Please answer the given financial question based on the context.
Context: 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: .
||2013|2012|2011|
|expected volatility|28.9% ( 28.9 % )|27.8% ( 27.8 % )|27.3% ( 27.3 % )|
|risk-free interest rate|0.7% ( 0.7 % )|0.8% ( 0.8 % )|1.7% ( 1.7 % )|
|dividend yield|3.2% ( 3.2 % )|3.2% ( 3.2 % )|2.7% ( 2.7 % )|
|expected life ( in years )|4.5|4.5|4.4|
|contractual life ( in years )|7.0|7.0|7.0|
.
Question: what was the percentage change in the expected volatility from 2012 to 2013


Answer: The answer is:0.03957