# The Iron Law of Bond Math

March 24, 2023

One financial reality we often have trouble wrapping our heads around is one person’s asset is another’s liability. Perhaps you have some money in a bank account and a mortgage. You think in terms of your own balance sheet. The money in your bank account (your “deposits”) are an asset on your balance sheet. Your mortgage is a liability. But from the bank’s standpoint it is the opposite. Your deposits are their liability. If you ask for your deposits back the bank must hand you cash. Your mortgage is the bank’s asset. You pay them every month!

It is also horribly misunderstood. Fractional reserve banking is often spoken with a negative connotation. The greedy banks pay you low rates and lend your money out at high rates! They are conjuring dollars up out of the ether and that will make the dollar worthless! Buy gold and Bitcoin! Or something? These are things you read on the internet. Scorning the fractional reserve banking system is fashionable. I suppose the term “fractional reserve” sounds kind of nefarious?

I will take the unpopular argument that fractional reserve banking is a net positive. Primarily because I like the house I live in. I walked into a bank at 28 years old and they loaned me \$500K at 3% over 30 years to buy the house I wanted. I was not independently wealthy. I had a solid (though not especially long) credit history and enough cash to make a down payment and leave enough left over for a rainy day. And they loaned me \$500K at 3% because of the whole fractional reserve thing. The bank looked at me and said something like, “well he and the rest of the community have all these deposits with us we only pay ~0.1% on. We’ll loan him \$500K at 3% and collect a 2.9% spread.” Without the fractional reserve system, banks would likely only lend to the wealthy. The middle class is built on fractional reserve banking.

Though one potential problem with our banking system is that it ceases to function if everyone decides to withdraw their money simultaneously. That is not a unique problem. Most aspects of our society will not function properly if everyone does the same thing at the same time. If everyone gets on the interstate it will become a parking lot. If everyone goes to the grocery store one afternoon there will be no food. If everyone decides to fill up their gas tank there will be no gas. And if everyone withdraws their money from banks simultaneously, they will not be able to get it. This is how the world works. If you find this unsatisfactory, you don’t have to take part in it! You can keep your cash under a mattress or in a lockbox at the bank. The bank can’t loan out your dollars sitting in a safe deposit box – it doesn’t even know they are there! Just be sure not to get a loan from a bank for a house, car, or business. Then you’re in the thick of the fractional reserve banking system.

But sometimes there are problems. Let’s say it is 2020 and you run a bank. The whole COVID thing happens, and the Federal Reserve takes interest rates to zero and basically aims a giant money cannon** at the economy. They fired the cannon and this is what happened to bank deposits:[ii]﻿

That steepening of the curve in 2020 is the money cannon. Banks were sitting on all this cash from the money cannon (“borrowing short”) and needed to lend long to earn a spread. Short term rates were historically low. The two-year treasury yield dropped to 0.09%.[iii] That means if a bank invested \$100,000,000 in two-year treasury, they earned \$90,000. If you are running a bank or any business it is hard to stomach a gross return of \$90,000 annually on \$100M of capital. So the banks were incentivized to buy longer term securities. The longer the term for which you loan money, the more you should get paid for the loan. That is how lending works. When the two-year yield was 0.09%, the 30-year treasury yield was 1.97%.[iv] Now the bank’s \$100M yields \$1,970,000 annually. That is more like it. It is not hard to guess what banks bought when short-term interest rates were sitting on the floor in 2020 and 2021.

And here is the thing, buying a 2-year or a 30-year U.S. Treasury exposes you to the same amount of credit risk: zero! They are both issues of the U.S. government, and U.S. government securities are considered risk-free. That is the first lesson you learn in Finance 101. “Risk-free” refers to their credit risk – there is no risk of default. Remember the money cannon. It is hard to default when you have a money cannon.

So the banks don’t seem (so far, knock on wood) to have issues with credit risk exposure (that was the problem in 2008). But they have loaded up on interest rate risk. The first thing you learn in Finance 101 is the risk-free thing. The second thing you learn in Finance 101 is interest rate risk, which is the Iron Law of Bond Math:

When interest rates go up, bond prices go down.

Say I pay \$1,000 for a bond that yields 2%/yr. for 10 years. I hand the issuer \$1,000, they pay me \$20/yr. (2%) for the next ten years and then they give me my \$1,000 back. That’s how a bond works. Suppose one year after my purchase interest rates begin rising. Now the same issuer is selling 10-year bonds with a 5% yield. That is a real bummer. I’m earning 2%/yr. when I could be earning 5%/yr. on a bond with the same issuer (read: same credit risk) and term. I would like to swap my lame 2% bond for the good stuff that pays 5%. There is one problem: who will buy my 2% bond when they could buy a similar bond paying five? The only way they will buy my 2% bond is if I sell at a discount – they will not pay \$1,000. They will pay less. The moment interest rates rose, the value of my bond fell. The Iron Law of Bond Math.

When I bought the 2% bond, I was expecting to be paid 2%/yr. for 10 years and then repaid my \$1,000. The fact interest rates have risen doesn’t impact any of that. It only impacts the value of the 2% bond I own on paper. It will still pay me \$1,000 at the end of the 10-year term, but no one will buy it from me for \$1,000 now. They will buy it for \$784.70. I won’t bore you with the formula, but that is the bond’s market value in this scenario. If it were a 30-year bond, rather than a 10-year, it would be worth even less (\$543.27) given a rise in interest rates from 2% to 5%. This makes sense – interest rates are higher, so a buyer is going to require a deeper discount to be stuck with an asset paying 2% for 29 more years than one they’re “only” stuck with for nine more years.

