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The Flaw of Averages: Why We Underestimate Risk in the Face of Uncertainty by Sam L. Savage

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CHAPTER 19
The Scholtes Revenue Fallacy
One of the ways a bank makes money is to borrow the stuff at a low interest rate (which it can do because it has excellent credit) and loan it to you and me at a higher interest rate (which we have to pay because our credit is not as good as a bank’s). The difference between the interest a bank pays and the interest it charges is called the margin. Suppose the bank pays 4 percent per year for its money and loans it to its best customers at 6 percent. The margin on those accounts is 2 percent. If the bank is also willing to loan money to less creditworthy customers for 14 percent, then those accounts would have a margin of 10 percent. In reality, banks lend money at a whole range of margins depending on the borrower’s credit score, age, income, and other considerations.
The bank’s amount of net revenue depends not only on the margin, but also on the balance, that is, the amount of money owed. For example, an account with a 6 percent margin and a $600 balance would yield annual net revenue of 6 percent times $600, or $36. Of course, there is an overhead cost associated with maintaining the loan, let’s say $25 per account per year. So the profit would be $36 - $25 = $11 for that account. Now imagine that 6 percent and $600 turn out to be the average balance and margin of all accounts. Then the bank makes an average profit of $11 per account. Right? You wish.
This is a subtle but insidious example of the Strong Form of the Flaw of Averages, ...

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