Data Update 3 for 2024: Interest Rates in 2023 - A Rule-breaking Year!

In my last post, I looked at equities in 2023, and argued that while they did well during 2023, the bounce back were uneven, with a few big winning companies and sectors, and a significant number of companies not partaking in the recovery. In this post, I look at interest rates, both in the government and corporate markets, and note that while there was little change in levels, especially at the long end of the maturity spectrum, that lack of change called into question conventional market wisdom about interest rates, and in particular, the notions that the Fed sets interest rates and that an inverted yield curve is a surefire predictor of a recession. As we start 2024, the interest rate prognosticators who misread the bond markets so badly in 2023  are back to making their 2024 forecasts, and they show no evidence of having learned any lessons from the last year.

Government Bond/Bill Rates in 2023

    I will start by looking at government bond rates across the world, with the emphasis on US treasuries, which suffered their worst year in history in 2022, down close to 20% for the year, as interest rates surged. That same phenomenon played out in other currencies, as government bond rates rose in Europe and Asia during the year, ravaging bond markets globally.

US Treasuries 

    Investors in US treasuries, especially in the longer maturities, came into 2023, bruised and beaten rising inflation and interest rates. The consensus view at the start of the year was that US treasury rates would continue to rise, with the rationale being that the Federal Reserve was still focused on knocking inflation down, and would raise rates during the yearl. Implicit in this view was the belief that it was the Fed that had created bond market carnage in 2022, and in my post on interest rates at the start of 2023, I took issue with this contention, arguing that it was inflation that was the culprit.

1. A Ride to Nowhere - US Treasury Rates in 2023

    It was undoubtedly a relief for bond market investors to see US treasury markets settle down in 2023, though there were bouts of volatility, during the course of the year.  The graph below looks at US treasury rates, for maturities ranging from 3 months to 30 years, during the course of 2022 and 2023:

Download data

As you can see, while treasury rates, across maturities, jumped dramatically in 2022, their behavior diverged in 2023. At the short end of the spectrum, the three-month treasury bill rate rose from 4.42% to 5.40% during the year, but the 2-year rate decreased slightly from 4.41% to 4.23%, the ten-year rate stayed unchanged at 3.88% and the thirty-year rate barely budged, going from 3.76% to 4.03%. The fact that the treasury bond rate was 3.88% at both the start and the end of the year effectively also meant that the return on a ten-year treasury bond during 2023 was just the coupon rate of 3.88% (and no price change). 

2. The Fed Effect: Where's the beef?

   I noted at the start of this post that the stock answer than most analysts and investors, when asked why treasury rates rose or fell during much of the last decade has been "The Fed did it". Not only is that lazy rationalization, but it is just not true, and for many reasons. First, the only rate that the Fed actually controls is the Fed funds rate, and it is true that the Fed has been actively raising that rate in the last two years, as you can see in the graph below:   

In 2022, the Fed raised the Fed funds rate seven times, with the rate rising from close to zero (lower limit of zero and an upper limit of 0.25%) to 4.25-4.50%, by the end of the year. During 2023, the Fed continued to raise rates, albeit at a slower rate, with four 0.25% raises.

    Second, the argument that the Fed's Fed Funds rate actions have triggered increases in interest rates in the last two years becomes shaky, when you take a closer look at the data. In the table below, I look at all of the Fed Fund hikes in the last two years, looking at the changes in 3-month, 2-year and 10-year rates leading into the Fed actions.  Thus, the Fed raised the Fed Funds rate on June 16, 2022 by 0.75%, to 1.75%, but the 3-month treasury bill rate had already risen by 0.74% in the weeks prior to the Fed hike,  to 1.59%. 

In fact, treasury bill rates consistently rise ahead of the Fed's actions over the two years. This may be my biases talking, but to me, it looks like it is the market that is leading the Fed, rather than the other way around. 

    Third, even if you are a believer that the Fed has a strong influence on rates, that effect is strongest on the shortest term rates and decays as you get to longer maturities. In 2023, for instance, for all of the stories about FOMC meeting snd the Fed raising rates, the two-year treasury declined and the ten-year did not budge. To understand what causes long term interest rates to move, I went back to my interest rate basics, and in particular, the Fisher equation breakdown of a nominal interest rate (like the US ten-year treasury rate) into expected inflation and an expected real interest rate:

Nominal Interest Rate = Expected Inflation + Expected real interest rate

If you are willing to assume that the expected real interest rate should converge on the growth rate in the real economy in the long term, you can estimate what I call an intrinsic riskfree rate:

Intrinsic Riskfree Rate = Expected Inflation + Expected real growth rate in economy

In the graph below, I take first shot at estimating this intrinsic riskfree rate, by adding the actual inflation rate each year to the real GDP growth rate in that year, for the US:

Download data

I will not oversell this graph, since my assumption about real growth equating to real interest rates is up for debate, and I am using actual inflation and growth, rather than expectations. That said, it is remarkable how well the equation does at explaining the movements in the ten-year US treasury bond rate over time. The rise treasury bond rates in the 1970s can be clearly traced to higher inflation, and the low treasury bond rates of the last decade had far more to do with low inflation and growth, than with the Fed. In 2023, the story of the year was that inflation tapered off during the course of the year, setting to rest fears that it would stay at the elevated levels of 2022. That explains why US treasury rates stayed unchanged, even when the Fed raised the Fed Funds rate, though the 3-month rate remains a testimonial to the Fed's power to affect short term rates. 

3. Yield Curves and Economic Growth

    It is undeniable that the slope of the yield curve, in the US, has been correlated with economic growth, with more upward sloping yield curves presaging higher real growth, for much of the last century. In an extension of this empirical reality, an inversion of the yield curve, with short term rates exceed long term rates, has become a sign of an impending recession. In a post a few years ago, I argued that if  the slope of the yield curve is a signal, it is one with a great deal of noise (error in prediction). If you are a skeptic about the inverted yield curves as a recession-predictor, that skepticism was strengthened in 2022 and 2023:

Download data

As you can see, the yield curve has been inverted for all of 2023, in all of its variations (the difference between the ten-year and two-year rates, the difference between the two-year rate and the 3-month rate and the difference between the ten-year rate and the 3-month T.Bill rate). At the same time, not only has a recession not made its presence felt, but the economy showed signs of strengthening towards the end of the year. It is entirely possible that there will be a recession in 2024 or even in 2025, but what good is a signal that is two or three years ahead of what it is signaling? 

