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%
27.3%
28.6%
Risk-free interest rate
0.8%
1.7%
2.4%
Dividend yield
3.2%
2.7%
2.9%
Expected life (in years)
4.5
4.4
4.3
Contractual life (in years)
7.0
7.0
7.0

.

Question: Analyse this data from a financial earnings document. what was the percent of the change in the dividend yield from 2011 to 2012
Choices:
0.16667
-0.89889
0.18519
-73.25926
0.5
Correct choice index: 2