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Financial Instruments (Tables) | 6 Months Ended
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Jun. 30, 2022
Derivative Instruments and Hedging Activities Disclosure [Abstract] |
Notional exposure of derivative instruments | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | June 30, 2022 | ​ | December 31, 2021
​ |  | Long Notional Exposure |  | Short Notional Exposure |  | Long Notional Exposure |  | Short Notional Exposure
​ | ​ | ​ | (in millions)
Primary underlying risk: | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Equity contracts | ​ | $ | 1,300 | ​ | $ | 4,398 | ​ | $ | 1,582 | ​ | $ | 5,986
Credit contracts(1) |  | ​ | — |  | ​ | 1,336 | ​ | ​ | — |  | ​ | 2,081
(1) | The short notional amount on our credit default swap positions was approximately $5.9 billion at June 30, 2022. However, because credit spreads cannot compress below zero, our downside short notional exposure to loss is approximately $1.3 billion as of June 30, 2022. The short notional amount on our credit default swap positions was approximately $6.6 billion as of December 31, 2021. However, because credit spreads cannot compress below zero, our downside short notional exposure to loss is approximately $2.1 billion as of December 31, 2021.
Fair value and income recognized for derivatives not designated as hedging instruments | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | Derivative Assets | ​ | Derivative Liabilities
​ |  | June 30, 2022 |  | December 31, 2021 |  | June 30, 2022 |  | December 31, 2021
​ | ​ | ​ | (in millions)
Equity contracts | ​ | $ | 205 | ​ | $ | 68 | ​ | $ | 942 | ​ | $ | 1,317
Credit contracts | ​ |  | 826 | ​ |  | 1,075 | ​ |  | — | ​ |  | —
Sub-total | ​ |  | 1,031 | ​ |  | 1,143 | ​ |  | 942 | ​ |  | 1,317
Netting across contract types(1) | ​ |  | (140) | ​ |  | (532) | ​ |  | (140) | ​ |  | (532)
Total(1) | ​ | $ | 891 | ​ | $ | 611 | ​ | $ | 802 | ​ | $ | 785
(1) | Excludes netting of cash collateral received and posted. The total collateral posted at June 30, 2022 and December 31, 2021 was $1,224 million and $1,906 million, respectively, across all counterparties, which are included in cash held at consolidated affiliated partnerships and restricted cash in the condensed consolidated balance sheets.
The following table presents the amount of gain (loss) recognized in the condensed consolidated statements of operations for our Investment segment’s derivatives not designated as hedging instruments:
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | Gain (loss) Recognized in Income (1)
​ | ​ | Three Months Ended June 30, | ​ | Six Months Ended June 30,
​ |  | 2022 |  | 2021 |  | 2022 |  | 2021
​ | ​ | (in millions)
Equity contracts | ​ | $ | 392 | ​ | $ | (310) | ​ | $ | 483 | ​ | $ | (634)
Credit contracts | ​ |  | (35) | ​ |  | (41) | ​ |  | (320) | ​ |  | (2)
​ | ​ | $ | 357 | ​ | $ | (351) | ​ | $ | 163 | ​ | $ | (636)
(1) | Gains (losses) recognized on derivatives are classified in net (loss) gain from investment activities in our condensed consolidated statements of operations for our Investment segment.

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