Other Currencies

    The rise in interest rates that I chronicled for the United States played out in other currencies, as well. While not all governments issue local-currency bonds, and only a subset of these are widely traded, there  is information nevertheless in a comparison of these traded government bond rates across time:

Note that these are all local-currency ten-year bonds issued by the governments in question, with the German Euro bond rate standing in as the Euro government bond rate. Note also that during 2022 and 2023, the movements in these government bond rates mimic the US treasuries, rising strongly in 2022 and declining or staying stable in 2023.

    These government bond rates become the basis for estimating risk-free rates in these currencies,  essential inputs if you are valuing your company or doing a local-currency project analysis; to value a company in Indian rupees, you need a rupee riskfree rate, and to do a project analysis in Japanese yen, a riskfree rate in yen is necessary. While there are some who use these government bond rates as riskfree rates, it is worth remembering that governments can and sometimes do default, even on local currency bonds, and that these government bond rates contain a spread for default risk. I use the sovereign ratings for countries to estimate and clean up for that default risk, and estimate the riskfree rates in different currencies at the start of 2024:

Download data

Unlike the start of 2022, when five currencies (including the Euro) had negative riskfree rates, there are only two currencies in that column at the start of 2024; the Japanese yen, a habitual member of the low or negative interest rate club, and the Vietnamese Dong, where the result may be an artifact of an artificially low government bond rate (lightly traded). Understanding that riskfree rates vary across currencies primarily because of difference in inflation expectations is the first step to sanity in dealing with currencies in corporate finance and valuation.

Corporate Borrowing

    As riskfree rates fluctuate, they affect the rates at which private businesses can borrow money. Since no company or business can print money to pay off its debt, there is always default risk, when you lend to a company, and to protect yourself as a lender, it behooves you to charge a default or credit spread to cover that risk:

Cost of borrowing for a company = Risk free Rate + Default Spread

The question, when faced with estimating the cost of debt or borrowing for a company, is working out what that spread should be for the company in question. Many US companies have their default risk assessed by ratings agencies (Moody's, S&P, Fitch), and  this practice is spreading to other markets as well. The bond rating for a company then becomes a proxy for its default risk, and the default spread then becomes the typical spread that investors are charging for bonds with that rating. In the graph below, I look at the path followed by bonds in different ratings classes - AAA, AA, A, BBB, BB, B and CCC & below - in 2022 and 2023:

As with US treasuries, the default spread behaved very differently in 2023, as opposed to 2022. In 2022, the spreads rose strongly across ratings classes, and more so for the lowest ratings, over the course of the year. During 2023, default spreads reversed course, declining across the ratings classes, with larger drops again in the lowest ratings classes.

    One perspective that may help make sense of default spread changes over time is to think of the default spread as the price of risk in the bond market, with changes reflecting the ebbs and flows in fear in the market. In my last data update, I measured the price of risk in the equity market in the form on an implied equity risk premium, and chronicled how it rose sharply in 2022 and dropped in 2023, paralleling the movements in default spreads. The fact that fear and risk premiums in equity and bond markets move in tandem should come as no surprise, and the graph below looks at the equity risk premiums and default spreads on one rating (Baa) between 1928 and 2023:

Download data

For the most part, equity risk premiums and default spreads move together, but there have been periods where the two have diverged; the late 1990s, where equity risk premiums plummeted while default spreads stayed high, preceding the dot-com crash in 2001, and the the 2003-2007 time periods, where default spreads dropped but equity risk premiums stayed elevated, ahead of the 2008 market crisis. Consequently, it is comforting that the relationship between the equity risk premium and the default spread at the start of 2024 is close to historic norms and that they have moved largely together for the last two years.

Looking to 2024

    If there are lessons that can be learned from interest rate movements in 2022 and 2023, it is that notwithstanding all of the happy talk of the Fed cutting rates in the year to come, it is inflation that will again determine what will happen to interest rates, especially at the longer maturities, in 2024. If inflation continues its downward path, it is likely that we will see longer-term rates drift downwards, though it would have to be accompanied by significant weakening in the economy for rates to approach levels that we became used to, during the last decade. If inflation persists or rises, interest rates will rise, no matter what the Fed does. 

YouTube Video

Data

1. US Treasury Rates in 2022 and 2023
2. Intrinsic Riskfree Rates and T.Bond Rates - 1954 to 2023
3. ERP and Default Spreads: 1960 - 2023

Data Update Posts for 2024

1. Data Update 1 for 2024: The Data Speaks, but what is it saying?
2. Data Update 2 for 2024: A Stock Comeback - Winning the Expectations Game!
3. Data Update 3 for 2024: Interest Rates in 2023 - A Rule-breaking Year

Data Update 2 for 2024: A Stock Comeback - Winning the Expectations Game!

Heading into 2023, US equities looked like they were heading into a sea of troubles, with inflation out of control and a recession on the horizon. While stocks had their ups and downs during the year, they ended the year strong, and recouped, at least in the aggregate, most of the losses from 2022. That positive result notwithstanding, the recovery was uneven, with a big chunk of the increase in market capitalization coming from seven companies (Facebook, Amazon, Apple, Microsoft, Alphabet, NVidia and Tesla) and wide divergences in performance across stocks, in performance. As we move into 2024, it looks like expectations have been reset, with most forecasters now expecting the economy to glide in for a soft landing and interest rates to decline, and while that may seem like good news, it will represent a challenge for equity market investors.

Looking Back

    Almost a year ago, I wrote a post about what 2023 held for stocks, and it reflected the dark mood in markets, and in the face of investor gloom, looked at how the expectations game would play out for equities. In that post, I noted that if inflation subsided quickly, and the economy stayed out of a recession, stocks had upside, and that is the scenario that played out in 2023.  Stocks ended the year well, with November and December both delivering strong up movements, and while this left investors feeling good about the year, it was a rocky year. In the graph below, I look at the monthly levels on the index and price returns, by month:

On a month-to-month basis, stocks started the year well and had a good first half, before entering a tough third quarter where they gave back most of those gains. Over the course of the year, the S&P 500 rose from 3840 to 4770, an increase of 24.23% for the year, which when added to the dividend yield of 1.83% translated into a return of 26.06% for the year:

To get historical context, I compared the returns in 2023 to annual returns on the S&P 500 going back to 1928:

Download historical return data

It was a good year, ranking 24th out of the 95 years of data that I have in my dataset, a relief after the -18.04% return in 2022. 

