THE GOLDMAN SACHS GROUP, INC.  AND SUBSIDIARIES Management’s Discussion and Analysis Scenario Analyses.
We conduct various scenario analyses including as part of the Comprehensive Capital Analysis and Review (CCAR) and Dodd-Frank Act Stress Tests (DFAST), as well as our resolution and recovery planning.
See “Equity Capital Management and Regulatory Capital — Equity Capital Management” below for further information.
These scenarios cover short-term and longterm time horizons using various macroeconomic and firmspecific assumptions, based on a range of economic scenarios.
We use these analyses to assist us in developing our longer-term balance sheet management strategy, including the level and composition of assets, funding and equity capital.
Additionally, these analyses help us develop approaches for maintaining appropriate funding, liquidity and capital across a variety of situations, including a severely stressed environment.
Balance Sheet Allocation In addition to preparing our consolidated statements of financial condition in accordance with U. S.  GAAP, we prepare a balance sheet that generally allocates assets to our businesses, which is a non-GAAP presentation and may not be comparable to similar non-GAAP presentations used by other companies.
We believe that presenting our assets on this basis is meaningful because it is consistent with the way management views and manages risks associated with the firm’s assets and better enables investors to assess the liquidity of the firm’s assets.
The table below presents our balance sheet allocation.
## Table 0 ##
1.
Includes $17.29 billion and $18.24 billion as of December 2015 and December 2014, respectively, of direct loans primarily extended to corporate and private wealth management clients that are accounted for at fair value.2.
See Note 9 to the consolidated financial statements for further information about loans receivable.
The following is a description of the captions in the table above: ‰ Global Core Liquid Assets and Cash.
We maintain liquidity to meet a broad range of potential cash outflows and collateral needs in a stressed environment.
See “Liquidity Risk Management” below for details on the composition and sizing of our “Global Core Liquid Assets” (GCLA).
In addition to our GCLA, we maintain other operating cash balances, primarily for use in specific currencies, entities, or jurisdictions where we do not have immediate access to parent company liquidity.
‰ Secured Client Financing.
We provide collateralized financing for client positions, including margin loans secured by client collateral, securities borrowed, and resale agreements primarily collateralized by government obligations.
As a result of client activities, we are required to segregate cash and securities to satisfy regulatory requirements.
Our secured client financing arrangements, which are generally short-term, are accounted for at fair value or at amounts that approximate fair value, and include daily margin requirements to mitigate counterparty credit risk.
‰ Institutional Client Services.
In Institutional Client Services, we maintain inventory positions to facilitate market making in fixed income, equity, currency and commodity products.
Additionally, as part of marketmaking activities, we enter into resale or securities borrowing arrangements to obtain securities which we can use to cover transactions in which we or our clients have sold securities that have not yet been purchased.
The receivables in Institutional Client Services primarily relate to securities transactions.
‰ Investing & Lending.
In Investing & Lending, we make investments and originate loans to provide financing to clients.
These investments and loans are typically longerterm in nature.
We make investments, directly and indirectly through funds and separate accounts that we manage, in debt securities, loans, public and private equity securities, real estate entities and other investments.
‰ Other Assets.
Other assets are generally less liquid, nonfinancial assets, including property, leasehold improvements and equipment, goodwill and identifiable intangible assets, income tax-related receivables, equitymethod investments, assets classified as held for sale and miscellaneous receivables.
17.
SHARE-BASED COMPENSATION We have a stock option and incentive plan which allows us to grant stock options and restricted stock to employees and nonemployee directors.
The total shares authorized under the plan are 8,900,000 of which 5,367,875 shares are available for future grant as of December 31, 2007.
Prior to January 1, 2006, we accounted for share-based compensation under the recognition and measurement provisions of Accounting Principles Board Opinion No.25 (“APB 25”), Accounting for Stock Issued to Employees, and related Interpretations, as permitted by SFAS No.123, Accounting for Stock-Based Compensation.
Accordingly, we did not record any compensation expense for stock options, as the exercise price of the option was equal to the quoted market price of the stock on the date of grant.
Effective January 1, 2006, we adopted SFAS No.123R, Share-Based Payment, which requires all share-based payments to employees, including grants of employee stock options, to be recognized in the statement of income based on their fair values.
This accounting utilizes a “modified grantdate” approach in which the fair value of an equity award is estimated on the grant date without regard to service or performance vesting conditions.
We adopted SFAS 123R using the “modified prospective” transition method.
Under this transition method, compensation expense is recognized beginning January 1, 2006 based on the requirements of SFAS 123R for all share-based payments granted after December 31, 2005, and based on the requirements of SFAS 123 for all awards granted to employees prior to January 1, 2006 that remain unvested as of that date.
Results of operations for prior years have not been restated.
