Please answer the given financial question based on the context.
Context: republic services , inc . notes to consolidated financial statements 2014 ( continued ) in december 2008 , the board of directors amended and restated the republic services , inc . 2006 incentive stock plan ( formerly known as the allied waste industries , inc . 2006 incentive stock plan ( the 2006 plan ) ) . allied 2019s stockholders approved the 2006 plan in may 2006 . the 2006 plan was amended and restated in december 2008 to reflect that republic services , inc . is the new sponsor of the plan , that any references to shares of common stock is to shares of common stock of republic services , inc. , and to adjust outstanding awards and the number of shares available under the plan to reflect the 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 waste industries , inc . and its subsidiaries who were not employed by republic services , inc . prior to such date . at december 31 , 2012 , there were approximately 15.5 million shares of common stock reserved for future grants under the 2006 plan . stock options we use a 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 period 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 , 2012 , 2011 and 2010 were $ 4.77 , $ 5.35 and $ 5.28 per option , respectively , which were calculated using the following weighted-average assumptions: .
||2012|2011|2010|
|expected volatility|27.8% ( 27.8 % )|27.3% ( 27.3 % )|28.6% ( 28.6 % )|
|risk-free interest rate|0.8% ( 0.8 % )|1.7% ( 1.7 % )|2.4% ( 2.4 % )|
|dividend yield|3.2% ( 3.2 % )|2.7% ( 2.7 % )|2.9% ( 2.9 % )|
|expected life ( in years )|4.5|4.4|4.3|
|contractual life ( in years )|7.0|7.0|7.0|
.
Question: what was the percent of the change in the dividend yield from 2011 to 2012


Answer: The answer is:0.18519