We continue to be in the midst of an unprecedented period of low interest rates and low yields for investments with the credit quality we prefer which presents a strong headwind to achieving our target rate for investment spread. In response, we have been reducing policyholder crediting rates for new annuities and existing annuities since the fourth quarter of 2011. In addition, options costs for certain index strategies have been increasing in the last several quarters which has caused an increase in our aggregate cost of money. We continue to have flexibility to reduce our crediting rates if necessary and could decrease our cost of money by approximately 63 basis points if we reduce current rates to guaranteed minimums. In addition, starting in 2017 we began to invest in asset classes that were not traditionally in our portfolio, focusing on investments with less liquidity that provide higher yields and have a track record of positive credit performance. Investment yields available to us in 2018 increased compared to 2017 due to an increase in interest rates on the asset classes we targeted for purchase and investment in new asset classes as noted above. We are looking to improve our investment yield through the opportunistic replacement of lower yielding securities with higher yielding securities. During 2018 we sold $2.1 billion in book value of lower yielding securities for a yield pick-up of approximately 170 basis points on these investments. As book yields on the securities sold were less than market yields, we recognized losses of approximately $50 million with $38 million recognized in net realized gains (losses), and $12 million recognized as OTTI. These losses should be recovered from the higher yields on the securities acquired with the proceeds from the sales in less than two years. While we anticipate pursuing additional portfolio realignment opportunities in 2019, we would not expect the size to be as large as in 2018.
We specialize in the sale of individual annuities (primarily fixed index deferred annuities). Under U.S. generally accepted accounting principles ("GAAP"), premium collections for deferred annuities are reported as deposit liabilities instead of as revenues. Similarly, cash payments to policyholders are reported as decreases in the liabilities for policyholder account balances and not as expenses. Sources of revenues for products accounted for as deposit liabilities are net investment income, surrender charges assessed against policy withdrawals and fees deducted from policyholder account balances for lifetime income benefit riders, net realized gains (losses) on investments and changes in fair value of derivatives. Components of expenses for products accounted for as deposit liabilities are interest sensitive and index product benefits (primarily interest credited to account balances and changes in the liability for lifetime income benefit riders), changes in fair value of embedded derivatives, amortization of deferred sales inducements and deferred policy acquisition costs, other operating costs and expenses and income taxes.
Annuity deposits by product type collected during 2018, 2017 and 2016, were as follows:
Net income for the year ended December 31, 2017 was negatively impacted by $35.9 million related to the revaluation of our net deferred tax assets using the newly enacted federal tax rate as a result of Tax Reform. Net income for the year ended December 31, 2017 was also negatively impacted by an $18.4 million pretax loss on the extinguishment of our $400 million notes due 2021 (the “2021 Notes”), which reduced net income by $10.8 million. See Note 9 to our audited consolidated financial statements.
Net income is also impacted by the change in fair value of derivatives and embedded derivatives which fluctuates from year to year based upon changes in fair values of call options purchased to fund the annual index credits for fixed index annuities and changes in the interest rate used to discount the embedded derivative liability. Net income for the year ended December 31, 2018 was positively impacted by an increase in the discount rate used to estimate our embedded derivative liabilities while net income for the years ended December 31, 2017 and 2016 was negatively impacted by a decrease in the discount rate used to estimate our embedded derivative liabilities.
Net income for 2018, 2017 and 2016 includes effects from revisions to assumptions as follows:
The most significant revisions made during 2017 as a result of our quarterly reviews were account balance true-ups which were favorable to us due to stronger index credits than we assumed due to strong equity market performance and adjustments to generally decrease lapse rate assumptions to reflect better persistency experienced than assumed. The favorable impact of the account balance true-ups and lapse rate assumption changes was partially offset by reductions in estimated future gross profits attributable to revisions to assumptions used in determining the liability for lifetime income benefit riders as well as an increase in estimated expenses associated with a reinsurance agreement with an unaffiliated reinsurer.
