How Correlated is LIBOR with Bank Funding Costs?
The title of this post is the title of a note by three Fed authors: How Correlated is LIBOR with Bank Funding Costs?
From the title and the resources available to the authors, especially in term of data, I was expecting something good. I have been disappointed. The disappointment is about what is said by also what is not said.
The note is based on "funding cost". For a quant like me, it is not very clear what their number means exactly. It is described as "annualized total interest expense/total liabilities". As it is from official reporting (FR Y-9C) this may be based on accounting/accrual interest and notional amounts, not on real daily MTM and actual interests. My understanding is that a long term funding with fixed coupon bond would have the same "funding cost" for their full life. The cost would probably not include any hedging that the bank would have done for its interest rate risk. Moreover those cost seems to be measured on a quarterly basis, but obviously the hedging by banks is done on a daily basis, not on a quarterly basis.
The main discussion is about "correlation". After reading the note, I'm not sure what correlation is computed. Is it the correlation between the level of the rates or between their daily changes. Wording in the paper seems to indicate it is the level. For hedging purposes, the most relevant measure of correlation would probably be the daily changes.
In the table with correlations, the 3-month SOFR in advance rate appears the "highest" the most frequently. This seems to indicate in effect some accrual/delay issue in the data. The 3-month SOFR in arrears compare to 3-month LIBOR is 2-1-3 (win-lost-draw). Not a clear winner. SOFR in-arrears (pushed by regulators and ISDA) is never the best in Table 1, while OIS (term rate) is the best half of the time. One possible other conclusion from the same study with the same data is that among the proposed fallback, SOFR in arrears in the worst choice and term rate the best choice.
All or nothing: The paper seems to implicitly suppose that the full balance sheet is compare to LIBOR or RFR. The reality is that some parts are more fed fund based and some more LIBOR-like based. The test, should they have relevant data, would be to check which part is RFR and which is LIBOR (or AMERIBOR) based. Maybe 50%/50% would be better than any one individually. It is strange that regulators, correctly, insist on funding diversification, but then write a note with underlying hypothesis that only one unique data source/hedging/comparison should be allowed, in absence of any diversification. I have never heard anybody claiming that LIBOR-3M should be used for everything, but this is the claim that this Fed note seems to "debunk". They could have done a good comparison by using a hedging pattern with SOFR or EFFR for some parts (secured funding) and LIBOR for "LIBOR funding" (their terminology), Figure 2 seems to indicate that the have the data on liability sources for this.
The everything includes depo-like liabilities and bonds from ON to 30Y (irrespective of maturity). In the "post-crisis non-GSIBs" part of the analysis, all correlations are below 50%. In a FRTB framework, the 5Y v 3M correlation is 55%. One possible hypothesis for further analysis could also be that there is a large maturity discrepancy between the arbitrary 3-month used by the authors and the bank's balance sheets. Long term funding is a relatively large part of the composition of GSIB Bank liabilities according to Figure 2, so this not an unrealistic hypothesis to test. It would be interesting to do the same exercise with LIBOR-ON v LIBOR-3M and SOFR. We may find that LIBOR-ON is more correlated to SOFR than to LIBOR-3M. In that direction, instead of saying that LIBOR is not the most correlated with funding pattern, one could argue that 3-months is not the most correlated with funding pattern and so quarterly data is not the most relevant for this study.
All the analysis is done on average funding cost. According to the data used, LIBOR is more a marginal cost of funding. Should the same analysis be done on marginal cost?
In their conclusions, the authors indicated: "loan margins would need to adjust to account for the differences between these types of rates". Does this sentence means that a credit sensitive margin would be necessary in some cases?
The conclusion seems also to implicitly associate "not the most correlated" to "useless". While diversification of balance sheet from Figure 2 should naturally lead to a "all are useful, but in different proportions" conclusion.
I don't have deep conclusion from this Fed notes. The data does not appear relevant from a quantitative risk management point of view, the data analysis is very unimaginative and almost irrelevant. The conclusion, beyond the negatively worded sentence against LIBOR, does not conclude anything. This is a pity, with the data and resources available to the authors, something interesting and useful could have been done.
From the title and the resources available to the authors, especially in term of data, I was expecting something good. I have been disappointed. The disappointment is about what is said by also what is not said.
The note is based on "funding cost". For a quant like me, it is not very clear what their number means exactly. It is described as "annualized total interest expense/total liabilities". As it is from official reporting (FR Y-9C) this may be based on accounting/accrual interest and notional amounts, not on real daily MTM and actual interests. My understanding is that a long term funding with fixed coupon bond would have the same "funding cost" for their full life. The cost would probably not include any hedging that the bank would have done for its interest rate risk. Moreover those cost seems to be measured on a quarterly basis, but obviously the hedging by banks is done on a daily basis, not on a quarterly basis.
