If the title of this post sounds familiar, it is because is one of Disney’s most iconic rides, one that I have taken hundreds of times, first with my own children and more recently, with my grandchildren. It is a mainstay of every Disney theme park, from the original Disneyland in Anaheim to the newer theme parks in Paris, Hong Kong and Shanghai. For those of who have never been on it, it is the favored ride for anyone who is younger than five in your group, since you spend ten minutes in a boat going through the world as Disney would like you to see it, full of peace, happiness, and goodwill. In this post, I will expand my analysis of data in 2024, which has a been mostly US-centric in the first four of my posts, and use that data to take you on my version of the Disney ride, but on this trip, I have no choice but to face the world as is, with all of the chaos it includes, with tariffs and trade wars looming.  Returns in 2024     Clearly, the most obvious place to start this post is with market performance, and in the table below, I report the percentage change in index level, for a subset of indices, in 2024: The best performing index in 2024, at least for the subset of indices that I looked at, was the Merval, up more than 170% in 2024, and that European indices lagged the US in 2024. The Indian and Chinese markets cooled off in 2024, posting single digit gains in price appreciation.     There are three problems with comparing returns in indices. First, they are indices and reflect a subset of stocks in each market, with different criteria determining how each index is constructed, and varying numbers of constituents. Second, they are in local currencies, and in nominal terms. Thus, the 172.52% return in the Merval becomes less impressive when inflation in Argentina is taken into account. It is for this reason that I chose to compute returns differently, using the following constructs: I included all publicly traded stocks in each market, or at least those with a market capitalization available for them. I converted all of the market capitalizations into US dollars, just to make them comparable. I aggregated the market capitalizations of all stocks at the end of 2023 and the end of 2024, and computed the percentage change. The results, broken down broadly by geography are in the table below: As you can see, the aggregate market cap globally was up 12.17%, but much of that was the result of a strong US equity market. Continuing a trend that has stretched over the last two decades, investors who tried to globally diversify in 2024 underperformed investors who stayed invested only in the United States.      I do have the percentage changes in market cap, by country, but you should take those results with a grain of salt, since there are countries with just a handful of listings, where the returns are distorted. Looking at countries with at least ten company listings, I have a list of the ten best and worst performing countries in 2024: Argentina's returns in US dollar terms is still high enough to put it on top of the list of best-performing countries in the world in 2024 and Brazil is at the top of the list of worst performing countries, at least in US dollar terms. The Currency Effect     As you can see comparing the local index and dollar returns, the two diverge in some parts of the world, and the reason for the divergence is movements in exchange rates. To cast light on this divergence, I looked at the US dollar's movements against other currencies, using three variants of US dollar indices against emerging market currencies, developed market currencies and broadly against all currencies: FRED The dollar strengthened during 2024, more (10.31%) against emerging market currencies than against developed market currencies (7.66%), and it was up broadly (9.03%).     I am no expert on exchange rates, but learning to deal with different currencies in valuation is a prerequisite to valuing companies. Since I value companies in local currencies, I am faced with the task of estimating risk free rates in dozens of currencies, and the difficulty you face in estimating these rates can vary widely (and be close to impossible in some) across currencies. In general, you can break down risk free estimation, in different currencies, in three groupings, from easiest to most difficult: My process for estimating riskfree rates in a currency starts with a government issuing a long term bond in that currency, and if the government in question has no default risk, it stops there. Thus, the current market interest rate on a long term Swiss government bond, in Swiss Francs, is the risfree rate in that currency. The process gets messier, when there is a long-term, local currency bond that is traded, but the government issuing the bond has default risk. In that case, the default spread on the bond will have to be netted out to get to a riskfree rate in the currency.  There are two key estimation questions that are embedded in this approach to estimating riskfree rates. The first is the assessment of whether there is default risk in a government, and I use a simplistic (and flawed) approach, letting the local currency sovereign rating for the government stand in as the measure; I assume that AAA rated government bonds are default-free, and that any rating below is a indication of default risk. The second is the estimation of the default spread, and in my simplistic approach, I use one of two approaches - a default spread based upon the sovereign rating or a sovereign credit default swap spread. At the start of 2025, there were just about three dozen currencies, where I was able to find local-currency government bonds, and I estimated the riskfree rates in these currencies; Download data At the risk of stating the obvious (and repeating what I have said in earlier posts), there is no such thing as a global riskfree rate, since riskfree rates go with currencies, and riskfree rates vary across currencies, with all or most of the difference attributable to differences in expected inflation. High inflation currencies will have high riskfree rates, low inflation currencies low riskfree rates and deflationary currencies can negative riskfree rates.     It is the recognition that differences in riskfree rates are primarily due to differences in expected inflation that gives us an opening to estimate riskfree rates in currencies without a government bond rate, or even to run a sanity check on the riskfree rates that you get from government bonds. If you start with a riskfree rate in a currency where you can estimate it (say US dollars, Swiss Francs or Euros), all you need to estimate a riskfree rate in another currency is the differential inflation between the two currencies. Thus, if the US treasury bond rate (4.5%) is the riskfree rate in US dollars, and the expected inflation rates in US dollars and Brazilian reals are 2.5% and 7.5% respectively, the riskier rate in Brazilian reals: Riskfree rate in $R = (1+ US 10-year T.Bond Rate) * (1 + Expected inflation rate in $R)/ (1+ Expected inflation rate in US $) - 1 = 1.045 *(1.075/1.025) -1 = 9.60% In approximate terms, this can be written as Riskfree rate in $R = US 10-year T.Bond Rate + (Expected inflation rate in $R) - Expected inflation rate in US $) - 1 = 4.5% - (7.5% - 2.5%) = 9.50% While obtaining an expected inflation rate for the US dollar is easy (you can use the difference between the ten-year US treasury bond rate and the ten-year US TIPs rate), it can be more difficult to obtain this number in Egyptian pounds or in Zimbabwean dollars, but you can get estimates from the IMF or the World Bank.  The Risk Effect     There are emerging markets that have delivered higher returns than developed markets, but in keeping with a core truth in investing and business, these higher returns often go hand-in-hand with higher risk. The logical step in looking across countries is measuring risk in countries, and bringing that risk into your analysis, by incorporating that risk by demanding higher expected returns in riskier countries.     That process of risk analysis and estimating risk premiums starts by understanding why some countries are riskier than others. The answers, to you, may seem obvious, but I find it useful to organize the obvious into buckets for analysis. I will use a picture in posts on country risk before to capture the multitude of factors that go into making some countries riskier than others: To get from these abstractions to country risk measures, I make a lot of compromises, putting pragmatism over purity. While I take a deeper look at the different components of country risk in my annual updates on country risk (with the most recent one from 2024), I will cut to the chase and focus explicitly on my approach to estimating equity risk premiums, using my 2025 data update to illustrate: With this approach, I estimated equity risk premiums, by country, and organized by region, here is what the world looked like, at the start of 2025: Download equity risk premiums by country Note that I attach the implied equity risk premium for the S&P 500 of 4.33% (see my data update 3 from a couple of weeks ago) to all Aaa rated countries (Australia, Canada, Germany etc.) and an augmented premium for countries that do not have Aaa ratings, with the additional country risk premium determined by local currency sovereign ratings.      I am aware of all of the possible flaws in this approach. First, treating the US as default-free is questionable, now that it has threatened default multiple times in the last decade and has lost its Aaa rating with every ratings agency, other than Moody's. That is an easily fixable problem, though, since if you decide to use S&P's AA+ rating for the US, all it would require is that you net out the default spread of 0.40% (for a AA+ rating at the start of 2025) from the US ERP to get a mature market premium of 3.93% (4.33% minus 0.40%). Second, ratings agencies are not always the best assessors of default risk, especially when there are dramatic changes in a country, or when they are biased (towards or against a region). That too has a fix, at least for the roughly 80 countries where there are trade sovereign CDS spreads, and those sovereign CDS spreads can be used instead of the ratings-based spreads for those countries. The Pricing Effect    As an investor, the discussions about past returns and risk may miss the key question in investing, which is pricing. At the right price, you should be willing to buy stocks even in the riskiest countries, and especially so after turbulent (down) years. At the wrong price, even the safest market with great historical returns are bad investments. To assess pricing in markets, you have to scale the market cap to operating metrics, i.e., estimate a multiple, and while easy enough to do, there are some simple rules to follow in pricing.      The first is recognizing that every multiple has a market estimate of value in the numerator, capturing either just equity value (market cap of equity), total firm value (market cap of equity + total debt) or operating asset (enterprise) value (market cap of equity + total debt - cash): Depending on the scalar (revenues, earnings, book value or cash flow), you can compute a variety of multiples, and if you add on the choices on timing for the scaling variables (trailing, current, forward), the choices multiply. To the question of which multiple is best, a much debated topic among analysts, my answer is ambivalent, since you can use any of them in pricing, as long as you ask the right follow-up questions.      