QE, Stock Prices, and TINA

The U.S. economy as quantified by GDP has been sputtering along in slow growth mode for a number of years. It took a huge hit in 2020 due to covid shutdowns and has not nearly recovered. But stock prices have been rocketing upwards, and this past year is no exception. Markets took a cliff-dive in March, but have since way overshot to the upside.

Here is a plot of the past five decades of U.S. GDP and of the Wilshire 5000 index, which approximates the total stock market capitalization in the U.S.:

Chart Source: St. Louis Fed, as plotted by Lyn Alden Schwartzer

These two curves have crisscrossed each other over the past five decades, but in recent years the stock market has roared to the upside. One of Warren Buffet’s favorite metrics as to whether stock are overvalued is to consider the ratio of these two quantities, i.e. the market-capitalization-to-GDP (Cap/GDP) ratio:

Source: Lyn Alden Schwartzer

The ratio is much higher than it has even been. The last time it got this high was in 2000, and that did not end well.

Continue reading

Peering Inside the Balance Sheet of the Fed

A balance sheet gives a snapshot of a corporation’s assets and liabilities. The difference between total assets and total liabilities is (by definition) the value of the equity owned by the owners or shareholders of the company.

With, say, a manufacturing firm, the assets would include tangible items such as buildings and equipment and inventory, and intangibles such as cash, bank accounts, and accounts receivable. Liabilities may include mortgages and other loans, and accounts payable such as taxes, wages, pensions, and bills for purchased goods.

The balance sheet for a bank is different. The “Assets” are mainly loans that the bank has made, plus some securities (such as US Treasury bonds) that the bank has purchased. These assets pay interest to the bank. The money the bank used to make these loans and purchase these securities came mainly from customer deposits or other borrowings by the bank (which are considered “Liabilities” of the bank), and also from paid-in capital from the bank owners/shareholders. [1]  As usual, the current equity of the bank is assets minus liabilities. Thus:

Source:  BBVA

The Federal Reserve System is a complex beast. We will not delve into all the components and moving parts, but just take a look at the overall balance sheet.

Unlike other banks, the Fed has the magical power of being able to create money out of thin air. Technically, what the Fed can do with that money is mainly make loans, i.e. buy interest-bearing securities such as government bonds. The Fed makes its transactions through affiliated banks, so it credits a bank’s reserve account with a million dollars, if it buys from that bank a million dollars’ worth of bonds. Those bonds then become part of the Fed’s “assets”, while the reserve account of the bank at the Fed (which is a liability of the Fed) becomes larger by a million dollars. Since the Fed is not a for-profit bank, the “Equity” entry on its balance sheet is nearly zero. Thus, total assets are essentially equal to total liabilities.

The Fed also has the power of literally printing money, in the form of Federal Reserve Notes (printed dollar bills). These, too, are classified as liabilities. Thus, you are probably carrying in your wallet right now some of the liabilities of the central bank of the United States.

Before 2008, the balance sheet of the Fed was under a trillion dollars. Nearly all the “Liabilities” were the Federal Reserve Notes and nearly all the “Assets” were US Treasury securities. The reserve accounts of the affiliated Depository Institutions was minuscule. All that changed with the Global Financial Crisis of 2008-2009. To help stabilize the financial system, the Fed started buying lots of various types of securities, including mortgage-backed securities (MBS) [2]. The Fed thus propped up the value of these securities, and injected cash (liquidity) into the system.

Here is a plot of how the assets of the Fed ballooned in the wake of the GFC, from about $ 0.9 trillion to over $ 4 trillion:

Source: Investopedia

The initial purchases in 2008 were US Treasuries, which the Fed had prior authorization to do. To buy other securities, especially the mortgage products, required congressional authorization. The increased liabilities of the Fed which offset these purchases were mainly in the form of larger reserve accounts of the affiliated banks. The Fed started paying interest on these reserve accounts, to keep short term interest rates above zero at all times (otherwise the whole money market in the U.S. might implode).

 With the Fed relentlessly buying the mortgage and bond products, the interest rates on long-term mortgages and bonds was kept low. This was deemed good for economic growth. The Fed tried to sell off some securities to taper down its balance sheet in 2018, but that effort blew up in its face – – the stock market started crashing in response in late 2018, and so the Fed backtracked . You can look at weekly tables of the Fed balance sheet here.

