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Financial Instruments (Tables) | 12 Months Ended
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Dec. 31, 2020
Derivative Instruments and Hedging Activities Disclosure [Abstract] |
Notional exposure of derivative instruments | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | December 31, 2020 | ​ | December 31, 2019
​ |  | Long Notional Exposure |  | Short Notional Exposure |  | Long Notional Exposure |  | Short Notional Exposure
​ | ​ | ​ | (in millions)
Primary underlying risk: | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Equity contracts | ​ | $ | — | ​ | $ | 8,623 | ​ | $ | 806 | ​ | $ | 13,113
Credit contracts(1) |  | ​ | — |  | ​ | 2,099 | ​ | ​ | — | ​ | ​ | 622
(1) | The short notional amount on our credit default swap positions was approximately $6.3 billion at December 31, 2020. However, because credit spreads cannot compress below zero, our downside short notional exposure to loss is approximately $2.1 billion as of December 31, 2020. The short notional amount on our credit default swap positions was approximately $4.7 billion as of December 31, 2019. However, because credit spreads cannot compress below zero, our downside short notional exposure to loss is $622 million as of December 31, 2019.
Fair value and income recognized for derivatives not designated as hedging instruments | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | Asset Derivatives | ​ | Liability Derivatives
​ |  | December 31, 2020 |  | December 31, 2019 |  | December 31, 2020 |  | December 31, 2019
​ | ​ | ​ | (in millions)
Equity contracts | ​ | $ | 4 | ​ | $ | 291 | ​ | $ | 852 | ​ | $ | 1,058
Credit contracts | ​ |  | 1,012 | ​ |  | — | ​ |  | 1 | ​ |  | 266
Sub-total | ​ |  | 1,016 | ​ |  | 291 | ​ |  | 853 | ​ |  | 1,324
Netting across contract types(1) | ​ |  | (231) | ​ |  | (109) | ​ |  | (231) | ​ |  | (109)
Total(1) | ​ | $ | 785 | ​ | $ | 182 | ​ | $ | 622 | ​ | $ | 1,215
(1) | Excludes netting of cash collateral received and posted. The total collateral posted at December 31, 2020 and 2019 was $872 million and $903 million, respectively, across all counterparties, which are included in cash held at consolidated affiliated partnerships and restricted cash in the consolidated balance sheets.
The following table presents the amount of gain (loss) recognized in the consolidated statements of operations for our Investment segment’s derivatives not designated as hedging instruments:
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | Gain (Loss) Recognized in Income(1)
​ | Year Ended December 31,
​ | 2020 |  | 2019 |  | 2018
​ | ​ | ​ | ​ | ​ | ​ | ​
Equity contracts | $ | (1,583) | ​ | $ | (2,152) | ​ | $ | 603
Credit contracts |  | 1,088 | ​ |  | (342) | ​ |  | 129
Commodity contracts |  | — | ​ |  | (8) | ​ |  | 66
​ | $ | (495) | ​ | $ | (2,502) | ​ | $ | 798
(1) | Gains (losses) recognized on derivatives are classified in net gain (loss) from investment activities in our consolidated statements of operations for our Investment segment.

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