Economics

Are Stock Prices Random?

A lot of people spend a lot of time trying to understand stock prices:  Are they predictable?  Are they random?  Can you make money by identifying trends?  Can you beat the market and make a fortune?

A prevailing theory is that stock prices are essentially random walks; that is, no more predictable than a coin flip.  The amount a price goes up or down at any given moment might follow some pattern (small movement is more likely than large movement, for example), but whether that movement is up or down is basically random.  Now, what random means to mathematicians can get kind of complicated, but that’s another story.

I thought it might be interesting to compare actual stock prices to a randomly-generated trend line.  After playing around with a spreadsheet and experimenting with different parameters, I produced the following two graphs:

Stock Graphs

One of these graphs represents 200 days of prices of the Dow Jones Industrial average; the other represents a quantity that moves up or down randomly, by some random amount.  Figuring out how to get a good-looking random graph took some time, and is an interesting challenge in and of itself.

So, can you tell which is the Dow and which is a coin toss?  More importantly, how much would you be willing to bet on it?

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By patrick honner, ago

Tighter Airline Seats

new airline seatThere is an interesting article in the Times about a new kind of airline seat.  Amusingly called the SkyRider, it’s more squat than seat.  I think the look on this guy’s face says it all.

Not surprisingly, this is all about money–and a lot of it.  This seat has a pitch of 23 inches; pitch is airline jargon for the distance between a point on a seat and the identical point on the next seat, sort of like the wavelength of a wave.  On typical commercial aircraft, pitch is closer to 32 inches.  An airline could therefore install many more of these new seats, and of course, more seats means more tickets means more money.

For instance, on an aircraft with 20 rows of seats with a 32-inch pitc you could get almost 28 rows of SkyRiders in there.  That’s 8 extra rows, so about 48 extra tickets.  At two or three hundred dollaras per ticket, that’s a nice increase in revenue–on the order of an extra $10000 per flight.  You could even charge less for these seats and still make more money.

As bad as this sounds, it’s not nearly as objectionable as paying to use the bathroom on a plane.

By patrick honner, ago

Bagel-nomics

bagelI have a natural tendency toward the quantitative side of things.  That, together with a substantial history of employment in the food service industry, has doomed me to forever over-analyze menu prices.

I recently realized that my local bagel shop has been charging me an outrageous premium for premium cream cheese.  The cost of a bagel is 95 cents, and a bagel with cream cheese is $1.90; these are pretty standard prices around town.

But here’s the kicker:  a bagel with scallion cream cheese at this place is $3.25.  That’s an additional $1.35–not for the cream cheese, mind you, but for the upgrade of scallion cream cheese over plain cream cheese.

Scallions.  Scallions are like onion weeds.  I buy a bundle of ten of them for 40 cents, use three of them, and then toss the rest, probably because they’ve wilted within two days of purchase.  They are expendable stalks at the bottom of the vegetable pyramid–savory and crisp, yes, but almost literally a dime-a-dozen.  If anything, scallion cream cheese should be cheaper than plain cream cheese, because whatever volume of cream cheese is being replaced by the scallions is almost certainly more valuable than the scallions themselves.

The guys behind the counter seemed sympathetic to my argument, but they still charged me $3.25.

By patrick honner, ago

More on Kovalchuk’s Contract

kovalchuk 2The National Hockey League has approved the new contract between the New Jersey Devils and Ilya Kovalchuk.  As discussed in an earlier post, the NHL voided the initial contract between the two parties, essentially on the grounds that it violated the spirit of the league’s salary cap rules.

The Devils originally signed Kovalchuk to a 17-year, $102 million contract.  By the NHL’s salary cap rules, this would have counted as 102/17 = 6 million dollars per year against the team’s salary cap (their yearly spending limit on players).

However, it was fairly clear from the structure of the deal that neither side expected the final five years to be played out.  Kovalchuk was to earn the league minimum for those five years, and he would have been in his 40s.  So the league viewed this really as a 12-year, $98 million dollar deal, which should count 8 million dollars plus per year against the team’s cap.

Through clever accounting, the team had created an extra $2 million per year in financial flexibility, but the league saw the matter differently.  The league, team, and player eventually compromised on a 15-year, $100 million deal (a 6.67 million dollar cap hit), and some changes have been made to the league’s salary cap policy so problems like this won’t arise in the future.  Until the next loophole is discovered, anyway

By patrick honner, ago

Football Economics

This is a nice, short profile of David Romer, an economist and lifelong sports fan who briefly turned his attention to football some years ago.

http://www.nytimes.com/2010/09/05/sports/football/05romer.html

In 2002, Romer wrote the first serious academic paper asking the question “When should football teams go for it on 4th down?”, applying rigorous analytical from economics and mathematics.

belichickHere’s the simple summary:  a touchdown in football is (usually) worth 7 points, and a field goal is worth 3 points.  A team will often face the situation that, on 4th down, they can either kick a field goal with a relatively high probability of success (say 80-90%), or they can go for it on 4th down (which has something closer to a 40-50% success rate) and continue to try for the touchdown (not a guarantee).

Romer’s conclusion was basically that teams should go for it on 4th down far more often than they do.  This is essentially an expected value argument:  if, by going for it, you get 7 points about 40% of the time, that’s an average of 2.8 points per attempt; if, by kicking the field goal, you get 3 points about 80% of the time, that’s an average of 2.4 points per attempt.  So in the long run, going for it will produce more points.

However, the fact is that teams rarely go for it on 4th down, usually only trying this strategy in desperate times.  So what account for the difference between the theoretical conclusion and the practice of professionals?

By patrick honner, ago
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