The most significant revisions during 2016 as a result of our quarterly reviews were adjustments to lower future spread assumptions as actual investment spreads being earned showed investment spread and gross profits being less than what we were assuming in our models due to decreases in the average yield on invested assets resulting from the continued low interest rate environment. We also made adjustments to extend the period of time in which we assume investment spread will grade up to our long-term spread targets by an additional two years as yields obtained on investment purchases were much lower than we had anticipated as a result of the overall decline in investment yields that followed the Brexit vote. In addition, revisions to assumptions used in determining the liability for lifetime income benefit riders during 2016 resulted in a decrease in estimated future gross profits.
The 2018, 2017 and 2016 revisions to the liability for lifetime income benefit riders were consistent with the revisions used in the calculation of amortization of deferred policy acquisition costs and deferred sales inducements described above. The 2018 revisions were primarily attributable to account balance true-ups and future investment spread assumptions. The impact of the account balance true-ups and future investment spread changes was partially offset by the lapse rate assumptions changes described above. The 2017 revisions were primarily due to the lapse rate assumption changes described above and changes to our account value growth projections. The 2016 revisions were primarily due to actual index credits on policies being lower than projected over the past four quarters.
Non-GAAP operating income, a non-GAAP financial measure (see reconciliation to net income in Item 6. Selected Consolidated Financial Data) increased 49% to $425.7 million in 2018 and 133% to $285.1 million in 2017 from $122.3 million in 2016.
Non-GAAP operating income is not a substitute for net income determined in accordance with GAAP. The adjustments made to derive non-GAAP operating income are important to understand our overall results from operations and, if evaluated without proper context, non-GAAP operating income possesses material limitations. As an example, we could produce a low level of net income in a given period, despite strong operating performance, if in that period we experience significant net realized losses from our investment portfolio. We could also produce a high level of net income in a given period, despite poor operating performance, if in that period we generate significant net realized gains from our investment portfolio. As an example of another limitation of non-GAAP operating income, it does not include the decrease in cash flows expected to be collected as a result of credit loss OTTI. Therefore, our management reviews net realized investment gains (losses) and analyses of our net investment income, including impacts related to OTTI write-downs, in connection with their review of our investment portfolio. In addition, our management examines net income as part of their review of our overall financial results.
Annuity product charges (surrender charges assessed against policy withdrawals and fees deducted from policyholder account balances for lifetime income benefit riders) increased 12% to $224.5 million in 2018 and 16% to $200.5 million in 2017 from $173.6 million in 2016. The components of annuity product charges are set forth in the table that follows:
The average yield earned on average invested assets was 4.47%, 4.46% and 4.51% for 2018, 2017 and 2016, respectively. The increase in yield earned on average invested assets in 2018 was attributable to the investment of new premiums and portfolio cash flows at rates above the overall portfolio yield and higher yields being earned on our floating rate investments. The decrease in yield earned on average invested assets in 2017 was attributable to investment of new premiums and portfolio cash flows during those periods at rates below the overall portfolio yield. The average yield on fixed income securities purchased and commercial mortgage loans funded was 4.79%, 4.16% and 3.66% for the years ended December 31, 2018, 2017 and 2016, respectively. The impact from these items was also impacted by non-trendable investment income items which added eight basis points to the average yield on invested assets in 2018 and 2017 and six basis points to the average yield on invested assets in 2016, respectively.
Change in fair value of derivatives consists of call options purchased to fund annual index credits on fixed index annuities, and an interest rate swap and interest rate caps that hedge our floating rate subordinated debentures. The components of change in fair value of derivatives are as follows:
The change in fair value of derivatives is also influenced by the aggregate costs of options purchased. The aggregate cost of options has increased primarily due to an increased amount of fixed index annuities in force as well as an increase in the cost of options for certain index strategies which began during the second half of 2017. The aggregate cost of options is also influenced by the amount of policyholder funds allocated to the various indices and market volatility which affects option pricing. See Critical Accounting Policies - Policy Liabilities for Fixed Index Annuities.
