AMERICAN TOWER CORPORATION AND SUBSIDIARIES NOTES TO CONSOLIDATED FINANCIAL STATEMENTS assessments in each of the tax jurisdictions resulting from these examinations.
The Company believes that adequate provisions have been made for income taxes for all periods through December 31, 2010.12.
STOCK-BASED COMPENSATION The Company recognized stock-based compensation of $52.6 million, $60.7 million and $54.8 million for the years ended December 31, 2010, 2009 and 2008, respectively.
Stock-based compensation for the year ended December 31, 2009 included $6.9 million related to the modification of the vesting and exercise terms for certain employee’s equity awards.
The Company did not capitalize any stock-based compensation during the years ended December 31, 2010 and 2009.
Summary of Stock-Based Compensation Plans—The Company maintains equity incentive plans that provide for the grant of stock-based awards to its directors, officers and employees.
Under the 2007 Equity Incentive Plan (“2007 Plan”), which provides for the grant of non-qualified and incentive stock options, as well as restricted stock units, restricted stock and other stock-based awards, exercise prices in the case of non-qualified and incentive stock options are not less than the fair market value of the underlying common stock on the date of grant.
Equity awards typically vest ratably over various periods, generally four years, and generally expire ten years from the date of grant.
Stock Options—As of December 31, 2010, the Company had the ability to grant stock-based awards with respect to an aggregate of 22.0 million shares of Common Stock under the 2007 Plan.
The fair value of each option grant is estimated on the date of grant using the Black-Scholes option pricing model based on the assumptions noted in the table below.
The risk-free treasury rate is based on the U. S.  Treasury yield in effect at the accounting measurement date.
The expected life (estimated period of time outstanding) was estimated using the vesting term and historical exercise behavior of Company employees.
The expected volatility was based on historical volatility for a period equal to the expected life of the stock options.
Key assumptions used to apply this pricing model are as follows:
## Table 0 ##
The weighted average grant date fair value per share during the years ended December 31, 2010, 2009 and 2008 was $15.03, $8.90 and $9.55, respectively.
The intrinsic value of stock options exercised during the years ended December 31, 2010, 2009 and 2008 was $62.7 million, $40.1 million and $99.1 million, respectively.
As of December 31, 2010, total unrecognized compensation expense related to unvested stock options was approximately $27.7 million and is expected to be recognized over a weighted average period of approximately two years.
The amount of cash received from the exercise of stock options was approximately $129.1 million during the year ended December 31, 2010.
During the year ended December 31, 2010, the Company realized approximately $0.3 million of state tax benefits from the exercise of stock options.
PRUDENTIAL FINANCIAL, INC.  Notes to Consolidated Financial Statements The pension and postretirement expected long-term rates of return on plan assets for 2016 were determined based upon an approach that considered the allocation of plan assets as of December 31, 2015.
Expected returns are estimated by asset class as noted in the discussion of investment policies and strategies below.
Expected returns on asset classes are developed using a building-block approach that is forward looking and are not strictly based upon historical returns.
The building blocks for equity returns include inflation, real return, a term premium, an equity risk premium, capital appreciation, effect of active management, expenses and the effect of rebalancing.
The building blocks for fixed maturity returns include inflation, real return, a term premium, credit spread, capital appreciation, effect of active management, expenses and the effect of rebalancing.
The Company applied the same approach to the determination of the expected rate of return on plan assets in 2017.
The expected rate of return for 2017 is 6.25% and 7.00% for pension and postretirement, respectively.
The assumptions for foreign pension plans are based on local markets.
There are no material foreign postretirement plans.
Assumed health care cost trend rates have a significant effect on the amounts reported for the health care plan.
A one-percentage point increase and decrease in assumed health care cost trend rates would have the following effects:
## Table 1 ##
Plan Assets The investment goal of the domestic pension plan assets is to generate an above benchmark return on a diversified portfolio of stocks, bonds and other investments.
The cash requirements of the pension obligation, which include a traditional formula principally representing payments to annuitants and a cash balance formula that allows lump sum payments and annuity payments, are designed to be met by the bonds and short-term investments in the portfolio.
The pension plan risk management practices include guidelines for asset concentration, credit rating and liquidity.
