4 ms·

This paper is talking about intraday or overnight lending between banks... cases where loans have a term of less than 1 day. Yes, "to get people to forgo the us

This paper is talking about intraday or overnight lending between banks... cases where loans have a term of less than 1 day. Yes, "to get people to forgo the use of their own money, you have to pay them something". The length of time the lender forgoes the use of their own money is a factor in the rate the borrower pays. As loan term tends toward zero, interest rate should tend toward zero as well. That's what central banks control, but often choose a non-zero value.

mikeash 9y ago
I can see why interest should tend towards zero, but why would the rate?
- jganetsk 9y ago
  Intuition: if you were my friend, and I gave you a loan for 5 minutes (maybe because your wallet is in your car and we are paying a restaurant bill), how much interest would I expect you pay it back with? Zero (think about Venmo payments). And the only way to have a zero-interest loan for a non-zero amount of time is setting the rate at zero. This loan has an extremely short term (5 minutes) and is extremely low risk (it's a small amount of money and we are friends). So all real loans should have a non-zero interest rate, but the rate should asymptotically approach zero as we decrease the term and the risk. If not zero, then what would you choose? What should be the floor on interest rates? If we think about the interbank lending market, once the aggregate supply of reserves is beyond what is necessary to settle daily payments, the interest rate falls to the floor (the rate the Fed pays on reserves). In this case, why should the Fed choose a non-zero floor? There are many answers the Fed could provide, and they do. But they definitely need to provide that answer, which is what the paper is claiming. And the paper also suggests that zero works pretty well, for a variety of reasons.
  - tomrod 9y ago
    > And the only way to have a zero-interest loan for a non-zero amount of time is setting the rate at zero. This assumption is where things break. You could have an interest rate whose nominal contribution for five minutes that rounds down below 1 mil, the smallest unit of currency. A five-minute interest rate of 0.00098% would result in rounding the interest on $5 to zero. However, taken over the course of 5 minute increments through a year, and you arrive at $14.01 dollars: $5 * ((1 + 0.0000098)^(12 5-min increments/hour * 24 hours/day * 365 days/year)) = $14.01 Plenty of folks would love a 280% annual return.
  - mikeash 9y ago
    I don’t think framing it in terms of friends is useful. I’d make that loan to be kind. I wouldn’t do it as part of a business arrangement, so a stranger would probably be out of luck. If I were in the business of making five minute loans, I’d charge an astronomical interest rate to cover the fixed transaction costs.
    - tomatocracy 9y ago
      I think you're getting side-tracked into credit risk which is not what the paper is about at all. But your example is useful to understand why credit risk is not as simple as that. For a start, considered in the context of formal loans, lending money to a friend in that situation is far from a risk-free bet - because my friend might have got it wrong and left his wallet at home, not in his car in which case in 5 minutes time he'll default on payment. Of course I'll almost certainly get my money back eventually (since otherwise I'd either have just said I'd give him the money or declined to either lend or gift it), but now your talking about the risk that I'm deprived of my money for longer than I had anticipated as well as having the the cost of using my time in chasing him for it, so I'd want some interest to compensate for that risk. In reality, what we do is (to some extent) to agree a social convention that "next time it will probably be the other way around" so that those potential losses even out between us and it makes sense that we reduce our administrative burden by not charging each other for them in the form of interest. What is true is that as the time a loan is outstanding reduces, ability to judge the repayment risk is likely to improve to some extent in most cases. However even this isn't universal - for example if I lend against you receiving payment on an invoice just issued and where yuou have given your customer 30-day payment terms, I'm likely to have better certainty lending on a 60-day repayment term than a 1-day repayment term.
      - mikeash 9y ago
        I don’t think I was discussing risk at all, unless some part of my comment implied a statement about risk that I hadn’t thought of.

mikeash 9y ago

I can see why interest should tend towards zero, but why would the rate?

jganetsk 9y ago
Intuition: if you were my friend, and I gave you a loan for 5 minutes (maybe because your wallet is in your car and we are paying a restaurant bill), how much interest would I expect you pay it back with? Zero (think about Venmo payments). And the only way to have a zero-interest loan for a non-zero amount of time is setting the rate at zero. This loan has an extremely short term (5 minutes) and is extremely low risk (it's a small amount of money and we are friends). So all real loans should have a non-zero interest rate, but the rate should asymptotically approach zero as we decrease the term and the risk. If not zero, then what would you choose? What should be the floor on interest rates? If we think about the interbank lending market, once the aggregate supply of reserves is beyond what is necessary to settle daily payments, the interest rate falls to the floor (the rate the Fed pays on reserves). In this case, why should the Fed choose a non-zero floor? There are many answers the Fed could provide, and they do. But they definitely need to provide that answer, which is what the paper is claiming. And the paper also suggests that zero works pretty well, for a variety of reasons.
- tomrod 9y ago
  > And the only way to have a zero-interest loan for a non-zero amount of time is setting the rate at zero. This assumption is where things break. You could have an interest rate whose nominal contribution for five minutes that rounds down below 1 mil, the smallest unit of currency. A five-minute interest rate of 0.00098% would result in rounding the interest on $5 to zero. However, taken over the course of 5 minute increments through a year, and you arrive at $14.01 dollars: $5 * ((1 + 0.0000098)^(12 5-min increments/hour * 24 hours/day * 365 days/year)) = $14.01 Plenty of folks would love a 280% annual return.
- mikeash 9y ago
  I don’t think framing it in terms of friends is useful. I’d make that loan to be kind. I wouldn’t do it as part of a business arrangement, so a stranger would probably be out of luck. If I were in the business of making five minute loans, I’d charge an astronomical interest rate to cover the fixed transaction costs.
  - tomatocracy 9y ago
    I think you're getting side-tracked into credit risk which is not what the paper is about at all. But your example is useful to understand why credit risk is not as simple as that. For a start, considered in the context of formal loans, lending money to a friend in that situation is far from a risk-free bet - because my friend might have got it wrong and left his wallet at home, not in his car in which case in 5 minutes time he'll default on payment. Of course I'll almost certainly get my money back eventually (since otherwise I'd either have just said I'd give him the money or declined to either lend or gift it), but now your talking about the risk that I'm deprived of my money for longer than I had anticipated as well as having the the cost of using my time in chasing him for it, so I'd want some interest to compensate for that risk. In reality, what we do is (to some extent) to agree a social convention that "next time it will probably be the other way around" so that those potential losses even out between us and it makes sense that we reduce our administrative burden by not charging each other for them in the form of interest. What is true is that as the time a loan is outstanding reduces, ability to judge the repayment risk is likely to improve to some extent in most cases. However even this isn't universal - for example if I lend against you receiving payment on an invoice just issued and where yuou have given your customer 30-day payment terms, I'm likely to have better certainty lending on a 60-day repayment term than a 1-day repayment term.
    - mikeash 9y ago
      I don’t think I was discussing risk at all, unless some part of my comment implied a statement about risk that I hadn’t thought of.