How was the ISDA fallback spread adjustment calculated when LIBOR ceased, and why was a spread needed at all?

The ISDA fallback spread adjustment bridges the structural difference between LIBOR (an unsecured term lending rate) and SOFR (a secured overnight rate). Without this spread, switching from LIBOR to SOFR would systematically transfer value from one counterparty to the other, since LIBOR historically exceeded SOFR by a credit and term premium.\n\nWhy a Spread Is Necessary:\n\nLIBOR = Risk-Free Rate + Bank Credit Premium + Term Premium\nSOFR approximates Risk-Free Rate (secured overnight)\n\nHistorically, 3-month USD LIBOR exceeded compounded SOFR by approximately 15 to 45 basis points. Simply replacing LIBOR with SOFR would reduce the floating leg by this amount, benefiting the floating-rate payer at the expense of the receiver.\n\nHow the Spread Was Calculated:\n\nISDA selected a methodology based on a historical median approach:\n\n1. Calculate the daily spread: LIBOR(t) - Compounded SOFR(t) for each business day over a 5-year lookback period\n2. Take the median of these daily spreads\n3. The lookback window ends on March 5, 2021 (the date the FCA announced LIBOR cessation dates)\n\n| USD LIBOR Tenor | ISDA Fallback Spread |\n|---|---|\n| Overnight | 0.644 bps |\n| 1-Month | 11.448 bps |\n| 3-Month | 26.161 bps |\n| 6-Month | 42.826 bps |\n| 12-Month | 71.513 bps |\n\nWhy Median Instead of Mean:\n\nThe median was chosen because:\n- It is robust to outliers (the 2008 crisis produced extreme LIBOR-OIS spreads)\n- It better represents the \"normal\" relationship between the rates\n- The mean would have been heavily influenced by the spike during 2007-2009\n\nWorked Example:\nRedwood Capital holds a receive-fixed swap originally referencing 3-month USD LIBOR. After LIBOR cessation on June 30, 2023:\n\n- Old floating leg: 3M LIBOR (e.g., 5.55%)\n- New floating leg: Compounded SOFR in arrears + 26.161 bps\n- If compounded SOFR for the period is 5.28%, the adjusted rate is 5.28% + 0.26161% = 5.542%\n\nThe spread adjustment ensures the floating leg payment is approximately equivalent to what it would have been under LIBOR, making the transition value-neutral in expectation.\n\nOngoing Implications:\n- The spread is fixed permanently — it does not update as market conditions change\n- As the credit environment evolves, the actual LIBOR-SOFR spread would have differed from the fixed fallback\n- New contracts should reference SOFR directly (no spread needed since they were never priced off LIBOR)\n\nStudy benchmark transitions comprehensively in our FRM course materials.