pre_text: vertex pharmaceuticals incorporated notes to consolidated financial statements ( continued ) d . stock-based compensation ( continued ) the company uses the black-scholes valuation model to estimate the fair value of stock options at the grant date . the black-scholes valuation model uses the option exercise price as well as estimates and assumptions related to the expected price volatility of the company 2019s stock , the period during which the options will be outstanding , the rate of return on risk-free investments , and the expected dividend yield for the company 2019s stock to estimate the fair value of a stock option on the grant date . the company validates its estimates and assumptions through consultations with independent third parties having relevant expertise . the fair value of each option granted under the stock and option plans during 2006 was estimated on the date of grant using the black- scholes option pricing model with the following weighted average assumptions : the weighted-average valuation assumptions were determined as follows : 2022 expected stock price volatility : in 2006 , the company changed its method of estimating expected volatility from relying exclusively on historical volatility to relying exclusively on implied volatility . options to purchase the company 2019s stock with remaining terms of greater than one year are regularly traded in the market . expected stock price volatility is calculated using the trailing one month average of daily implied volatilities prior to grant date . 2022 risk-free interest rate : the company bases the risk-free interest rate on the interest rate payable on u.s . treasury securities in effect at the time of grant for a period that is commensurate with the assumed expected option term . 2022 expected term of options : the expected term of options represents the period of time options are expected to be outstanding . the company uses historical data to estimate employee exercise and post-vest termination behavior . the company believes that all groups of employees exhibit similar exercise and post-vest termination behavior and therefore does not stratify employees into multiple groups in determining the expected term of options . 2022 expected annual dividends : the estimate for annual dividends is $ 0.00 , because the company has not historically paid , and does not intend for the foreseeable future to pay , a dividend . expected stock price volatility 57.10 % (  % ) risk-free interest rate 4.74 % (  % ) expected term 5.64 years .
post_text: .
table: 2006
table: Expected stock price volatility 57.10%
table: Risk-free interest rate 4.74%
table: Expected term 5.64 years
table: Expected annual dividends —
question: Analyse this data from a financial earnings document. in 2006 what was the ratio expected stock price volatility to risk-free interest rate