To compare how stocks are priced globally, I will use three of these multiples. The first is the price earnings ratio, partly because in spite of all of its faults, it remains the most widely used pricing metric in the world. The second is the polar opposite on the pricing spectrum, which is the enterprise value to sales multiple, where rather than focus on just equity value, I look at operating asset value, and scale it to the broadest of operating metrics, which is revenue. While it takes a lot to get from revenues to earnings, the advantage of using revenues is that it is number least susceptible to accounting gaming, and also the one where you are least likely to lose companies from your sample. (Thousands and thousands of companies in my sample have negative net income, making trailing PE not meaningful, but very few (usually financial service firms) have missing revenues). The third pricing metric I look at is the enterprise value to EBITDA, a multiple that has gone from being lightly used four decades ago to a banking punchline today, where EBITDA represents a rough measure of operating cash flow). With each of these multiples, I make two estimation choices: I stay with trailing values for net income, revenues and EBITDA, because too many of the firms in my 48,000 firm sample have no analysts following them, and hence no forward numbers. I compute two values for each country (region), an aggregated version and the median value. While the latter is simple, i.e., it is the median number across all companies in a country or region, the former is calculated across all companies, by aggregating the values across companies. Thus, the aggregated PE ratio for the United States is 20.51, and it computed by adding up the market capitalizations of all traded US stocks and dividing by the sum of the net income earned by all traded firms, including money losers. Think of it a weighted-average PE, with no sampling bias. With these rules in place, here is what the pricing metrics looked like, by region, at the start of 2025: The perils of investing based just upon pricing ratios should be visible from this table. Two of the cheapest regions of the world to invest in are Latin America and Eastern Europe, but both carry significant risk with them, and the third, Japan, has an aging population and is a low-growth market. The most expensive market in the world is India, and no amount of handwaving about the India story can justify paying 31 times earnings, 3 times revenue and 20 times EBITDA, in the aggregate, for Indian companies. The US and China also fall into the expensive category, trading at much higher levels than the rest of the world, on all three pricing metrics.     Within each of these regions, there are differences across countries, with some priced more richly than others. In the table below, I look at the ten countries, with at least 5 companies listed on their exchanges, that trade at the lowest median trailing PE ratios, and the ten countries that are more expensive using that same metric: Many of the markets are in the world that trade at the lowest multiples of trailing earnings are in Africa. With Latin America, it is a split decisions, where you have two countries (Colombia and Brazil) on the lowest PE list and one (Argentina) on the highest PE list. In some of the countries, there is a divergence between the aggregated version and the trailing PE, with the aggregated PE higher (lower) than the median value, reflecting larger companies that trade at lower (higher) PE ratios than the rest of the market.     Replacing market cap with enterprise value, and net income with revenues, gives you a pricing multiple that lies at the other end of the spectrum, and ranking countries again, based on median EV to sales multiples, here is the list of the ten most expensive and cheapest markets: On an enterprise value to sales basis, you see a couple of Asian countries (Japan and South Korea) make the ten lowest list, but the preponderance of Middle Eastern countries on ten highest lists may just be a reflection of quirks in sample composition (more financial service firms, which have no revenues, in the sample). The Year to come     This week has been a rocky one for global equities, and the trigger for the chaos has come from the United States. The announcements, from the Trump administration, of the intent to impose 25% tariffs on Canada and Mexico may have been delayed, and perhaps may not even come into effect, but it seems, at least to me, a signal that globalization, unstoppable for much of the last four decades, has crested, and that nationalism, in politics and economics, is reemerging.      As macroeconomists are quick to point out, using the Great Depression and Smoot-Hawley's tariffs in the 1930 to illustrate, tariffs are generally not conducive to global economic health, but it is time that they took some responsibility for the backlash against free global trade and commerce. After all, the notion that globalization was good for everyone was sold shamelessly, even though globalization created winners (cities, financial service firms) and losers (urban areas, developed market manufacturing) , and much of what we have seen transpired over the last decade (from Brexit to Trump) can be viewed as part of the backlash. In spite of the purse clutching at the mention of tariffs, they have been part of global trade as long as there has been trade, and they did not go away after the experiences with the depression. I agree that the end game, if tariffs and trade wars become commonplace, will be a less vibrant global economy, but as with any major macroeconomic shocky, there will be winners and losers.      There is, I am sure, a sense of schadenfreude among many in emerging markets, as they watch developed markets start to exhibit the behavior (unpredictable government policy, subservient central banks, breaking of legal and political norms) that emerging markets were critiqued for decades ago, but the truth is that the line between developed and emerging markets has become a hazy one. After the fall of the Iron Curtain, George H.W. Bush (the senior) declared a "new world order", a proclamation turned out to be premature, since the old world order quickly reasserted itself. The political and economic developments of the last decade may signal the arrival of a new world order, though no one in quite sure whether it will be better or worse than the old one.  YouTube Video Data Updates for 2025 Data Update 1 for 2025: The Draw (and Danger) of Data! Data Update 2 for 2025: The Party continued for US Equities Data Update 3 for 2025: The times they are a'changin'! Data Update 4 for 2025: Interest Rates, Inflation and Central Banks! Data Update 5 for 2025: It's a small world, after all! Data Links Riskfree rates, by currency, in January 2025 Equity risk premiums, by country, in January 2025 Pricing ratios, by country, in January 2025

I am going to start this post with a confession that my knowledge of the architecture and mechanics of AI are pedestrian and that there will be things that I don't get right in this post. That said, DeepSeek's abrupt entry into the AI conversation has the potential to change the AI narrative, and as it does, it may also change the storylines for the many companies that have spent the last two years benefiting from the AI hype. I first posted about AI in the context of valuing Nvidia, in June 2023, when there was still uncertainty about whether AI had legs. A little over a year later, in September 2024, that question about AI seemed to have been answered in the affirmative, for most investors, and I posted again after Nvidia had a disappointing earnings report, arguing that it reflected a healthy scaling down of expectations. As talk of AI disrupting jobs and careers also picked up, I also posted a piece on the threat that AI poses for all of us, with its capacity to do our jobs, at low or no cost, and what I saw as the edges I could use to keep my bot at bay. For those of you who have been tracking the market, the AI segment in the market has held its own since September, but even before the last weekend, there were signs that investors were sobering up on not only how big the payoff to AI would be, but how long they would have to wait to get there.  The AI story, before DeepSeek     The AI story has been building for a while, reflecting the convergence of two forces in technology - more computing power, often in smaller and smaller packages, and the accumulation of data, on technology platforms and elsewhere. That said, the AI story broke out to the public on November 30, 2022, when OpenAI launched ChatGPT, and it made its presence felt in homes, schools and businesses almost instantaneously. It is that wide presence in our daily lives that laid the foundations for the AI story, where evangelists sold us on the notion that AI solutions would make our lives easier and take away the portions of our work that we found most burdensome, and that the businesses that provided these solutions would be worth trillions of dollars.     As the number of potential applications of AI proliferated, thus increasing the market for AI products and services, another part of the story was also being put into play. AI was framed as being made possible by the marriage of incredibly powerful computers and deep troves of data, effectively setting the stage for the winners, losers, and wannabes in the story. The first set of companies were perceived as benefiting from building the AI architecture, with the advance spending on this architecture coming from the companies that hoped to be players in the AI product and service markets: Computing Power: In the AI story that was told, the computers that were needed were so powerful that they needed customized chips, more powerful and compact than any made before, and one company (Nvidia), by virtue of its early start and superior chip design capabilities, stood well above the rest. Not only did Nvidia have an 80% market share of the AI chip market, as assessed in 2024, the lead and first-mover advantage that the company possessed would give it a dominant market share, in the much larger AI chip market of the future. Along the way, the the AI story picked up supercomputing companies, as passengers, again on the belief that Ai systems would find a use for them. Power: In the AI story, the coupling of powerful computing and immense data happens in data centers that are power hogs, requiring immense amounts of energy to keep going. Not surprisingly, a whole host of power companies have stepped into the breach, with some increasing capacity entirely to service these data centers. Some of them were new entrants (like Constellation Energy), whereas others were more traditional power companies (Siemens Energy) who saw an opening for growth and profitability in the AI space.  Data: A third beneficiary from the architecture part of the AI story were the cloud businesses, where the big data, collected for the AI systems would get stored. The big tech companies with cloud arms, particularly Microsoft (Azure) and Amazon (AWS) have benefited from that demand, as have other cloud businesses. Since the companies involved in building the AI infrastructure are the ones that are most tangibly (and immediately) benefiting from the AI boom, they are also the companies that have seen the biggest boost in market cap, as the AI story heated up. In the graph, I have picked on a subset of high-profile companies that were part of the AI market euphoria and looked at the consequent increase in their market capitalizations: Using the ChatGPT introduction on November 30, 2022, as the starting point for the AI buzz, in public consciousness and markets, the returns in 2023 and 2024 are a composite (albeit a rough) measure of the benefits that AI has generated for these companies. Note that the biggest percentage winner, at least in this group was Palantir, up 1285% in the last two years, but the biggest winner in absolute terms was Nvidia, which gained almost $ 3 trillion in value in 2023 and 2024.     