The pension plan does not invest in leveraged derivatives.
Derivatives such as futures contracts are used to reduce transaction costs and change asset concentration, while interest rate swaps and futures are used to adjust duration.
The investment goal of the domestic postretirement plan assets is to generate an above benchmark return on a diversified portfolio of stocks, bonds, and other investments, while meeting the cash requirements for the postretirement obligation that includes a medical benefit including prescription drugs, a dental benefit and a life benefit.
The postretirement plan risk management practices include guidelines for asset concentration, credit rating, liquidity and tax efficiency.
The postretirement plan does not invest in leveraged derivatives.
Derivatives such as futures contracts are used to reduce transaction costs and change asset concentration, while interest rate swaps and futures are used to adjust duration.
The plan fiduciaries for the Company’s pension and postretirement plans have developed guidelines for asset allocations reflecting a percentage of total assets by asset class, which are reviewed on an annual basis.
Asset allocation targets as of December 31, 2016 are as follows:
## Table 2 ##
To implement the investment strategy, plan assets are invested in funds that primarily invest in securities that correspond to one of the asset categories under the investment guidelines.
However, at any point in time, some of the assets in a fund may be of a different nature than the specified asset category.
Assets held with Prudential Insurance are in either pooled separate accounts or single client separate accounts.
Pooled separate accounts hold assets for multiple investors.
Each investor owns a “unit of account.
” Single client separate accounts hold assets for only one investor, the domestic qualified pension plan, and each security in the fund is treated as individually owned.
Assets held with a bank are either in common/collective trusts or single client trusts.
Common or collective trusts hold assets for more than one investor.
Each investor owns a “unit of account.
” Single client trusts hold assets for only one investor, the domestic qualified pension plan, and each security in the fund is treated as individually owned.
Retirement Operating Results The following table sets forth the Retirement segment’s operating results for the periods indicated.
## Table 3 ##
(1) Certain of our Retirement segment’s non-U.
S.  dollar-denominated earnings are from longevity reinsurance contracts, which are denominated in British pounds sterling, and are therefore subject to foreign currency exchange rate risk.
Effective January 1, 2016, the financial results of our Retirement segment include the impact of an intercompany arrangement with our Corporate and Other operations designed to mitigate the impact of exchange rate changes on the segment’s U. S.  dollar-equivalent earnings.
For more information related to this intercompany arrangement, see “—Results of Operations—Impact of Foreign Currency Exchange Rates,” above.
Adjusted Operating Income 2016 to 2015 Annual Comparison.
Adjusted operating income increased $81 million.
Results for 2016 reflected a net benefit of $6 million from our annual review and update of assumptions and other refinements, driven by favorable updates to actuarial assumptions, while results for 2015 reflected no net impact from our annual review and update of assumptions.
Excluding this favorable comparative impact, adjusted operating income increased $74 million, primarily driven by higher net investment spread results, partially offset by a lower contribution from reserve experience, higher general and administrative expenses, net of capitalization, and lower fee income.
The increase in net investment spread results primarily reflected higher net prepayment fee income, growth in account values and higher income on non-coupon investments, partially offset by lower reinvestment rates net of crediting rate reductions on full service general account stable value products.
The lower contribution from reserve experience primarily reflected lower mortality gains on a comparative basis for pension risk transfer contracts.
The increase in general and administrative expenses, net of capitalization, was primarily driven by increased legal costs.
The decrease in fee income primarily reflected lower margins on full service account values.
This decrease was partially offset by growth in account values and increased billed revenues.2015 to 2014 Annual Comparison.
Adjusted operating income decreased $284 million.
Results for 2015 reflected no net impact from our annual review and update of assumptions, while results for 2014 reflected a $13 million net charge.
Excluding this favorable comparative impact, adjusted operating income decreased $297 million, primarily driven by lower net investment spread results, higher general and administrative expenses, net of capitalization, and lower fee income, partially offset by a higher contribution from reserve experience.
The decrease in net investment spread results primarily reflected lower income on non-coupon investments, lower reinvestment rates, lower income on derivatives used in portfolio management and lower net prepayment fee income, partially offset by growth in account values.
The increase in general and administrative expenses, net of capitalization, was primarily driven by business growth and costs associated with strategic initiatives.