Anyway, the GFC and its aftermath provided the precedent for massive purchases of “stuff” by the Fed. When the Covid shutdown of the economy hit in March of this year, the Fed very quickly went into high gear. Its balance sheet shot up from $4 trillion to $7 trillion in just a few months. It bought not only Treasuries and MBS, but corporate bonds. This was way outside the Fed’s original charter, but the crisis was so intense that nobody seemed to care whether these actions were legal or not. And now, to finance the huge deficit spending of the federal government in the wake of the shutdowns, the Fed has been buying up nearly the entire issuance of Treasury bonds and notes.

These actions may have long term consequences we will explore in later posts [3]. For now, the Fed has made it clear that it will keep interests rates near zero for at least the next couple of years. Invest accordingly.

ENDNOTES

[1] Huge caveat: This statement gives the impression that a bank must first receive say a thousand dollar deposit before it can make a thousand dollar loan. That is not the case. The reality is just the opposite: the act of making a thousand dollar loan actually CREATES a corresponding thousand dollar deposit. This is very counterintuitive, and I won’t try to explain or justify this point here.

[2] Technically, the Fed is not “buying” the mortgage-backed security (MBS). Rather, it is making a “loan” to the bank, and holding the MBS as collateral against that loan.

[3] It is now harder to take the federal deficit seriously as a constraint on spending:  the government can issue unlimited bonds to fund deficits, which the Fed will purchase to keep interest rates low. Yes, the government has to pay interest on those bonds, but the Fed has to return most of that interest to the Treasury, so the real cost to the government of that extra debt is low.

Aggregate Demand Regimes

Is inflation correlated with output growth?

Consider the AD-AS model which is often expressed in growth rates. Economists will often say that the short-run supply curve is flatter in the short-run and vertical in the long-run. In other words, aggregate demand policy can have SR output effects, and only has LR price effects.  Sounds good.

But there is a lot of baggage hiding behind “can have effects”. Often we’ll say that lackadaisical businesses cause a flatter SRS and that businesses with rational expectations have a vertical one. Also sounds good.

What causes the steepness of the SR supply curve? I’m sure that there are multiple determinants in regard to expectations. Here’s what got me on this topic. David Andolfatto shared the below graph and asked “Does lowflation necessarily mean low growth?.

Good question. My answer includes expectations concerning the monetary policy regime. Specifically, my answer was “It does in a regime of volatile and uncertain nominal income. Surprise AD growth pushes us up the SRAS.” Andolfatto called me out and in the right way, asking “What’s the evidences for this?

[…crickets…]

I had no evidence. I had the AS-AD model in hand and some logic – but no evidence. My logic is as follows. In a monetary regime that includes a constant rate of AD growth, output and price growth are inversely correlated. If NGDP grows at 5% always, then inflation falls when output growth rises. In other words, AD is exactly what people expect – illustrated as a vertical SRAS curve.

However, expectations are different in a regime of erratic AD. Let’s say that the rate of AD growth is unknown, but that the variance is known. If this is the world that you live in, then you make hay when the sun shines. Businesses sell more in periods of higher income. And, because they’re marching up the marginal cost curve, prices also rise. Alternatively, it may be that output growth is inflexible and prices rise as a goods are rationed.

Regardless of the truth, the above explanation is just story-telling. I had no evidence. What would the evidence even be? Here’s what I settled on. First, let’s express the AS-AD model in quarterly growth rates. In order to get a handle on monetary regime AD variance, I calculated the standard deviation of the NGDP growth rate by Fed Chair. Presumably, the Fed chair has a decent amount to do with monetary policy and the rear that occupies that chair is an indicator of when a regime begins and ends. I calculated the correlation between the GDP deflator and RGDP growth rates by regime. Below is the scatter plot.

What does it tell us? It tells us that regimes of stable AD growth experience a negative correlation between inflation and output growth. It also tells us that a AD growth volatility is associated with a positive correlation between inflation and output growth. So,  Does lowflation necessarily mean low growth? It does in a regime of volatile and uncertain nominal income.

(Of course this is all casual. It makes sense to me at first blush though. Having said that, the line of best fit also looks like it’s driven by the 2 extremely variable times: McCabe & Powell.)