The investments in that AI architecture were being made, with the expectation that companies that invested in the architecture would be able to eventually profit from developing and selling AI products and services. Since the AI storyline required immense upfront investing in computing power and access to big data, the biggest investors in AI architecture were big tech companies, with Microsoft and Meta being the largest customers for Nvidia chips in 2024. In the table below, I look at the Mag Seven, not inclusive of Nvidia, and examine the returns that they have made in 2023 and 2024: As you can see, the Mag Seven carried the market in the two years, each adding a trillion (or close, in the case of Tesla) dollars in value in the last two years, with some portion of that value attributable to the AI story. With requirements for large investment up front acting as entry barriers, the expectation was these big tech companies would eventually not only be able to develop AI products and services that their customers would want, but charge premium prices (and earn higher margins).     In the picture below, I have tried to capture the essence of AI story, with the potential winners and losers at each stage: There are parts to this story where there is much to be proved, especially on the AI product and service part, and while investors can be accused of becoming excessively exuberant about the story, it is a plausible one. In fact, my most recent (in September 2024) valuation of Nvidia bought into core elements of the story, though I still found it overvalued: Nvidia valuation in September 2024 (Pre DeepSeek) Note that the big AI story plays out in these inputs in multiple places: AI chip market: My September 2024 estimate for the size of the AI chip market was $500 billion, which in turn was justifiable only because the AI product and service market was expected to huge ($3 trillion and beyond). Nvidia market share: In my valuation, I assumed that Nvidia's lead in the AI chip business would give the company a head start, as the business grew, and to the extent that demand is sticky (i.e., once companies start build data centers with Nvidia chips, it would be difficult for them to switch to a competitor), Nvidia would maintain a dominant market share (60%) of the expanded AI chip market. Nvidia margins: Nvidia has had immense pricing power, posting nosebleed-level gross and operating margins, while TSMC (its chip maker) has generated only a fraction of the benefits, and its biggest customers (the big tech companies) have been willing to pay premium prices to get a head start in building their AI architecture. Over time, I assumed that Nvidia would see its margins drop, but even with the drop, their target margin (60%) would resemble those of very successful, software companies, not chip making companies. My concern in September 2024, and in fact for the bulk of the last two years, was not that I had doubts about the core AI story, but that investors were overpaying for the story. That is partly why, I have shed portions of my holdings in Nvidia, selling half my holdings in the summer of 2023 and another quarter in the summer of 2024. The AI Story, after DeepSeek     I teach valuation, and have done so for close to forty years. One reason I enjoy the class is that you are never quite done with a valuation, because life keeps throwing surprises at you. The first session of my undergraduate valuation class was last Wednesday (January 22), and during the course of the class, I talked about how a good valuation connects narrative to numbers, and followed up by noting that even the most well thought through narratives will change over time. I am not sure how much of that message got through to my studentls, but the message was delivered much more effectively by DeepSeek's entry into the AI story over the weekend, and the market shakeup that followed when markets opened on Monday (January 27). A DeepSeek Primer     The DeepSeek story is still being told, and there is much we do not know. For the moment, though, here is what we know. In 2010, Liang Wenfeng, a software engineer, founded DeepSeek as a hedge fund in China, with the intent of using artificial intelligence to make money. Unable to get traction in that endeavor, and facing government hostility on speculative trading, he pivoted in 2023 into AI, putting together a team to create a Chinese competitor to OpenAI. Since the intent was to come up with a product that could be sold at bargain prices, DeepSeek did what disruptors have always done, which is look for an alternate path to the same destination (providing AI products that work). Rather than invest in expensive infrastructure (supercomputers and data centers), DeepSeek used much cheaper, less powerful chips, and instead of using immense amounts of data, created an AI prototype that could work with less data, using rule-based logic to fill in the gap. While there has been chatter about DeepSeek for weeks, it became publicly accessible at the end of last week (ending January 24), and within hours, was drawing rave reviews from people well versed in tech, as it matched beat ChatGPT at many tasks, and even performed better on scientific and math queries.      There are parts of this story that are clearly for public consumption, more side stories than main story,, and it is best to get them out of the way, before looking at the DeepSeek effect. Cost of development: The notion that DeepSeek was developed for just a few million dollars is fantasy, and while there may have been a portion of the development that cost little, the total was probably in the hundreds of millions of dollars and required a lot more resources (including perhaps even Nvidia chips) than the developers are letting on. No matter what the true cost of development is finally revealed to be, it will be a fraction of the money spent by the existing players in building their systems. Performance tests: The tests of DeepSeek versus OpenAI (or Claude and Gemini) suggests that DeepSeek not only holds it own against the establishment, but even outperforms them on some tasks. That is impressive, but the leap that some are making to concede the entire AI product and service market to DeepSeek is unwarranted. There are clearly aspects of the AI products and service business, where the DeepSeek approach (of using less powerful computing and data) will be good enough, but there will be other aspects of the AI business, where the old paradigm of super computing power and vast data will still hold. A Chinese company: The fact that DeepSeek was developed in China throws a political twist into the story that will undoubtedly play a role in how it develops, but the genie is out of the bottle, even if other governments try to stop its adoption. Adding to the noise is the decision by the company to make DeepSeek open-source, effectively allowing others to adapt and build their own versions. Fair or foul: Finally, there has been some news on the legal front, where OpenAI has argued that DeepSeek unlawfully used data that was generated by OpenAI in building their offering, and while part of that lawsuit may just be showboating, it is possible that portions of the story are true and that legal consequences will follow. While we can debate the what's and why's in this story, the market reaction this week to the story has been swift and decisive. I graph the performance of the five AI stocks highlighted in the earlier section, throwing in the Meta and Microsoft for good measure, on a daily basis in 2025. As you can see in this chart, Nvidia Broadcom, Constellation and Vistra have had terrible weeks, losing more than 10% in the last week, but just for perspective, also note that Constellation and Vistra are still up strongly for the year. Meta and Microsoft were unaffected, and so was Palantir, Clearly, the DeepSeek story is playing out differently for different companies in the AI space, but its overall market impact has been substantial, and for the most part, negative.     What is it that makes the DeepSeek story so compelling? First, is the technological aspect of coming up with a product, with far less in resources that the establishment, and I have nothing but admiration for the DeepSeek creators, but the part of the story that stands out is that the they chose not to go with the prevailing narrative (the one where Nvidia chips and huge data bases are a necessity) and instead asked the question of what the end products and services would look like, and whether there was an easier, quicker and cheaper way of getting there. In hindsight, there are probably others who are looking at DeepSeek and wondering why they did not choose the same path, and the answer is that it takes courage to go against the conventional wisdom, especially when, as AI did over the last two years, it sweeps everyone (from tech titans to individual investors) along with its force.     The truth is that even if DeepSeek is stopped through legal or government action or fails to deliver on its promises, what its entry has done to the AI story cannot be undone, since it has broken the prevailing narrative. I would not be surprised if there are a dozen other start-ups, right now, using the DeepSeek playbook to come up with their own lower-cost competitors to prevailing players. Put simply, the AI story's weakest links have been exposed, and if this were the tale about the Emperor's new clothes, the AI emperor is, if not naked, is having a wardrobe malfunction, for all to see. The Story Effect     In this first week, as is to be expected, the response has been anything but reasoned. If you are a voracious reader of financial news (I am not), you have probably seen dozens of “thought pieces” from both technology and market experts claiming to foretell the future, and even among the few that I have read, the views range the spectrum on how DeepSeek changes the AI story.      In my writings on narrative and numbers, where I talk about how every valuation tells a story, I also talk about how stories are dynamic, with a story break representing radical change (where a great story can crash and burn or a small story can break out to become a big one), a story change can be a significant narrative alteration (where a story adds or loses a dimension with big value effects) or a story shift (where the core story remains unchanged, but the parameters can change). Using the pre-DeepSeek story as a starting point, you can classify the narratives on what is coming on the story break/story change/story shift continuum: With all the caveats, including the fact that I am an AI novice, with a deeper understanding of potato chips than computer chips, and that it is early in the game, I am going to take a stand on where in this continuum I see the DeepSeek effect falling. I believe that DeepSeek does change the AI story, by creating two pathways to the AI product and service endgame. On one path that will lead to what I will term the “low intensity” AI market, it has opened the door to lower cost alternatives, in terms of investments in computing power and data, and competitors will flock in. That said, there will remain a segment of the AI market, where the old story will prevail, and the path of massive investments in computer chips and data centers leading to premium AI products and services will be the one that has to be taken.     