# S&P back of the envelope, from Duncan Coker

May 16, 2013 |

Some back of the envelope numbers on S&P500  futures daily changes last 10years for your perusal:

```Year       %up       Max       Min        SDev

2003      55%       28           -29         10

2004      57%       18           -21         8

2005      54%       21           -21         8

2006      53%       26           -25         8

2007      52%       44           -57         14

2008      50%       127         -100         27

2009      56%       54           -42         14

2010      58%       48           -41         12

2011      51%       59           -85         18

2012      51%       42           -35         12

2013      65%       25           -38         11
```

## Alex Castaldo ponders:

The standard deviation for a binomial is the famous sqrt(N p q) and the standard deviation for a proportion is sqrt(p q / N).  Assume p=0.54 q=0.46 and N=252 days per year. Then sd= 3.1%. The proportions for 2003 through 2012 are within usual confidence intervals.

But for the year 2013 we have only N=95 trading days so far. In that case sd= 5.1%.  So the observed 65% is about 2.16 standard deviations above the expected.  Yes, it is statistically significant but not hugely so.

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