely the first splits were not conducted as a signal; they were meant to draw in more investors by making the stock easier to buy. Only later, I imagine, did market actors begin to interpret splits as a sign that a firm was prospering. 

Neil Irwin best captured the absurdity of the idea of drawing in more investors with a split:
"The logic, presumably, is that there may be people who really want to invest in Apple, yet want to do so in chunks smaller than $530, (which raises a question of why somebody who can’t come up with $530 to invest would be investing in individual stocks to begin with)."
So maybe it is just about signaling. But, even that aspect is troubling. If a firm's prospects could be measured on a one-dimensional index (call it theta (0 < theta < infinity)), firms may decide to split their stock when theta reaches a certain value theta0. Market actors will subsequently learn that a split is an indication that management believes theta=theta0, and incorporate this into their information portfolio.

Grasping and impatient firms may then try to goose their share prices by splitting at, say, 0.9theta0. This will lead firms who would have waited until theta0 to split at 0.9theta0. Market actors will then adjust their beliefs about splits to mean a firm has theta=0.9theta0. The graspers may then split at 0.8theta0. This spiral will continue until market actors begin to believe that splits have no meaningful informational value. 

Yet we still see that market actors believe splits have informational value. Is the answer that there are no impatient and grasping firms? That seems unlikely. I think the most plausible explanation for (positive) market reactions to splits is that many market actors (lone wolves and institutional investors alike) have no idea what in world a given split means, except that it means that the price will go up, so they buy (hoping they are) on the up-slope.

Irwin's post has a link to Dhar, Goetzmann, Zhu, and Moscow, which found that the lower prices created by splits attracts individual idiots and has no impact on institutional investors. Irwin cites this as Warren Buffett's reason for never splitting BRK.A. Matthew Yglesias speculates that the Apple split could be aimed at getting inclusion on the Dow index, but notes that this would not likely generate much value.

However one chooses to look at it, a meaningful impact from stock splits is generally incompatible with EMH.

22 April 2014

2014 Patriots Draft: Historical Comparisons

I recently posted a study of Belichick-era Patriots draft picks, based on the expected draft position of the Patriots in 2014. In this post, I will compare the "average player" taken by the Patriots at those positions since 2000 with the "average player" taken league-wide over the same span.



Games per year: 14.26 / 12.83 = 1.11
(This indicates that Patriots draftees in this range play 11% more games per year on average than their peers.)

Starts per year: 13.06 / 8.17 = 1.60

Pro Bowl trips: 2.33 / 0.63 = 3.70
All-Pro selections: 0.33 / 0.14 = 2.36

Years as primary starter: 7.00 / 3.45 = 2.03

Career length*: 7.67 / 5.90 = 1.30

Weighted career approximate value**: 51.67 / 27.07 = 1.91

Belichick grade***: 1.66

This is outstanding. Belichick-drafted players in this range could be thought of as 66% better than the league average in this range.



Games per year: 8.96 / 11.03 = 0.81
Starts per year: 5.82 / 6.27 = 0.93

Pro Bowl trips: 0.00 / 0.35 = 0.00
All-Pro selections: 0.00 / 0.04 = 0.00

Years as primary starter: 2.20 / 2.60 = 0.85

Career length: 4.60 / 5.36 = 0.86

Weighted career approximate value: 15.02 / 20.31 = 0.75

Belichick grade: 0.80

This is a lesser area for Belichick. Players he has drafted have consistently underperformed their peers.



Games per year: 5.29 / 10.44 = 0.51
Starts per year: 1.21 / 4.24 = 0.29

Pro Bowl trips: 0.00 / 0.10 = 0.00
All-Pro selections: 0.00 / 0.05 = 0.00

Years as primary starter: 0.17 / 1.61 = 0.11

Career length: 2.83 / 4.67 = 0.61

Weighted career approximate value: 1.83 / 13.20 = 0.14

Belichick grade: 0.33

This is abysmal. There's really no other way to put it. For Belichick, this range, in relative terms, has been a failure.


#130 (Patriots) (league)

Games per year: 8.58 / 8.41 = 1.02
Starts per year: 4.10 / 2.70 = 1.52

Pro Bowl trips: 0.00 / 0.03 = 0.00
All-Pro selections: 0.00 / 0.00 = [N/A]

Years as primary starter: 0.80 / 0.90 = 0.89

Career length: 4.00 / 3.95 = 1.01

Weighted career approximate value: 10.80 / 8.71 = 1.24

Belichick grade: 1.14

This is a value area for Belichick. He drafts players in this range that are 14% better than their peers.


#140 (Patriots) (league)

Games per year: 8.42 / 9.24 = 0.91
Starts per year: 1.17 / 2.98 = 0.39

Pro Bowl trips: 0.00 / 0.18 = 0.00
All-Pro selections: 0.00 / 0.08 = 0.00

Years as primary starter: 0.00 / 1.45 = 0.00

Career length: 2.5 / 4.42 = 0.57

Weighted career approximate value: 3 / 10.79 = 0.28

Belichick grade: 0.52

Belichick players are about half as good as their peers in this range. It's not the train wreck that #93 is, but this is not good, by any measure. 


#198 (Patriots) (league)

Games per year: 7.99 / 6.01 = 1.33
Starts per year: 2.04 / 1.90 = 1.07

Pro Bowl trips: 1.29 / 0.14 = 9.21
All-Pro selections: 0.29 / 0.02 = 14.50

Years as primary starter: 1.71 / 0.72 = 2.38

Career length: 3.71 / 3.12 = 1.19

Weighted career approximate value: 25.67 / 8.06 = 3.18

Belichick grade: 2.14

This is obviously Belichick's best range, given the inclusion of Tom Brady. Even excluding Brady, Belichick's score for this range is 1.64, which is still very good.