Note that the entry characteristics for the two paths will also determine the profitability and payoffs from their respective AI product and service markets (that will eventually exist). The “low entry cost” pathway is more likely to lead to commoditization, with lots of competitors and low pricing power, whereas the “high entry cost” path with its requirements for large upfront investment and access to data will create a more restrictive market, with higher priced and more profitable AI products and services. This story leaves me with a judgment call to make about the relative sizes of the markets for the two pathways. I am generalizing, but much of what consumers have seen so far as AI offerings fall into the low cost pathway and I would not be surprised, if that remains true for the most part. The DeepSeek entry has now made it more likely that you and I (as consumers) will see more AI products and services offered to us, at low cost or even for free. There is another segment of the AI products and services market, though, with businesses (or governments) as customers, where significant investments made and refinements will lead to AI products and services, with much higher price points. In this market, I would not be surprised to see networking benefits manifest, where the largest players acquire advantages, leading to winner-take-all markets.      In telling this story, I understand that not only am I going to be wrong, perhaps decisively, but also that it could unravel in record time. I make this leap, not out of arrogance or a misplaced desire to change how you think, but because I own a slice of Nvidia (one quarter of the holding that I had two years ago, but still large enough to make a difference in my portfolio), and I cannot value the company without an AI story in place. That said, the feedback loop remains open, and I will listen not only to alternate opinions but also follow real world developments, in the interests of telling a better story. The Value Effect     Now that my AI story is in the open, I will use it to revisit my valuation of Nvidia, and incorporate my new AI story in that valuation. Even without working through the numbers, it is very difficult to see a scenario where the entry of DeepSeek makes Nvidia a more valuable company, with the biggest change being in the expected size of the AI chip market: table.tableizer-table { font-size: 12px; border: 1px solid #CCC; font-family: Arial, Helvetica, sans-serif; } .tableizer-table td { padding: 4px; margin: 3px; border: 1px solid #CCC; } .tableizer-table th { background-color: #104E8B; color: #FFF; font-weight: bold; } In September 2024 (pre DeepSeek)In January 2025 (post DeepSeek) AI chip market size in 2035$500 billion$300 billion Nvidia's market share60%60% Nvidia's operating margin60%60% Nvidia's risk (cost of capital)10.52% _> 8.49%11.79% -> 8.50% (Higher riskfree rate + higher ERP) With the changes made, and updating the financials to reflect an additional quarter of data,  you can see my Nvidia valuation in the picture below: Nvidia valuation in January 2025 (Post DeepSeek) There are two (unsurprising) results in this valuation. The value per share that I estimate for Nvidia dropped from $87 in September 2024 to $78 in January 2025, much of that change driven by the smaller AI chip market that comes out of the DeepSeek disruption (with the rest of the decline arising for higher riskfree rates and the equity risk premiums). The other is that the stock is overvalued, at its current price of $123 per share, even after the markdown this week. Since I found Nvidia overvalued in September 2024, when the big AI story was still in place, and Nvidia was trading at $109, $14 lower than todays price, estimating a lower value and comparing to a higher price makes it even more over valued..     More generally, the value effect of the DeepSeek disruption will be disparate, more negative for some companies in the AI space than others, and perhaps even positive for a few and I have attempted to capture those effects in the picture below, comparing DeepSeek to a bomb, and looking at the damage zones from the blast: In my view, the damage, in the near and long term, from DeepSeek will be to the businesses that have been the lead players in building the AI architecture. In addition to Nvidia (and its AI chip business), this includes the energy and gas businesses that have benefited from the tens of billions spent on building AI data centers. It is not that they will currently contracts, but that it is likely that you will see a slowing down of commitments to spend money on AI, as companies examine whether they need them. More companies are therefore likely to follow Apple's path of cautious entry than Meta and Microsoft's headfirst dive into the AI businesses. As for the businesses that are aiming for the AI products and services market, the effect will depend upon how much these products and services need data and computing power. If the proposed AI products and services are low-grade, i.e., they are more rule-based and mechanical and less dependent on incorporating intuition and human behavior, the effect of DeepSeek will be significant, with lower costs to entry and a commoditized marketplace, with lower margins and intense competition, If on the other hand, the AI products and services are high grade, i.e,, trying to imitate human decision making in the face of uncertainty, the effects of the DeepSeek entry are likely to be minimal and perhaps even non-existent. Thus, I would expect a business that is working on an AI product for financial accounting to find its business landscape changed more than Palantir, working on complex AI products for the defense department or commercial businesses. There is a grouping of companies, primarily big tech firms with large platforms, like Meta and Microsoft, where there may be buyer’s remorse about money already spent on AI (buying Nvidia chips and building data centers) but the DeepSea disruption may make it easier to develop low-cost, low-tech AI products and services that they can offer their platform users (either for free or at low costs) to keep them in their ecosystems.     When faced with a development that could change the way we live and work, it is natural, especially in the early phases, to give that development a catchy name, and use it as a rationale for investing large amounts (if you are a business) or pushing up what you would pay for the businesses in the space (if you are an investor). In my early piece on AI, I talked about four developments in my lifetime that I would classify as revolutionary – personal computers in the 1980s, the internet in the 1990s, the smartphone in the first decade of the twenty first century and social media in the last decade, and how each of these started as catchall buzzwords, before investors and businesses learned to discriminate. Cisco, AOL and Amazon were all born in the internet era, but they had very different business models, and as the internet matured, faced very different end games. I hope that the DeepSeek entry into the AI narrative, and its disparate effects on different businesses in this space, will lead us to be more focused in our AI conversations. Thus, rather than describe a company as an AI company or describe the AI market as “huge”, we should be more explicit about what part of the AI business a company fits into (architecture, software, data or products/services) and apply the same degree of discrimination when talking about AI markets. If you also buy into my reasoning, you may want to follow up by asking whether the AI offering is more likely to fall into the premium or commoditized grouping. The Bottom Line     My early entry into Nvidia and my holdings of many of the other Mag Seven stocks have allowed me to ride the AI boom, I have remained a skeptic about the product and service side of AI, for much of the last two years. I can attribute that wariness partly to my age, since I cannot think of a single AI offering that has been made to me in the last two years that I would pay a significant additional amount for. I see AI icons on almost everything that I use, from Zoom to Microsoft Word/Powerpoint/Excel to Apple mail. I must admit that they do neat things, including reword emails to not only clean up for mistakes but change the tone, but I can live without those neat add-ons. Since I work in valuation and corporate finance, not a day goes by without someone contacting me about a new AI product or service in the space. Having tried a few out, my response to many of these products and services is that, at least for me, they don’t do enough for me to bother. In many ways, DeepSeek confirms a long-standing suspicion on my part that most AI products and services that we will see, as consumers and even as businesses, fall into the “that’s cute” or “how neat” category, rather than into the “that would change my life”, If that is the case, it has also struck me as overkill to expend tens of billions of dollars building data centers to develop these products, akin to using a sledgehammer to tap a nail into the wall. Every major innovation of the last few decades, has had its reality check, and has emerged the stronger for it, and this may the first of many such reality checks for AI.     I know that much of what I have said here goes against the "happy talk" narrative about AI, emanating from tech titans and business visionaries. I know that Reid Hoffman and Sam Altman believe that AI will be world-changing, in a good way, relieving us of the pain of tasks that are boring and time consuming, and even replacing flawed "human" decisions with be more reasoned AI decisions. They are smart men, but I have two reasons for being cautions. The first is that I have had exposure to smart people in almost every walk of life - smart academics, smart bankers, smart software engineers, smart venture capitalists and yes, even smart regulators - but most of them have had blind spots, perhaps because they hang out with people who think like them. The second, and this perhaps follows from the first, is that I am old enough to have heard this evangelist pitch for a revolutionary change before. In the 1980s, I remember being told that personal computers would eliminate the drudgery of working through ledger sheets with calculators and pencils, but as young financial analysts will tell you today, it has just created a fresh and  perhaps even more soul-sucking drudgery, where monstrously large spreadsheets govern their workdays. In the 1990s, the advocates for the internet painted a picture of the world where access to online information would make us all more informed and wiser, but in hindsight, all it has done is weaken our reasoning muscles (by letting us look up answers online) and made us misinformed. In this century, social media too was born on the promise that it would keep us connected with friends, even if they were thousands of miles away, and happier, because of those connections, but as my good friend, Jonathan Haidt, and others have chronicled, it has left many in its orbit more isolated and less happy than before.  YouTube Video Nvidia Valuations Nvidia valuation in September 2024 (Pre DeepSeek) Nvidia valuation in January 2025 (Post DeepSeek)