    The solid comeback in stocks, though, came with caveats. The first is that it was an uneven recovery, if you break stocks down be sector, which I have, for both US and global stocks, in the table below: 

As you can see, technology was the biggest winner of the year, up almost 58% (44%) for US (global) stocks, with communication services and consumer discretionary as the next best performers. Energy, one of the few survivors of the 2022 market sell-off, had a bad year, as did utilities and consumer staples. Breaking equities down by sub-region, and looking across the globe, I computed the change in aggregate market capitalization, by region:

While US stocks accounted for about $9.5 trillion of the $14 trillion increase in equity market capitalization across the world, two regions did even better, at least on a percentage basis. The first was Eastern Europe and Russia, coming back from a massive sell-off in the prior two years and the other was India, which saw an increase of $1 trillion in market cap, and a 31.3% increase in market capitalization.

Looking forward

    While there is comfort in looking backwards, slicing and dicing data in the hope of getting clues for the future, investing is about the future. Much as we like to believe that history repeats itself, and find patterns even when they do not exist, the nature of markets makes them difficult to forecast, precisely because they are driven not by what actually happens to the economy, inflation and other fundamentals, but by how these results compare to expectations. Going into 2024, investors are clearly in a better mood about what is to come this year, than they were a year ago, but they are pricing in that better mood. To capture the market's mood, I back out the expected return (and equity risk premium) that investors are pricing in, through an implied equity risk premium:

Put simply, the expected return is an internal rate of return derived from the pricing of stocks, and the expected cash flows from holding them, and is akin to a yield to maturity on bonds. 

    To see how expectations and pricing have changed over the course of the year, I compare the implied equity risk premium (ERP) from the start of 2023 with the same number at the start of 2024

2023 ERP & 2024 ERP

At the start of 2023, in the midst of the market's pessimism of what the coming years would deliver, stocks were priced to earn a 9.82% annual return and a 5.94% equity risk premium. In contrast, at the start of 2024, the lifting of fear has led to higher prices, a more upbeat forecast of earnings and an expected return of 8.48% and an equity risk premium of 4.60%. I do compute this expected return and the equity risk premium at the start of each month, and the last 24 months have been a roller coaster ride:

While equity risk premiums and expected returns rose strongly in 2022, registering the largest single-year increase in history, they declined over 2023, as hope has gained an upper hand over fear.

    To the question of whether 8.48% is a reasonable expectation for an annual return for US stocks, and 4.60% a sufficient equity risk premium, I looked at the historical estimates for these numbers going back to 1960:

Download historical ERP

While stocks had expected returns exceeding 10% for much of the 1970s and 1980s, the culprit was high interest rates, and as interest rates have declined in this century, expected returns have come down as well. The post-2008 time period also was a period of historically low interest rates, and expected returns bottomed out in 2021, before rising again in 2022.  In the table below, I look at the expected returns and equity risk premiums at the start of 2022, 2023 and 2024 against the distribution of the corresponding variables between 1960 and 2024:

Download historical ERP

It is comforting, if you are an equity investor, to see that the expected returns are only slightly lower than the median value over the longer period, and the equity risk premium is above historical norms.

    Needless to say, there are other metrics, measuring the cheapness or expensiveness of equities, that investors may find more troubling. In particular, the earnings yield (the inverse of the PE ratio) for US equities will give investors pause:

Download historical EP

Note that the EP ratio, after a surge last year, has dropped back towards 2022 levels, with the caveat being that treasury bond rates are much higher now than they were then, an attractive alternative to equities that did not exist two years ago.

Taking a Stand

   I am not a market timer, but I do value the market at regular intervals, more to get a measure of what the market is pricing in, than to forecast future movements. In valuing the index, I follow the intrinsic value rulebook, where the value is determined by expectations of cash flows in the future, discounted back to adjust their risk. 

• To get expected cash flows, I start with expectations of earnings from the equities that comprise the index. For the S&P 500, the most widely followed equity index, I use the consensus estimates of aggregate earnings for 2024 and 2025, from analysts. I know that mistrust of analysts runs high, and the perception that they are cheerleaders for individual companies is often well founded, but I will stick with these forecasts for a simple reason. Having tracked analyst forecasts for four decades,I have found that analyst estimates of aggregated earnings for the index are unbiased, with analysts under estimating earnings in almost as many years as they over estimate them. 
• The cash flows to equity investors, especially in the United States, have increasingly taken the form of buybacks, not just supplementing but supplanting dividends. In 2023, dividends and buybacks on the S&P 500 index amounted to $1.367 trillion, 164.25 in index units, with 57.6% of these cash flows coming from buybacks. As a percent of earnings, the cumulative cash returned represented 74.8% of earnings in that year, representing a decline from payout ratios during this century (2000-2022); the median payout ratio for this period was 83%.

With these earnings and cash flows as starting points, and assuming that the treasury bond rate of 3.88% is a fair interest rate, I value the S&P 500:

Download valuation spreadsheet

Note that I forecast earnings beyond 2025, by assuming that growth scales down to the growth rate of the economy, estimated to be roughly equal to the riskfree rate. Unlike early in 2023, when stocks looked slightly under valued, with consensus earnings numbers and prevailing rates, stocks look over valued by about 9.2%, with a similar structure today.