The main discussion is about "correlation". After reading the note, I'm not sure what correlation is computed. Is it the correlation between the level of the rates or between their daily changes. Wording in the paper seems to indicate it is the level. For hedging purposes, the most relevant measure of correlation would probably be the daily changes.
In the table with correlations, the 3-month SOFR in advance rate appears the "highest" the most frequently. This seems to indicate in effect some accrual/delay issue in the data. The 3-month SOFR in arrears compare to 3-month LIBOR is 2-1-3 (win-lost-draw). Not a clear winner. SOFR in-arrears (pushed by regulators and ISDA) is never the best in Table 1, while OIS (term rate) is the best half of the time. One possible other conclusion from the same study with the same data is that among the proposed fallback, SOFR in arrears in the worst choice and term rate the best choice.
All or nothing: The paper seems to implicitly suppose that the full balance sheet is compare to LIBOR or RFR. The reality is that some parts are more fed fund based and some more LIBOR-like based. The test, should they have relevant data, would be to check which part is RFR and which is LIBOR (or AMERIBOR) based. Maybe 50%/50% would be better than any one individually. It is strange that regulators, correctly, insist on funding diversification, but then write a note with underlying hypothesis that only one unique data source/hedging/comparison should be allowed, in absence of any diversification. I have never heard anybody claiming that LIBOR-3M should be used for everything, but this is the claim that this Fed note seems to "debunk". They could have done a good comparison by using a hedging pattern with SOFR or EFFR for some parts (secured funding) and LIBOR for "LIBOR funding" (their terminology), Figure 2 seems to indicate that the have the data on liability sources for this.
The everything includes depo-like liabilities and bonds from ON to 30Y (irrespective of maturity). In the "post-crisis non-GSIBs" part of the analysis, all correlations are below 50%. In a FRTB framework, the 5Y v 3M correlation is 55%. One possible hypothesis for further analysis could also be that there is a large maturity discrepancy between the arbitrary 3-month used by the authors and the bank's balance sheets. Long term funding is a relatively large part of the composition of GSIB Bank liabilities according to Figure 2, so this not an unrealistic hypothesis to test. It would be interesting to do the same exercise with LIBOR-ON v LIBOR-3M and SOFR. We may find that LIBOR-ON is more correlated to SOFR than to LIBOR-3M. In that direction, instead of saying that LIBOR is not the most correlated with funding pattern, one could argue that 3-months is not the most correlated with funding pattern and so quarterly data is not the most relevant for this study.
All the analysis is done on average funding cost. According to the data used, LIBOR is more a marginal cost of funding. Should the same analysis be done on marginal cost?
In their conclusions, the authors indicated: "loan margins would need to adjust to account for the differences between these types of rates". Does this sentence means that a credit sensitive margin would be necessary in some cases?
The conclusion seems also to implicitly associate "not the most correlated" to "useless". While diversification of balance sheet from Figure 2 should naturally lead to a "all are useful, but in different proportions" conclusion.
My conclusion
I have send some questions to the authors about the data used and the analysis performed. I will report on the answers if I receive anything relevant.
Note added 2020-07-18: The title contains LIBOR while LIBOR is only a small part of the paper, most of it is related to SOFR. A more neutral title would have been "How correlated are some rates with Bank Funding Costs?". This is specially the case as SOFR has three versions (in advance, in arrears and term) while LIBOR has only one version. A more natural analysis would have included also three versions for LIBOR (ON in advance, ON in arrears and term). With such a choice of title, one can guess that the authors wanted a priori to say something about LIBOR, not to analyze funding rate correlations. The question is what "a priori" was it? Negative of positive? With their conclusion, we know the answer to that question.
Note added 2020-07-19: I have received an answer from one of the authors. It confirms that what they call "funding cost" is not on a MTM basis. This means that it is probably relevant for long term costs, but not to understand correlation with market interest rate on a quarterly basis. It also indicated that the correlation are between changes of rates on a quarterly basis (not the rate level as I inferred from the paper). The data available does not provide cost by categories (like LIBOR funding, secured, long term) but provide notional amounts. Adding a realistic weighted mixture of LIBOR and SOFR would have been possible among the market rates analyzed.
Note Added 2020-08-04: I have been contacted by someone in the "Public Affairs Office" of the Federal Reserve Board to known if I wouldn't mind sending to them what I wrote about the note. I was happy to do so and indicated that "I correct factual errors I’m made aware of with acknowledgement and accept all relevant public comments on my blogs". I have not received any feedback. I can only conclude from it that my post does not contain any factual error and that no comment from the authors is appropriate.
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