It was an interesting year for interest rates in the United States, one in which we got more evidence on the limited power that central banks have to alter the trajectory of market interest rates. We started 2024 with the consensus wisdom that rates would drop during the year, driven by expectations of rate cuts from the Fed. The Fed did keep its end of the bargain, cutting the Fed Funds rate three times during the course of 2024, but the bond markets did not stick with the script, and market interest rates rose during the course of the year. In this post, I will begin by looking at movements in treasury rates, across maturities, during 2024, and the resultant shifts in yield curves. I will follow up by examining changes in corporate bond rates, across the default ratings spectrum, trying to get a measure of how the price of risk in bond markets changed during 2024. Treasury Rates in 2024     Coming into 2024, interest rates had taken a rollicking ride, surging in 2022, as inflation made its come back, before settling in 2023. At the start of 2024, the ten-year treasury rate stood at 3.88%, unchanged from its level a year prior, but the 3-month treasury bill rate had climbed to 5.40%. In the chart below, we look the movement of treasury rates (across maturities) during the course of 2024: Download daily data During the course of 2024, long term treasury rates climbed in the first half of the year, and dropped in the third quarter, before reversing course and increasing in the fourth quarter, with the 10-year rate ending  the year at 4.58%, 0.70% higher than at the start of the year. The 3-month treasury barely budged in the first half of 2024, declined in the third quarter, and diverged from long term rates and continued its decline in the last quarter, to end the year at 4.37%, down 1.03% from the start of the year. I have highlighted the three Fed rate actions, all cuts to the Fed Funds rate, on the chart, and while I will come back to this later in this post, market rates rose after all three.     The divergence between short term and long term rates played out in the yield curve, which started 2024, with a downward slope, but flattened out over the course of the year: Download daily data Writing last year about the yield curve, which was then downward sloping, I argued that notwithstanding prognostications of doom,  it was a poor prediction of recessions. This year, my caution would be to not read too much, at least in terms of forecasted economic growth, into the flattening or even mildly upward sloping yield curve.      The increase in long term  treasury rates during the course of the year was bad news for treasury bond investors, and the increase in the 10-year treasury bond rate during the course of the year translated into an annual return of -1.64% for 2024: With the inflation of 2.75% in 2024 factored in, the real return on the 10-year bond is -4.27%. With the 20-year and 30-year bonds, the losses become larger, as time value works its magic. It is one reason that I argue that any discussion of riskfree rates that does not mention a time horizon is devoid of a key element. Even assuming away default risk, a ten-year treasury is not risk free, with a one time horizon, and a 3-month treasury is definitely not riskfree, if you have a 10-year time horizon. The Drivers of Interest Rates     Over the last two decades, for better or worse, we (as investors, consumers and even economics) seem to have come to accept as a truism the notion that central banks set interest rates. Thus, the answer to questions about past interest rate movements (the low rates between 2008 and 2021, the spike in rates in 2022) as well as to where interest rates will go in the future has been to look to central banking smoke signals and guidance. In this section, I will argue that the interest rates ultimately are driven by macro fundamentals, and that the power of central banks comes from preferential access to data about these fundamentals, their capacity to alter those fundamentals (in good and bad ways) and the credibility that they have to stay the course. Inflation, Real Growth and Intrinsic Riskfree Rates     It is worth noting at the outset that interest rates on borrowing pre-date central banks (the Fed came into being in 1913, whereas bond markets trace their history back to the 1600s), and that lenders and borrowers set rates based upon fundamentals that relate specifically to what the former need to earn to cover  expected inflation and default risk, while earning a rate of return for deferring current consumption (a real interest rate). If you set the abstractions aside, and remove default risk from consideration (because the borrower is default-free), a riskfree interest rate in nominal terms can be viewed, in its simplified form, as the sum of the expected inflation rate and an expected real interest rate: Nominal interest rate = Expected inflation + Expected real interest rate This equation, titled the Fisher Equation, is often part of an introductory economics class, and is often quickly forgotten as you get introduced to more complex (and seemingly powerful) monetary economics lessons. That is a pity, since so much of misunderstanding of interest rates stems from forgetting this equation. I use this equation to derive what I call an "intrinsic riskfree rate", with two simplifying assumptions: Expected inflation: I use the current year's inflation rate as a proxy for expected inflation. Clearly, this is simplistic, since you can have unusual events during a year that cause inflation in that year to spike. (In an alternate calculation, I use an average inflation rate over the last ten years as the expected inflation rate.) Expected real interest rate: In the last two decades, we have been able to observe a real interest rate, at least in the US, using inflation-protected treasury bonds(TIPs). Since I am trying to estimate an intrinsic real interest rate, I use the growth rate in real GDP as my proxy for the real interest rate. That is clearly a stretch when it comes to year-to-year movements, but in the long term, the two should converge. With those simplistic proxies in place, my intrinsic riskfree rate can be computed as follows: Intrinsic riskfree rate = Inflation rate in period t + Real GDP growth rate in period t In the chart below, I compare my estimates of the intrinsic riskfree rate to the observed ten-year treasury bond rate each year: Download data While the match is not perfect, the link between the two is undeniable, and the intrinsic riskfree rate calculations yield results that help counter the stories about how it is the Fed that kept rates low between 2008 and 2021, and caused them to spike in 2022.  While it is true that the Fed became more active (in terms of bond buying, in their quantitative easing phase) in the bond market in the last decade, the low treasury rates between 2009 and 2020 were driven primarily by low inflation and anemic real growth. Put simply, with or without the Fed, rates would have been low during the period. In 2022, the rise in rates was almost entirely driven by rising inflation expectations, with the Fed racing to keep up with that market sentiment. In fact, since 2022, it is the market that seems to be leading the Fed, not the other way around. Entering 2025, the gap between intrinsic and treasury rates has narrowed, as the market consensus settles in on expectations that inflation will stay about the Fed-targeted 2% and that economic activity will be boosted by tax cuts and a business-friendly administration. The Fed Effect     I am not suggesting that central banks don't matter or that they do not affect interest rates, because that would be an overreach, but the questions that I would like to address are about how much of an impact central banks have, and through what channels. To the first question of how much of an impact, I started by looking at the one rate that the Fed does control, the Fed Funds rate, an overnight interbank borrowing rate that nevertheless has resonance for the rest of the market. To get a measure of how the Fed Funds rate has evolved over time, take a look at what the rate has done between 1954 and 2024: As you can see the Fed Funds was effectively zero for a long stretch in the last decade, but has clearly spiked in the last two years. If the Fed sets rates story is right, changes in these rates should cause market set rates to change in the aftermath, and in the graph below, I look at monthly movements in the Fed Funds rate and two treasury rates - the 3-month T.Bill rate and the 10-year T.Bond rate. The good news for the "Fed did it" story is that the Fed rates and treasury rates clearly move in unison, but all this chart shows is that Fed Funds rate move with treasury rates contemporaneously, with no clear indication of whether market rates lead to Fed Funds rates changing, or vice versa. To look at whether the Fed funds leads the rest of the market, I look at the correlation between changes in the Fed Funds rate and changes in treasury rates in subsequent months.  As you can see from this table, the effects of changes in the Fed Funds rate on short term treasuries is positive, and statistically significant, but the relationship between the Fed Funds rate and 10-year treasuries is only 0.08, and barely meets the statistical significance test. In summary, if there is a case to be made that Fed actions move rates, it is far stronger at the short end of the treasury spectrum than at the long end, and with substantial noise in predictive effects. Just as an add on, I reversed the process and looked to see if the change in treasury rates is a good predictor of change in the Fed Funds rate and obtained correlations that look very similar.  In short, the evidence is just as strong for the hypothesis that market interest rates lead the Fed to act, as they are for "Fed as a leader" hypothesis.     As to why the Fed's actions affect market interest rates, it has less to do with the level of the Fed Funds rate and more to do with the market reads into the Fed's actions. Ultimately, a central bank's effect on market interest rates stems from three factors: Information: It is true that the Fed collects substantial data on consumer and business behavior that it can use to make more reasoned judgments about where inflation and real growth are headed than the rest of the market, and its actions often are viewed as a signal of that information. Thus, an unexpected increase in the Fed Funds rate may signal that the Fed sees higher inflation  than the market perceives at the moment, and a big drop in the Fed Funds rates may indicate that it sees the economy weakening at a time when the market may be unaware. Central bank credibility: Implicit in the signaling argument is the belief that the central bank is serious in its intent to keep inflation in check, and that is has enough independence from the government to be able to act accordingly. A central bank that is viewed as a tool for the government will very quickly lose its capacity to affect interest rates, since the market will tend to assume other motives (than fighting inflation) for rate cuts or raises. In fact, a central bank that lowers rates, in the face of high and rising inflation, because it is the politically expedient thing to do may find that market interest move up in response, rather than down. Interest rate level: If the primary mechanism for central banks signaling intent remains the Fed Funds rate (or its equivalent in other markets), with rate rises indicating that the economy/inflation is overheating and rate cuts suggesting the opposite, there is an inherent problem that central banks face, if interest rates fall towards zero. The signaling becomes one sided i.e., rates can be raised to put the economy in check, but there is not much room to cut rates. This, of course, is exactly what the Japanese central bank has faced for three decades, and European and US banks in the last decade, reducing their signal power. The most credible central banks in history, from the Bundesbank in Deutsche Mark Germany to the Fed, after the Volcker years, earned their credibility by sticking with their choices, even in the face of economic disruption and political pushback. That said, in both these instances, central bankers chose to stay in the background, and let their actions speak for themselves. Since 2008, central bankers, perhaps egged on by investors and governments, have become more visible, more active and, in my view, more arrogant, and that, in a strange way, has made their actions less consequential. Put simply, the more the investing world revolves around FOMC meetings and the smoke signals that come out of them, the less these meetings matter to markets.  