Author: Zachary Bartsch

Fiscal Trends: USA’s 250th (And the Government’s 237th)

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We celebrate 250 years since the Declaration of Independence was signed on July 4th, 1776. That’s the day that we celebrate our country’s birth. So, it’s very American of us to celebrate the day that we merely declared independence (not the day that the revolutionary war ended). We simply said we were independent from the crown. Regardless, we celebrate 250 years as a people. BUT, our government is only 237 years old.  The current constitution replaced the articles of confederation in 1789.  So there are some caveats to the whole semiquincentennial thing.

An important distinction that is baked into the American pie is that we are not our government. Our government is younger than we are. Our government has a piggy bank called ‘US Treasury’. It can spend and borrow for the US national government. It can also impose tax liabilities on the population in order to service those outlays. Now that it’s the government’s 237th birthday, what’s its basic financial track record?

I like to think in the long run, for better or for worse, and I don’t like to get hysterical. So, let’s look at the full span of the 237 years – well – 235 years. The oldest annual data that we have is from Bicentennial Historical Statistics, which goes back to 1792. Below are the series for Federal Receipts and Outlays (revenue and spending).

The blue line is in nominal dollars and the orange line is the natural log so that we can see the changes in growth rates more easily. These aren’t inflation adjusted numbers, so we should expect to see some inflationary patterns. Long-run inflation was pretty stable prior to the 1913 Federal Reserve act and wee can see that reflected in both series. There was some drift upward in terms of revenue and expenditures. But the primary pattern was one of punctuated rises followed by plateaus. That’s a pretty standard ratcheting leviathan pattern. There’s a bump up for the big events in the first half of our history: the War of 1812, Civil War in 1861, and World War I in 1917.

Then, after the great depression and leaving the gold standard (mostly), in about 1933 we start to see the consistent positive trend in cash flows. In fact, it’s amazing how consistent the raw nominal series is.  We can see where World War II is in the series, but after that we appear to have traded punctuated increases for steady increases. Even the higher inflation rates of the 1970s look pretty muted and on trend (Btw, the blip in 1976 is a record-keeping artifact. There was a 3 month gap-period when the US government changed its fiscal year start/end). Even the new growth in total cashflows seems to be slightly bending downward and growing a little more slowly.

But rest assured, spending has exceeded revenues. Below is the long run deficit. I don’t take the log for this one since there are negative numbers. It’s hard to tell from the line graph, but the first big and persist swing in the deficit arrived after the Fed was established and the onset of WWI. The deficit hit $9 billion in 1918, which was 10x the prior peak of $0.9 billion at the end of the civil war in 1865. Notice that the above government revenues stayed flat or fell after 1920, but the outlays began trending upward before the revenues. The deficit doesn’t really start its long, steady march until 1932. Of course, for the past quarter century, the national government has been in a deficit mess (even if you measure the proportion of GDP).

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What the Fed Knew, and When

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I’ve recently gone back and started listening to the archived episodes of the ‘Macro Musings’ podcast hosted by David Beckworth. The show started in 2016. At that time, there was still a sense of malaise after the 2007-2008 Great Financial Crisis (GFC) and the slow recovery that followed it. We were also in a prolonged low-interest rate environment.

A recurring theme is whether the Fed should have engaged in expansionary policy earlier than they did in response to the GFC. There are multiple ways to answer. It’s not helpful to say ‘knowing what we know now’. The Fed didn’t have that opportunity. It’s a little bit more helpful to say ‘if the Fed had a different target or different tools’.  The target and tools are higher-order policy decisions and changing them can be helpful in the future. But they typically can’t be changed with the flip of a switch. After all, the 2% inflation target itself rolled out over the course of decades.

The most awkward/damning question is “Given the target, tools, and data that the fed actually had, did they make the right decision?”. If the answer is ‘no’, then that warrants a serious investigation of individuals, groups, processes, etc. I don’t mean a legal investigation. I mean the decentralized kind in which public and expert trust can be affected.