The changes in index credits were attributable to changes in the level of appreciation of the underlying indices (see discussion above under Change in fair value of derivatives) and the amount of funds allocated by policyholders to the respective index options. Total proceeds received upon expiration of the call options purchased to fund the annual index credits were $1.3 billion, $1.6 billion and $0.3 billion for the years ended December 31, 2018, 2017 and 2016, respectively. The decrease in interest credited in 2018 and 2017 was primarily due to a decrease in the average rate credited to the annuity liabilities outstanding receiving a fixed rate of interest. The average amount of annuity liabilities outstanding (net of annuity liabilities ceded under coinsurance agreements) increased 6% to $49.9 billion in 2018 and 8% to $46.8 billion in 2017 from $43.5 billion in 2016. The decrease in benefits recognized for lifetime income benefit riders in 2018 was primarily due to the impact of revisions of assumptions used in determining the liability for lifetime income benefit riders which caused a decrease of $53.6 million in the liability in 2018 as compared to an increase of $21.6 million in the liability in 2017. The decrease in the liability in 2018 due to assumption revisions was partially offset by an increase in the number of policies with lifetime income benefit riders which correlates to the increase in fees discussed in Annuity product charges. The decrease in benefits recognized for lifetime income benefit riders in 2017 was due to the impact of revisions of assumptions used in determining the liability for lifetime income benefit riders being less in 2017 than it was in 2016 which was partially offset by an increase in the number of policies with lifetime income benefit riders which correlates to the increase in fees discussed in Annuity product charges. See Net income above for discussion of the changes in the assumptions used in determining reserves for lifetime income benefit riders for the years ended December 31, 2018, 2017 and 2016.
Change in fair value of embedded derivatives includes changes in the fair value of our fixed index annuity embedded derivatives (see Notes 5 to our audited consolidated financial statements). The components of change in fair value of embedded derivatives are as follows:
The change in fair value of the fixed index annuity embedded derivatives resulted from (i) changes in the expected index credits on the next policy anniversary dates, which are related to the change in fair value of the call options acquired to fund those index credits discussed above in Change in fair value of derivatives; (ii) changes in the discount rate used in estimating our embedded derivative liabilities; and (iii) the growth in the host component of the policy liability. The amounts presented as "Other changes in difference between policy benefit reserves computed using derivative accounting vs. long-duration contracts accounting" represents the total change in the difference between policy benefit reserves for fixed index annuities computed under the derivative accounting standard and the long-duration contracts accounting standard at each balance sheet date, less the change in fair value of our fixed index annuities embedded derivative. See Critical Accounting Policies-Policy Liabilities for Fixed Index Annuities.
The decrease in interest expense in 2018 was due to the repayment of our outstanding $100 million term loan and the redemption of our $400 million 6.625% notes due 2021 with the proceeds from the issuance of $500 million aggregate principal amount of senior unsecured notes due 2027 which bear interest at 5.0% per year and will mature on June 15, 2027 (the "2027 Notes"). This lowered our senior notes costs to 5% from 6.625%. The increase in interest expense in 2017 was attributable to interest expense on the $100 million variable rate term loan originated on September 30, 2016 and prepaid on June 16, 2017 and interest expense on the 2027 Notes issued on June 16, 2017 which were partially offset by a decrease in interest expense as a result of the redemption of the 2021 Notes on July 17, 2017. See Note 9 to our audited consolidated financial statements.
Other operating costs and expenses increased 16% to $129.3 million in 2018 and increased 9% to $111.7 million in 2017 from $102.2 million in 2016 and are summarized as follows:
The increases in reinsurance risk charges expense during 2018 and 2017 were due to the growth in our policyholder liabilities subject to a reinsurance agreement pursuant to which we cede excess regulatory reserves to an unaffiliated reinsurer. The increase in risk charge expense in 2017 due to growth in the policyholder liabilities subject to the reinsurance was partially offset by a lower risk charge percentage which was included in an October 1, 2016 amendment to the reinsurance agreement. The regulatory reserves ceded at December 31, 2018, 2017 and 2016 were $780.0 million, $737.3 million and $638.1 million, respectively.
