Financial derivatives involve, to varying degrees, interest rate, market and credit risk.
For interest rate swaps and total return swaps, options and futures contracts, only periodic cash payments and, with respect to options, premiums are exchanged.
Therefore, cash requirements and exposure to credit risk are significantly less than the notional amount on these instruments.
Further information on our financial derivatives is presented in Note 1 Accounting Policies and Note 17 Financial Derivatives in the Notes To Consolidated Financial Statements in Item 8 of this Report, which is incorporated here by reference.
Not all elements of interest rate, market and credit risk are addressed through the use of financial or other derivatives, and such instruments may be ineffective for their intended purposes due to unanticipated market changes, among other reasons.
The following table summarizes the notional or contractual amounts and net fair value of financial derivatives at December 31, 2012 and December 31, 2011.
Table 54: Financial Derivatives Summary
## Table 0 ##
(a) Represents the net fair value of assets and liabilities.2011 VERSUS 2010 CONSOLIDATED INCOME STATEMENT REVIEW Summary Results Net income for 2011 was $3.1 billion, or $5.64 per diluted common share, compared with $3.4 billion, or $5.74 per diluted common share, for 2010.
The decrease from 2010 was primarily due to an $850 million, or 6%, reduction in total revenue, a $492 million, or 6%, increase in noninterest expense and the impact of the $328 million after-tax gain on the sale of GIS recognized in 2010, partially offset by a $1.3 billion, or 54%, decrease in the provision for credit losses in 2011.
In addition, 2010 net income attributable to common shareholders was also impacted by a noncash reduction of $250 million in connection with the redemption of TARP preferred stock.
Net Interest Income Net interest income was $8.7 billion for 2011 down from $9.2 billion in 2010.
The net interest margin decreased to 3.92% in 2011 compared with 4.14% for 2010, primarily due to the impact of lower purchase accounting accretion, a decline in the rate on average loan balances and the low interest rate environment partially offset by lower funding costs.
Noninterest Income Noninterest income was $5.6 billion for 2011 and $5.9 billion for 2010.
Noninterest income for 2011 reflected higher asset management fees and other income, higher residential mortgage banking revenue, and lower net other-thantemporary impairments (OTTI), that were offset by a decrease in corporate service fees primarily due to a reduction in the value of commercial mortgage servicing rights, lower service charges on deposits from the impact of Regulation E rules pertaining to overdraft fees, a decrease in net gains on sales of securities and lower consumer services fees due, in part, to a decline in interchange fees on individual debit card transactions in the fourth quarter partially offset by higher transaction volumes throughout 2011.
Asset management revenue, including BlackRock, increased $34 million to $1.1 billion in 2011 compared to 2010.
The increase was driven by strong sales performance by our Asset Management Group and somewhat higher equity earnings from our BlackRock investment.
Discretionary assets under management at December 31, 2011 totaled $107 billion compared with $108 billion at December 31, 2010.
## Table 1 ##
(a) Includes the impact of RBC Bank (USA), which we acquired on March 2, 2012.
(b) Includes the impact of National City, which we acquired on December 31, 2008.
(c) Includes the impact of National City except for the following Selected Ratios: Net interest margin, Noninterest income to total revenue, Efficiency, Return on Average common shareholders’ equity, Return on Average assets, Dividend payout and Average common shareholders’ equity to average assets.
(d) Represents the sum of interest-bearing money market deposits, interest-bearing demand deposits, and noninterest-bearing deposits.
(e) Includes long-term borrowings of $19.3 billion, $20.9 billion, $24.8 billion, $26.3 billion and $33.6 billion for 2012, 2011, 2010, 2009 and 2008, respectively.
Borrowings which mature more than one year after December 31, 2012 are considered to be long-term.
(f) Amounts for 2012, 2011 and 2010 include cash and money market balances.
(g) Calculated as taxable-equivalent net interest income divided by average earning assets.
The interest income earned on certain earning assets is completely or partially exempt from federal income tax.
As such, these tax-exempt instruments typically yield lower returns than taxable investments.
To provide more meaningful comparisons of net interest margins for all earning assets, we use net interest income on a taxable-equivalent basis in calculating net interest margin by increasing the interest income earned on tax-exempt assets to make it fully equivalent to interest income earned on taxable investments.