A concept that Beckworth often mentions concerning Fed culpability/performance during the GFC is the problem of data revisions. Currently, we know what the revised data says about NGDP, inflation, employment, etc. But the Fed only had the contemporary numbers and immediate revisions. In a world where economic growth is lousy or stellar in a range of 1-3%, small revisions can matter a lot. For example, below are the 2001q1 NGDP revision values over time.

Revisions occurred twice by 2002q2, revising NGDP down by more than 2%. Subsequent revisions raised the value on record to nearly +3% of the initial estimate, before settling at a less elevated value. Sheesh! In a world where a 1% swing is a big deal, how can we possibly expect the Fed to succeed at managing aggregate demand?

Things are not so scary as they might seem. The Fed doesn’t much care about revisions to an individual quarter. Rather, they care about the direction of change over time. Whether future revisions increase GDP by 2% is unimportant. What’s important is whether one period’s value is lower relative to the earlier value. That’s the relevant difference that tells us how the economy is changing.

Now, in 2026, our current understanding of NGDP during the GFC follows the below pattern starting in 2005q1 (lest I omit important pre-trends). NGDP growth had weakened in 2007q4, turning negative in 2008q1. Weak growth resumed in 2008q2. Then we had near-zero or negative growth for the next five quarters. Of course, we’re now approaching twenty years later, so we have the huge benefit of hindsight and revisions. Keep in mind that the contemporary numbers aren’t available until the subsequent quarter. By the yard stick of NGPD, the Fed should have been loosening by Q3 or certainly Q4 of 2008 if they cared about supporting total spending. Maybe as early as Q2 is they were especially sensitive.  

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Consumer Debt Delinquency & Write-Offs

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I wrote a post about debt delinquency way back in 2023. At the time, people were concerned about an impending recession. I argued that, if there were to be a recession, then debt defaults would not be the cause. The delinquency numbers were low and stable. Though delinquencies did rise some, no recession materialized. I’ll say a little more about how to interpret the numbers and give an update.

There exists a stock of loan balances. Most loans are in good standing with scheduled payments being made. This is good debt. Some debt is delinquent, meaning that payments are not being made. This is bad debt. What happens to bad debt? Sometimes those borrowers catch up on their payments and their loan balances switch to being good debt. Borrowers can also transform their bad debt into good debt by restructuring it with new terms. Temporary administrative adjustments can also change the classification from bad to good debt. At any moment, the total stock of debt is composed of good and delinquent debt. We can express these as proportions of all debt.

But the lenders also recognize that not all bad debt will be made good. For one reason or another, sometimes borrowers just don’t repay. It doesn’t make sense to list delinquent debt as a balance sheet asset if it will never be paid. Rather than accumulating more bad debt every year that will never be paid, banks ‘charge off’ some of that bad debt. Charging off bad debt lets banks realize losses and makes for a more realistic balance sheet. The flow of charge offs is deducted from the stock of delinquent debt.

If banks charge off some delinquent debt, then the proportion of delinquent debt should be lower in the next period, all else constant. But all else isn’t constant. Some good debt will become delinquent and some delinquent debt will become good. Though, after a charge off it’s true that delinquent debt is less than it would have been otherwise. Below, I denote the net flow of good & bad debt transitions as ‘r’ and solve for it.

The variable ‘r’ is the net transition to good or to bad debt after charge offs. If r>0, then net new delinquencies occurred faster than banks realized their losses with charge offs. Is that good or bad? A higher rate of net new delinquencies can be bad because it reflects that people aren’t paying their contractually obligated debts. But it can also be good if the new delinquencies are a result of experimental entrepreneurship and an innovative economy. The bad interpretation is probably relevant cyclically as a short or medium run variable. The innovation interpretation probably changes in the medium or long run as a structural variable.

Let’s look at the numbers. There are several categories of loans, but let’s start with just consumer loans.

