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On beta adjustment for basis risk, I could only find an online definition:

Gap reports modified to mollify the errors caused by basis risk. The essential concept of beta-adjusted gap is that all interest rates do not change by the same amounts, but that there is an identifiable relationship, a correlation, between changes in various interest rates. Some rates are more sensitive to change than other rates. In beta-adjusted gap analysis, the volumes of assets and liabilities subject to repricing are weighted to reflect the historical sensitivity of the yields or costs of those assets and liabilities relative to some benchmark yield or cost.

Is there any more detailed explanation on this topic, how the beta adjustment was done?

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