Fair value | Fair value Recurring fair value measurements We hold fixed maturity securities and short-term investments, which are carried at fair value. The fair value of fixed maturity securities and short-term investments are estimated primarily based on information derived from third-party pricing services (“pricing services”), internal models and/or broker quotes, which use a market approach, income approach or a combination of the market and income approach depending on the type of instrument and availability of information. In general, a market approach is utilized if there is readily available and relevant market activity for an individual security. In certain cases where market information is not available for a specific security but is available for similar securities, that security is valued using market information for similar securities, which is also a market approach. When market information is not available for a specific security (or similar securities) or is available but such information is less relevant or reliable, an income approach or a combination of a market and income approach is utilized. For securities with optionality, such as call or prepayment features (including asset-backed securities), an income or combination approach may be used. These valuation techniques may change from period to period, based on the relevance and availability of market data. Further, while we consider the valuations provided by pricing services and broker quotes to be of high quality, management determines the fair value of our investment securities after considering all relevant and available information. In general, we first obtain valuations from pricing services. If prices are unavailable for public securities, we obtain broker quotes. For all securities, excluding certain private fixed maturity securities, if neither a pricing service nor broker quotes valuation is available, we determine fair value using internal models. For certain private fixed maturity securities where we do not obtain valuations from pricing services, we utilize an internal model to determine fair value since transactions for similar securities are not readily observable and these securities are not typically valued by pricing services. Given our understanding of the pricing methodologies and procedures of pricing services, the securities valued by pricing services are typically classified as Level 2 unless we determine the valuation process for a security or group of securities utilizes significant unobservable inputs, which would result in the valuation being classified as Level 3. Broker quotes are typically based on an income approach given the lack of available market data. As the valuation typically includes significant unobservable inputs, we classify the securities where fair value is based on our consideration of broker quotes as Level 3 measurements. For private fixed maturity securities, we utilize an income approach where we obtain public bond spreads and utilize those in an internal model to determine fair value. Other inputs to the model include rating and weighted-average life, as well as sector which is used to assign the spread. We then add an additional premium, which represents an unobservable input, to the public bond spread to adjust for the liquidity and other features of our private placements. We utilize the estimated market yield to discount the expected cash flows of the security to determine fair value. We utilize price caps for securities where the estimated market yield results in a valuation that may exceed the amount that would be received in a market transaction. When a security does not have an external rating, we assign the security an internal rating to determine the appropriate public bond spread that should be utilized in the valuation. While we generally consider the public bond spreads by sector and maturity to be observable inputs, we evaluate the similarities of our private placement with the public bonds, any price caps utilized, liquidity premiums applied, and whether external ratings are available for our private placements to determine whether the spreads utilized would be considered observable inputs. We classify private securities without an external rating or public bond spread as Level 3. In general, a significant increase (decrease) in credit spreads would have resulted in a significant decrease (increase) in the fair value for our fixed maturity securities as of June 30, 2023. For remaining securities priced using internal models, we determine fair value using an income approach. We maximize the use of observable inputs but typically utilize significant unobservable inputs to determine fair value. Accordingly, the valuations are typically classified as Level 3. Our assessment of whether or not there were significant unobservable inputs related to fixed maturity securities was based