# Briefly Speaking, from Victor Niederhoffer

October 30, 2008 |

Some of the sophisticated media, including the most used ones are subtle in how they bias their news for their own man in the election. They report original studies using their own data that in the last 20 elections the market has moved better under their favored administration than in their least favored one in the first year. With 25 elections, and a starting point, and one of four years, or cumulatives to work with, and leaving out that the main reason the market is down is that the election is in the bag already, they leave it to the reader to overcome their natural aversion to favor the administration that will enable them in their platform to keep more of their after service gains.

The attempt to propagandize using stats in an indirect way, rather subtle compared to their usual attempts to objectively debunk any claims that the other side makes against their favorite,(thereby maintaining their je na sais quoi with their founder and his votaries), elicits an important formula. The variation or standard error of a mean without replacement is considerably lower than its variation with replacement. Thus, a sample of the stats that we all use when searching for regularities in past patterns are based on replacement. The standard error withour replacement is lower than the standard error with replacement by a factor sqrt ( 1 - n/N) where n is the sample size and N the population. Thus with a sample of 10 from a population of 25 where the standard deviation is 25 %, the standard error would not be the usual 25/3 but 8 x 3/4 = 6. 25% of the area of a normal curve is within 0.7e standard dev from the mean. That means that we would expect 1/2 of all means of 10 observations from such a distribution to be greater than 4 away from the grand mean of say 10 percentage points. The average difference between the better performaing group and the worse performing group would be approximately 8 percantage points. When we look for regularities we generally don't choose just one split but 3 or 4 or 10 until we find the best one. That runs into another statistical problem relating to the average difference between succesive samples from a distribution. A short approximation for that is contained in Kendall and Stuart, but looks to be approximately equal to an average difference for a normal distribution of 2/3 of a standard deviation (one must check that). Thus if we take the best of 2 cuts of 10 from a distrition like the above, we could expect the best one to be 8 away( 4 +2/3 x 6 ) from the grand mean a full 80% more than the grand mean approximately 1/2 of the time. This explains why so many of the regularities discovered with many different qualifiers, if's and or buts, stops et al are purely artifices of randomness rather than propaganda as above. It also explains why such programs as artificial interaction detector and cart often give such spurious results. The whole subject cries out the artful simulater.

## Steve Ellison replies:

The Political Economist studied this last month:

I've run the numbers myself. Superficially at least, the Democratic claims are true: Since 1948, the Standard & Poor's 500 total return (capital gains plus dividends) has averaged 15.6% when a Democrat was in the White House and only 11.1% when a Republican was in the White House.

You get a similar result if you look at growth in real gross domestic product. Under Democratic presidents, the average since 1948 has been 4.2%. Under Republican presidents it has been only 2.8%.

But it's not so simple when you study that 'study.' … While stocks could be expected to react very quickly to changes and expectations of changes in the political environment, the whole economy doesn't just turn on a dime. So when we compare real GDP growth under Democratic and Republican presidents, maybe we should lag the results by a couple years. That is, we'll assume that the growth in a given year was the result of the president's policies from two years ago.

When we do that … we find that the economy performed pretty much exactly the same regardless of the president's party: 3.5% under Democrats and 3.4% under Republicans.

But then who ever said that the president alone determines the economy or the stock market? It's Congress that makes the laws. The president just signs them. Based on congressional control, the study results look very different. Under Republican Congresses, stocks have averaged a 19% return, while under Democratic Congresses only 11.9%. Real GDP growth, lagged two years, has averaged 3.7% under Republican Congresses, and only 3.2% under Democratic ones.