Timeline of the Global Financial Crisis, Part 1: January-September, 2008

The sudden shutdown of much of the economy of the U.S. and of the world starting in February and March of 2020 led to deep concern, if not panic, in world financial markets. Millions of people were suddenly unemployed or furloughed, millions of small businesses faced bankruptcy, and stocks plunged some 30% in the fastest fall of global markets in history. Demand collapsed, and prices for nearly all financial assets fell. Trillions of dollars of financial transactions were in danger of unravelling.

The Federal Reserve immediately rode to the rescue, slashing interest rates and buying up all kinds of financial assets. These purchases of bonds and similar products injected cash into the markets to provide much-needed liquidity, and kept the system on track. In late March, the U.S. federal government authorized trillions of dollars of payments to individuals and businesses to stave off bankruptcy, and forbade foreclosures on mortgages, to keep people from losing their homes (at least in the near term). Banks and governments in other nations took similar measures. By May, it was clear that the worst scenarios had been averted, even though there will be significant lingering consequences of the Covid shutdowns.

The speed and scale of the Fed and government responses in March, 2020, may be attributed in part to learnings from the 2008-2009 Global Financial Crisis (GFC). In that crisis, the severity of the problem was not understood at first. There was naturally reluctance to take unprecedented actions to do what was perceived as bailing out of irresponsible banks and other companies. Over a period of many months, various measures were implemented to address some immediate needs, but then more and more problems kept cropping up. It was a macroeconomic game of whack-a-mole.

As a bit of a history lesson, here is a timeline of the main financial events of January-September, 2008. These descriptions are taken, with only minor editing, from an article by Kimberly Amadeo in The Balance.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

January 2008: Fed Tries to Stop Housing Bust

Easy credit and expectations of always-increasing home prices led to a speculative run-up in housing in 2002-2006. Mortgages were given to people who really could not afford them, and billions of dollars of those unsound sub-prime mortgages were repackaged and sold into the broad financial system. That all began to unravel in 2006-2007. In response to a struggling housing market, the Federal Market Open Committee began lowering the fed funds rate. It dropped the rate to 3.5% on January 22, 2008, then to 3.0% a week later. Economic analysts thought lower rates would be enough to restore demand for homes.

It didn’t help the millions of homeowners who had adjustable-rate mortgages.

February 2008: Bush Signs Tax Rebate as Home Sales Continue to Plummet

President Bush signed a tax rebate bill to help the struggling housing market. The bill increased limits for Federal Housing Administration loans and allowed Freddie Mac to repurchase jumbo loans.

February’s homes sales fell 24% year-over-year. It reached 5.03 million according to the National Association of Realtors. The median resale home price was $195,900, down 8.2% year-over-year.  Foreclosures were up.

March 2008: Fed Begins Bailouts

The Fed Chair realized the Fed needed to take aggressive action. It had to prevent a more serious recession. Falling oil prices meant the Fed was not concerned about inflation. When inflation isn’t a concern, the Fed can use expansionary monetary policy. The Fed’s goal was to lower the LIBOR benchmark interest rate, and keep adjustable-rate mortgages affordable. In its role of “bank of last resort,” it became the only bank willing to lend.

It increased its Term Auction Facility program to $50 billion. It also initiated a series of term repurchase transactions. These were 28-day term repurchase agreements with primary dealers. The Fed’s goal was to pump $100 billion into the economy.

March 11: The Fed announced it would lend $200 billion in Treasury notes to bail out bond dealers. They were stuck with mortgage-backed securities and other collateralized debt obligations. They couldn’t resell them on the secondary market. The subprime mortgage crisis dried up the secondary market for these debt products.

No one knew who had the bad debt or how much was out there. All buyers of debt instruments became afraid to buy and sell from each other. No one wanted to get caught with bad debt on their books. The Fed was trying to keep liquidity in the financial markets.

But the problem was not just one of liquidity, but also of solvency. Banks were playing a huge game of musical chairs, hoping that no one would get caught with more bad debt. The Fed tried to buy time by temporarily taking on the bad debt itself. It protected itself by only holding the debt for 28 days and only accepting AAA-rated debt.

March 14: The Federal Reserve held its first emergency weekend meeting in 30 years. On March 17, it announced it would guarantee Bear Stearns‘ bad loans. It wanted JP Morgan to purchase Bear and prevent bankruptcy. Bear Stearns’ had about $10 trillion in securities on its books. If it had gone under, these securities would have become worthless. That would have jeopardized the global financial system.