Forecasting Rates     I am wary of Fed watchers and interest rate savants, who claim to be able to sense movements in rates before they happen for two reasons. First, their track records are so awful that they make soothsayers and tarot card readers look good. Second, unlike a company's earnings or risk, where you can claim to have a differential advantage in estimating it, it is unclear to me what any expert, no matter how credentialed, can bring to the table that gives them an edge in forecasting interest rates. In my valuations, this skepticism about interest rate forecasting plays out in an assumption where I do not try to second guess the bond market and replace current treasury bond rates with fanciful estimates of normalized or forecasted rates. If you look back at my S&P 500 valuation in my second data post for this year, you will see that I left the treasury bond rate at 4.58% (its level at the start of 2025) unchanged through time.      If you feel the urge to play interest forecaster, I do think that it is good practice to make sure that your views on the direction of interest rates are are consistent with the views of inflation and growth you are building into your cash flows. If you buy into my thesis that it is changes in expected inflation and real growth that causes rates to change in interest rates, any forecast of interest rates has be backed up by a story about changing inflation or real growth. Thus, if you forecast that the ten-year treasury rate will rise to 6% over the next two years, you have to follow through and explain whether rising inflation or higher real growth (or both) that is triggering this surge, since that diagnosis have different consequences for value. Higher interest rates driven by higher inflation will generally have neutral effects on value, for companies with pricing power, and negative effects for companies that do not. Higher interest rates precipitated by stronger real growth is more likely to be neutral for the market, since higher earnings (from the stronger economy) can offset the higher rates. The most empty forecasts of interest rates are the ones where the forecaster's only reason for predicting higher or lower rates is central banks, and I am afraid that the discussion of interest rates has become vacuous over the last two decades, as the delusion that the Fed sets interest rates becomes deeply engrained. Corporate Bond Rates in 2024     The corporate bond market gets less attention that the treasury bond market, partly because rates in that market are very much driven by what happens in the treasury market. Last year, as the treasury bond rate rose from 3.88% to 4.58%, it should come as no surprise that corporate bond rates rose as well, but there is information in the rate differences between the two markets. That rate difference, of course, is the default spread, and it will vary across different corporate bonds, based almost entirely on perceived default risk.  Default spread = Corporate bond rate - Treasury bond rate on bond of equal maturity Using bond ratings as measures of default risk, and computing the default spreads for each ratings class, I captured the journey of default spreads during 2024: During 2024, default spreads decreased over the course of the year, for all ratings classes, albeit more for the lowest rated bonds. Using a different lexicon, the price of risk in the bond market decreased during the course of the year, and if you relate that back to my second data update, where I computed a price of risk for equity markets (the equity risk premium), you can see the parallels. In fact, in the graph below, I compare the price of risk in both the equity and bond markets across time: In most years, equity risk premiums and bond default spreads move in the same direction, as was the case in 2024. That should come as little surprise, since the forces that cause investors to spike up premiums (fear) or bid them down (hope and greed) cut across both markets. In fact, lookin a the ratio of the equity risk premium to the default spread, you could argue that equity risk premiums are too high, relative to bond default spreads, and that you should see a narrowing of the difference, either with a lower equity premium (higher stock prices) or a higher default spread on bonds.     The decline of fear in corporate bond markets can be captured on another dimension as well, which is in bond issuances, especially by companies that face high default risk. In the graph below, I look at corporate bond issuance in 2024, broken down into investment grade (BBB or higher) and high yield (less than BBB).  Note that high yield issuances which spiked in 2020 and 2021, peak greed years, almost disappeared in 2022. They made a mild comeback in 2023 and that recovery continued in 2024.      Finally, as companies adjust to a new interest rate environment, where short terms rates are no longer close to zero and long term rates have moved up significantly from the lows they hit before 2022, there are two other big shifts that have occurred, and the table below captures those shifts: First, you will note that after a long stretch, where the percent of bond that were callable declined, they have spiked again. That should come as no surprise, since the option, for a company, to call back a bond is most valuable, when you believe that there is a healthy chance that rates will go down in the future. When corporates could borrow money at 3%, long term, they clearly attached a lower likelihood to a rate decline, but as rates have risen, companies are rediscovering the value of having a  calculability option. Second, the percent of bond issuances with floating rate debt has also surged over the last three years, again indicating that when rates are low, companies were inclined to lock them in for the long term with fixed rate issuances, but at the higher rates of today,  they are more willing to let those rates float, hoping for lower rates in future years. In Conclusion     I spend much of my time in the equity market, valuing companies and assessing risk. I must confess that I find the bond market far less interesting, since so much of the focus is on the downside, and while I am glad that there are other people who care about that, I prefer to operate in a space where there there is more uncertainty. That said, though, I dabble in bond markets because what happens in those markets, unlike what happens in Las Vegas, does not stay in bond markets. The spillover effects into equity markets can be substantial, and in some cases, devastating. In my posts looking back at 2022, I noted how a record bad year for bond markets, as both treasury and corporate bonds took a beating for the ages, very quickly found its ways into stocks, dragging the market down. On that count, bond markets had a quiet year in 2024, but they may be overdue for a clean up. YouTube Data Updates for 2025 Data Update 1 for 2025: The Draw (and Danger) of Data! Data Update 2 for 2025: The Party continued for US Equities Data Update 3 for 2025: The times they are a'changin'! Data Update 4 for 2025: Interest Rates, Inflation and Central Banks! Data Links Intrinsic risk free rates and Nominal interest rates Bond Default Spreads and Equity Risk Premiums

In my first two data posts for 2025, I looked at the strong year that US equities had in 2024, but a very good year for the overall market does not always translate into equivalent returns across segments of the market. In this post, I will remain focused on US equities, but I will break them into groupings, looking for differences. I first classify US stocks by sector, to see return variations across different industry groupings. I follow up by looking at companies broken down by market capitalization,  with an eye on whether the much-vaunted small cap premium has made a comeback. In the process, I also look how much the market owes its winnings to its biggest companies, with the Mag Seven coming under the microscope. In the next section, I  look at stock returns for companies in different price to book deciles, in a simplistic assessment of the value premium. With both the size and value premiums, I will extend my assessment over time to see how (and why) these premiums have changed, with lessons for analysts and investors. In the final section, I look at companies categorized by price momentum coming into 2024, to track whether winning stocks in 2023 were more likely to be winners or losers in 2024. US Stocks, by Sector (and Industry)        It is true that you very seldom see a market advance that is balanced across sectors and industries. This market (US stocks in 2024) spread its winnings across sectors disproportionately, with four sectors - technology, communication services, consumer discretionary and financials - delivering returns in excess of 20% in 2024, and three sectors - health care, materials and real estate delivering returns close to zero: Sector Returns - Historical (with $ changes in millions) The performance of technology stocks collectively becomes even more impressive, when you look at the fact that they added almost $4.63 trillion in market cap just in 2024, and that over the last five (ten) years, the sector has added $11.3 trillion ($13.6 trillion) in market cap.     I  break the sectors down into 93 industries, to get a finer layer of detail, and there again there are vast differences between winning and losing industry groups, based upon stock price performance in 2024: $ changes in millions While most of the industries on the worst-performing list represent old economy companies (steel, chemicals, rubber & tires), green energy finds itself on the list as well, perhaps because the "virtue trade" (where impact and socially conscious investors bought these companies for their greenness, rather than business models) lost its heft. The top two performers, in 2024, on the best performing industry list, semiconductors and auto & truck, owe much of their overall performance to super-performers in each one (Nvidia with semiconductors and Tesla with auto & truck), but airline companies also had a good year, though it may be premature to conclude that they have finally found working business models that can deliver profitability on a continuous basis. US Stocks, by Market Cap     For much of the last century, the conventional wisdom has been that small companies, with size measured by market cap, deliver higher returns than larger companies, on a risk-adjusted basis, with the debate being about whether that was because the risk measures were flawed or because small cap stocks were superior investments. That "small cap premium" has found its way into valuation practitioners playbooks, manifesting as an augmentation (of between 3-5%) on the cost of equity of small companies.  