The adoption of SFAS 123R, compared to the previous accounting for share-based compensation under APB 25, reduced 2006 income before income taxes and minority interest by $17.5 million, net income by $12.5 million, and both basic and diluted net earnings per common share by $0.12.
The impact on net income and net earnings per common share if we had applied the recognition provisions of SFAS 123 to stock options for 2005 was as follows (in thousands, except per share amounts):
## Table 1 ##
As required by SFAS 123R and discussed further in Note 14, upon adoption in 2006, we reclassified $11.1 million of unearned compensation related to restricted stock from deferred compensation to common stock.
We classify all share-based awards as equity instruments.
Substantially all awards have graded vesting which is recognized on a straight-line basis over the vesting period.
As of December 31, 2007, compensation expense not yet recognized for nonvested share-based awards was approximately $52.3 million, which is expected to be recognized over a weighted average period of 1.3 years.
STOCK OPTIONS Stock options granted to employees vest at the rate of one third each year and expire seven years after the date of grant.
Stock options granted to nonemployee directors vest in increments from six months to three and a half years and expire ten years after the date of grant.
In 2005, we discontinued our broad-based employee stock option plan under which options were made available to substantially all employees; however, existing options continue to vest at the rate of one third each year and expire four years after the date of grant.
Following are the expense, cash flow, and tax effects related to stock options on the Company’s financial statements from the adoption of SFAS 123R (in thousands):
## Table 2 ##
The additional compensation expense is included in salaries and employee benefits in the statement of income with the corresponding increase included in common stock in shareholders’ equity.
For 2005, the tax benefit realized as a reduction of income taxes payable and included in common stock was $13.5 million.
On October 22, 2007, the Company announced it had received notification from the SEC that its patent-pending Employee Stock Option Appreciation Rights Securities (“ESOARS”) was sufficiently designed as a market-based method for valuing employee stock options under SFAS 123R.
The SEC staff did not object to the Company’s view that the market-clearing price of ESOARS in the Company’s auction conducted May 4-7, 2007 was a reasonable estimate of the fair value of the underlying employee stock options.
The Company used the results of that auction to value its employee stock options granted on May 4, 2007.
The value established was $12.06 per option, which the Company estimated was approximately 14% below its Black-Scholes model valuation on that date.
The number of stock options granted on that date were 963,680, or 91.4% of the total stock options granted in 2007.
The Company used the ESOARS value for the remainder of 2007 in determining compensation expense for this grant of stock options, and recorded the related estimated future ESOARS settlement obligation as a liability in the balance sheet.
For all other stock options granted in 2007, and previously in 2006 and 2005, the Company used the Black-Scholes option pricing model to estimate the fair values of stock options in determining compensation expense.
The following summarizes the weighted average of fair value and the significant assumptions used in applying the Black-Scholes model for options granted:
## Table 3 ##
The methodology used to estimate the fair values of stock options is consistent with the estimates used for the 2005 pro forma presentation previously shown.
The assumptions for expected dividend yield, expected volatility and expected life reflect management’s judgment and include consideration of historical experience.
Expected volatility is based in part on historical volatility.
The risk-free interest rate is based on the U. S.  Treasury yield curve in effect at the time of grant for periods corresponding with the expected life of the option.
The following summarizes our stock option activity for the three years ended December 31, 2007:
## Table 4 ##
We issue new authorized shares for the exercise of stock options.
The total intrinsic value of stock options exercised was approximately $59.0 million in 2007 and $50.8 million in 2006.