Income tax expense decreased in 2018 as Tax Reform reduced the statutory federal income tax rate from 35% to 21% effective January 1, 2018. The lower tax rate offset the expected increase in income tax expense from the increase in income before income taxes. Income tax expense increased in 2017 due to an increase in income before income taxes and the impact of Tax Reform discussed below. The effective income tax rates were 19.0%, 44.8% and 36.1% for 2018, 2017 and 2016, respectively.
Income tax expense and the resulting effective tax rate are based upon two components of income before income taxes ("pretax income") that are taxed at different tax rates. Life insurance income is generally taxed at an effective rate of approximately 21.6% reflecting the absence of state income taxes for substantially all of the states that the life insurance subsidiaries do business in. The income for the parent company and other non-life insurance subsidiaries (the "non-life insurance group") is generally taxed at an effective tax rate of 29.5% reflecting the combined federal / state income tax rates. Prior to Tax Reform, life insurance income was generally taxed at an effective rate of approximately 35.6% while income for the non-life insurance group was generally taxed at an effective tax rate of 41.5% reflecting the combined federal / state income tax rates. The effective income tax rates resulting from the combination of the income tax provisions for the life / non-life sources of income vary from year to year based primarily on the relative size of pretax income from the two sources.
The effective income tax rate for 2018 was impacted by capital losses being carried back to periods in which a 35% statutory tax rate was in effect. The impact of the higher capital loss carry back rate reduced income tax expense by approximately $2.5 million for the year ended December 31, 2018. In addition, the effective tax rate for the year ended December 31, 2018 benefited from a discrete tax item for a worthless stock deduction related to a wholly-owned subsidiary which reduced income tax expense by approximately $7.4 million.
The effective income tax rate for 2018 and 2017 was impacted by a discrete tax item related to share-based compensation that reduced income tax expense for 2018 and 2017 by approximately $2.7 million and $2.8 million, respectively.
The increase in unrealized losses from December 31, 2017 to 2018 was primarily due to an increase in interest rates in addition to price deterioration due to wider credit spreads during the year ended December 31, 2018. The 10-year U.S. Treasury yield rates at December 31, 2018 and 2017 were 2.69% and 2.40%, respectively. The 30-year U.S. Treasury yields at December 31, 2018 and 2017 were 3.02% and 2.74%, respectively.
We hold fixed maturity securities with international exposure. As of December 31, 2018, 24% of the carrying value of our fixed maturity securities was comprised of corporate debt securities of issuers based outside of the United States and debt securities of foreign governments. All of our fixed maturity securities with international exposure are denominated in U.S. dollars. Our investment professionals analyze each holding for credit risk by economic and other factors of each country and industry. The following table presents our international exposure in our fixed maturity portfolio by country or region:
Our commercial mortgage loan portfolio consists of mortgage loans collateralized by the related properties and diversified as to property type, location and loan size. Our mortgage lending policies establish limits on the amount that can be loaned to one borrower and other criteria to attempt to reduce the risk of default. Our commercial mortgage loans on real estate are reported at cost, net of loan loss allowances and deferred prepayment fees. At December 31, 2018 and 2017, the largest principal amount outstanding for any single mortgage loan was $23.8 million and $21.2 million, respectively, and the average loan size was $3.8 million and $3.5 million, respectively. In addition, the average loan to value ratio for the overall portfolio was 53.6% at both December 31, 2018 and 2017, respectively, based upon the underwriting and appraisal at the time the loan was made. This loan to value is indicative of our conservative underwriting policies and practices for making commercial mortgage loans and may not be indicative of collateral values at the current reporting date. Our current practice is to only obtain market value appraisals of the underlying collateral at the inception of the loan unless we identify indicators of impairment in our ongoing analysis of the portfolio, in which case, we either calculate a value of the collateral using a capitalization method or obtain a third party appraisal of the underlying collateral. The commercial mortgage loan portfolio is summarized by geographic region and property type in Note 4 of our audited consolidated financial statements of this Form 10-K, which is incorporated by reference in this Item 7.