To get a sense of how market capitalization was related to returns, I classified all publicly traded US companies, by market cap, and looked at their returns in 2024. The returns across deciles are volatile, and while the lowest deciles in terms of market cap deliver higher percent returns, looking at the top and bottom halves of the market, in terms of market cap, you can see that there is not much setting apart the two groups.      To make an assessment of how the performance of small cap stocks in 2024 falls in the historical spectrum, I drew on Ken French's research return data, one of my favorite data sources, and looked at the small cap premium as the difference in compounded annual returns between the lowest and highest deciles of companies, in terms of market cap: My small cap premium spreadsheet, based on Ken French data In this graph, you can see the basis for the small cap premium, but only if go back all the way to 1927, and even with that extended time period, it is far stronger with equally weighted than with value weighted returns; the 1927-2024 small cap premium is 2.07% with value-weighted returns and 6.69% in  equally weighted terms. It should be noted that even its heyday, the small cap premium had some disconcerting features including the facts that almost of it was earned in one month (January) of each year, and that it was sensitive to starting and end points for annual data, with smaller premium in mid-year starting points. To see how dependent this premium is on the front end of the time period, I estimated the small cap premium with different starting years in the graph (and the table), and as you can see the small cap premium drops to zero with any time period that starts in 1970 and beyond. In fact, the small cap premium has become a large cap premium for much of this century, with small cap returns lagging large cap returns by about 4-4.5% in the last 20 years.     The market skew towards large cap companies can be seen even more dramatically, if you break stocks down by percentile, based upon market cap, and look at how much of the increase in market cap in US equities is accounted for by different percentile groupings: US Stocks: Market Cap Change Breakdown Looking across 6000 publicly traded stocks in 2024, the top percentile (about 60 stocks) accounted for 74% of the increase in market cap, and the top ten percent of all stocks delivered 94% of the change in total market capitalization.     Zeroing in even further and looking at the biggest companies in the top percentile, the Mag Seven, the concentration of winners at the very top is clear: $ changes in millions In 2024, seven companies (Apple, Amazon, Meta, Alphabet, Microsoft, Nvidia and Tesla) increased in market cap by $5.6 trillion, almost of the entire market's gain for the year. While it is not uncommon for stock market returns to be delivered by a few winners at the top,  with the Mag Seven, the domination extends over a decade, and in the last ten years (2014-2024), these seven companies have added $15.8 trillion in market cap, about 40% of the increase in market capitalization across all US stocks over the decade.     For years now, some investors have bet on a reversal in this trend line, with small cap stocks coming back in favor, and these investors have lagged the market badly. To get a better handle on why large cap stocks have acquired a dominant role, in markets, I look at three explanations that I have seen offered for the phenomenon: Momentum story: Momentum has always been a strong force in markets, in both directions, with price increases in stocks (decreases) followed by more price increases (decreases). In effect, winning stocks continue to win, drawing in new funds and investors, but when these same stocks start losing, the same process plays out in reverse. A reasonable argument can be made that increasing access to information and easing trading, for both individual and institutional investing, with a boost from social media, has increased momentum, and thus the stock prices of large cap stocks. The dark side of this story, though, is that if the momentum ever shifted, these large cap stocks could lose trillions in value. Passive investing: Over the last two decades, passive investing (in the form of index funds and ETFs) has taken market share from active investors, accounting for close to  50% of all invested funds in 2024. That shift has been driven by active investing underperformance and a surge in passive investing vehicles that are accessible to all investors. Since many passive investing vehicles hold all of the stocks in the index in proportion to their market cap, there presence and growth creates fund flows into large cap stocks and keeps their prices elevated. Here again, the dark side is that if fund flows reverse and became negative, i.e., investors start pulling money out of markets, large cap stocks will be disproportionately hurt. Industry economics: In writing about the disruption unleashed by tech start-ups, especially in the last two decades, I have noted the these disruptors have changed industry economics in many established businesses, replacing splintered, dispersed competition with consolidation. Thus, Meta and Alphabet now have dominant market shares of the advertising business, just as Uber, Lyft and Grab have consolidated the car service business. As industries consolidate, we are likely to see them dominated by a few, big winners, which will play out in the stock market as well. It is possible that antitrust laws and regulatory authorities will try to put constraints on these biggest winners, but as I noted in my post on the topic, it will not be easy. In my view, the small cap premium is not coming back, and given that it has been invisible for five decades now, the only explanation for why appraisers and analysts hold on to it is inertia. That said, the large cap premium that we have seen in the last two decades, was businesses have transitioned from splintered to consolidated structure, will also fade. Where does that leave us? Picking a company to invest in, based upon its market capitalization, will be, at best, a neutral strategy, and that should surprise no one. The Value Premium?     Just as the small cap premium acquired standing as conventional wisdom in the twentieth century, the data and research also indicated that stocks that trade at low price to book ratios earned higher returns that stocks that trade at high price to book ratios, in what was labeled as the value premium. As with the size premium, low price to book (value) stocks have struggled to deliver in the twenty first century, and as with the small size premium, investors have waited for it to return. To see how stocks in different price to book classes performed in 2024, I looked at returns in 2024, for all US stocks, broken down into price to book deciles: Deciles created based on price to book ratios at start of 2024 In 2024, at least, it was the companies in the top decile (highest price to book ratios) that delivered the best returns in 2024, and stocks in the lowest decile lagged the market.      Here again, Ken French's data is indispensable in gaining historical perspective, as I looked the difference in annual returns between the top decile and bottom decile of stocks, classified by price to book, going back to 1927: My value premium spreadsheet, based on Ken French data In this graph, I am computing the premium earned by low price to book stocks, in the US, with different starting points. Thus, if you go back to 1927 and look at returns on the lowest and highest deciles, the lowest decile earned an annual premium of 2.43%. That premium remains positive until you get to about 1990, when it switches signs; the lowest price to book stocks have earned 0.87% less annually between 1990 and 2024, than the highest price to book stocks. As was the case with the small cap premium, the premium earned by low price to book stocks over high price to book stocks has faded over time, spending more time in negative territory in the last 20 years, than positive.      Value investors, or at least the ones that use the conventional proxies for cheapness (low price to book or low PE ratios), have felt the effects, significantly under performing the market for much of the last two decades. While some of them still hold on to the hope that this is just a phase that will reverse, there are three fundamentals at play that may indicate that the low price to book premium will not be back, at least on a sustained basis: Price to book ≠ Value: It is true that using low price to book as an indicator of value is simplistic, and that there are multiple other factors (good management, earnings quality, moats) to consider before making a value judgment. It is also true that as the market's center of gravity has shifted towards companies with intangible assets, the troubles that accountants have had in putting a number on intangible asset investments has made book value less and less meaningful at companies, making it a poorer and poorer indicator of what a company's assets are worth. Momentum: In markets, the returns to value investing has generally moved inversely with the strength of momentum. Thus, the same forces that have strengthened the power of momentum, that we noted in the context of the fading of the small cap premium, have diluted the power  of value investing. Structural Shifts: At the heart of the premium earned by low price to book ratios is mean reversion, with much of the high returns earned by these stocks coming from moving towards the average (price to book) over time. While that worked in the twentieth century, when the US was the most mean-reverting and predictable market/economy of all time, it has lost its power as disruption and globalization have weakened mean reversion. So, what does this mean for the future? I see no payoff in investing in low price to book stocks and waiting for the value premium to return. As with market cap, I believe that the value effect will become volatile, with low price to book stocks winning in some years and high price to book stocks in others, and investing in one or another of these groups, just on the basis of their price to book ratios, will no longer deliver excess returns.     