Additional selected information on stock options at December 31, 2007 follows:

Tables referenced above, in order (Table 0 first):
<table><tr><td></td><td>As of December</td></tr><tr><td><i>$ in millions</i></td><td>2015</td><td>2014</td></tr><tr><td>Global Core Liquid Assets (GCLA)</td><td>$199,120</td><td>$182,947</td></tr><tr><td>Other cash</td><td>9,180</td><td>7,805</td></tr><tr><td>GCLA and cash</td><td>208,300</td><td>190,752</td></tr><tr><td>Secured client financing</td><td>221,325</td><td>210,641</td></tr><tr><td>Inventory</td><td>208,836</td><td>230,667</td></tr><tr><td>Secured financing agreements</td><td>63,495</td><td>74,767</td></tr><tr><td>Receivables</td><td>39,976</td><td>47,317</td></tr><tr><td>Institutional Client Services</td><td>312,307</td><td>352,751</td></tr><tr><td>Public equity</td><td>3,991</td><td>4,041</td></tr><tr><td>Private equity</td><td>16,985</td><td>17,979</td></tr><tr><td>Debt<sup>1</sup></td><td>23,216</td><td>24,768</td></tr><tr><td>Loans receivable<sup>2</sup></td><td>45,407</td><td>28,938</td></tr><tr><td>Other</td><td>4,646</td><td>3,771</td></tr><tr><td>Investing & Lending</td><td>94,245</td><td>79,497</td></tr><tr><td>Total inventory and related assets</td><td>406,552</td><td>432,248</td></tr><tr><td>Other assets</td><td>25,218</td><td>22,201</td></tr><tr><td>Total assets</td><td>$861,395</td><td>$855,842</td></tr></table>
<table><tr><td>Net income, as reported</td><td>$480,121</td></tr><tr><td>Deduct: Total share-based compensation expense determined under fair value based method for stock options, net of related taxeffects</td><td>-9,793</td></tr><tr><td>Pro forma net income</td><td>$470,328</td></tr><tr><td>Net earnings per common share:</td><td></td></tr><tr><td>Basic – as reported</td><td>$5.27</td></tr><tr><td>Basic – pro forma</td><td>5.16</td></tr><tr><td>Diluted – as reported</td><td>5.16</td></tr><tr><td>Diluted – pro forma</td><td>5.08</td></tr></table>
<table><tr><td></td><td> 2007</td><td> 2006</td></tr><tr><td>Compensation expense:</td><td></td><td></td></tr><tr><td>Additional amount recorded</td><td>$15,828</td><td>17,542</td></tr><tr><td>Reduction of income tax expense</td><td>4,987</td><td>4,968</td></tr><tr><td>Cash flows received from exercise of stock options</td><td>59,473</td><td>79,511</td></tr><tr><td>Tax benefit realized from reduction of income taxes payable:</td><td></td><td></td></tr><tr><td>Reduction of goodwill for tax benefit of vested stock options converted in the Amegy acquisition and exercised during the year</td><td>$2,069</td><td>4,189</td></tr><tr><td>Included in common stock as net stock options exercised</td><td>10,365</td><td>11,769</td></tr><tr><td>Reduction of deferred tax assets and current income tax expense</td><td>1,038</td><td>1,323</td></tr><tr><td>Total tax benefit</td><td>$13,472</td><td>17,281</td></tr></table>
<table><tr><td></td><td> 2007</td><td> 2006</td><td> 2005</td></tr><tr><td>Weighted average of fair value for options granted</td><td>$15.15</td><td>15.02</td><td>15.33</td></tr><tr><td>Weighted average assumptions used:</td><td></td><td></td><td></td></tr><tr><td>Expected dividend yield</td><td>2.0%</td><td>2.0%</td><td>2.0%</td></tr><tr><td>Expected volatility</td><td>17.0%</td><td>18.0%</td><td>25.0%</td></tr><tr><td>Risk-free interest rate</td><td>4.42%</td><td>4.95%</td><td>3.95%</td></tr><tr><td>Expected life (in years)</td><td>5.4</td><td>4.1</td><td>4.1</td></tr></table>
<table><tr><td></td><td> Number of shares</td><td> Weighted average exercise price</td></tr><tr><td>Balance at December 31, 2004</td><td>7,633,775</td><td>$51.98</td></tr><tr><td>Granted</td><td>912,905</td><td>71.37</td></tr><tr><td>Assumed in acquisition</td><td>1,559,693</td><td>47.44</td></tr><tr><td>Exercised</td><td>-1,872,753</td><td>50.00</td></tr><tr><td>Expired</td><td>-519,521</td><td>66.53</td></tr><tr><td>Forfeited</td><td>-216,533</td><td>55.46</td></tr><tr><td>Balance at December 31, 2005</td><td>7,497,566</td><td>52.79</td></tr><tr><td>Granted</td><td>979,274</td><td>81.14</td></tr><tr><td>Exercised</td><td>-1,631,012</td><td>49.43</td></tr><tr><td>Expired</td><td>-52,398</td><td>50.00</td></tr><tr><td>Forfeited</td><td>-106,641</td><td>62.89</td></tr><tr><td>Balance at December 31, 2006</td><td>6,686,789</td><td>57.62</td></tr><tr><td>Granted</td><td>1,054,772</td><td>82.82</td></tr><tr><td>Exercised</td><td>-1,681,742</td><td>80.88</td></tr><tr><td>Expired</td><td>-136,805</td><td>58.37</td></tr><tr><td>Forfeited</td><td>-112,031</td><td>75.00</td></tr><tr><td>Balance at December 31, 2007</td><td>5,810,983</td><td>64.82</td></tr><tr><td>Outstanding stock options exercisable as of:</td><td></td><td></td></tr><tr><td>December 31, 2007</td><td>3,866,627</td><td>$57.15</td></tr><tr><td>December 31, 2006</td><td>4,409,971</td><td>50.73</td></tr><tr><td>December 31, 2005</td><td>4,663,707</td><td>49.04</td></tr></table>

Question: What's the current increasing rate of Expired for Number of shares?
Answer: 1.61088
Reasoning program: add(-136805,52398), divide(#0,-52398)