    As with any market valuation, there are risks embedded in this value. First, the consensus view that the economy will come in for a soft landing may be wrong, with a recession or a stronger recovery both in the cards; the earnings numbers will be lower than analyst estimates in a recession and higher with a stronger economy. Second, while the market is building in expectations of interest rates declining in 2024, a significant portion of that optimism comes from a delusion that the Fed can raise or lower rates at well. After all, the treasury bond rate, a much stronger driver of equity values than short term treasury rates, remained unchanged in 2023, even as the Fed repeatedly raised the Fed Fund rates, and it is very likely that the future path of the treasury bond rate will depend more on the vagaries of inflation than on the whims of Jerome Powell. In the graph below, I look at the fair index level as a function of assumptions about earnings surprises and interest rates:

Note that I report the fair index values currently, and to convert them into target levels for the index a year from now, you have to take the future value of the index, using the expected return on stocks (net of dividend yield). For instance, to get the expected index level at the end of 2024, if rates stay at around 4% and earnings come in 10%  above expectations, is as follows:

Fair value of the index in current terms = 5202

Expected annual return on equities = T.Bond rate + ERP = 4% + 5% = 9%

Expected price appreciation on equities = Expected annual return - Dividend yield = 9% - 1.5% = 7.5%

Expected index level on 12/31/2024 (r =4%, Earnings 10% above expected) = 5202 (1.075) = 5592

As you can see, you would need earnings to come in above expectations, for the current index level (4750 on January 16) to be justified, with lower interest rates providing an assist. While what-if tables like the one above are useful tools for dealing with uncertainties, a more complete assessment of uncertainty requires that I be explicit about the uncertainties I face on each input, resulting in a simulation:

Simulation run with Crystal Ball, an Excel add-on

Not surprisingly, with uncertainties built in, the fair value of the index has a wide range, but using the first and ninth decile, a reasonable range for the fair value would 3670 - 5200, and at the January 16 closing level of 4750, there is about a  70% chance that the market is over valued.

    I am sure that you will disagree with one or more of the inputs that I have used to value the index, and I welcome that disagreement. Rather than point out to me the error of my ways, please download the spreadsheet containing the intrinsic valuation, and you should be able to replace my assumptions about earnings, cash payout and interest rates, and arrive at your own estimates of index value. 

Caveat emptor!

    Before you take my market prognostications at face value, please consider my open disclosure that I am a terrible market timer and try to avoid it in my investing. In short, I do not plan to act on my  market valuation by buying puts on the index, or scaling down by portfolio's equity exposure. If you are wondering why I bother valuing the index, there are two reasons. First, there are times in the past, when the overvaluation of the market is so large that it operates as a red flag on investing in equities, as an asset class, in general. That signal worked in early 2000 but did not in early 2008, and it is thus a noisy one. Second, and more generally, though, valuing the market allows you to make sense of, and tolerance for, bullish and bearish views on the market that may diverge from your own views.  Thus, investors and analysts who believe that rates will continue to decline, with a strong economy delivering higher-than-expected earnings, will see significant upside in this market, just as investors and analysts who believe that stubbornly higher inflation will cause rates to rise, and that earnings will come in well below expectations will be more likely to be part of the doomsday crowd. Just as in 2023, there will  be times in 2024 when one side or the other will think that it has decisively won the argument, just to see a reversal in the next period.

YouTube Video

Datasets

1. Historical Returns on Stocks, Bonds, Gold and Real Estate - 1928 -2023
2. Historical Implied Equity Risk Premiums and Expected Returns - 1960- 2023

Spreadsheets

1. Implied ERP calculator - January 1, 2024
2. Valuation of the S&P 500 on January 1, 2024

The School Bell Rings: Time for Class!

Continuing an annual ritual of long standing, ahead of starting my spring teaching at NYU starting in a couple of weeks, I would like to invite you, if you are interested, to come along for the ride. I know! I know! Most of you are not enrolled at NYU, paying nosebleed prices, and that is prerequisite to be in the classroom, but thanks to technology and a loose reading of the rules that constrain me, you can get a close approximation of the classroom experience, wherever you are in the world, with broadband being your only constraint.

My Teaching Journey

   I am a product of my life experiences, and at the risk of boring you, I would like to give you a short history of the lucky breaks and choices that have led me to where I am today. I came to the United States in 1979, and having lived here much of my life, I feel nothing but gratitude for the kindness and opportunities that this country has offered me. I started in the MBA program at University of California at Los Angeles (UCLA) in 1979, at the tail-end of its basketball glory days, fully expecting to move on to a career in consulting or investment banking, when I was done. To ease my financial constraints, I became a teaching assistant in the second year of my MBA program, and in what I can only describe as a moment of grace, I realized that teaching was what I wanted to do with the rest of my life. 

    Recognizing the need for a doctorate as an entree into college teaching, I stayed on at UCLA to get my Phd. In 1984, I moved on to the University of California at Berkeley, as a visiting lecturer, teaching anything that needed to be taught. The six classes that I prepped for in those two years ranged from banking to investments to corporate finance, and while I have never worked harder, much of what I teach today came out of those classes. In 1986, I joined New York University's business school as an assistant professor, and asked to teach Security Analysis, a class made legendary by Ben Graham, who taught it at Columbia University in the 1950s. By 1986, though, it was showing its age, more a collection of topics about institutions and types of securities, than a cohesive class. I balked at teaching this motley collection of topics and wanted to teach a class on valuation, but I was told that there was not enough stuff in valuation to fill a class. I learned early in my academic life that if you want to get anything done in an academic setting, it is better to do it subversively than it is to ask (and get) official permission. In the fall of 1986, I taught a valuation class in my security analyst slot, and with no cameras in the classroom or complaints from students, no one was any wiser. In spring 2024, I will be teaching valuation again to the MBAS, for the 59th time, and I have an identical class that I will delivering to undergraduates during the semester. 

    The very first class that I taught at Berkeley in 1984 was an introductory corporate finance class (BA 130, for those who are from Berkeley and remember the class codes) and I have continued to teach that class as well to the MBAs at Stern, usually in the first year of the program. Since many MBAs consider taking both my corporate finance and valuation classes, I am asked what the difference is between the classes, and my explanation is that in corporate finance, we look at first principles in finance from the inside of businesses, as owners or managers, whereas in valuation, you look at those same principles, as investors or potential investors in these companies, from the outside in. In the years that I have taught these two classes, I find myself using my corporate finance framework constantly, when valuing companies, and bringing my understanding of valuation into play, when examining how companies should make investing, financing and dividend decisions.