on our observations obtained through the course of managing our investment portfolio, including interaction with other market participants, observations related to the availability and consistency of pricing and/or rating, and understanding of general market activity such as new issuance and the level of secondary market trading for a class of securities. Additionally, we considered data obtained from pricing services to determine whether our estimated values incorporate significant unobservable inputs that would result in the valuation being classified as Level 3. A summary of the inputs used for our fixed maturity securities and short-term investments based on the level in which instruments are classified is included below. We have combined certain classes of instruments together as the nature of the inputs is similar. Level 1 measurements There were no fixed maturity securities classified as Level 1 as of June 30, 2023, and December 31, 2022. Level 2 measurements Fixed maturity securities: Third-party pricing services In estimating the fair value of fixed maturity securities, approximately 89% of our portfolio was priced using third-party pricing services as of June 30, 2023. These pricing services utilize industry-standard valuation techniques that include market-based approaches, income-based approaches, a combination of market-based and income-based approaches or other proprietary, internally generated models as part of the valuation processes. These third-party pricing vendors maximize the use of publicly available data inputs to generate valuations for each asset class. Priority and type of inputs used may change frequently as certain inputs may be more direct drivers of valuation at the time of pricing. Examples of significant inputs incorporated by pricing services may include sector and issuer spreads, seasoning, capital structure, security optionality, collateral data, prepayment assumptions, default assumptions, delinquencies, debt covenants, benchmark yields, trade data, dealer quotes, credit ratings, maturity and weighted-average life. We conduct regular meetings with our pricing services for the purpose of understanding the methodologies, techniques and inputs used by the third-party pricing providers. The following table presents a summary of the significant inputs used by our pricing services for certain fair value measurements of fixed maturity securities that are classified as Level 2 as of June 30, 2023: (Amounts in thousands) Fair value Primary methodologies Significant inputs U.S. government, agencies and GSEs $ 110,538 Price quotes from trading desk, broker feeds Bid side prices, trade prices, Option Adjusted Spread (“OAS”) to swap curve, Bond Market Association OAS, Treasury Curve, Agency Bullet Curve, maturity to issuer spread State and political subdivisions $ 426,528 Multi-dimensional attribute-based modeling systems, third-party pricing vendors Trade prices, material event notices, Municipal Market Data benchmark yields, broker quotes Non-U.S. government $ 11,206 Matrix pricing, spread priced to benchmark curves, price quotes from market makers Benchmark yields, trade prices, broker quotes, comparative transactions, issuer spreads, bid-offer spread, market research publications, third-party pricing sources U.S. corporate $ 2,105,532 Multi-dimensional attribute-based modeling systems, broker quotes, price quotes from market makers, internal models, OAS-based models Bid side prices to Treasury Curve, Issuer Curve, which includes sector, quality, duration, OAS percentage and change for spread matrix, trade prices, comparative transactions, Trade Reporting and Compliance Engine (“TRACE”) reports Non-U.S. corporate $ 495,138 Multi-dimensional attribute-based modeling systems, OAS-based models, price quotes from market makers Benchmark yields, trade prices, broker quotes, comparative transactions, issuer spreads, bid-offer spread, market research publications, third-party pricing sources Residential mortgage-backed $ 9,474 OAS-based models, single factor binomial models, internally priced Prepayment and default assumptions, aggregation of bonds with similar characteristics, including collateral type, vintage, tranche type, weighted-average life, weighted-average loan age, issuer program and delinquency ratio, pay up and pay down factors, TRACE reports Other asset-backed $ 1,196,812 Multi-dimensional attribute-based modeling systems, spread matrix priced to swap curves, price quotes from market makers Spreads to daily updated swap curves, spreads derived from trade prices and broker quotes, bid side prices, new issue data, collateral performance, analysis of prepayment speeds, cash flows, collateral loss analytics, historical issue analysis, trade data from market makers, TRACE reports Internal models A portion of our Level 2 U.S. corporate and non-U.S. corporate securities are valued using