The Anne Hathaway Effect

I recently stumbled upon this article in the Huffington Post which claims that every time Anne Hathaway gets a lot of Internet attention (for releasing a movie, hosting the Oscars, or what have you), the stock price for Berkshire Hathaway shoots up. The author, Dan Mirvish, justifies the plausibility of this by saying that "My guess is that all those automated, robotic trading programming are picking up the same chatter on the internet about "Hathaway" as the IMDb's StarMeter, and they're applying it to the stock market." 


The data they use to support the claim is that 

Oct. 3, 2008 - Rachel Getting Married opens: BRK.A up .44%Jan. 5, 2009 - Bride Wars opens: BRK.A up 2.61%
Feb. 8, 2010 - Valentine's Day opens: BRK.A up 1.01%
March 5, 2010 - Alice in Wonderland opens: BRK.A up .74%
Nov. 24, 2010 - Love and Other Drugs opens: BRK.A up 1.62%
Nov. 29, 2010 - Anne announced as co-host of the Oscars: BRK.A up .25%

I think the first commenter put it well when s/he said 

"First!"

Nah, just kidding. Here's what they really said:

This is junk statistics if I've ever seen it. There may be something to the automated trading idea, but these data are proof of nothing. How about the hundreds of other times Ms. Hathaway was in the news and the stock didn't rise so dramatical­ly? How volatile is this stock normally? Are these percentage increases anything out of the ordinary?
Exasperate­d, I decided to d a quick test. I downloaded the BRK.A data from Jan. 1, 2008 to Mar. 18, 2011 from YAHOO Finance and did a trivial analysis of it in Matlab. Just looking at the difference between open and close prices, the stock was up 0.25% or more 308 times over this period. The stock was up 2.61% or more 47 times over this period. Those two percentage­s are the lowest and highest in Mr. Mirvish's "data."
As a scientist and math lover I've disappoint­ed to see this story making the rounds with so little skepticism­. It's a statement for the level of understand­ing of statistics and probabilit­y by the general public.

Looks like I'm not the only mathbuster out there. 


My first complaint about this (and backing up commenter number 1) is that, as someone who does not follow stocks at all, I have no idea if a .74% increase in BRK.A is anything notable.  Having downloaded the stock prices since 2008 from Google Finance, I can tell you that it isn't.  When Rachel Getting Married opened, the .44% increase was in the 68th percentile of changes in price... including negative changes. It was only in the 32nd percentile of positive changes. Even the biggest change of 2.61% is only in the 92nd percentile overall. Certainly not a tail event.  Getting to the point, it's not like every time Anne Hathaway gets naked with Jake Gyllenhaal, the stock holders all go out and by themselves a brand new G6. It's a pretty normal fluctuation. 

Over the period from 2008 to yesterday, the stock increased about 47% of the time. Since we are apparently completely disregarding the magnitude of the change, the probability of getting all positive changes when randomly selecting 6 dates out of the 828 trading days is quite small. But what would be the chances of looking at, say, 10 different dates and finding that 6 or more of them are positive?? If we ignore the issue of replacement (which shouldn't be horribly important since the sample size is 828 and we are only sampling 10), the probability of getting exactly 6 is about 18%, and the probability of getting 6 or more is about 31%. 


Given that the hypothesis is that the stock price is getting this little upward nudge because of Internet chatter, I checked out Google Trends to find other likely dates that the stock should increase under this hypothesis. Luckily, Google even shows you what the major news stories are on some of the major peaks, so it is easy to figure out the date.

Google Trends for Anne Hathaway
The top line is search volume and the bottom is news volume. They pick out many of the same spikes.

Two big peaks we see on here that haven't already been accounted for in the original post are B, Anne Hathaway Proclaims Love For ‘Family Guy,’ ‘Aqua Teen,’ Fulfills Nerd Vision Of Idealized Woman, on February 23, 2009 and C, Anne Hathaway spends spare time studying physics, on February 2, 2010. On these two dates, BRK.A saw a 1.82% and .11% decrease respectively.  Further, when on June 20, 2008 the Los Angeles Times posted a story called Anne Hathaway versus Jessica Alba  resulting in the very visible spike in 2008 (I guess everyone likes a good ladyfight), BRK.A experienced a -.79% change. On the opening day of Get Smart, June 20, 2008, BRK.A fell .79%, and if we go back just a little bit further to December 9, 2005, the day that Brokeback Mountain had its major opening in the US, BRK.A dropped .07%. In fact, the sample correlation between Anne Hathaway's Internet search traffic and the price of BRK.A for 2008 to yesterday was just .01-- basically uncorrelated.** 


Given all of this, I'm really hoping that Dan Mirvish didn't run out and by up a bunch of BRK.A hoping that his post would force the price up a bit. :) 


**This, of course, does not rule out the case that the fancy trading algorithms only act based on spikes in search volume, not normal activity, but just sayin'...