$200 billion in less than 48 hours

Subreddit, the overnight rate increased by 3.25% in just 44 hours.<br><br> Given that the overnight rate-setting establishes the rate at which banks lend money to each other, and considering that overnight money lent to banks tends to stend its way far into the future, at the same rate, it means that you can multiply all of that overnight debt across the entire financial system.<br><br>We can assume that the overnight rate is the lowest rate in the system, so I'll call it 30% for the rate of interest paid by overnight loans.<br><br>If we call `Y` the amount of overnight debt, then the total amount of debt is the infinite series:<br><br>`Y` + `1.3 * Y / 1.3` + `(1.3 * Y / 1.3)^2 + ...`<br><br>For this entire series, we can calculate the sum in closed form:<br><br>`Y + 1.3 * Y / 1.3 + (1.3 * Y / 1.3)^2 = ...`<br>= `Y * (1 + 1 / 1.3 + 1 / 1.3^2 + ...)`<br>= `Y * (1 / (1 - 1 / 1.3))`<br>= `Y * 1.3 / 0.3`<br>= `Y * 13 / 3`<br><br>So basically, for every dollar that is in the overnight rate being paid at `30%`, results in the total system-wide interest rate being roughly `4 * 30% = 130%`.<br><br>In other words, roughly four times as much debt being across the system at overnight rates.<br><br>So if the overnight rate has just increased by `3.25%`, then that is equivalent to roughly:<br><br>`4 * 3.25% = 13%`<br><br>So if `Y` is the overnight rate, then the entire system has overnight debt that is at least `4` times the size of `Y`.<br><br>Or rather, every dollar essentially counts as at least `4` dollars in the economy, and thus a rate increase of `3.25%` would be effectively equivalent to a rate increase of:<br><br>`4 x 3.25% = 13%`<br><br>Which is to say, the overnight rate increased by `5.65%` in 48 hours, but the rest of the system has already suffered a rate increase of at least `13%`.<br><br>But we still have to multiply this by roughly `4`, resulting in a `56%` in the last week.<br><br>Which is to say, at least `3%` of `5 trillion` is `150 billion`, and in overnight rates that would have been far more than at least `4` times that amount, at least `600 billion`.<br><br>In the last 48 hours, the Fed has:<br><br>1. Increased the discount rate by `5.65%` in 48 hours<br>2. Increased the effective fed funds rate by `4%` in 24 hours<br>3. Effectively increased the financial system-wide rate by `13%` in 48 hours<br>4. Effectively increased the financial system-wide rate by `56%` in 240 hours<br><br>I guess you could say that the overnight rate is like the head of the octopus.<br><br>Like, the tentacles are what matter.