This is basically what happened to banks in 2022. They were flush with deposits in 2020 and 2021 and bought safe (from credit risk) fixed income securities, many with long durations, to earn their spread. Then 2022 came around and the Fed put the money cannon in the closet and did this to interest rates:[v]﻿

The Iron Law of Bond Math still applies to securities held by banks. Suddenly the bank’s assets are worth a lot less money. This is not necessarily a problem in the normal course of banking business. Regulatory requirements mandate they keep some reserves on hand to give back to customers when they ask for them. There are all sorts of very strict regulations.

When banks buy bonds, they must classify them in of two ways: “available for sale” (AFS) or “held to maturity” (HTM). A simplified way to think about this is AFS securities are available to sell to pay out depositors when they ask for their money back. AFS securities are marked to market – that is, their market value is updated on the bank’s books each day. When interest rates go up, they record the decline in value of their AFS portfolio. Securities designated HTM are designed to be held to maturity and are not marked to market each day. The bank loans out \$1,000, classifies it as HTM, an interest rate hike causes that loan to be worth \$800, but it is still recorded as a \$1,000 asset on the bank’s balance sheet. The bank says (with the regulator’s approval), “who cares if the value declined from \$1,000 to \$800? We’re holding it to maturity and at maturity we’ll get our \$1,000 back.”  The balance sheet records that loan as a \$1,000 asset and they bury the fact that the present value of that asset is only \$800 in the footnotes. As long as the bank’s AFS securities are enough to repay depositors, everything is fine.

Silicon Valley Bank (SVB) has been in the news lately as a rather large bank that suddenly failed. One of SVB's problems was a rather undiversified client base. The bank was well known in the venture capital and private equity sectors – over 1,000 such firms held capital there.[vi] And 85% of the bank’s deposits were uninsured – that is, exceeded the \$250,000 FDIC insurance limit.[vii] I am not sure what is typical for a bank, but I am almost certain most banks have a much smaller percentage of uninsured deposits. And the VC and PE communities are pretty small – they all know each other and subscribe to the same newsletters. Once such newsletter – The Diff by Byrne Hobart – is required reading in the VC community. On February 23rd he wrote about SVB’s balance sheet. Notably, he read the convoluted language in the footnotes to the balance sheet where SVB explained the heavy losses their HTM portfolio had taken (Iron Law of Bond Math) and translated it as, “on a mark-to-market basis, they were broke last quarter…”[viii] The VC and PE depositors read that and got nervous. It is not certain that Hobart’s newsletter sparked the run on SVB, but that is the speculation.[ix] People started withdrawing their deposits, forcing the bank to sell its AFS securities at a loss (Iron Law of Bond Math) to pay out those depositors. It wasn’t enough so SVB attempted to raise \$2.25 billion in equity capital to plug the hole, but the capital raise failed.[x] When a bank announces they have some liquidity problems and are raising capital to plug the hole, depositors think, “hmm that doesn’t sound great, I’m going to monitor this situation.” Then the bank says, “ah yes that capital, we didn’t get it” and it translates as, “hey everyone, we have a serious problem” and the depositors get on the phone and say something like “hello, JP Morgan? I’d like to open an account.”

This has created jitters that have reverberated throughout the banking sector and into the economy. You have probably felt them over the last few weeks. Perhaps you received an email from your bank saying something along the lines of  “we’re fine, please, please don’t panic.” People naturally recall the last banking crisis in 2008 and start to get nervous. An important distinction is 2008 was a credit crisis – banks made loans that couldn’t be repaid. “Subprime” was the buzz word. Those subprime loans defaulted, and all sorts of derivatives conjured from those assets went to zero too. That is a credit crisis. It was quite bad. 2023 is similar to 2008 in that there are some issues in the banking sector (scary!) but it is different in that there are no indications (so far) of a credit crisis (much less scary!). The loans banks have made seem to be fine, their market value is just temporarily depressed because interest rates rose so quickly in 2022. The Iron Law of Bond Math came for the banks.

So people are trying to figure out what to do. The first step is understanding FDIC limits. If your bank account is beneath the \$250K FDIC limit, you have nothing to worry about. Your bank can have the biggest bank run of all time and Uncle Sam has promised to make you whole. To the extent you have uninsured funds sitting at the bank it is a situation worth monitoring. There is a good chance everything will be just fine. Banks failing make for great headlines, but they aren’t as rare as people think. It is not something that always leads to economic calamity:[xi]﻿

The Iron Law of Bond Math came for the banks in 2023. But given the present interest rate environment, it can work in your favor.

Sean Cawley, CFP®

*Fractional reserve banking isn’t alchemy! It’s perfectly legitimate and very effective, which I hope I make clear in the proceeding paragraph. Regulations frown upon investment advisors making jokes, but I’m trying to make a discussion about banking something other than hopelessly boring. I thought the alchemy bit was mildly humorous. It is a joke!

**The joke thing again – Jerome Powell doesn’t actually have a money cannon. It is all done via a computer. Not a cannon.

**But if I were the chairman of the Federal Reserve, let me assure you that I would actually have a money cannon created and then at press conferences announcing an interest rate cut I wouldn’t have to give a boring prepared speech. I would just fire off the money cannon and it would be much more fun for everyone.

*** 4% for 30 days! That sounds too good to be true! Remember, treasury yields are annualized. So, \$100,000 at 4% annualized is about \$333 over a 30-day period. You are not going to make a killing here, but we’re talking about treasuries! And it is still ~11x more than the average savings account yield.

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[ii] YCharts, US Commercial Bank Deposits, 10 Years.

[iii] YCharts, 2-Year Treasury Rate & 30 Year Treasury Rate, 01/01/2021 – 02/05/2021.

[iv] YCharts, 2-Year Treasury Rate & 30 Year Treasury Rate, 01/01/2021 – 02/05/2021.