March 18: The Federal Open Market Committee (FOMC) lowered the fed funds rate by 0.75% to 2.25%. It had halved the interest rate in six months. That put downward pressure on the dollar, which increased oil prices.

That same day, federal regulators agreed to let Fannie Mae and Freddie Mac take on another $200 billion in subprime mortgage debt. The two government-sponsored enterprises would buy mortgages from banks. This process is known as buying on the secondary market. They then package these into mortgage-backed securities and resell them on Wall Street. All goes well if the mortgages are good, but if they turn south, then the two GSEs would be liable for the debt.

The Federal Housing Finance Board also took action. It authorized the regional Federal Home Loan Banks to take an extra $100 billion in subprime mortgage debt. The loans had to be guaranteed by Fannie and Freddie Mac

Fed Chair Ben Bernanke and U.S. Treasury Secretary Hank Paulson thought this would take care of the problem. They underestimated how extensive the crisis had become. These bailouts only further destabilized the two mortgage giants.

April – June: Fed Lowers Rate and Buys More Toxic Bank Debt

April 30: The FOMC lowered the fed funds rate to 2%.

April 7 and April 21: The Fed added another $50 billion each through its Term Auction Facility.

May 20: The Fed auctioned another $150 billion through the Term Auction Facility.

By June 2, the Fed auctions totaled $1.2 trillion. In June, the Federal Reserve lent $225 billion through its Term Auction Facility. This temporary stop-gap measure of adding liquidity had become a permanent fixture.

July 11, 2008: IndyMac Bank Fails

July 11: The Office of Thrift Supervision closed IndyMac Bank. Los Angeles police warned angry IndyMac depositors to remain calm while they waited in line to withdraw funds from the failed bank. About 100 people worried they would lose their deposit. The Federal Deposit Insurance Corporation (FDIC) only insured amounts up to $100,000. This was later raised to $250,000.

July 23: Treasury Secretary Paulson made the Sunday talk show rounds. He explained the need for a bailout of Fannie Mae and Freddie Mac. The two agencies themselves held or guaranteed almost half of the $12 trillion of the nation’s mortgages.

Wall Street’s fears that these loans would default caused Fannie’s and Freddie’s shares to tumble. This made it more difficult for private companies to raise capital themselves. Paulson reassured talk show listeners that the banking system was solid, even though other banks might fail like IndyMac.

July 30: Congress passed the Housing and Economic Recovery Act. It gave the Treasury Department authority to guarantee as much as $25 billion in loans held by Fannie Mae and Freddie Mac.

September 7: Treasury Nationalizes Fannie and Freddie

The FHFA placed Fannie and Freddie under conservatorship. It allowed the government to run the two until they were strong enough to return to independent management. 

The FHFA allowed Treasury to purchase preferred stock of the two to keep them afloat. They could also borrow from the Treasury. Last but not least, Treasury was allowed to purchase their mortgage-backed securities. 

The Fannie and Freddie bailout initially cost taxpayers $187 billion. But over time, they two paid back all costs plus added $58 billion in profit to the general fund. 

September 15, 2008: Lehman Brothers Bankruptcy Triggered Global Panic

Paulson urged Lehman Brothers to find a buyer. Only two banks were interested: Bank of America and British Barclays.

Bank of America didn’t want a loan. It wanted the government to cover $65 billion to $70 billion in anticipated losses. Paulson said no. The U.S. Treasury had no legal authority to invest capital in Lehman Brothers, as Congress hadn’t yet authorized the Troubled Asset Relief Program. Barclays announced its British regulators would not approve a Lehman Brothers deal.

Since Lehman Brothers was an investment bank, the government could not nationalize it like it did government enterprises Fannie Mae and Freddie Mac. For that same reason, no federal regulator, like the FDIC, could take it over.  Moreover, the Fed couldn’t guarantee a loan as it did with Bear Stearns. Lehman Brothers didn’t have enough assets to secure one. 

When Lehman’s declared bankruptcy, financial markets reeled. The Dow fell 504 points, its worst decline in seven years. U.S. Treasury bond prices rose as investors fled to their relative safety. Oil prices tanked.

Later that day, Bank of America announced it would purchase struggling Merrill Lynch for $50 billion. 

