pre_text: republic services , inc . notes to consolidated financial statements 2014 ( continued ) the plan to reflect the allied acquisition . the 2006 plan , as amended and restated , provides for the grant of non- qualified stock options , incentive stock options , shares of restricted stock , shares of phantom stock , stock bonuses , restricted stock units , stock appreciation rights , performance awards , dividend equivalents , cash awards , or other stock-based awards . awards granted under the 2006 plan prior to december 5 , 2008 became fully vested and nonforfeitable upon the closing of the acquisition . awards may be granted under the 2006 plan , as amended and restated , after december 5 , 2008 only to employees and consultants of allied and its subsidiaries who were not employed by republic prior to such date . as of december 31 , 2013 , there were approximately 15.6 million shares of common stock reserved for future grants under the 2006 plan . stock options we use a lattice binomial option-pricing model to value our stock option grants . we recognize compensation expense on a straight-line basis over the requisite service period for each separately vesting portion of the award , or to the employee 2019s retirement eligible date , if earlier . expected volatility is based on the weighted average of the most recent one year volatility and a historical rolling average volatility of our stock over the expected life of the option . the risk-free interest rate is based on federal reserve rates in effect for bonds with maturity dates equal to the expected term of the option . we use historical data to estimate future option exercises , forfeitures ( at 3.0% ( 3.0 % ) for each of the periods presented ) and expected life of the options . when appropriate , separate groups of employees that have similar historical exercise behavior are considered separately for valuation purposes . the weighted-average estimated fair values of stock options granted during the years ended december 31 , 2013 , 2012 and 2011 were $ 5.27 , $ 4.77 and $ 5.35 per option , respectively , which were calculated using the following weighted-average assumptions: .
post_text: .
table: 2013 2012 2011
table: Expected volatility 28.9% 27.8% 27.3%
table: Risk-free interest rate 0.7% 0.8% 1.7%
table: Dividend yield 3.2% 3.2% 2.7%
table: Expected life (in years) 4.5 4.5 4.4
table: Contractual life (in years) 7.0 7.0 7.0
question: Analyse this data from a financial earnings document. what was the percentage change in the expected volatility from 2012 to 2013