The delinquency rate is higher than it was after the pandemic stimulus checks, but is still lower than historical rates. The charge off rate is also near the historical average. Below right graphs ‘r’ and it’s always greater than zero, meaning that there’s always more people transitioning from good debt to delinquency than the reverse. There was more debt becoming delinquent as post-pandemic interest rates rose, but net delinquency transitions have been falling since 2024q1 until 2026q1 when they mildly up-ticked. In other words, the aggregate consumer debt picture looks pretty average except for the secular decline in rates of delinquency. I don’t know why that is. Maybe banks have gotten better are identifying risk? Or maybe newer forbearance rules are friendlier to borrowers who need to pause payments?

Below are the same two graphs for single-family residential mortgages. These delinquencies are close to historical lows and charge offs are average. However, the ‘r’ graph below has been rising for a decade and is currently at a twelve-year high. Since the data only goes back so far, it’s hard to say whether the low numbers of the late twenty-teens were an aberration of the post GFC, low interest rate environment or whether we should be concerned. It is worth noting that the ‘r’ values are often below zero, which means that people do often come back from delinquency. We know it’s not simply charge offs doing the work there since the charge off rate has been steady and very low.

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Relative Measures of Portfolio Performance

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This is the third and final installment of my series on portfolio performance measures among separate assets groups. First, I summarize the earlier posts, then I introduce relative performance measures. I start with the Markowitz cloud of possible portfolio weights, returns, and volatilities.

Absolute measures of performance contrast the realized portfolio performance with the performances that were possible simply by calculating the difference in, say, return or volatility. The drawback of this method is that different spreads of statistics can affect these differences apart from portfolio performance. That is, even if a portfolio of assets return was very high, some reference return can still be much higher and make the performance look poor.

Quasi-relative measures tackle this problem of different spreads by calculating the percentile of possible returns or volatilities. This allows us to compare portfolio returns to what was possible even among portfolios of different assets with Markowitz clouds of different volatility ranges. The drawback of quasi-relative measures is that the return at some percentile of possible returns is not the same as the return of the same percentile among possible portfolios. Said another way, each possible rate of return in the Markowitz cloud is not equally as likely. So, a low percentile among possible returns be due to a very high and unlikely return.

It should be obvious that returns and volatilities among possible portfolio weights are not equally likely. To help visualize the idea, see the below 3D quadratic for a simplified example that represents a portfolio of three assets. The x-axis represents returns and the z-axis represents standard deviation. The y-axis represents the weight on  the 3rd assets (returns and weights map directly to one another linearly). The set of possible portfolios lie on the surface of the quadratic function.

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Quasi-Relative Measures of Portfolio Performance

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Last week I discussed absolute measures of portfolio performance and management, specifically between two portfolios that are composed of different assets (utilities and tech). I began with comparing the basics of return, standard deviation, and Sharpe ratio to some other possible portfolio in the Markowitz cloud. But, simply comparing the difference between these possible portfolios can be sensitive to the spread of stats within a specific Markowitz cloud. In other words, it’s not scale independent. A larger spread of possible stats can make a portfolio look bad due to the spread return/standard deviation/Sharpe ratio alone.

In this post I introduce quasi-relative measures. Again, I lean on the Markowitz cloud. They’re pasted below (Utilities on the left, tech on the right).

If we can somehow express the returns, volatilities, and Sharpe ratios on a common scale that is independent of the level values, then we can make the realized portfolios more comparable. One thing that we can do is to express a stat as a weighted linear average between the maximum and minimum possible values. Conditional on the realized standard deviation, there exists a maximum and minimum of possible return. Something like the below. Rho is the weight on the maximum return. It’s also the proportion of possible conditional returns that are lower than the realized return.

The unconditional version is the same, but would be relative to the global maximum and minimum stats. We can represent the weigh on the maximum return and the percentile among possible returns as gamma.

A final quasi-relative measure of performance is the dissimilarity index between the realized portfolio weights and some reference portfolio weights. This provides a measure of how much the asset weights would need to change in order to adjust the portfolio.  If changing portfolio weights is costly, then it’s also a measure of the transaction cost of reallocation. It’s quasi-relative because it is independent of the spread of possible performance stats.