This adjustment is not permitted under accounting principles generally accepted in the United States of America (GAAP) on the Consolidated Income Statement.
The taxable-equivalent adjustments to net interest income for the years 2012, 2011, 2010, 2009 and 2008 were $144 million, $104 million, $81 million, $65 million and $36 million, respectively.
RESIDENTIAL MORTGAGE-BACKED SECURITIES At December 31, 2012, our residential mortgage-backed securities portfolio was comprised of $31.4 billion fair value of US government agency-backed securities and $6.1 billion fair value of non-agency (private issuer) securities.
The agency securities are generally collateralized by 1-4 family, conforming, fixed-rate residential mortgages.
The non-agency securities are also generally collateralized by 1-4 family residential mortgages.
The mortgage loans underlying the non-agency securities are generally non-conforming (i. e. , original balances in excess of the amount qualifying for agency securities) and predominately have interest rates that are fixed for a period of time, after which the rate adjusts to a floating rate based upon a contractual spread that is indexed to a market rate (i. e. , a “hybrid ARM”), or interest rates that are fixed for the term of the loan.
Substantially all of the non-agency securities are senior tranches in the securitization structure and at origination had credit protection in the form of credit enhancement, overcollateralization and/or excess spread accounts.
During 2012, we recorded OTTI credit losses of $99 million on non-agency residential mortgage-backed securities.
All of the losses were associated with securities rated below investment grade.
As of December 31, 2012, the noncredit portion of impairment recorded in Accumulated other comprehensive income for non-agency residential mortgagebacked securities for which we have recorded an OTTI credit loss totaled $150 million and the related securities had a fair value of $3.7 billion.
The fair value of sub-investment grade investment securities for which we have not recorded an OTTI credit loss as of December 31, 2012 totaled $1.9 billion, with unrealized net gains of $114 million.
COMMERCIAL MORTGAGE-BACKED SECURITIES The fair value of the non-agency commercial mortgagebacked securities portfolio was $5.9 billion at December 31, 2012 and consisted of fixed-rate, private-issuer securities collateralized by non-residential properties, primarily retail properties, office buildings, and multi-family housing.
The agency commercial mortgage-backed securities portfolio was $2.0 billion fair value at December 31, 2012 consisting of multi-family housing.
Substantially all of the securities are the most senior tranches in the subordination structure.
There were no OTTI credit losses on commercial mortgagebacked securities during 2012.
ASSET-BACKED SECURITIES The fair value of the asset-backed securities portfolio was $6.5 billion at December 31, 2012 and consisted of fixed-rate and floating-rate, private-issuer securities collateralized primarily by various consumer credit products, including residential mortgage loans, credit cards, automobile loans, and student loans.
Substantially all of the securities are senior tranches in the securitization structure and have credit protection in the form of credit enhancement, over-collateralization and/or excess spread accounts.
We recorded OTTI credit losses of $11 million on assetbacked securities during 2012.
All of the securities are collateralized by first lien and second lien residential mortgage loans and are rated below investment grade.
As of December 31, 2012, the noncredit portion of impairment recorded in Accumulated other comprehensive income for asset-backed securities for which we have recorded an OTTI credit loss totaled $52 million and the related securities had a fair value of $603 million.
For the sub-investment grade investment securities (available for sale and held to maturity) for which we have not recorded an OTTI loss through December 31, 2012, the fair value was $47 million, with unrealized net losses of $3 million.
The results of our security-level assessments indicate that we will recover the cost basis of these securities.
Note 8 Investment Securities in the Notes To Consolidated Financial Statements in Item 8 of this Report provides additional information on OTTI losses and further detail regarding our process for assessing OTTI.
If current housing and economic conditions were to worsen, and if market volatility and illiquidity were to worsen, or if market interest rates were to increase appreciably, the valuation of our investment securities portfolio could be adversely affected and we could incur additional OTTI credit losses that would impact our Consolidated Income Statement.
LOANS HELD FOR SALE Table 15: Loans Held For Sale
## Table 2 ##
We stopped originating commercial mortgage loans held for sale designated at fair value in 2008 and continue pursuing opportunities to reduce these positions at appropriate prices.
At December 31, 2012, the balance relating to these loans was $772 million, compared to $843 million at December 31, 2011.