internal models. The fair value of these fixed maturity securities was $181.6 million and $72.2 million, respectively, as of June 30, 2023. Internally modeled securities are primarily private fixed maturity securities where we use market observable inputs such as an interest rate yield curve, published credit spreads for similar securities based on the external ratings of the instrument and related industry sector of the issuer. Additionally, we may apply certain price caps and liquidity premiums in the valuation of private fixed maturity securities. Price caps and liquidity premiums are established using inputs from market participants. Short-term investments: The fair value of short-term investments classified as Level 2 is determined after considering prices obtained by pricing services. Level 3 measurements Broker quotes A portion of our U.S. corporate and other asset-backed securities are valued using broker quotes. Broker quotes are obtained from third-party providers that have current market knowledge to provide a reasonable price for securities not routinely priced by pricing services. Brokers utilized for valuation of assets are reviewed annually. The fair value of our Level 3 fixed maturity securities priced by broker quotes was $23.3 million as of June 30, 2023. Internal models A portion of our U.S. corporate and non-U.S. corporate securities are valued using internal models. The primary inputs to the valuation of the bond population include quoted prices for identical assets, or similar assets in markets that are not active, contractual cash flows, duration, call provisions, issuer rating, benchmark yields and credit spreads. Certain private fixed maturity securities are valued using an internal model using market observable inputs such as the interest rate yield curve, as well as published credit spreads for similar securities, which includes significant unobservable inputs. Additionally, we may apply certain price caps and liquidity premiums in the valuation of private fixed maturity securities. Price caps are established using inputs from market participants. For structured securities, the primary inputs to the valuation include quoted prices for identical assets, or similar assets in markets that are not active, contractual cash flows, weighted-average coupon, weighted-average maturity, issuer rating, structure of the security, expected prepayment speeds and volumes, collateral type, current and forecasted loss severity, average delinquency rates, vintage of the loans, geographic region, debt service coverage ratios, payment priority with the tranche, benchmark yields and credit spreads. The fair value of our Level 3 fixed maturity securities priced using internal models was $282.7 million as of June 30, 2023. The following tables set forth our assets by class of instrument that are measured at fair value on a recurring basis as of the dates indicated: June 30, 2023 (Amounts in thousands) Total Level 1 Level 2 Level 3 Fixed maturity securities: U.S. government, agencies and GSEs $ 110,538 $ — $ 110,538 $ — State and political subdivisions 426,528 — 426,528 — Non-U.S. government 11,206 — 11,206 — U.S. corporate 2,509,479 — 2,287,178 222,301 Non-U.S. corporate 640,050 — 567,326 72,724 Residential mortgage-backed 9,474 — 9,474 — Other asset-backed 1,207,764 — 1,196,812 10,952 Total fixed maturity securities 4,915,039 — 4,609,062 305,977 Short-term investments 10,849 — 10,849 — Total $ 4,925,888 $ — $ 4,619,911 $ 305,977 December 31, 2022 (Amounts in thousands) Total Level 1 Level 2 Level 3 Fixed maturity securities: U.S. government, agencies and GSEs $ 44,769 $ — $ 44,769 $ — State and political subdivisions 419,856 — 419,856 — Non-U.S. government 9,349 — 9,349 — U.S. corporate 2,646,863 — 2,426,237 220,626 Non-U.S. corporate 652,844 — 557,690 95,154 Residential mortgage-backed 11,043 — 11,043 — Other asset-backed 1,100,036 — 1,096,555 3,481 Total fixed maturity securities 4,884,760 — 4,565,499 319,261 Short-term investments 3,047 — 3,047 — Total $ 4,887,807 $ — $ 4,568,546 $ 319,261 We had no liabilities recorded at fair value as of June 30, 2023, and December 31, 2022. The following tables present additional information about assets measured at fair value on a recurring basis and for which we have utilized significant unobservable (Level 3) inputs to determine fair value as of or for the dates indicated: Beginning balance as of April 1, 2023 Total realized and unrealized gains (losses) Purchases Sales Settlements Transfer into Level 3 (1) Transfer out of Level 3 (1) Ending balance as of June 30, 2023 Total gains (losses) attributable to assets still held (Amounts in thousands) Included in net income Included in OCI Included in net income Included in OCI Fixed maturity securities: U.S. corporate $ 216,330 $ (8) $ (4,021) $ 18,000 $ — $ (8,000) $ — $ — $ 222,301 $ (7) $ (4,842) Non-U.S. corporate 74,131 