    In the 1990s, I was asked to pinch hit for a colleague and manage a semester-long class of sessions with outside speakers, all of whom were successful investors and portfolio managers. As I watched these investors come in and pitch their ideas about how markets worked and the best way to beat these markets to the students in the class, I noticed that while the speakers all shared success, they had very different perspectives about markets and divergent investment philosophies. At the end of that class, I put together a class on investment philosophies, not with the intent of picking the best one, but instead offering the entire menu, so that students could decide for themselves whether they wanted to be technical analysts, momentum trades, value investors, venture capitalists of market timers. 

Pre-Season Prep

    If you are new to finance or valuation, and especially if you have a non-quantitative background (a liberal arts major, a job in strategy or marketing, for example), I don't blame you for feeling intimidated at the prospect of taking a corporate finance, valuation or investment philosophies class. Investment bankers, consultants and portfolio managers often speak in a language that is foreign to those not in the space, and create an aura of mystery and layers of complexity around what they do. In my view, much of this is smoke and mirrors, and there is nothing in finance that is beyond your reach, if you are willing to use common sense and commit to doing a little bit of work that is outside your comfort zone. In particular, there are three disciplines that can help you in any finance class or analysis, and the payoff to spending time on each of them is significant.

1. The Language of Finance: Much as I take issue with the rigidity of accounting rules and the incapacity of accounting to be imaginative, the data that we use in finance is expressed in accounting terms. If you really don't understand the difference between operating earnings and net income, or know what accounting balance sheets can (and cannot) measure, you will have trouble doing any type of corporate financial analysis or valuation. That said, accounting classes are not only overkill but they also actively create perspectives that can get in the way of sensible financial analysis. A few years ago, I created my own version of an accounting class, reflecting my selfish interests in accounting data, and you can find this online, if your accounting is rusty:

If you are an accountant or have an accounting degree, you may find my treatment of accounting rules to be sacrilegious, but I have a very different end game.

2. The Building Blocks of Finance: Over the decades, finance has become specialized, but it is astonishing how much of finance is still build around basic building blocks. Since many of the students in my NYU finance classes come in with a foundational class in finance already under their belt, I used to take it for granted that they had mastered those building blocks. Over time, I have learned that this is not always true, and I have a short class on foundational finance, which includes discussions of  what risk is, and how to measure it, the time value of money and the basic macroeconomic drivers of interest rates and exchange rates.

If you are well versed in these areas already, you should skip this class and move on, but it cannot hurt to refresh the basics.

3. The Data Wranglers: We live in the age of big data, and as I watch those marketing big data make tall claims about what it can do for businesses, It is worth remembering that finance discovered the power of data decades ago, and that its effects on practice have been mixed. In particular, we have discovered that having more financial data does not always lead to better decisions and that our behavioral quirks can lead us to skew and ignore data. It is for that reason that I find myself turning more and more to statistics, a discipline designed to take large amounts of contradictory data and make sense of that data. Again, I have a short course that I put together that covers the statistical concepts needed in finance, from summary statistics (averages, medians) to measures of relationships (correlations, covariances) to predictive and analytics tools (regressions, simulations):    

If you are a statistics maven, you will undoubtedly find my discussion of statistical topics to be simplistic and naive, but if you are not, I hope that this revisiting of statistical concepts helps.

Learning Choices

    If I have not already talked you out of taking my classes, and you are still interested, the classes exist in multiple formats, and you can make your choice, based upon time available, preferences and end games.

The Classes

    In the first section of this post, I described the history of the three classes that I teach - the corporate finance class that I first taught at Berkeley in 1984 and have taught every year since, the valuation class that I sneaked in, as a replacement for security analysis, into my NYU classroom in 1986, and my investment philosophies class, born out of my experience listening to great investors talk about how they make money. 

     I describe my corporate finance class as an applied, big-picture class. It is a big-picture class because it is really a class about how to run a business, from a financial principles perspective, and every decision that a business makes is ultimately a corporate finance decision. The class tries to answer three core questions that every business, small or large, public or private, faces - the investment question (of whether and how much to invest in new projects/assets, the financing question of how much to borrow and in what form and the dividend question of how much cash to return to shareholders, if at all:

  

It is an applied class, because I answer each of these questions for a mix of companies that range the spectrum from large to small, developed to emerging market and from public to private - Disney, Vale, Tara Motors, Baidu, Deutsche Bank and a privately owned bookstore in New York Since these are real businesses exposed to changes in real time, there will be surprises that they deliver during the next few months that will become fodder for discussion. 

    The corporate finance class ends with a valuation segment, where I link the decisions that companies make on the investing, financing and dividend dimension to value. I pick up on that segment in the valuation class, which I describe grandiosely as a class about valuing and pricing just about anything and from any perspective:

Rather than use case studies and abstractions, this class is built around valuing businesses in real time, and the companies that hit the news during the course of the next few months will find their way into my classroom versions of the valuation class. While it is offered to both undergraduates and MBAs, the class is identical in terms of content, and you can pick either to follow.

    The investment philosophies class covers the spectrum of investment philosophies, and I have classified them in the picture below, based upon whether they are built around value or pricing. If you find that contrast mystifying, tune in to the class, and I will clarify:

The end game with this class is not to sell you on the best investment philosophy, but the one that best fits you, based upon what you bring to the game.

Class Format

    My classes are available in three formats. The first is the classroom format, where you can watch recordings of my undergraduate and MBA classes at Stern this semesters, shortly after they are delivered in real time. In that format, you will also have access to all of the materials that I use in the classroom, including lectures notes and exams/quizzes, and if you really want to get close to classroom-experience, you can  do the project that everyone in class is required to do. You will not get credit or a grade, and you are not enrolled the class, but you don't have to pay tuition. The second is a free online version that I have created for each class, with the lectures shrunk (in substance and time) to be more attuned to an online audience. You can access these online classes on my website, and as with the classroom classes, be able to download lecture notes and quizzes. The third is an online and paid version offered by NYU, where there are professional recordings of the online lectures, administered and grades quizzes and exams and virtual office hours. You will get an official certificate of course completion with this class, but NYU will extract its (financial) pound of flesh in the form of a tuition payment.