We have a process by which we evaluate the credit quality of each of our commercial mortgage loans. This process utilizes each loan's debt service coverage ratio as a primary metric. A summary of our portfolio by debt service coverage ratio (based on most recent information collected) follows:
At December 31, 2018, we had no commercial mortgage loans that were delinquent (60 days or more past due at the reporting date) in their principal and interest payments.
Our insurance subsidiaries continue to have adequate cash flows from annuity deposits and investment income to meet their policyholder and other obligations. Net cash flows from annuity deposits and funds returned to policyholders as surrenders, withdrawals and death claims were $1.2 billion for the year ended December 31, 2018 compared to $1.3 billion for the year ended December 31, 2017 with the decrease attributable to a $341.4 million (after coinsurance) increase in funds returned to policyholders, which was partially offset by a $202.9 million increase in net annuity deposits after coinsurance. We continue to invest the net proceeds from policyholder transactions and investment activities in high quality fixed maturity securities and fixed rate commercial mortgage loans.
The maximum distribution permitted by law or contract is not necessarily indicative of an insurer's actual ability to pay such distributions, which may be constrained by business and regulatory considerations, such as the impact of such distributions on surplus, which could affect the insurer's ratings or competitive position, the amount of premiums that can be written and the ability to pay future dividends or make other distributions. Further, state insurance laws and regulations require that the statutory surplus of our life subsidiaries following any dividend or distribution must be reasonable in relation to their outstanding liabilities and adequate for their financial needs. Along with solvency regulations, the primary driver in determining the amount of capital used for dividends is the level of capital needed to maintain desired financial strength ratings from rating agencies. Both regulators and rating agencies could become more conservative in their methodology and criteria, including increasing capital requirements for our insurance subsidiaries which, in turn, could negatively affect the cash available to us from insurance subsidiaries. As of December 31, 2018, we estimate American Equity Life has sufficient statutory capital and surplus, combined with capital available to the holding company, to maintain this rating objective. However, this capital may not be sufficient if significant future losses are incurred or a rating agency modifies its rating criteria and access to additional capital could be limited.
The transfer of funds by American Equity Life is also restricted by a covenant in our line of credit agreement which requires American Equity Life to maintain a minimum risk-based capital ratio of 275% and a minimum level of statutory surplus equal to the sum of 1) 80% of statutory surplus at June 30, 2016, 2) 50% of the statutory net income for each fiscal quarter ending after June 30, 2016, and 3) 50% of all capital contributed to American Equity Life after June 30, 2016. American Equity Life's risk-based capital ratio was 360% at December 31, 2018. Under this agreement, we are also required to maintain a maximum ratio of adjusted debt to total adjusted capital of 0.35.
Cash and cash equivalents of the parent holding company at December 31, 2018, were $68.9 million. In addition, as discussed in Note 9 to our audited consolidated financial statements, we have a $150 million revolving line of credit agreement, with no borrowings outstanding at December 31, 2018. This revolving line of credit terminates on September 30, 2021, and borrowings are available for general corporate purposes of the parent company and its subsidiaries. We also have the ability to issue equity, debt or other types of securities through one or more methods of distribution. The terms of any offering would be established at the time of the offering, subject to market conditions.
Statutory accounting practices prescribed or permitted for our life subsidiaries differ in many respects from those governing the preparation of financial statements under GAAP. Accordingly, statutory operating results and statutory capital and surplus may differ substantially from amounts reported in the GAAP basis financial statements for comparable items. Information as to statutory capital and surplus and statutory net income for our life subsidiaries as of December 31, 2018 and 2017 and for the years ended December 31, 2018, 2017 and 2016 is included in Note 12 to our audited consolidated financial statements.