We sold $32 million in unpaid principal balances of these commercial mortgage loans held for sale carried at fair value in 2012 and sold $25 million in 2011.

Tables referenced above, in order (Table 0 first):
<table><tr><td></td><td colspan="2">December 31, 2012</td><td colspan="2">December 31, 2011</td></tr><tr><td>In millions</td><td>Notional/ ContractualAmount</td><td>Net Fair Value (a)</td><td>Notional/ Contractual Amount</td><td>Net Fair Value (a)</td></tr><tr><td> Derivatives designated as hedging instruments under GAAP</td><td></td><td></td><td></td><td></td></tr><tr><td>Total derivatives designated as hedging instruments</td><td>$29,270</td><td>$1,720</td><td>$29,234</td><td>$1,772</td></tr><tr><td> Derivatives not designated as hedging instruments under GAAP</td><td></td><td></td><td></td><td></td></tr><tr><td>Total derivatives used for residential mortgage banking activities</td><td>$166,819</td><td>$588</td><td>$196,991</td><td>$565</td></tr><tr><td>Total derivatives used for commercial mortgage banking activities</td><td>4,606</td><td>-23</td><td>2,720</td><td>-21</td></tr><tr><td>Total derivatives used for customer-related activities</td><td>163,848</td><td>30</td><td>158,095</td><td>-132</td></tr><tr><td>Total derivatives used for other risk management activities</td><td>1,813</td><td>-357</td><td>4,289</td><td>-327</td></tr><tr><td>Total derivatives not designated as hedging instruments</td><td>$337,086</td><td>$238</td><td>$362,095</td><td>$85</td></tr><tr><td>Total Derivatives</td><td>$366,356</td><td>$1,958</td><td>$391,329</td><td>$1,857</td></tr></table>
<table><tr><td></td><td colspan="5">At or for the year ended December 31</td></tr><tr><td>Dollars in millions, except as noted</td><td>2012 (a) (b)</td><td>2011 (b)</td><td>2010 (b)</td><td>2009 (b)</td><td>2008 (c)</td></tr><tr><td> BALANCESHEETHIGHLIGHTS</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Assets</td><td>$305,107</td><td>$271,205</td><td>$264,284</td><td>$269,863</td><td>$291,081</td></tr><tr><td>Loans</td><td>185,856</td><td>159,014</td><td>150,595</td><td>157,543</td><td>175,489</td></tr><tr><td>Allowance for loan and lease losses</td><td>4,036</td><td>4,347</td><td>4,887</td><td>5,072</td><td>3,917</td></tr><tr><td>Interest-earning deposits with banks</td><td>3,984</td><td>1,169</td><td>1,610</td><td>4,488</td><td>14,859</td></tr><tr><td>Investment securities</td><td>61,406</td><td>60,634</td><td>64,262</td><td>56,027</td><td>43,473</td></tr><tr><td>Loans held for sale</td><td>3,693</td><td>2,936</td><td>3,492</td><td>2,539</td><td>4,366</td></tr><tr><td>Goodwill and other intangible assets</td><td>10,869</td><td>10,144</td><td>10,753</td><td>12,909</td><td>11,688</td></tr><tr><td>Equity investments</td><td>10,877</td><td>10,134</td><td>9,220</td><td>10,254</td><td>8,554</td></tr><tr><td>Noninterest-bearing deposits</td><td>69,980</td><td>59,048</td><td>50,019</td><td>44,384</td><td>37,148</td></tr><tr><td>Interest-bearing deposits</td><td>143,162</td><td>128,918</td><td>133,371</td><td>142,538</td><td>155,717</td></tr><tr><td>Total deposits</td><td>213,142</td><td>187,966</td><td>183,390</td><td>186,922</td><td>192,865</td></tr><tr><td>Transaction deposits (d)</td><td>176,705</td><td>147,637</td><td>134,654</td><td>126,244</td><td>110,997</td></tr><tr><td>Borrowed funds (e)</td><td>40,907</td><td>36,704</td><td>39,488</td><td>39,261</td><td>52,240</td></tr><tr><td>Total shareholders’ equity</td><td>39,003</td><td>34,053</td><td>30,242</td><td>29,942</td><td>25,422</td></tr><tr><td>Common