Class Format	Cost	Credit	Timing	Sessions	Material	Personal Interaction
Classroom	$0	None	Taught Jan - May 2024, but flexible on your part	Twenty six 80-minute recorded sessions (MBA) or twenty eight 75-minute sessons (Undergraduate)	Lecture notes, additional material, quizzes/exams and final project	None, unless you are an NYU student in the class
Onliine (Free)	$0	None	Flexible	26-36 online 10-20 minutes recorded sessions	Lecture notes, post-class tests	None
Online (NYU Certificate)	$2,200	Certification	Jan - May 2024	26-36 online 10-20 minutes recorded sessions	Lecture notes, post-class tests, quizzes/exams, project	One live virtual office hour every two weeks.

I want to emphasize that if you decide to follow the classroom or online versions of the class, it is entirely informal and that it has nothing to do with NYU. There is no registration, recording or access to NYU resources that come with taking these classes.  If you take the certificate class, you will have a more formal relationship with NYU. 

    In choosing between these alternatives (and I really am completely okay with any choice you make), here are some things to consider:

1. Financial constraints: If you are budget-constrained, your choice is a simple one. Since my NYU certificate classes are available, with almost nothing held back, for free on my webpage, why pay for these classes? The corollary to this proposition, however, is if you do choose to take the certificate class, please recognize that NYU sets the prices and complaining to me that the price is too high accomplishes nothing.
2. Time constraints: You have lives to live, work to do and families that you want to spend time with, and adding one of my classes to the list of things to do will eat into your time. The NYU certificate classes run on a semester clock, and if it looks like you will be busy for the next few months, you may find yourself unable to finish the class. Unlike some university-offered certificate classes, I do require those who take these certificate classes show me through a project and exams that they understand the material, and I don't give free passes. The two free versions (classroom and free online) do not operate on a calendar. In short, you can start with the regular class in January 2024 and stretch out the class over 12 months or 18 months, if you want to.
3. End game: Much as we all like to buy into the notion that learning is what matters, the truth is that some of you may want to use proof of that learning as a ticket to improve your standing in life (get a different job, move up in the ranks). With the free versions, you may very well learn just as much as those taking the class in the classroom, but you will get no credit for the class. Of course, you will get the certificate if you take the NYU certificate version, but NYU will extract its pound of flesh.
4. Updating: You will  be watching recorded lectures in all three versions of the class, but the timing of these recordings will be different. With the classroom format, you will get an updated 2024 version and in real time, but with the online versions (free and certificate), the sessions will reflect when they were recorded. While my framework and fundamentals remain the same, the examples I will be using will reflect this updating (or lack of it).
5. Personal preferences: The online sessions (free and certificate) are shorter (10-20 minutes) and thus more easily amenable to online consumption. Watching an 80-minute session online is not easy, especially in a world of TikTok and short YouTube videos. You may want to try both formats, before you decide.

The links to all of the classes in their different formats is below:

Class	Link
Accounting 101	https://pages.stern.nyu.edu/~adamodar/New_Home_Page/webcastacctg.htm
Foundations of Finance	https://pages.stern.nyu.edu/~adamodar/New_Home_Page/webcastfoundationsonline.htm
Statistics	https://pages.stern.nyu.edu/~adamodar/New_Home_Page/webcaststatistics.htm
Corporate Finance (MBA)	https://pages.stern.nyu.edu/~adamodar/New_Home_Page/webcastcfspr24.htm
Corporate Finance (Online Free)	https://pages.stern.nyu.edu/adamodar/New_Home_Page/webcastcfonline.htm
Corporate Finance (NYU Certificate)	https://execed.stern.nyu.edu/products/corporate-finance-with-aswath-damodaran
Valuation (MBA)	https://pages.stern.nyu.edu/~adamodar/New_Home_Page/webcasteqspr24.htm
Valuation (Undergrads)	https://pages.stern.nyu.edu/~adamodar/New_Home_Page/webcasteqUGspr24.htm
Valuation (Online Free)	https://pages.stern.nyu.edu/~adamodar/New_Home_Page/webcastvalonline.htm
Valuation (NYU Certificate)	https://execed.stern.nyu.edu/products/advanced-valuation-with-aswath-damodaran
Inv Philosophies(Online Free)	https://pages.stern.nyu.edu/~adamodar/New_Home_Page/invphil.htm
Inv Philosophies (NYU Certificate)	https://execed.stern.nyu.edu/products/investment-philosophies-with-aswath-damodaran

Note that the certificate classes for the spring 2024 will be open for enrollment only until Sunday, January 14, 2024, and that the corporate finance certificate class is available only in the fall.

Sequencing

    I like all the classes I teach, and if you asked which one you should take, I would be unable to answer, partly because it depends on what you plan to do in the future. If your question is about sequence, i.e., which classes should be taken first, that too will depend on what your background is and your end game. To help you make these choices, I put together a flow chart:

In fact, you may short circuit this sequencing and take only a portion of a class. Thus, if you are involved in banking or project financing, you may choose to take only the capital structure part of the corporate finance class, and if you are a trader, your focus may be on the pricing portion of the valuation class. 

The Joy of Learning

    As I watch young children experience the joy of learning, it reinforces my belief that human beings love to learn and that the tragedy of education systems is that they seem to be designed to destroy that love. It would be hubris on my part to claim that I will make you rediscover that love, but I do know that one reason I teach is to expose people to how much I enjoy learning new things or relearning old lessons. I hope that you can see that joy and that some of it rubs off on you! 

YouTube Video

Data Update 1 for 2024: The data speaks, but what does it say?

    In January 1993, I was valuing a retail company, and I found myself wondering what a reasonable margin was for a firm operating in the retail business. In pursuit of an answer to that question, I used company-specific data from Value Line, one of the earliest entrants into the investment data business, to compute an industry average. The numbers that I computed opened my eyes to how much perspective on the high, low, and typical values, i.e., the distribution of margins, helped in valuing the company, and how little information there was available, at least at that time, on this dimension. That year, I computed these industry-level statistics for five variables that I found myself using repeatedly in my valuations, and once I had them, I could not think of a good reason to keep them secret. After all, I had no plans on becoming a data service, and making them available to others cost me absolutely nothing. In fact, that year, my sharing was limited to the students in my classes, but in the years following, as the internet became an integral part of our lives, I extended that sharing to anyone who happened to stumble upon my website. That process has become a start-of-the-year ritual, and as data has become more accessible and my data analysis tools more powerful, those five variables have expanded out to more than two hundred variables, and my reach has extended from the US stocks that Value Line followed to all publicly traded companies across the globe on much more wide-reaching databases. Along the way, more people than I ever imagined have found my data of use, and while I still have no desire to be a data service, I have an obligation to be transparent about my data analysis processes. I have also developed a practice in the last decade of spending much of January exploring what the data tells us, and does not tell us, about the investing, financing and dividend choices that companies made during the most recent year. In this, the first of the data posts for this year, I will describe my data, in terms of geographic spread and industrial breakdown, the variables that I estimate and report on, the choices I make when I analyze data, as well as caveats on best uses and biggest misuses of the data. 