September 16, 2008: Fed Buys AIG for $85 Billion

The American International Group Inc. turned to the Federal Reserve for emergency funding. The company had insured trillions of dollars of mortgages throughout the world. If it had fallen, so would the global banking system. Bernanke said that this bailout made him angrier than anything else. AIG took risks with cash from supposedly ultra-safe insurance policies. It used it to boost profits by offering unregulated credit default swaps.

October 8, 2008: The Federal lent another $37.8 billion to AIG subsidiaries in exchange for fixed-income securities.

November 10, 2008: The Fed restructured its aid package. It reduced its $85 billion loan to $60 billion. The $37.8 billion loan was repaid and terminated.The Treasury Department purchased $40 billion in AIG preferred shares. The funds allowed AIG to retire its credit default swaps rationally, stave off bankruptcy, and protect the government’s original investment. 

September 17, 2008: Economy Almost Collapsed

Due to losses from Lehman’s bankruptcy, investors fled money market mutual funds. That’s where companies obtain their short-term cash.

September 16: The Reserve Primary Fund “broke the buck.” It didn’t have enough cash on hand to pay out all the redemptions that were occurring.

September 17: The attack spread. Investors withdrew a record $172 billion from their money market accounts. During a typical week, only about $7 billion is withdrawn. If it had continued, companies couldn’t get money to fund their day-to-day operations. In just a few weeks, shippers wouldn’t have had the cash to deliver food to grocery stores. We were that close to a complete collapse. 

September 19, 2008: Paulson and Bernanke Meet with Congress

U.S. Treasury Secretary Henry Paulson (L) speaks as Federal Reserve Board Chairman Ben Bernanke (R) listens during a hearing before the House Financial Services Committee on Capitol Hill September 24, 2008 in Washington, DC. Photo: Alex Wong/Getty Images

September 19: Paulson and Bernanke met with Congressional leaders to explain the crisis. Republicans and Democrats alike were stunned by the somber warnings. They realized that credit markets were only a few days away from a meltdown. 

The leaders were prepared to work together in a bipartisan fashion to craft a solution. But many rank-and-file members of Congress were not on board. 

Bernanke announced the Fed would lend the money needed by banks and businesses to operate so they wouldn’t have to pull out the cash in money market funds. This, along with the announcement of the bailout package, calmed the markets enough keep the economy functioning.

September 20, 2008: Treasury Submits Legislation to Congress

On September 20, Paulson submitted a three-page document that asked Congress to approve a $700 billion bailout. Treasury would use the funds to buy up mortgage-backed securities that were in danger of defaulting. By doing so, Paulson wanted to take these debts off the books of banks, hedge funds, and pension funds that held them.

When asked what would happen if Congress didn’t approve the bailout, Paulson replied, “If it doesn’t pass, then heaven help us all.”

September 21, 2008: The End of the “Greed Is Good” Era

Goldman Sachs and Morgan Stanley, two of the most successful investment banks on Wall Street, applied to become regular commercial banks. They wanted the Fed’s protection.

September 26, 2008: WaMu Goes Bankrupt

Washington Mutual Bank went bankrupt when its panicked depositors withdrew $16.7 billion in 10 days. It had insufficient capital to run its business. The FDIC then took over. The bank was sold to J.P. Morgan for $1.9 billion.

September 29, 2008: Stock Market Crashes as Bailout Rejected

A trader gestures as he works on the floor of the New York Stock Exchange September 29, 2008 in New York City. U.S. stocks took a nosedive in reaction to the global credit crisis and as the U.S. House of Representatives rejected the $700 billion rescue package, 228-205. Photo by Spencer Platt/Getty Images

The stock market collapsed when the U.S. House of Representatives rejected the bailout bill. Opponents were rightly concerned that their constituents saw the bill as bailing out Wall Street at the expense of taxpayers. But they didn’t realize that the future of the global economy was at stake.

Stock investors did, sending the ​Dow Jones Industrial Average down 770 points. It was the most in any single day in history. It didn’t stop there. Global markets panicked: The Morgan Stanley Capital International World Index dropped 6% in one day, the most since its creation in 1970.

To restore financial stability, the Federal Reserve doubled its currency swaps with foreign central banks in Europe, England, and Japan to $620 billion. The governments of the world were forced to provide all the liquidity for frozen credit markets.