8 (1,309) — — (106) — — 72,724 8 (1,310) Other asset-backed 984 2 (24) 9,991 — (1) — — 10,952 2 (24) Total $ 291,445 $ 2 $ (5,354) $ 27,991 $ — $ (8,107) $ — $ — $ 305,977 $ 3 $ (6,176) Beginning balance as of April 1, 2022 Total realized and unrealized gains (losses) Purchases Sales Settlements Transfer into Level 3 (1) Transfer out of Level 3 (1) Ending balance as of June 30, 2022 Total gains (losses) attributable to assets still held (Amounts in thousands) Included in net income Included in OCI Included in net income Included in OCI Fixed maturity securities: U.S. corporate $ 243,463 $ (13) $ (13,386) $ — $ — $ — $ — $ (13,410) $ 216,654 $ (13) $ (12,893) Non-U.S. corporate 84,418 (84) (3,933) 3,009 — (105) — — 83,305 (84) (3,931) Other asset-backed — — 57 14,997 — — — — 15,054 — 57 Total $ 327,881 $ (97) $ (17,262) $ 18,006 $ — $ (105) $ — $ (13,410) $ 315,013 $ (97) $ (16,767) ______________ (1) The transfers into and out of Level 3 for fixed maturity securities were related to changes in the primary pricing source and changes in the observability of external information used in determining the fair value, such as external ratings or credit spreads. Beginning balance as of January 1, 2023 Total realized and unrealized gains (losses) Purchases Sales Settlements Transfer into Level 3 (1) Transfer out of Level 3 (1) Ending balance as of June 30, 2023 Total gains (losses) attributable to assets still held (Amounts in thousands) Included in net income Included in OCI Included in net income Included in OCI Fixed maturity securities: U.S. corporate $ 220,626 $ (21) $ 3 $ 21,000 $ (6,899) $ (12,408) $ — $ — $ 222,301 $ (16) $ (1,093) Non-U.S. corporate 95,154 (717) 1,458 3,759 (3,543) (23,387) — — 72,724 16 122 Other asset-backed 3,481 5 (10) 9,991 — (1) — (2,514) 10,952 5 (28) Total $ 319,261 $ (733) $ 1,451 $ 34,750 $ (10,442) $ (35,796) $ — $ (2,514) $ 305,977 $ 5 $ (999) (Amounts in thousands) Beginning balance as of January 1, 2022 Total realized and Purchases Sales Settlements Transfer into Level 3 (1) Transfer out of Level 3 (1) Ending balance as of June 30, 2022 Total gains Included Included Included in net income Included in OCI Fixed maturity securities: U.S. corporate $ 220,733 $ (28) $ (30,170) $ 39,969 $ — $ (440) $ — $ (13,410) $ 216,654 $ (28) $ (29,677) Non-U.S. corporate 83,664 (168) (9,270) 13,009 — (211) — (3,719) 83,305 (168) (8,975) Other asset-backed 24,223 — (1,567) 14,997 — — — (22,599) 15,054 — 57 Total $ 328,620 $ (196) $ (41,007) $ 67,975 $ — $ (651) $ — $ (39,728) $ 315,013 $ (196) $ (38,595) ______________ (1) The transfers into and out of Level 3 for fixed maturity securities were related to changes in the primary pricing source and changes in the observability of external information used in determining the fair value, such as external ratings or credit spreads. Purchases, sales, issuances and settlements represent the activity that occurred during the period that results in a change of the asset but does not represent changes in fair value for the instruments held at the beginning of the period. The amount presented for realized and unrealized gains (losses) included in net income for fixed maturity securities primarily represents amortization and accretion of premiums and discounts on certain fixed maturity securities recorded within net investment income. The following table presents a summary of the significant unobservable inputs used for certain asset fair value measurements that are based on internal models and classified as Level 3 as of June 30, 2023: (Amounts in thousands) Valuation technique Fair value (1) Unobservable input Range (bps) Weighted- average (2) (bps) Fixed maturity securities: U.S. corporate Internal models $ 220,136 Credit spreads 64 - 263 146 Non-U.S. corporate Internal models $ 62,527 Credit spreads 92 - 197 147 ______________ (1) Certain classes of instruments classified as Level 3 are excluded as a result of not being material or due to limitations in being able to obtain the underlying inputs used by certain third-party sources, such as broker quotes, used as an input in determining fair value. (2) Unobservable inputs weighted by the relative fair value of the associated instrument. We have certain financial instruments that are not recorded at fair value, including cash and cash equivalents and accrued investment income, the carrying value of which approximate fair value due to the short-term nature of these instruments and are not included in this disclosure. Liabilities not required to be carried at fair value The following represents our estimated fair value of financial liabilities that are not required to be carried at fair value, classified as Level 2, as of the dates indicated: June 30, 2023 December 31, 2022 (Amounts in thousands) Carrying amount Fair value Carrying amount Fair value Long-term borrowings $ 744,100 $ 737,790 $ 742,830 $ 739,020 |