The Sample

    While there are numerous services, including many free ones, that report data statistics, broken down by geography and industry, many look at only subsamples (companies in the most widely used indices, large market cap companies, only liquid markets), often with sensible rationale – that these companies carry the largest weight in markets or have the most reliable information on them. Early in my estimation life, I decided that while this rationale made sense, the sampling, no matter how well intentioned, created sampling bias. Thus, looking at only the companies in the S&P 500 may give you more reliable data, with fewer missing observations, but your results will reflect what large market cap companies in any sector or industry do, rather than what is typical for that industry.

    Since I am lucky enough to have access to databases that carry data on all publicly traded stocks, I choose all publicly traded companies, with a market price that exceeds zero, as my universe, for computing all statistics. In January 2024, that universe had 47,698 companies, spread out across all of the sectors in the numbers and market capitalizations that you see below:

Data on Damodaran Online

Geographically, these companies are incorporated in 134 countries, and while you can download the number of companies listed, by country, in a dataset at the end of this post, I break the companies down by region into six broad groupings – United States, Europe (including both EU and non-EU countries, but with a few East European countries excluded), Asia excluding Japan, Japan, Australia & Canada (as a combined group) and Emerging Markets (which include all countries not in the other groupings), and the pie chart below provides a picture of the number of firms and market capitalizations of each grouping:

Data on Damodaran Online

Before you take issue with my categorization, and I am sure that there are countries or at least one country (your own) that I have miscategorized, I have three points to make, representing a combination of mea culpas and explanations. First, these categorizations were created close to twenty years ago, when I first started looking a global data, and many countries that were emerging markets then have developed into more mature markets now. Thus, while much of Eastern Europe was in the emerging market grouping when I started, I have moved those countries that have either adopted the Euro or grown their economies strongly into the Europe grouping. Second, I use these groupings to compute industry averages, by grouping, as well as global averages, and nothing stops you from using the average of a different grouping in your valuation. Thus, if you are from Malaysia, and you believe strongly that Malaysia is more developed than emerging market, you should look at the global averages, instead of the emerging market average. Third, the emerging market grouping is now a large and unwieldy one, including most of Asia (other than Japan), Africa, the Middle East, portions of Eastern Europe and Russia and Latin America. Consequently, I do report industry averages for the two fastest growing emerging markets in India and China.

The Variables

    As I mentioned at the start of this post, this entire exercise of collecting and analyzing data is a selfish one, insofar as I compute the data variables that I find useful when doing corporate financial analysis, valuation, or investment analysis. I also have quirks in how I compute widely used statistics like accounting returns on capital or debt ratios, and I will stay with those quirks, no matter what the accounting rule writers say. Thus, I have treated leases as debt in computing debt ratios all through the decades that I have been computing this statistic, even though accounting rules did not do so until 2019, and capitalized R&D, even though accounting has not made that judgment yet. 

    In my corporate finance class, I describe all decisions that companies make as falling into one of three buckets – investing decisions, financing decision and dividend decisions. My data breakdown reflects this structure, and here are some of the key variables that I compute industry averages for on my site:

		Corporate Governance & Descriptive
		1. Insider, CEO & Institutional holdings
		2. Aggregate operating numbers
		3. Employee Count & Compensation
Investing Principle		Financing Principle		Dividend Principle
Hurdle Rate	Project Returns	Financing Mix	Financing Type	Cash Return	Dividends/Buybacks
1. Beta & Risk	1. Return on Equity	1. Debt Ratios & Fundamentals	1. Debt Details	1. Dividends and Potential Dividends (FCFE)	1.Buybacks
2. Equity Risk Premiums	2. Return on (invested) capital	2. Ratings & Spreads	2. Lease Effect	2. Dividend yield & payout
3. Default Spreads	3. Margins & ROC	3. Tax rates
4. Costs of equity & capital	4. Excess Returns on investments	4. Financing Flows
	5. Market alpha

Many of these corporate finance variables, such as the costs of equity and capital, debt ratios and accounting returns also find their way into my valuations, but I add a few variables that are more attuned to my valuation and pricing data needs as well.

	Valuation		Pricing
Growth & Reinvestment	Profitability	Risk	Multiples
1. Historical Growth in Revenues & Earnings	1. Profit Margins	1. Costs of equity & capital	1. Earnings Multiples
2. Fundamental Growth in Equity Earnings	2. Return on Equity	2. Standard Deviation in Equity/Firm Value	2. Book Value Multiples
3. Fundamenal Growth in Operating Earnings			3. Revenue Multiples
4. Long term Reinvestment (Cap Ex & Acquisitons)			4. EBIT & EBITDA multiples
5. R&D
6. Working capital needs

Thus, I compute pricing multiples based on revenues (EV to Sales, Price to Sales), earnings (PE, PEG), book value (PBV, EV to Invested Capital) or cash flow proxies (EV to EBITDA). In recent years, I have also added employee statistics (number of employees and stock-based compensation) and measures of goodwill (not because it provides valuable information but because of its potential to cause damage to your analysis). 

    My data is primarily micro-focused, since there are other services that are much better positioned to provide macro data (on inflation, interest rates, exchange rates etc.). My favorite remains the Federal Reserve data site in St. Louis (know as FRED, and one of the great free data resources in the world), but there are a few macro data items that I estimate, primarily because they are not as easily available, or if available, are exposed to estimation choices. Thus, I report annual historical returns on asset classes (stocks, bonds, real estate, gold) going back to 1928, mostly because data services seem to focus on individual asset classes and partly because I want to make sure that returns are computed the way I want them to be. I also have implied equity risk premiums (forward-looking and dynamic estimate of what investors are pricing stocks to earn in the future) for the S&P 500 going back annually to 1960 and monthly to 2008, and equity risk premiums for countries. 