[Again, these descriptions are taken nearly verbatim from 2008 Financial Crisis Timeline, by Kimberly Amadeo. See her article for coverage of the rest of 2008, and the ending of the recession in 2009.]

How Much Money Is There?

It is not straightforward to define what “money” is in a modern national economy. Simply tallying the amount of coins and paper currency is inadequate. Most buying and selling is now done by shifting numbers between abstract bank accounts, not by pushing a bundle of bills across a table.  Thus, these bank accounts serve the functions of money (medium of exchange and store of value). The question then arises as to which of these financial accounts to regard as money.

Among financial assets, there is a broad spectrum of liquidity. Typically you can write a check on your checking account which, when it clears, provides immediate and final settlement for a purchase.  On the other hand, if you want to tap your brokerage account with its holdings of Apple stock to buy a television, you would typically have to sell (liquidate) your stock. A third party would have to be willing to give you something more money-like (e.g. credit your money market fund at your brokerage) in exchange for the stock at some negotiated price. Then you might have to transfer the funds from your brokerage fund into your bank checking account before you can actually buy that TV.  Because of all these intermediate steps, and the fluctuating value of the stock before you complete the sale, the stock holding would not be counted as “money”, even though its value enabled you to ultimately make your purchase.

There are a number of measures of money in modern economies. In the U.S. some of these are:

M0: The total of all physical currency (coins and paper bills).

MB (“Monetary Base”): The total of all physical currency (coins and bill) plus Federal Reserve  Deposits (special deposits that only banks can have at the Fed). This is money essentially created by the government plus the Federal Reserve, which does not necessarily enter the private economy to be spent.

M1: Physical currency circulating outside of the Fed and private banking system, plus the amount of demand deposits, travelers’ checks and other checkable deposits. This is highly “liquid” money, i.e. accepted and used for transactions in the private economy.

M2: M1 + most savings accounts, money market accounts, retail money market mutual funds, and small denomination time deposits (certificates of deposit of under $100,000). The funds in these additional savings and money market accounts can in general be easily transferred to checkable accounts, and thus could go towards making purchases if desired.

MZM: “Money Zero Maturity” is one of the most popular aggregates in use by the Fed because its velocity has historically been the most accurate predictor of inflation. It is M2 – time deposits + institutional money market funds.

Below is a chart showing the growth in the U.S. in the past fifteen years of M0 (total currency, labeled “currency in circulation), MB, M1, and M2. The grayed areas are recessions, i.e. 2008-2009 and the present.  [1]

Various Measures of “Money” in the U.S.

The M1 money supply (green line) was about $1.4 trillion ( $1,400 billion on the chart) in 2005, was fairly steady for several years, then started a steady ramp up to $4 trillion by January, 2020. Due to the extraordinary events associated with the Covid-19 shutdown (government stimulus package plus Fed purchases of securities), M1 jumped up to $ 5.4 trillion by August of this year. M2 followed similar trends, though on a much larger scale, rising to$18.3 trillion this year. This compares to a current U. S. total GDP of about $21 trillion.

The lowest line on the chart is the physical currency (blue line), which has grown slowly but steadily. The “Total MB” (red) line, was essentially on top of the blue line up until the 2008-2009 recession. Since MB = physical currency plus reserves, this meant that the amount of money in the reserve balances at the Fed of the private banks was nearly zero before 2008. The reserves jumped up (difference between the red and blue lines) in 2009, with the onset of massive purchases of securities by the Fed (“quantitative easing”). The Fed buys these securities from the banks, and credits their reserve accounts. The Fed has tried to taper down its holdings in recent years (red line declining 2015-2019), but suddenly purchased trillions more this spring (red line jumping up in 2020).  Most pundits hold that all this Fed money injected into the financial system has been the major cause of the enormous rise in stock prices in the past decade, especially in the past six months.

[1] Chart produced on the St. Louis Fed “FRED” site, https://fred.stlouisfed.org/categories/24 . This site has a wealth of economic data. Unfortunately, it is not easy to change units, so I was stuck with “billions” instead of “trillions” for the axis labels. Also, the M0 and MB numbers were only available in “millions”, so I had to divide those numbers by 1000 to get them to fit on the plot with M1 and M2. The grayed out spots on the graph labels is where I blotted out the “ /1000 ” which the plotting software put in. It would have been cleaner, in retrospect, to have exported the data to Excel and replotted it there.