In the normal course of business, we enter into financing transactions, lease agreements, or other commitments. These commitments may obligate us to certain cash flows during future periods. The following table summarizes such obligations as of December 31, 2018.
Models and other valuation methodologies using significant inputs that are unobservable for financial instruments and include situations where there is little, if any, market activity for the financial instrument. The inputs into the determination of fair value require significant management judgment or estimation. Financial instruments that are included in Level 3 are securities for which no market activity or data exists and for which we used discounted expected future cash flows with our own assumptions about what a market participant would use in determining fair value.
Management's assessment of all available data when determining fair value of our investments is necessary to appropriately apply fair value accounting.
The independent pricing services provide quoted market prices when available. Quoted prices are not always available due to market inactivity. When quoted market prices are not available, the third parties use yield data and other factors relating to instruments or securities with similar characteristics to determine fair value for securities that are not actively traded. We generally obtain one value from our primary external pricing service. In situations where a price is not available from this service, we may obtain quotes or prices from additional parties as needed. In addition, for our callable United States Government sponsored agencies we obtain multiple broker quotes and take the average of the broker prices received. Market indices of similar rated asset class spreads are considered for valuations and broker indications of similar securities are compared. Inputs used by the broker include market information, such as yield data and other factors relating to instruments or securities with similar characteristics. Valuations and quotes obtained from third party commercial pricing services are non-binding and do not represent quotes on which one may execute the disposition of the assets.
We validate external valuations at least quarterly through a combination of procedures that include the evaluation of methodologies used by the pricing services, comparison of the prices to a secondary pricing source, analytical reviews and performance analysis of the prices against trends, and maintenance of a securities watch list. Additionally, as needed we utilize discounted cash flow models or perform independent valuations on a case-by-case basis using inputs and assumptions similar to those used by the pricing services. Although we do identify differences from time to time as a result of these validation procedures, we did not make any significant adjustments as of December 31, 2018 and 2017.
The liability for lifetime income benefit riders is based on estimates of the present value of benefit payments expected to be paid in excess of projected policy values recognizing the excess over the expected lives of the underlying policies based on the actual and present value of expected assessments including spreads and product charges and fees. The inputs used in the calculation of the liability for lifetime income benefit riders include actual policy values, actual income account values, actual payout factors, actual roll-up rates and our best estimate assumptions for future policy growth, future policy decrements, the ages at which policyholders are expected to elect to begin to receive lifetime income benefit payments, the percentage of policyholders who elect to receive lifetime income benefit payments and the type of income benefit payments selected upon election. The assumptions are reviewed quarterly and revisions to the assumptions are made based on historical results and our best estimates of future experience. The liability for lifetime income benefit riders is included in policy benefit reserves in the consolidated balance sheets and the change in the liability is included in interest sensitive and index product benefits in the consolidated statements of operations. See Results of Operations for the Three Years Ended December 31, 2018 in this Item 7 for a discussion and presentation of the actual effects of assumption revisions.
For annuity products, these costs are being amortized generally in proportion to expected gross profits from investment spreads, including the cost of hedging the fixed indexed annuity obligations, and, to a lesser extent, from product charges net of expected excess payments for lifetime income benefit riders, and mortality and expense margins. Current and future period gross profits/margins for fixed index annuities also include the impact of amounts recorded for the change in fair value of derivatives and the change in fair value of embedded derivatives. Current period amortization is adjusted retrospectively through an unlocking process when estimates of current or future gross profits/margins (including the impact of realized investment gains and losses) to be realized from a group of products are revised. Our estimates of future gross profits/margins are based on actuarial assumptions related to the underlying policies terms, lives of the policies, yield on investments supporting the liabilities and level of expenses necessary to maintain the polices over their entire lives. Revisions are made based on historical results and our best estimates of future experience. See Results of Operations for the Three Years Ended December 31, 2018 in this Item 7 for a discussion and presentation of the actual effects of unlocking.