The decrease in fee income primarily reflected lower margins on full service account values and net outflows of investment-only stable value account values, partially offset by higher income from longevity reinsurance account values.
The more favorable reserve impacts reflected higher mortality gains for pension risk transfer contracts.
Revenues, Benefits and Expenses 2016 to 2015 Annual Comparison.
Revenues increased $1,055 million.
Premiums increased $851 million primarily driven by pension risk transfer transactions.
This increase in premiums resulted in a corresponding increase in policyholders’ benefits, as discussed in benefits and expenses below.
Net investment income increased $181 million, primarily reflecting growth in account values as discussed below, higher prepayment fee income and higher income on non-coupon investments, partially offset by lower reinvestment rates.
Benefits and expenses increased $974 million.
Excluding the impact of our annual review and update of assumptions, as discussed above, benefits and expenses increased $981 million.
Policyholders’ benefits, including the change in policy reserves, increased $968 million, primarily related to the increase in premiums discussed above.
Interest credited to policyholders’ account balances increased $32 million, primarily driven by higher prepayment fee income credited to experience rated account balances and growth in account values as discussed below, partially offset by the impact of crediting rate reductions on full service general account stable value account values.2015 to 2014 Annual Comparison.
Revenues decreased $256 million.
Premiums decreased $68 million, primarily driven by more significant group annuity transactions in 2014, partially offset by ongoing premiums assumed for longevity reinsurance contracts sold in 2015.
Net investment income decreased $127 million, primarily reflecting lower income on non-coupon investments, lower reinvestment rates and lower prepayment fee income, partially offset by growth in account values.
Policy charges and fee income, asset management and service fees and other income decreased $61 million, primarily from lower fee income and lower income on derivatives used in portfolio management.
See below for a discussion of the change in the yields for PFI excluding the Closed Block division.
The decrease in net investment income yield attributable to the Closed Block division for 2016 compared to 2015 was primarily due to lower fixed income reinvestment rates and lower yields from non-coupon investments partially offset by higher fixed maturity prepayment fees and call premiums.
The net investment income yield attributable to the Closed Block division for 2015 decreased compared to 2014, due to lower yields on non-coupon investments and lower fixed income reinvestment rates.
The following table sets forth the income yield and investment income for each major investment category of our general account investments, excluding both the Closed Block division and the Japanese insurance operations’ portion of the general account which is presented separately below, for the periods indicated.
The yields are based on net investment income as reported under U. S.  GAAP and as such do not include certain interest related items, such as settlements of duration management swaps which are included in realized gains (losses).
## Table 4 ##
(1) Yields are based on quarterly average carrying values except for fixed maturities, equity securities and securities lending activity.
Yields for fixed maturities are based on amortized cost.
Yields for equity securities are based on cost.
Yields for fixed maturities and short-term investments and cash equivalents are calculated net of liabilities and rebate expenses corresponding to securities lending activity.
Yields exclude investment income on assets other than those included in invested assets.
(2) Includes investment income of our asset management operations and derivative operations,.
The decrease in net investment income yield attributable to our general account investments, excluding both the Closed Block division and the Japanese operations’ portfolio, for 2016, compared to 2015, was primarily the result of lower fixed income reinvestment rates and lower yields from non-coupon investments offset by higher fixed maturity prepayment fees and call premiums.
The decrease in net investment income yield attributable to our general account investments, excluding both the Closed Block division and the Japanese operations’ portfolio, for 2015, compared to 2014, was primarily the result of lower income from non-coupon investments and lower fixed income reinvestment rates.
The following table sets forth the income yield and investment income for each major investment category of our Japanese insurance operations’ general account for the periods indicated.
The yields are based on net investment income as reported under U. S.  GAAP and as such do not include certain interest related items, such as settlements of duration management swaps which are included in realized gains (losses).
## Table 5 ##
(1) Yields are based on quarterly average carrying values except for fixed maturities, equity securities and securities lending activity.
Yields for fixed maturities are based on amortized cost.
Yields for equity securities are based on cost.
Yields for fixed maturities and short-term investments and cash equivalents are calculated net of liabilities and rebate expenses corresponding to securities lending activity.
Yields exclude investment income on assets other than those included in invested assets.

