We reported net income of $126 million or $0.67 per share for the third quarter and adjusted diluted net operating income per share was also $0.67.
We grew our book value per share by 9% year-over-year.
We achieved this growth even after accounting for more than $100 million of dividends that we returned to stockholders over the past year.
During the third quarter, we wrote $26.6 billion of high-quality new mortgage insurance business and our primary insurance in-force grew by $4.3 billion from the second quarter to $241.6 billion at September 30.
We have seen continued improvement in the credit performance of our portfolio, with a 46% year-over-year decline in our total number of defaulted loans.
We saw 60% decline year-over-year in the number of new notices of default received in the quarter.
The cure-to-new default ratio in the third quarter of 2021 was 178%.
Based on September data from our own Radian Home Price Index continued strong housing demand and relatively limited supply in the market led to an annualized 17.6% increase in home prices across the country.
Our new mortgage insurance business was 90% purchase volume in the third quarter versus only 71% a year ago.
Based on updated market projections for our 2021 mortgage originations, we now expect the private mortgage insurance market to be approximately $575 million to $600 billion, which would be slightly lower than the record volume in 2020, but still represent the second highest MI volume year in history.
Looking ahead, total mortgage originations for 2022 are estimated to be approximately $3 trillion, reflecting a 10% increase in purchase originations and a 55% decrease in refinance activity.
Turning to our Homegenius segment, total revenues for the third quarter were $45.1 million, representing a 35% increase from the second quarter of 2021 and a 51% increase year-over-year.
This was primarily driven by an increase in our title revenue, which grew 106% year-over-year as well as growth in our valuation business.
In terms of capital strength, at September 30, Radian Group maintained a strong capital position with $1 billion of total holding company liquidity.
Additionally, at September 30, Radian Guaranty's PMIERs excess available assets, was $1.7 billion or a cushion of 49%.
Notably, the recent lifting of the preferred stock purchase agreement caps on layered risk, the newly proposed amendment to the Enterprise capital framework to reduce GSE-required capital levels and the various direct market actions such as eliminating the 50 basis point adverse market fee for refinance loans and expanding eligibility for the refi now and refi hospital programs represent a notable shift in focus.
To recap our financial results issued last evening, we reported GAAP net income of $164.1 million or $0.67 per diluted share for the third quarter of 2021 as compared to $0.80 per diluted share in the second quarter of 2021 and $0.70 per diluted share in the third quarter of 2020.
Adjusted diluted net operating income was $0.67 per share in the third quarter of 2021 compared to $0.75 in the second quarter of 2021 and $0.59 in the third quarter of 2020.
As Rick mentioned earlier, our new insurance written was $26.6 billion during the quarter compared to $21.7 billion in the second quarter of 2021 and $33.3 billion in the third quarter of 2020.
New insurance written for purchase transactions was $23.9 billion, an increase of 2% year-over-year and 43% compared to the second quarter of 2021.
Purchase volume accounted for 90% of our total new insurance written for the third quarter, an increase from 77% of volume in the prior quarter and 70.5% in the third quarter of 2020.
Primary insurance in-force increased $4.3 billion during the quarter to $241.6 billion.
On a year-over-year basis, primary insurance in-force has declined approximately 2%, primarily driven by sustained low persistency resulting from policy cancellations during a low interest rate, high refinance period.
It is important to note, however, the mix shift of our in-force portfolio during this past year, monthly premium insurance in-force, which drives the majority of our earned premiums, has grown 6% year-over-year compared to a 25% decline in single-premium insurance in-force.
Our quarterly annualized persistency rate was 67.5% this quarter, an increase from 66.3% in the second quarter of 2021 and 60% in the third quarter of 2020.
Moving now to our earned premiums and other revenues, total net premiums earned were $249.1 million in the third quarter of 2021 compared to $254.8 million in the second quarter of 2021 and $286.5 million in the third quarter of 2020.
Title premiums increased to $12.3 million in the third quarter of 2021 compared to $7.7 million in the second quarter of 2021.
Our direct in-force premium yield was 40.3 basis points this quarter compared to 41.1 basis points last quarter and 43.2 basis points in the third quarter of 2020.
Our Homegenius segment revenues were $45.1 million for the third quarter of 2021, representing a 35% increase compared to the second quarter of 2021 and a 51% increase compared to the third quarter of 2020.
Our reported home genius pre-tax operating loss before allocated corporate operating expenses was $600,000 for the third quarter of 2021 compared to a loss of $4.5 million for the second quarter of 2021.
Our reported Homegenius adjusted gross profit for the third quarter of 2021 was $17.9 million compared to $11.7 million for the second quarter of 2021.
As noted on Slide 22, we continue to make progress against our targets as communicated earlier this year, with Homegenius revenues still tracking toward our goal of $150 million for 2021.
Our investment income this quarter of $36 million was relatively flat compared to the prior quarter and same quarter prior year due to the lower investment yields, which were partially offset by additional investment balances from underwriting cash flow.
