SVB, the Power of Math, and World Pi Day

As the fintech and start-up community leaves a tumultuous weekend behind, we can now collectively take a deep breath and reflect on what transpired.

There will undoubtedly be a lot written about why SVB failed, what could have been done differently, and who should shoulder the blame.

The human psyche favours simple answers, and this tends to lead to a tendency where we want to find one primary cause for a big event. Reality, of course, is much more nuanced. When something big like a bank failure happens, there are a confluence of factors that come together, but our brains still crave that simple narrative.

If we look at SVB, the list of causes is long indeed: the fractional banking system has an inherent tendency towards bank runs, a very small percentage of the deposit base was protected by FDIC insurance which is designed to prevent such runs, the interest rate exposure on either side of the balance sheet was misaligned, they were very concentrated in one niche customer segment, the venture community can exhibit herd like behaviour, all moving at the speed of Twitter, they had a high Beta footloose deposit base, and so the list goes on.

But looking at that list there is one particular cause that is worth highlighting, especially in light of the fact that March 14th was World Pi Day (3.14), as this particular cause demonstrates the awesome power of simple math. That is the concept of bond duration, and what that did to their bond portfolio.

While there was a lot of publicity around the $1.8bn loss SVB realized when selling $21bn of bonds, there was another and bigger ticking time bomb on their balance sheet, which was the Held to Maturity (HTM) bond portfolio. As of September 2022, SVB had a bond portfolio in excess of $90bn, and the mark to market losses on that portfolio were a staggering $15.9bn, greater than their $11.5bn in tangible equity at that point in time, as was reported in their financial statements.

In other words, if SVB had been forced to sell its entire bond portfolio, the losses on that would have wiped out its entire equity book value plus some! But how is this possible – after all, bonds are supposed to be safe right? How can a bond portfolio crystalize such big losses?

It is very important to note here that there is nothing wrong with holding a bond portfolio to maturity, and in fact if one does so, there is no credit risk. And no loss would have crystalized. The bond does what it says on the label and you get the returns promised, it would just take many many years. The problem occurred because they had to sell today because of the run, and that laid bare the interest rate risk as explained below.

Let’s look at this interest rate risk, which brings us back to the power of math and the concept of bond duration which is fundamentally all about discounted cash flows and net present value. Here is a simple illustration.

If you buy a one-year maturity bond, with a 1% nominal coupon, when interest rates are also at 1%, that bond is worth par at your time of purchase. So you would pay $1,000, expect to get a $10 coupon plus the principal in one year’s time, discount that cash flow into the present with the 1% discount rate, and arrive at a $1,000 value. In other words, par.

Now, imagine that interest rates increase to 2% the instant you bought the above bond. Instead of discounting your expected $1,010 return on the bond by 1% to get $1,000, you would have to discount it by 2%, getting $990.19. Your bond is trading at a discount, and you just lost some money on your safe bond. Of course, if you hold your bond to maturity, you will still collect the $1,010 in one year’s time, but that money is only worth $990 today because we discount it at a higher rate. That is how bond math works.

But this was a one-year maturity bond, which incidentally has a duration of 1 (or close to it, depending on when the coupon gets paid) so the math was pretty simple.

If this had been a thirty-year maturity bond, we would first need to formulaically calculate the exact duration of the bond which is a measure how sensitive a bond’s price is to changes in interest rates. If we think of the cash flows flowing from the bond (the annual coupons and principal payment at the end) as bags of money positioned on a lever, the duration is the fulcrum point that balances this lever.

With a one-year bond that only pays one coupon at the end along with the principal, this fulcrum point is exactly 1. With a thirty-year bond that has a 1% coupon, it turns out that the fulcrum point is closer to 25 years.  

As a general rule, for every 1% increase or decrease in interest rates, a bond’s price will change approximately 1% in the opposite direction for every year of duration. So if we bought a thirty year bond, and rates went from 1% to 2% the day after we bought it, we would expect our bond to lose about 25% of its value, going from $1,000 to $750. So much for bonds being safe!

Now, clearly the folks that did this at SVB were aware of bond duration, and they had some sort of rate hedges and other instruments in place. However, the fact remains that they took on interest rate risk, and the duration math (as well as the rate environment) moved against them, and fast.

The fact that the Dodd-Frank rollback in the US (which happened in 2018) also reduced the buffer of shareholder funds needed to absorb such losses at banks did not help, and SVB was just under the $250bn threshold that would have come with more regulatory oversight and interest rate sensitivity stress testing.

While there are many learnings and insights from what happened, one is clearly to always work from first principles and be aware that the conventional wisdom around you may not necessarily be correct. As we just saw, bonds are safe only when held to maturity, and if you have to sell a long maturity bond early, math and markets can catch up with you.

When in doubt, always do the math. Much like Pi is a constant in math, make math a constant in your life.