Tables referenced above, in order (Table 0 first):
<table><tr><td></td><td>2010</td><td>2009</td><td>2008</td></tr><tr><td>Range of risk-free interest rate</td><td>1.41% – 2.39%</td><td>1.41% – 2.04%</td><td>1.44% – 3.05%</td></tr><tr><td>Weighted average risk-free interest rate</td><td>2.35%</td><td>1.71%</td><td>1.89%</td></tr><tr><td>Expected life of option grants</td><td>4.60 years</td><td>4.00 years</td><td>4.00 years</td></tr><tr><td>Range of expected volatility of underlying stock price</td><td>37.11% – 37.48%</td><td>36.00% – 36.63%</td><td>28.51% – 35.30%</td></tr><tr><td>Weighted average expected volatility of underlying stock price</td><td>37.14%</td><td>36.23%</td><td>29.10%</td></tr><tr><td>Expected annual dividends</td><td>N/A</td><td>N/A</td><td>N/A</td></tr></table>
<table><tr><td></td><td>Other PostretirementBenefits (in millions)</td></tr><tr><td>One percentage point increase</td><td></td></tr><tr><td>Increase in total service and interest costs</td><td>$7</td></tr><tr><td>Increase in postretirement benefit obligation</td><td>158</td></tr><tr><td>One percentage point decrease</td><td></td></tr><tr><td>Decrease in total service and interest costs</td><td>$6</td></tr><tr><td>Decrease in postretirement benefit obligation</td><td>106</td></tr></table>
<table><tr><td></td><td colspan="2">Pension</td><td colspan="2">Postretirement</td></tr><tr><td></td><td>Minimum</td><td>Maximum</td><td>Minimum</td><td>Maximum</td></tr><tr><td>Asset Category</td><td></td><td></td><td></td><td></td></tr><tr><td>U.S. Equities</td><td>2%</td><td>16%</td><td>27%</td><td>60%</td></tr><tr><td>International Equities</td><td>2%</td><td>16%</td><td>2%</td><td>23%</td></tr><tr><td>Fixed Maturities</td><td>50%</td><td>68%</td><td>4%</td><td>50%</td></tr><tr><td>Short-term Investments</td><td>0%</td><td>15%</td><td>0%</td><td>42%</td></tr><tr><td>Real Estate</td><td>2%</td><td>16%</td><td>0%</td><td>0%</td></tr><tr><td>Other</td><td>0%</td><td>16%</td><td>0%</td><td>0%</td></tr></table>
<table><tr><td></td><td colspan="3">Year ended December 31,</td></tr><tr><td></td><td>2016</td><td>2015</td><td>2014</td></tr><tr><td></td><td colspan="3">(in millions)</td></tr><tr><td>Operating results-1:</td><td></td><td></td><td></td></tr><tr><td>Revenues</td><td>$12,876</td><td>$11,821</td><td>$12,077</td></tr><tr><td>Benefits and expenses</td><td>11,864</td><td>10,890</td><td>10,862</td></tr><tr><td>Adjusted operating income</td><td>1,012</td><td>931</td><td>1,215</td></tr><tr><td>Realized investment gains (losses), net, and related adjustments</td><td>-281</td><td>255</td><td>591</td></tr><tr><td>Related charges</td><td>-272</td><td>-1</td><td>-4</td></tr><tr><td>Investment gains (losses) on trading account assets supporting insurance liabilities, net</td><td>-21</td><td>-581</td><td>151</td></tr><tr><td>Change in experience-rated contractholder liabilities due to asset value changes</td><td>25</td><td>490</td><td>-106</td></tr><tr><td>Income (loss) from continuing operations before income taxes and equity in earnings of operating joint ventures</td><td>$463</td><td>$1,094</td><td>$1,847</td></tr></table>
