For at least the last seven years, the highest and lowest price for IBM (NYSE:IBM) shares have traded within a range well defined by earnings per share. The actual data (source: Value Line) are:
Year 
Earnings per Share 
High Stock Price 
Low Stock Price 
2007 
$ 7.18 
$ 121.50 
$ 88.80 
2008 
$ 8.93 
$ 130.90 
$ 69.50 
2009 
$ 10.01 
$ 132.90 
$ 81.80 
2010 
$ 11.52 
$ 147.50 
$ 116.00 
2011 
$ 12.95 
$ 194.90 
$ 146.60 
2012 
$ 15.13 
$ 210.59 
$ 179.16 
2013 
$ 16.28 
$ 215.80 
$ 173.37 
A regression analysis was used to determine a good fit between earnings and prices. The High Stock Price over the past seven years is well approximated by the formula,
High Stock Price = 11.868 X (Earnings per Share) + $25.847
The Low Stock Price over the past seven years is well approximated by the formula,
Low Stock Price = 10.572 X (Earnings per Share)
The following graph displays the fit of the equations to the data.
Earnings per share
IBM is followed by several analysts who provide estimates of earnings for the current and next fiscal years. (Source: Yahoo Finance) The average estimates are displayed in the table below:
FY 2014 
FY 2015 

Number of Analysts 
26 
25 
Average Earnings Estimate 
$17.89 
$19.81 
Assuming these earnings estimates are credible, they can be used in the derived regression equations to estimate the range of trading values in 2014 and 2015.
FY 2014 
FY 2015 

Estimated lowest trading price 
$ 187.34 
$207.45 
Estimated highest trading price 
$ 233.96 
$255.73 
These estimates are extremely imprecise for a number of reasons. First, the original data are based upon one extreme value (maximum or minimum) over the course of a year. Second, the estimated maximums and minimums are for only one trading value over the course of a year into the future. Nevertheless, they do provide a very crude, but data based, guess about the most plausible trading range.
These trading ranges can be used to derive practical trading rules. While there are a number of ways to do this, I am dividing the trading range into thirds and regarding the lowest third as a buy range, and the highest third as the sell range. I propose the following trading rules:
BUY IF < 
SELL IF > 

FY 2014 
$202.88 
$218.42 
FY 2015 
$223.54 
$239.64 
At the current price of about $186, IBM would appear to be well within the BUY range. On the high end, a gain of up to 22% seems plausible over the next year and one half or so. The downside risk would appear to be relatively small.
Disclosure: I am long IBM. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.