Author: Zachary Bartsch

So Many Living Ex-Presidents

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If you count president Trump, the number of living former presidents is at a historic high of five (Clinton, G.W. Bush, Obama, Trump, Biden). The number of living ex-presidents can increase for three reasons. 1) More people becoming president, 2) ex-presidents having longer lifespans, and 3) presidents leaving office earlier in life. Why do we have so many right now?

The historical maximum number of people who both 1) leave office and 2) live simultaneously with others is five. It first happened in 1861 when Abraham Lincoln (16th) was president for just under a year before John Tyler (10th) died in 1862. Since then, the number of living ex-presidents has been mostly below four if not below 3.  The figures below graph the number of people living who have been US president. The left graph uses daily data and the right uses the annual average (weighted by day).

In fact, besides Washington, we’ve had four other periods when there were ZERO ex-presidents living. The first was under Grant (18th). This changes my perspective of that period. Living ex-presidents provide a sense of continuity – that something from the past continues today. They give us hope that our country will continue into the future. Grant presided over part of the reconstruction era. For part of this presidency, there was no one else who knew how he felt and no living person who had been in his position. What a tenuous time!*

The other presidents who, at some point, had no living predecessors were Theodore Roosevelt (26th), Herbert Hoover (31st), and Richard Nixon (37th). But since 1981, we’ve had three or more living presidents. So, most of us feel like that’s “normal”. Imagine if there was just Trump, and that’s it. That’d feel jarring.

1) Are More People Becoming President?

A presidential term is four years and only one president was in office for more than two terms, Franklin Roosevelt (32nd). Let’s take a 24-year trailing average. With 8-year tenures, the least number of presidents is 3. With 4-year tenures, the greatest number of presidents is 6. Assassinations and other deaths of sitting presidents can push the number higher. The graph below is the number of unique people to act as head of state over the prior 24 years (I say ‘unique’ because Cleveland (22nd & 24th) and Trump (45th & 47th) both served two non-consecutive terms).

We can conclude that the number of unique presidents is not exceptionally high at this time. The historical average is about 5.2 unique presidents. We’ve been below that since 1998 owing to a higher proportion of two-term presidents since then. Before Biden (46th), Bush (41st) was the last time that we had a one-term president. So, in terms of executive regimes, the 21st century has been unusually stable. But this stability also places downward pressure on the number of surviving ex-presidents. So, we’ve had many living ex-presidents despite our few regime changes. Reason 1) doesn’t explain why we have so many living ex-presidents now.

2) Are President Lifespans Longer?

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Uncertainty Increases Profits?

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Most people have an intuition that uncertainty can harm economic outcomes. Baker, Bloom, & Davis (2016) and Bloom (2009) demonstrated that industrial production and manufacturing decline in the face of policy uncertainty. The typical mechanism that people suggest is that uncertainty about the future causes people to engage in precautionary saving, resulting in fewer sales.

The theory continues that firms consequently decrease production as demand for their output declines. Firms aren’t interested in causing the quantities supplied and demanded to be equal. Rather, they don’t want to produce too many goods that don’t get sold or don’t get sold at an adequate markup. Production is costly.  A related theory is that more persistent or longer-run uncertainty can also depress investment, since the riskier future increases the tail risk of losses.

Rather than make a risky investment, one could instead just hold off and wait for some of that uncertainty to get resolved. There’s tradeoffs to this, of course. As future costs and benefits become clearer, they also get priced-in to asset values. So, there is an optimization problem. The possible downside outcome is big and uncertain. If the risk of the investment gets resolved and the downside outcome is still too likely or harmful, then a project manager did the ex-post ‘right thing’ by waiting.

But, if the downside risk disappears or is found to be very small, then waiting to invest in the project incurs an economic cost. Either 1) the profitable project and its associated profits will occur later and less valuably, or 2) other firms also resolve their uncertainty and bid up the price of the project’s inputs. Invest too early, and the downside is large and uncertain. Invest too late, and you may lose the potential upside partially or entirely.

But can uncertainty systematically increase profits?

Walter Oi said yes.

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By the Numbers: Florida’s Property Tax Amendment (2026)

Zachary Bartsch2 Comments

Voters this November will face a proposed amendment to the Florida state constitution on property tax reform. Currently, Florida has what’s called a ‘homestead’ exemption of $50,000. If a residential property is your primary residence, then your home’s assessed value is $50k less before taxes are calculated. There is no exemption for rental property or 2nd homes or vacation homes. The proposed amendment increases the exemption to $250k by 2028 and then indexes it to inflation.

First, let’s get an idea of the magnitudes. The median home in Florida is priced at about $400k and the average property tax rate is around 0.8%. Below compares the current consolidated tax bill against that of the proposed amendment. Given current home prices and local tax rates, the new exemption would have a huge impact on municipal governments who get the bulk of their revenue from property tax. In fact, there is no Florida state property tax, so the proposed amendment would adopt a new rule for municipalities and not the state government.

What Motivates the Amendment?

The current homestead exemption of $50k was established in 2008. A subsequent amendment in 2024 allowed half of that to be indexed to CPI-U. The average home price in Florida has risen 114% since 2008 and 84% since 2020. That’s a lot faster than inflation, but the tax burden is partially offset by a maximum of 3% annual increase in assessed value. Regardless, many individuals face a larger tax bill over time even independent of whether their income or use of public services has changed. Plenty people are feeling the squeeze.

What’s the Purpose of the Homestead Exemption?

The exemption is available for primary residences only. That means that rentals and vacation homes do not qualify. It’s important to keep in mind that, given some total revenue, every tax break for one group or activity implies a higher tax rate for others. So, clearly, the effect is to tax residents less and tax seasonal residents and visitors more. Florida doesn’t have an income tax, but it does have a sales tax, gasoline tax, and others that are disproportionately borne by non-residents. Given that higher income individuals tend to have higher home values, the homestead exemption is a way to lower the tax burden of lower income households. Obviously, the lowest income individuals are renters, but so are non-residents who Florida prefers to tax.

The Economics

Homeowners

The exemption is enjoyed by all primary residences, but helps low income owners the most. And, given a stable amount of municipal tax revenue, a higher homestead exemption requires that municipalities replace that revenue. This might take the form of higher local fees and taxes, making life harder for lower income people to, say, own a car or make purchase if taxes on those activities rise. Revenue stability might also be helped by higher property tax rates. The higher the property value is above $250k, the greater the average tax burden that is borne. So, someone with a very high property value may find themselves with an even higher property tax bill after municipalities adjust to the proposed statewide rule. In this sense, the new amendment would be a step in the direction of tax progressivity (a higher proportion taxed from those with higher income/wealth).

Indexing

Normally, I am in favor of indexing nominal values to CPI. In this case, we need to think about what the goal is. Let’s assume that the goals is to provide relief to lower income homeowners specifically and all primary residence homeowners generally. Does indexing to the CPI help? It depends!

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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 a new and positive trend in cash flows began. 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

Zachary Bartsch1 Comment

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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