shareholders’ equity</td><td>35,413</td><td>32,417</td><td>29,596</td><td>22,011</td><td>17,490</td></tr><tr><td> CLIENTASSETS(billions)</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Discretionary assets under management</td><td>$112</td><td>$107</td><td>$108</td><td>$103</td><td>$103</td></tr><tr><td>Nondiscretionary assets under management</td><td>112</td><td>103</td><td>104</td><td>102</td><td>125</td></tr><tr><td>Total assets under administration</td><td>224</td><td>210</td><td>212</td><td>205</td><td>228</td></tr><tr><td>Brokerage account assets (f)</td><td>38</td><td>34</td><td>34</td><td>32</td><td>29</td></tr><tr><td>Total client assets</td><td>$262</td><td>$244</td><td>$246</td><td>$237</td><td>$257</td></tr><tr><td> SELECTEDRATIOS</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Net interest margin (g)</td><td>3.94%</td><td>3.92%</td><td>4.14%</td><td>3.82%</td><td>3.37%</td></tr><tr><td>Noninterest income to total revenue</td><td>38</td><td>39</td><td>39</td><td>44</td><td>39</td></tr><tr><td>Efficiency</td><td>68</td><td>64</td><td>57</td><td>56</td><td>59</td></tr><tr><td>Return on</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Average common shareholders’ equity</td><td>8.31</td><td>9.56</td><td>10.88</td><td>9.78</td><td>6.52</td></tr><tr><td>Average assets</td><td>1.02</td><td>1.16</td><td>1.28</td><td>.87</td><td>.64</td></tr><tr><td>Loans to deposits</td><td>87</td><td>85</td><td>82</td><td>84</td><td>91</td></tr><tr><td>Dividend payout</td><td>29.0</td><td>20.2</td><td>6.8</td><td>21.4</td><td>104.6</td></tr><tr><td>Tier 1 common</td><td>9.6</td><td>10.3</td><td>9.8</td><td>6.0</td><td>4.8</td></tr><tr><td>Tier 1 risk-based</td><td>11.6</td><td>12.6</td><td>12.1</td><td>11.4</td><td>9.7</td></tr><tr><td>Common shareholders’ equity to total assets</td><td>11.6</td><td>12.0</td><td>11.2</td><td>8.2</td><td>6.0</td></tr><tr><td>Average common shareholders’ equity to average assets</td><td>11.5</td><td>11.9</td><td>10.4</td><td>7.2</td><td>9.6</td></tr><tr><td> SELECTEDSTATISTICS</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Employees</td><td>56,285</td><td>51,891</td><td>50,769</td><td>55,820</td><td>59,595</td></tr><tr><td>Retail Banking branches</td><td>2,881</td><td>2,511</td><td>2,470</td><td>2,513</td><td>2,581</td></tr><tr><td>ATMs</td><td>7,282</td><td>6,806</td><td>6,673</td><td>6,473</td><td>6,233</td></tr><tr><td>Residential mortgage servicing portfolio (billions)</td><td>$135</td><td>$131</td><td>$139</td><td>$158</td><td>$187</td></tr><tr><td>Commercial mortgage servicing portfolio (billions)</td><td>$282</td><td>$267</td><td>$266</td><td>$287</td><td>$270</td></tr></table>
<table><tr><td>In millions</td><td>December 312012</td><td>December 312011</td></tr><tr><td>Commercial mortgages at fair value</td><td>$772</td><td>$843</td></tr><tr><td>Commercial mortgages at lower of cost or market</td><td>620</td><td>451</td></tr><tr><td>Total commercial mortgages</td><td>1,392</td><td>1,294</td></tr><tr><td>Residential mortgages at fair value</td><td>2,096</td><td>1,415</td></tr><tr><td>Residential mortgages at lower of cost or market</td><td>124</td><td>107</td></tr><tr><td>Total residential mortgages</td><td>2,220</td><td>1,522</td></tr><tr><td>Other</td><td>81</td><td>120</td></tr><tr><td>Total</td><td>$3,693</td><td>$2,936</td></tr></table>

Question: by what percentage did total residential mortgages increase from 2011 to 2012?
Answer: 0.45861
Reasoning program: subtract(2220,1522), divide(#0,1522)