Below are the quasi-relative measures for each the utility and tech company portfolios.

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Absolute Measures of Portfolio Performance

Zachary Bartsch1 Comment

The basic idea is that we want to compare the performance of different portfolios or their managers. This is relatively easy as long as the portfolios contain the same assets. Then, the portfolios are simply characterized by the different weights among the different assets. But how do we compare the performance of portfolios whose assets are different? In finance, we usually assume that everyone can invest in everything. But there are plenty of cases in which that’s a bad assumption: when clients want exposure to particular industries, when there are statutory limitations on holding certain assets, or when an individual company is considering specific projects within the same company under conditions of scarce financing.

The most primitive step is to compare the return and standard deviation of two different portfolios. However, higher risk investments tend to have higher returns in dynamic equilibrium. So, if we were to compare the returns of a tech company to a utility company, then we’d often see the tech companies performing better. But, if we compare the volatilities, then the utility companies would tend to perform better. Sharpe stepped in with a ratio to express the excess return (benefit) per standard deviation (the cost). This way, we can compare the price of volatilities between two portfolios. We’ll stick with just these basic 3 measures: return, standard deviation, and Sharpe ratio. (Others do exist)

Let’s put some meat on this with an example. Say that we have two portfolios, each composed of different assets. There’s a utility portfolio that’s composed of NEE, DUK, and SO. There’s also a tech portfolio that’s composed of AMD, MSFT, and NVDA. Both portfolios have weights of (0.33, 0.33, 0.34).  The results of the utility versus the tech portfolio are:

  • Returns: 14.2% vs 136.3%
  • Standard Deviation: 14.9% vs 32%
  • Sharpe: 0.684 vs 4.134

Goodness me! The tech portfolio returns much more in absolute terms and much more per unit of risk. It’s twice as volatile as the utility portfolio, but the returns are almost ten times as high. If you could, then many of us would choose the tech portfolio over the utility portfolio. But, what if, for one reason or another, you can only invest in one of the two industries? Or, what if you want to invest your money with a skilled manager, rather than a risky one?

One way to tackle this problem is to introduce the Markowitz cloud. Specifically, we can essentially list out all of the possible portfolios along with their return and standard deviations. Then, we can compare the actual performance to the entire menu of possible performances within each set of assets. Below are the possible performances for the utility (left) versus the tech (right) portfolio. The actual portfolios are marked with an X.

One way to evaluate the two portfolios is to compare their return, standard deviation, and Sharpe ratio to the other candidates that were achievable with the same assets. As we can see, conditional on the assets, neither portfolio minimized the volatility, maximized return, nor maximized the Sharpe ratio. Furthermore, assuming that the realized rate of return was the goal, neither portfolio minimized the conditional volatility. Assuming that the realized volatility was the goal, neither portfolio maximized the conditional return. Below are two tables that describe some candidate alternatives and how they differ from the realized portfolio.

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Breakfast Pudding

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When I was a kid, my family didn’t get JELLO puddings – or any puddings for that matter. As an adult, I realized that a lot of those are just sugar, cornstarch, and stabilizers. So, they became less appetizing.

You’re going to laugh at me.

A few years ago my wife and I went to a nice little breakfast restaurant for brunch in old town Fredericksburg, VA. I got this coconut milk chia seed parfait. I was blown away. That seems silly to say, but it was really nice.

For years we spoke longingly of that chia parfait and we’d speculate about when we might go there again. It was one of those conversations that married people have.

“Hey, remember that really good thing?”

“Yeah, it was really good.”

“We should try that again sometime.”

Then one day, while visiting Virginia, we noticed that the restaurant had closed. It wasn’t surprising because the restaurant had only been ‘fine’, except for the healthy and delectable layered treat from years past.

Now we have a handful of kids and we try different things periodically to make the morning routines go more smoothly. Having a responsible treat to entice juveniles from their room isn’t the worst thing that we’ve tried.

