Quantitative Easing: Will Excess reserves in the Fed Cause Inflation?

There is a scary graph floating around that I have been seeing a lot. It shows the excess reserves that have been deposited into the Federal Reserve since they started their quantitative easing back in 2008-09. I have seen so many different takes on this, and misconceptions about what it actually means that I decided to take a really close look at it myself to dissect what is really going on.

excess reserves graphWhat a huge change, right? One can easily see that something big changed when the graph takes a sudden jump. But what really happened here, and what will be the consequences of it?

What Happened?

When the Fed needed to put money into the banking system it made it, and then gave it to the banks which sold them government debt in exchange for it (see Why do Bond Prices Change) This gave the banks a whole lot of cash in their Fed accounts which helped them stay in business after they saw their net worth tumble after housing prices crashed and they were stuck with whatever assets they had leveraged on their books.

So now, then entire banking system has more money in it, and interest rates are lower because the fed has artificially altered the prices of bonds. Now it is logical to think that if the bank just turned around and loaned out all of that money, there would be less reserves and more money floating around on the street which could lead to inflation. This is incorrect!!! Banks cannot control the amount of reserves in the system by way of lending.

How do Excess Reserves Work

As you can see, the reserves will eventually make their way back to the fed and they have not left the banking system at all meaning that the banks can loan all they want, and there would still be an excess of reserves in the system, because they have no control over it. The excess reserves are a function of the Feds policy and the amount of cash in circulation. Individual banks, however, may be short on reserves, and they would then have to go and borrow these from another bank to meet their requirements. In this case, if Bank A was short, then it would just borrow some extra reserves from Bank B, essentially re-borrowing the money it already lent to the business (at a much lower interest rate, of course).

Cash is the other thing that can affect the total amount of excess reserves because cash is not in any Fed account. When a bank needs cash for customers, the Fed debits its account and then sends it some cash which means the cash exists outside of the banking system, until it is redeposited again.

What are the Consequences of This?

The consequences, unlike most people seem to think, will not be inflation. If inflation does occur, it will be because the rate at which the money moves through the economy has sped up, not because there is too much of it being let out of the reserves.

For the Fed, they now have another way to influence interest rates. They can simply change the amount that they pay on excess reserves instead of changing interest rates through open market operations. As long as the Fed Funds rate sits below this, it should be the floor for interest rates.

For the banks, they now have sufficient reserves, and somewhere to put them to earn some interest on them. They shouldn’t have to worry too much about covering their own reserve requirements, or lending to other banks which could be perceived as too risky after what happened in ’08.

So there is no floodgate of money sitting in the banks waiting to be unleashed and igniting inflation.


How are Log Returns Different From Normal Returns?

Log returns aren’t an intuitive concept like simple arithmetic returns are. Everyone knows that if you have $1000 earning 10% over one year, then you will have $1100 after that one year is up. So why would you ever need anything different that this easy to understand concept?

Problems arise when things become more complicated,  especially with the addition of more periods (time).  The simple interest calculation that we are all familiar with is somewhat ‘inefficient’ across time because it doesn’t compound interest continuously. A log return will do just exactly that. The consequence of this is that log returns can be easily added over separate time periods while simple arithmetic returns cannot.

Arithmetic Return Example

Say you had $1000 and you achieved a return of 20% over the course of a year. You would end up with $1200 at the end of year 1. Great. What happens if you were to lose 20% the very next year?

CodeCogsEqnarithmetic returns example

Even though you have gained 20% and then lost 20%, you will have actually realized a -4% on your original investment of $1000. This is again because of the inherent inefficiency of calculating interest arithmetically.

How are Arithmetic Returns Inefficient?

Source: https://en.wikipedia.org/wiki/Compound_interest#mediaviewer/File:Compound_Interest_with_Varying_Frequencies.svgAs you can see from the picture the simple arithmetic interest follows the curve set by the continuous logarithmic interest, but it will always be somewhat inefficient, and the gap will continue to get bigger and bigger the farther out in time one goes.

Logarithmic Return Example

Say you had the same $1000 at the beginning of year 1. If you earned 20% logarithmic interest on that money, then by the end of year 1 you would have $1221.40…

logarithmic return equation

logarithmic return example

As you can see, going up 20% and going down 20% gives you the same result. This is because the interest compounds continually into infinitely small segments.

So Why Would You Ever Need This?

Imagine you have a bunch of different trades each with a different amount of time that you plan on holding it and each with a different amount that you made on it, some big, some small, some positive, some negative, you know how it is. Using the simple Arithmetic mean, it would be an absolute nightmare to try and calculate it. With the logarithmic return, you can just calculate the return on each trade and then add them up and it will accumulate properly. Remember that +20% and -20% came out flat in the logarithmic return, but +20% and -20% came out to be a -4% loser when using the arithmetic mean.

I think its also important to note that when the returns are small, the log and arithmetic returns will be very similar, it is only when the returns get bigger that they deviate very significantly.