<table><tr><td></td><td colspan="6">Year Ended December 31,</td></tr><tr><td></td><td colspan="2">2016</td><td colspan="2">2015</td><td colspan="2">2014</td></tr><tr><td></td><td>Yield-1</td><td>Amount</td><td>Yield-1</td><td>Amount</td><td>Yield-1</td><td>Amount</td></tr><tr><td></td><td colspan="6">($ in millions)</td></tr><tr><td>Fixed maturities</td><td>4.63%</td><td>$6,043</td><td>4.67%</td><td>$5,686</td><td>4.69%</td><td>$5,461</td></tr><tr><td>Trading account assets supporting insurance liabilities</td><td>3.80</td><td>721</td><td>3.79</td><td>688</td><td>3.96</td><td>730</td></tr><tr><td>Equity securities</td><td>6.49</td><td>232</td><td>6.07</td><td>197</td><td>6.49</td><td>191</td></tr><tr><td>Commercial mortgage and other loans</td><td>4.35</td><td>1,306</td><td>4.62</td><td>1,338</td><td>4.96</td><td>1,271</td></tr><tr><td>Policy loans</td><td>5.49</td><td>252</td><td>5.52</td><td>250</td><td>5.66</td><td>253</td></tr><tr><td>Short-term investments and cash equivalents</td><td>0.67</td><td>113</td><td>0.25</td><td>38</td><td>0.21</td><td>22</td></tr><tr><td>Other investments</td><td>5.96</td><td>344</td><td>6.17</td><td>356</td><td>10.03</td><td>598</td></tr><tr><td>Gross investment income before investment expenses</td><td>4.31</td><td>9,011</td><td>4.33</td><td>8,553</td><td>4.63</td><td>8,526</td></tr><tr><td>Investment expenses</td><td>-0.14</td><td>-248</td><td>-0.15</td><td>-239</td><td>-0.15</td><td>-209</td></tr><tr><td>Investment income after investment expenses</td><td>4.17%</td><td>8,763</td><td>4.18%</td><td>8,314</td><td>4.48%</td><td>8,317</td></tr><tr><td>Investment results of other entities and operations-2</td><td></td><td>82</td><td></td><td>114</td><td></td><td>124</td></tr><tr><td>Total investment income</td><td></td><td>$8,845</td><td></td><td>$8,428</td><td></td><td>$8,441</td></tr></table>
<table><tr><td></td><td colspan="6">Year Ended December 31,</td></tr><tr><td></td><td colspan="2">2016</td><td colspan="2">2015</td><td colspan="2">2014</td></tr><tr><td></td><td>Yield-1</td><td>Amount</td><td>Yield-1</td><td>Amount</td><td>Yield-1</td><td>Amount</td></tr><tr><td></td><td colspan="6">($ in millions)</td></tr><tr><td>Fixed maturities</td><td>3.14%</td><td>$3,472</td><td>3.23%</td><td>$3,190</td><td>3.06%</td><td>$3,301</td></tr><tr><td>Trading account assets supporting insurance liabilities</td><td>1.75</td><td>37</td><td>1.66</td><td>32</td><td>1.80</td><td>35</td></tr><tr><td>Equity securities</td><td>4.80</td><td>75</td><td>4.77</td><td>69</td><td>5.06</td><td>84</td></tr><tr><td>Commercial mortgage and other loans</td><td>4.23</td><td>445</td><td>4.45</td><td>390</td><td>4.20</td><td>294</td></tr><tr><td>Policy loans</td><td>4.05</td><td>95</td><td>3.93</td><td>84</td><td>3.93</td><td>88</td></tr><tr><td>Short-term investments and cash equivalents</td><td>0.78</td><td>9</td><td>0.32</td><td>5</td><td>0.24</td><td>4</td></tr><tr><td>Other investments</td><td>5.01</td><td>129</td><td>5.32</td><td>133</td><td>6.67</td><td>155</td></tr><tr><td>Gross investment income before investment expenses</td><td>3.26</td><td>4,262</td><td>3.35</td><td>3,903</td><td>3.18</td><td>3,961</td></tr><tr><td>Investment expenses</td><td>-0.12</td><td>-165</td><td>-0.13</td><td>-155</td><td>-0.12</td><td>-153</td></tr><tr><td>Total investment income</td><td>3.14%</td><td>$4,097</td><td>3.22%</td><td>$3,748</td><td>3.06%</td><td>$3,808</td></tr></table>

Question: what was the percent of the change in the intrinsic value of stock options from 2009 to 2010
Answer: 0.56359
Reasoning program: subtract(62.7,40.1), divide(#0,40.1)