At quarter end, the investment portfolio duration was approximately 4.5 years, unchanged from the prior quarter.
Moving now to our loss provision and credit quality, as noted on Slide 13, the mortgage provision for losses for the third quarter of 2021 was $16.8 million, an increase compared to $3.3 million in the second quarter of 2021 and a decrease compared to $87.8 million in the third quarter of 2020.
As shown on Slide 14, we had approximately 8,100 new defaults in both the third and second quarters of 2021 compared to approximately 21,000 in the third quarter of 2020.
Also, as noted on Slide 13, the provision for losses for the third quarter 2021 includes a positive development on prior defaults of $16.5 million.
We maintained our prior quarter assumptions for defaults reported since the start of the pandemic, including the default to claim rate assumption on new defaults at 8% for the third quarter of 2021.
As shown on Slide 16, 67% of all defaults were reported to be in a forbearance program as of September 30, 2021.
It should also be noted that approximately 89% of new defaults from the second quarter of 2020 and 85% of new defaults from the third quarter 2020 have cured as of the end of October.
Now turning to expenses; other operating expenses were $86.5 million in the third quarter of 2021, flat to the second quarter of 2021 and increased compared to $69.4 million in the third quarter of 2020.
The increase in other operating expenses as compared to the prior year is primarily related to an increase in incentive compensation expense, including long-term share-based incentive compensation as well as a $6.7 million decrease in ceding commissions associated with lower single premium acceleration.
Over the next year, we expect consolidated normalized quarterly operating expenses to grow from approximately $72 million to approximately $85 million which will depend largely on the timing and the execution of our Homegenius segment revenue growth strategy.
Our mortgage segment, however, should have relatively flat quarterly expenses at just under $60 million.
Moving now to taxes; our overall effective tax rate for the third quarter of 2021 was 21.8%.
Our annualized effective tax rate for 2021 and before discrete items remains generally consistent with the statutory rate of 21%.
Now moving to capital and available liquidity; Radian Guaranty's excess available assets over minimum required assets was $1.7 billion as of the end of the third quarter, which represents a 49% PMIERs cushion.
In connection with this transaction, Radian Guaranty will receive $484.1 million of fully collateralized aggregate excess of loss reinsurance coverage from Eagle Re at closing.
The excess of loss reinsurance will cover mortgage insurance losses on new defaults on an existing portfolio of eligible policies with risk in force of $10.8 billion that were issued predominantly between January 1, 2021 and July 31, 2021.
For Radian Group, as of September 30, 2021, we maintained $768 million of available liquidity compared to $923 million as of June 30, 2021.
Along with our recurring shareholder dividend payment, partially offset by a $36 million ordinary dividend paid by our Radian Reinsurance subsidiary.
Total liquidity, which includes the company's $267.5 million credit facility, was $1 billion as of September 30, 2021.
During the third quarter of 2021, we repurchased 7.1 million shares and year-to-date through October 31, we have purchased 13.3 million shares or approximately 7% of our outstanding shares at an average share price of $22.78 or an approximate 3% discount to our current book value.
As of October 31, we have approximately $95 million of remaining repurchase authorization which expires on August 31 of next year.
We have also continued to pay a dividend to common shareholders throughout the pandemic, including during the third quarter of 2021, as we returned approximately $27 million to shareholders through dividends during the quarter.
As a reminder, and as previously announced, we increased our quarterly dividend by 12% to $0.14 per share during the second quarter of this year.
The combination of dividend payments and share repurchase represent a return of capital of approximately 82% of our after-tax operating income for this year.
We wrote $26.6 billion of high-quality new mortgage insurance business, which helped grow our primary mortgage insurance in force to $241.6 billion, Homegenius revenues increased by 51% year-over-year.
During the quarter, we were recognized as a champion of Board Diversity by the Forum of Executive Women and raised a total of $165,000 for the NBA Open Store Foundation, an organization that shares our mission of enabling and protecting homeownership.

Summary:
We reported net income of $126 million or $0.67 per share for the third quarter and adjusted diluted net operating income per share was also $0.67.
Turning to our Homegenius segment, total revenues for the third quarter were $45.1 million, representing a 35% increase from the second quarter of 2021 and a 51% increase year-over-year.
To recap our financial results issued last evening, we reported GAAP net income of $164.1 million or $0.67 per diluted share for the third quarter of 2021 as compared to $0.80 per diluted share in the second quarter of 2021 and $0.70 per diluted share in the third quarter of 2020.
Adjusted diluted net operating income was $0.67 per share in the third quarter of 2021 compared to $0.75 in the second quarter of 2021 and $0.59 in the third quarter of 2020.
Our Homegenius segment revenues were $45.1 million for the third quarter of 2021, representing a 35% increase compared to the second quarter of 2021 and a 51% increase compared to the third quarter of 2020.