My wife, in her laudable creativity, refined a new creation that’s inspired by our now frustrated longing for a nice chia parfait.

Below is a recipe for peanut butter chocolate chia seed pudding. Basically, you mix it the night before and stir it again in the morning and it’s ready to go. It’s a crowd pleaser.

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Which Business Programs Require Economics?

Zachary Bartsch2 Comments

Disclaimer: This post might throw shade.

The vast majority of business majors across the US are required to take two or more Economics courses. You can look across the spectrum. All of the top 20 business schools require two or more econ classes. In fact, Wharton is the top-ranked business school and their business program is actually an *economics* program. They don’t have finance/accounting/business degrees. Instead, they have an Economics degree with the various business concentrations. Again – the top business school in the country is an Economics program.

What about at the other end of the spectrum? I live in Florida. Every single Florida state school requires both Micro and Macroeconomics for business majors. These schools include everything from Florida State University to the local Florida state college down the road. I didn’t look at other state-run higher education systems in other states. There are a lot of states…

I teach at a private Catholic university. We’re listed in something called ‘The Newman Guide’ which recommends 17 Catholic schools. Many of these are liberal arts schools, but the list also includes Catholic University of America, which is an R1. Most of these schools also require two or more Economics classes in their Business major programs. The only exception is University of Dallas, which has Economics in the core curriculum.*

So, overwhelmingly undergraduate business programs across the country require two economics courses. But, why? The students are often not happy to be there, and I’ve even heard business professors demean the math as performatively rigorous and superfluous. They argue that plenty of people get rich or are otherwise successful without all of the quantitative skills that economics leverages.

I think that the fear of math is both a red herring and a scapegoat. Rather, Economics confronts students with the liberal arts – whether they like it or not. Be careful. Liberal Arts are not the same as Humanities. They include argumentation, the ability to write and communicate, clear and consistent logic, and, yes, even math. Accounting can tell you how to keep track of the money, but it doesn’t include a theory for when you should produce more or less in contrast to your competitors. Finance does better since it has the time value of money and ‘with vs without’ analysis. That’s closer to marginal thinking. But finance lacks a theory of markets outside of portfolio theory and arbitrage.**

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How do Income Tax Brackets Work?

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I was listening to an episode of The Deduction, a podcast by the Tax Foundation. As if that first sentence isn’t evident enough, I was reminded of how confusing taxes are – period. Even experts disagree and see grey areas. As I was listening, I thought “man, they need a graph”. So, here we are.

Income Tax Vocabulary

The money that you are paid by your employer is your gross income. Not all of it is taxable. You can deduct money from your gross income to get your taxable income. Most people subtract the ‘standard deduction’ from their gross income, which is how I’ll proceed in this post. Since the standard deduction for 2026 is $16,100 for a single earner, that means that your taxable income is $16,100 less than your gross income. By following a formula, one can calculate the amount of money that they must pay the government. These payments can be all at once, throughout the year, or even directly from your paycheck. The total that’s due to the government by April 15 is called the total tax liability. Finally, the money that the government doesn’t take, and that you get to keep, is called your net income. It’s your income net of taxes.

If you’ve had a job, then you are probably most familiar with your gross income, what your employer pays you, and your net income, what you get to take home. The steps in between might include some hand-waving.

Marginal Tax Rates

One of the most confusing pieces of the income tax code is marginal income taxes. Below are the brackets for 2026.

Marginal Tax rates work like this: Every dollar that you earn faces a tax rate. If your taxable income would be below zero, then you pay zero in taxes. But if your taxable income is $5k, then it gets taxed at a rate of 10%. That part should be pretty straightforward. But what if your taxable income is $15k? According to the table, you face a tax rate of 10% for dollars earned up to $12,400. That would be a tax liability of $1,240. But the remainder of your $15k in taxable income exists in the next tax bracket. That portion of your taxable income faces a tax rate of 12%. Sticking with the example, $2,600 is in the 12% tax bracket, so the tax liability for that portion of your taxable income is $312 (=$2.6k*0.12). Therefore, your total tax liability would be the sum of your tax liabilities across all applicable tax brackets: $1,552 (=$1,240+$312).