#206 (Patriots) (league)

Games per year: 6.46 / 6.51 = 0.99
Starts per year: 1.53 / 1.69 = 0.90

Pro Bowl trips: 0.00 / 0.03 = 0.00
All-Pro selections: 0.00 / 0.00 = [N/A]

Years as primary starter: 0.43 / 0.53 = 0.81

Career length: 3.57 / 3.10 = 1.15

Weighted career approximate value: 7.00 / 7.18 = 0.98

Belichick grade: 1.00

This is Belichick's most "average" drafting position. 


#244 (Patriots) (league)

Games per year: 6.92 / 6.17 = 1.12
Starts per year: 2.00 / 1.55 = 1.29

Pro Bowl trips: 0.00 / 0.01 = 0.00
All-Pro selections: 0.00 / 0.00 = [N/A]

Years as primary starter: 0.33 / 0.46 = 0.72

Career length: 3.00 / 2.86 = 1.05

Weighted career approximate value: 7.00 / 5.01 = 1.40

Belichick grade: 1.20

This is another top value area for Belichick.


Overall grade: 1.11

This score indicates that, over the range of picks the Patriots have this year, Belichick has drafted 11% better than league average. Without Brady, his overall grade is still 1.04.



*Note that this number is computed using both active players and players out of football, and is therefore not to be interpreted as reflecting an entire career.

**See explanation here. See more explanation here.

***This is the total of the Patriots numbers divided by the total of the league numbers. A score of 1.0 represents a quality equal to that of the league. A score of 1.23 can be interpreted as 23% better than the league average.

21 April 2014

2014 Patriots Draft: A Historical Perspective

In preparation for the upcoming NFL Draft, I wanted to have a look at what the Patriots have done at or near the selections they've got this year. I gathered data on their past drafts from Pro Football Reference, and the projected picks from WEEI. I will look at all picks within three of the expected picks in order to gather a more meaningful amount of data. I will post a followup after the draft, as the likelihood the Patriots use all of these picks and no others asymptotically approaches zero. The statistics can be viewed as representative of an "average player" drafted in a given area by Belichick since 2000.


The picks currently held by the Patriots are as follows:
First round: No. 29 overall
Second round: No. 62 overall
Third round: No. 93 overall
Fourth round: Nos. 130 and 140 (140 is compensatory — the last pick of the fourth round)
Fifth round: None (pick dealt to Philadelphia in Isaac Sopoaga trade)
Sixth round: Nos. 198 (via Eagles as part of Sopoaga trade) and 206
Seventh round: No. 244


Players: Devin McCourty, Ben Watson, Logan Mankins

Games per year: 14.26
Starts per year: 13.06

Pro Bowl trips: 2.33
All-Pro selections: 0.33

Years as primary starter*: 7

Career length*: 7.67

All told, a Belichick selection in this area is a solid, if unspectacular, starter.



Players: Aaron Dobson, Terrence Wheatley, Brandon Spikes, Marquise Hill, Deion Branch

Games per year: 8.96
Starts per year: 5.82

Pro Bowl trips: 0
All-Pro selections: 0

Years as primary starter: 2.2

Career length: 4.6

This player is a marginal starter, and is likely viewed as a disappointment, considering draft position.



Players: Taylor Price, Jake Bequette, Duron Harmon, Kevin O'Connell, Guss Scott, Kenyatta Jones

Games per year: 5.29
Starts per year: 1.21

Pro Bowl trips: 0
All-Pro selections: 0

Years as primary starter: 0.17

Career length: 2.83

This player is a largely replaceable special teamer or backup.



Players: Greg Randall, Kareem Brown, Cedric Cobbs, Jonathan Wilhite, James Sanders

Games per year: 8.58
Starts per year: 4.10

Pro Bowl trips: 0
All-Pro selections: 0

Years as primary starter: 0.8

Career length: 4

This player, like #93, is primarily a special teamer or backup, but, interestingly, plays and starts more than #93, and over a longer career.



Players: Marcus Cannon, Dave Stachelski

Games per year: 8.42
Starts per year: 1.17

Pro Bowl trips: 0
All-Pro selections: 0

Years as primary starter: 0

Career length: 2.5

Small sample size here, but this player is primarily a backup, though one that plays a lot.



Players: Bo Ruud, Nate Ebner, Jake Ingram, Tom Brady, Leonard Myers, David Nugent, Kliff Kingsbury

Games per year: 7.99 (7.03)
Starts per year: 2.04 (0.11)

Pro Bowl trips: 1.29 (0)
All-Pro selections: 0.29 (0)

Years as primary starter: 1.71 (0)

Career length: 3.71 (2)

The main numbers here show a pretty good player, but there is an outlier in the list above that skews the statistics. Stripping out the outlier, the numbers in parentheses reflect a player that plays a lot, but over a short career, starting very infrequently.



Players: Ted Larsen, Thomas Welch, Myron Pryor, Justise Hairston, Corey Hilliard, Dan Stevenson, Le Kevin Smith

Games per year: 6.46
Starts per year: 1.53

Pro Bowl trips: 0
All-Pro selections: 0

Years as primary starter: 0.43

Career length: 3.57

This reflects another backup or special-teams player. Not bad for this low in the draft, however.



Players: Ethan Kelley, Mike Elgin, Brandon Deaderick

Games per year: 6.92
Starts per year: 2.00

Pro Bowl trips: 0
All-Pro selections: 0

Years as primary starter: 0.33

Career length: 3.00

This is another area in which the typical Belichick player is likely better than average, considering draft position.


I will follow up soon with comparisons of Belichick-era Patriots draft picks with league-wide averages in the Belichick era.



*Note that this number is computed using both active players and players out of football, and is therefore not to be interpreted as reflecting an entire career.