The Industry Groupings

    I am aware that there are industry groupings that are widely used, including industry codes (SIC and NAICS), I have steered away from these in creating my industry groupings for a few reasons. First, I wanted to create industry groupings that were intuitive to use for analysts looking for peer groups, when analyzing companies. Second, I wanted to maintain a balance in the number of groupings - having too few will make it difficult to differentiate across businesses and having too many will create groupings with too few firms for some parts of the world. The sweet spot, as I see it, is around a hundred industry groupings, and I get pretty close with 95 industry groupings; the table below lists the number of firms within each in my data:

No matter how carefully you create these groupings, you will still face questions about where individual companies fall, especially when each company can be assigned to one industry group. Is Apple a personal computer company, an entertainment company or wireless telecom company? While you can allow it to be in all three, when analyzing the companies, for purposes of computing industry averages, I had to assign each company to a single grouping. If you are interested in seeing which companies fall within each group, you can find it by clicking on this link. (Be patient. This is a large dataset and can take a while to download) 

Data Timing & Currency Effects

    In computing the statistics for each of the variables, I have one overriding objective, which is to make sure that they reflect the most updated data that I have at the time that I compute them, which is usually the first week of January. That does lead to what some of you may view as timing contradictions, since any statistic based upon market data (costs of equity and capital, equity risk premiums, risk free rates) is updated to the date that I do the analysis (usually the values at the close of the last trading day of the prior year – Dec 31, 2023, for 2024 numbers), but any statistic that uses accounting numbers (revenues, earnings etc.) will reflect the most recent quarterly accounting filing. Thus, when computing my accounting return on equity in January 2024, I will be dividing the earnings from the four quarters ending in September 2023 (trailing twelve month) by the book value of equity at the end of September 2022. Since this is reflecting of what investors in the market have access to at the start of 2024, it fulfils my objective of being the most updated data, notwithstanding the timing mismatch.

    There are two perils with computing statistics across companies in different markets. The first is differences in accounting standards, and there is little that I can do about that other than point out that these differences have narrowed over time. The other is the presence of multiple currencies, with companies in different countries reporting their financials in different currencies. The global database that I use for my raw data, S&P Capital IQ, gives me the option of getting all of the data in US dollars, and that allows for aggregation across global companies. In addition, most of the statistics I report are ratios rather than absolute values, and are thus amenable to averaging across multiple countries.

Statistical Choices

    In the interests of transparency, it is worth noting that there are data items where the reporting standards either don’t require disclosure in some parts of the world (stock-based compensation) or disclosure is voluntary (employee numbers). When confronted with missing data, I do not throw the entire company out of my sample, but I report the statistics only across companies that report that data.

    In all the years that I have computed industry statistics, I have struggled with how best to estimate a number that is representative of the industry. As you will see, when we take a closer look at individual data items in later posts, the simple average, which is the workhorse statistic that most services report for variables, is often a poor measure of what is typical in an industry, either because the variable cannot be computed for many of the companies in the industry, or because, even when computed, it can take on outlier values. Consider the PE ratio, for example, and assume that you trying to measure a representative PE ratio for software companies. If you follow the averaging path, you will compute the PE ratio for each software company and then take a simple average. In doing so, you will run into two problems. 

• First, when earnings are negative, the PE ratio is not meaningful, and if that happens for a large number of firms in your industry group, the average you estimate is biased, because it is only for the subset of money-making companies in the industry. 
• Second, since PE ratios cannot be lower than zero but are unconstrained on the upside, you will find the average that you compute to be skewed upwards by the outliers. 

Having toyed with alternative approaches, the one that I find offers the best balance is the aggregated ratio. In short, to compute the PE ratio for software companies, I add up the market capitalization of all software companies, including money-losers, and divide by the aggregated earnings across these companies, against including losses. The resulting value uses all of the companies in the sample, reducing sampling bias, and is closer to a weighted average, alleviating the outlier effect. For a few variables, I do report the conventional average and median, just for comparison. 

Using the data

    As I noted earlier, the datasets that I report are designed for my use, in corporate financial analysis and valuation that I do in real time. Thus, I plan to use the 2024 data that you see, when I value companies or do corporate financial analysis during the year, and if you are a practitioner doing something similar, it should work for you. You can find this current data at this link, organized to reflect the categories. 

    That said, there are some of you who are not doing your analysis in real time, either because you are in the appraisal business and must value your company as of the start of 2020 or 2021, or a researcher looking at changes over time. I do maintain the archived versions of my datasets for prior years on my webpage, and if you click on the relevant data, you can get the throwback data from prior years.

    There are two uses that my data is put to where you are on your own. The first is in legal disputes, where one or both sides of the dispute seem to latch on to data on my site to make their (opposing) cases. While I clearly cannot stop that from happening, please keep me out of those fights, since there is a reason I don’t do expert witness of legal appraisal work; courts are the graveyards for good sense in valuation. The other is in advocacy work, where data from my site is often selectively used to advance a political or business argument. My dataset on what companies pay as tax rates seems to be a favored destination, and I have seen statistics from it used to advance arguments that US companies pay too much or too little in taxes. 

    Finally, my datasets do not carry company-specific data, since my raw data providers (fairly) constrain me from sharing that data. Thus, if you want to find the cost of capital for Unilever or a return on capital for Apple, you will not find it on my site, but that data is available online already, or can be computed from the financial releases from these companies.

A Sharing Request

    I will end this post with words that I have used before in these introductory data posts. If you do use the data, you don’t have to thank me, or even acknowledge my contribution. Use it sensibly, take ownership of your analysis (don’t blame my data for your value being too high or low) and pass on knowledge. It is one of the few things that you can share freely and become richer as you share more. Also, as with any large data exercise, I am sure that there are mistakes that have found their way into the data, and if you find them, let me know, and I will fix them as quickly as I can!

YouTube Video

Sample Breakdown

1. Country Breakdown

Links to my data

1. Current Data
2. Archived Data

Data Update Posts for 2024

1. Data Update 1 for 2024: The data speaks, but what does it say?