There are some features of marginal tax rates that are worth mentioning. Since the tax rates on the lower taxable income brackets don’t change, earning more gross income never reduces your net income unless the tax rate exceeds 100% (which it doesn’t here). So, when someone says that their taxable income is in the 35% tax rate bracket, they probably just mean that their last dollar earned is there. They’re only paying 35% on the taxable income that’s above $256,225. They’re not paying 35% of all earned dollars to the Internal Revenue Service (IRS).

Below is a graph that details the different marginal tax rates with shaded areas. The blue line is the average tax rate. It’s calculated by dividing the tax liability by the gross income. Even though one might earn an income that’s greater than $257k where the marginal tax rate is 35% or greater, the average tax rate remains lower, topping out at about 30% in this figure. The average tax rate is lower than an earner’s top marginal tax rate because the income in those lower brackets never disappears or get taxed at a higher rate.

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The Arithmetic of Family Punctuality

Zachary Bartsch4 Comments

My children are getting more capable. They get more responsibility that comes with the independence that capability implies. Specifically, when getting ready in the morning they like to leave so that they arrive at school just barely on time. Except, when something comes up, they are rushed, flustered, short-tempered, and tardy. They lament that “if only the unforeseeable event X hadn’t happened, I would have been on time”.

It doesn’t matter what X is. Maybe they forgot to pack a lunch, or set out their clothes, or they have a flat tire on their bikes, or… whatever. The specific time-consuming event is unforeseeable. But, that *any* time-consuming event will occur is very foreseeable. What’s a Bayesian to do?

Before we even start the analysis, let’s acknowledge that being perfectly on time for some event usually involves stress and a lack of preparedness. Yes, you were ‘on time’, but given the probability of heavier traffic, difficulty finding a parking spot, or whatever, we know that tardiness is just one unforeseen event away.

Individual Punctuality

How long does it take to get somewhere? It takes both travel time and time preparing to depart. Let’s just generally call this ‘preparation’ time. Let’s assume that you complete everything that you would complete. That means that you aren’t forgoing a shower or breakfast or whatever lower priority you might choose to forgo to arrive at some obligation punctually.

Random events can occur either as you travel to work or as you prepare to depart, but let’s place the random travel events to the side and focus on what one can do to get out of the house ‘on time’. In my personal case, my children have a 30min interval during which they can arrive at school. They almost never arrive in the first 15min of that interval. That’s more of a policy choice than an accident. They don’t want to sit in a cold gymnasium for 20min if it’s avoidable. So, their planned arrival time has an effective 15min window.

Here is the problem. A time-consuming random event, X, is a right-skewed random variable. Discretely, the modal day includes X=0min. Though the most common delays are greater than 0min. See the distribution below. A 0min random event occurs 35% of the time. But, a time-consuming event happens 65% of the time. So, if you try to arrive exactly on time to your obligation, then you will be punctual 35% of the time and you will be tardy 65% of the time. That’s not a good look and not a good reputation to build – and that’s apart from building a habit of imprudence and the material consequence of not being ready for the task at hand.

Someone with just enough insight to be dangerous might say ‘Ah! Instead, leave with enough time to accommodate the expected unforeseen event’. Mathematically, that’s the weighted average. In this case, that’s six minutes. So, if you plan to arrive 6min early, then you will be punctual – on average. But even that’s not really what we’re after. We’d like to be on time for a preponderance of the days. Building in a 6-minute buffer does two things. 1) Every time that there is a 0min or 5min unforeseen event, you get to your destination 6min or 1min early. That’s good for your nerves, performance, and reputation. But, that also means that you’re late whenever there is a 10min, 15min, or 20min unforeseen event – and those occur 35% of the time!

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