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Why Loan-Weighted Average Interest Rates Reflect Capital Use

Article Quant Q&A · Author: marnix
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Summary

The note explains why banks often calculate average lending rates using loan sizes as weights. This measure represents the rate earned on the average dollar lent, so a small high-rate loan has limited influence on the bank-wide figure compared with a large loan. The weighting therefore helps summarize how the bank’s lending capital is being used.

The note also cautions against using that average alone to explain differences between banks. Loan size and interest rate may be related, and the overall figure does not show the reasons behind a higher or lower average. Comparing institutions calls for more detail, including loan characteristics and how long loans have been outstanding, since lending rates change over time.

Key ideas

  • Loan-size weighting estimates the average rate earned per dollar lent.
  • A small high-rate loan contributes little to the aggregate when its principal is small.
  • A bank-wide weighted average summarizes lending returns but does not explain their causes.
  • Comparisons between banks require details such as loan sizes and origination periods.

Tags

StatisticsFixed income
Full text
# The weight of interest rates


# The weight of interest rates












Why are average interest rates often weighed by loan (and deposit) sizes?

Since the size and interest rate of a loan are function of each other, I expect the resulting statistic to be hard to interpret.

## Answer by nbbo2 (score 1, accepted)

https://quant.stackexchange.com/a/30052

When a bank lends money at different rates for different purposes the weighted average interest rate measures how well the 'average dollar' is being utilized by the bank. (A very small amount lent at a very high rate for example does not impact overall bank profitability very much). The average is a kind of 'overview' statistic for the bank as a whole, but I agree with you that if you want to understand WHY Bank A has a higher average than Bank B you would have to look at more detail on the loans themselves, such as their size, how long they have been on the books (years ago interest rates were higher) etc. etc.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.