Since the fading of the small cap and value premiums can be traced at least partially to the strengthening of momentum, as a market force, I looked at the interplay between momentum and stock returns, by breaking companies into deciles, based upon stock price performance in the previous year (2023), and looking at returns in 2024: Deciles formed on percentage returns in 2023 As you can see, barring the bottom decile, which includes the biggest losers of 2023, where there was a strong bounce back (albeit less in dollar terms, than in percent), there was a strong momentum effect in 2024, with the biggest winners from last year (2023) continuing to win in 2024. In short, momentum continued its dominance in 2024, good news for traders who make money in its tailwinds, with the caveat that momentum is a fickle force, and that 2025 may be the year where it reverses. Implications     The US equity market in 2024 followed a pathway that has become familiar to investor in the last decade, with large companies, many with a tech focus, carried the market, and traditional strategies that delivered higher returns, such as investing in small cap or low price to book stocks, faltered. This is not a passing phase, and reflects the market coming to terms with a changed economic order and investor behavior. There are lessons from the year for almost everyone in the process, from investors to traders to corporate executive and regulators: For investors: I have said some harsh things about active investing, as practiced today, since much of it is based upon history and mean reversion. A mutual fund manager who screens stocks for low PE ratios and high growth, while demanding a hefty management fee, deserves to be replaced by an ETF or index fund, and that displacement will continue, pruning the active management population. For active investors who hold on to the hope that quant strategies or AI will let them rediscover their mojo, I am afraid that disappointment is awaiting them. For traders: Traders live and die on momentum, and as market momentum continues to get stronger, making money will look easy, until momentum shifts. Coming off a year like 2024, where chasing momentum would have delivered market-beating returns, the market may be setting up traders for a takedown. It may be time for traders to revisit and refine their skills at detecting market momentum shifts. For companies: Companies that measure their success through stock market returns may find that the market price has become a noisier judge of their actions. Thus, a company that takes a value destructive path that feeds into momentum may find the market rewarding it with a higher price, but it is playing a dangerous game that could turn against it.  For regulators: With momentum comes volatility and corrections, as momentum shifts, and those corrections will cause many to lose money, and for some, perhaps even their life savings. Regulators will feel the pressure to step in and protect these investors from their own mistakes, but in my view, it will be futile. In the markets that we inhabit, literally any investment can be an instrument for speculation. After all, Gamestop and AMC were fairly stolid stocks until they attracted the meme crowd, and Microstrategy, once a technology firm, has become almost entirely a Bitcoin play.  I recently watched Timothy Chalamet play Bob Dylan in the movie, A Complete Unknown,  and I was reminded of one of my favorite Dylan tunes, "The times they are a-changin".  I started my investing in the 1980s, in a very different market and time, and while I have not changed my investing principles, I have had to modify and adapt them to reflect a changed market environment. You may not agree with my view that both the small cap and value premiums are in our past, but it behooves you to question their existence.  YouTube Video Data Updates for 2025 Data Update 1 for 2025: The Draw (and Danger) of Data! Data Update 2 for 2025: The Party continued for US Equities Data Update 3 for 2025: The times they are a'changin'! Datasets My small cap premium calculator (based on Ken French data) My value premium calculator (based on Ken French data)

In my last post, I noted that the US has extended its dominance of global equities in recent years, increasing its share of market capitalization from 42% in at the start of 2023 to 44% at the start of 2024 to 49% at the start of 2025. That rise was driven by a surge in US equity values during 2024, with the S&P 500 delivering returns of close to 25%, all the more impressive, given that the index delivered returns in excess of 26% in 2023. In this post, I will zero in on US equities, in the aggregate, first by looking at month-by-month returns during 2024, and then putting their performance in the last two years in a historical context. I will follow up by trying to judge where markets stand at the start of 2025, starting with PE ratios, moving on to earnings yields and ending with a valuation of the index. US Equities in 2024     Entering 2024, there was trepidation about where stocks would go during the year especially coming off a a strong bounce back year in 2023, and there remained real concerns about inflation and a recession. The hopeful note was that the Fed would lower the Fed Funds rate during the course of the year, triggering (at least in the minds of Fed watchers) lower interest rates across the yield curve, Clearly, the market not only fought through those concerns, but did so in the face of rising treasury rates, especially at the long end of the spectrum.      While the market was up strongly for the year, it is worth remembering that the there were months during 2024, where the market looked shaky, as can be seen in the month to month returns on the S&P 500 during the course of 2025: The market’s weakest month was April 2025, and it ended the year or a weak note, down 2.50% in December. Overall, though the index was up 23.31% for the year, and adding the dividend yield of 1.57% (based upon the expected dividends for 2025 and the index at the start of the years) yields a total return 24.88% for the year: As is almost always the case, the bulk of the returns from equity came from price appreciation, with the caveat that the dividend yield portion has shrunk over the last few decades in the United States. Historical Context     To assess stock returns in 2024, it makes sense to step back and put the year's performance into historical perspective. In the graph below, I look at returns (inclusive of dividends) on the S&P 500 every year from 1928 to 2024.  Download historical data Across the 97 years that I have estimated annual returns, stocks have had their ups and downs, delivering positive returns in 71 years and negative returns in the other 26 years. The worst year in history was 1931, with stocks returning -43.84%, and the best year was 1954, when the annual return was 52.56%. If you wanted to pick a benchmark to compare annual returns to pass judgment on whether a year was above or below average, you can can go with either the annual return (11.79%) or the median return (14.82%) across the entire time period.     Looking at the 24.88% return in 2024 in terms of rankings, it ranks as the 27th best year across the last 97 years, indicating that while it was a good year, there have been far better years for US stocks. Combining 2023 and 2024 returns yield a cumulative a two-year return for the S&P 500 of 57.42%, making it one the ten best two-year periods in US market history.      The riskless alternative to investing in US stocks during this period, in US dollar terms, are US treasuries, and in 2024, that contest was won, hands down, by US equities: Equity risk premium earned in 2024, over 3-month  treasury bills  = Return on stocks - Return on 3-month treasuries (averaged over 2024)  = 24.88% -4.97% = 19.91% Equity risk premium earned in 2024, over 10-year treasuries = Return on stocks - Return on 10-year treasury = 24.88% -(-1.64%) = 26.52% The ten-year treasury return was negative, because treasury bond rates rose during 2024.      Equity risk premiums are volatile over time, and averaging them makes sense, and in the table below, I look at the premium that stocks have earned over treasury bills and treasury bonds, going back to 1928, using both simple averages (of the returns each year) and geometric averages (reflecting the compounding effect): Download historical data These returns are nominal returns, and inflation would have taken a bite out of returns each year. Computing the returns in real terms, by taking out inflation in each year from that year's returns, and recomputing the equity risk premiums: Download historical data Note that the equity risk premiums move only slightly, because inflation finds its way into both stock and treasury returns.     Many valuation practitioners use these historical averages, when forecasting equity risk premiums in the future, but it is a practice that deserves scrutiny, partly because it is backward looking (with the expectation that things will revert back to the way they used to be), but mostly because the estimates that you get for the equity risk premium have significant error terms (see standard errors listed below the estimates in the table). Thus, if are using the average equity risk premium for the last 97 years of 5.44% (7.00%), i.e., the arithmetic or geometric averages, it behooves you to also inform users that the standard error of 2.12% will create a range of about 4% on either side of the estimate. Pricing Questions     Coming into 2025, investors are right to be trepidatious, for many reasons, but mostly because we are coming off two extraordinarily good years for the market, and a correction seems due. That is, however, a poor basis for market timing, because stock market history is full of examples to the contrary. There are other metrics, though, which are signaling danger, and in this section, I will wrestle with what they tell us about stocks in 2025. PE ratios and Earnings Yields     Even as we get new and updated pricing metrics, it is undeniable that the most widely used metric of stock market cheapness or expensiveness is the price earnings ratio, albeit with variations in the earning number that goes into the denominator on timing (current, last 12 months or trailing or next 12 month of forward), share count (diluted, primary) and measurement (ordinary or extraordinary). In the graph below, I focus on trailing earnings for all companies in the S&P 500 and compute the aggregated PE ratio for the index to be 24.16 at the start of 2025, higher than the average value for that ratio in every decade going back to 1970.  Download data Just for completeness, I compute two other variants of the PE, the first using average earnings over the previous ten years (normalized) and the second using the average earnings over the last ten years, adjusted for inflation (CAPE or Shiller PE). At the start of 2025, the normalized PE and CAPE also come in at well above historical norms.     If I have terrified you with the PE story, and you have undoubtedly heard variants of this story from market experts and strategists for much of the last decade, I would hasten to add that investing on that basis would have kept you out of stocks for much of the last ten years, with catastrophic consequences for your portfolio. For some of this period, at least, you could justify the higher PE ratios with much lower treasury rates than historic norms,, and one way to see this is to compare the earnings yield, i.e., the inverse of the PE ratio, with the treasury yields, which is what I have done in the graph below: Download data If you compare the earnings yield to the ten-year treasury rate, you can see that for much of the last decade, going into 2022, the earnings yield, while low, was in excess of the ten-year rate. As rates have risen, though, the difference has narrowed, and at the start of 2025, the earnings yield exceeded the treasury rate. If you see market strategists or journalists talking about negative equity risk premiums, this (the difference between the earnings yield and the treasury rate) is the number that they are referencing.     At this stage, you may be ready to bail on stocks, but I have one final card to play. In a post in 2023, I talked about equity risk premiums, and the implicit assumptions that you make when you use the earning to price ratio as your measure of the expected return on stocks. It works only if you make one of two assumptions: That there will be no growth in earnings in the future, i.e., you will earn last year's earnings every year in perpetuity, making stocks into glorified bonds.  In a more subtle variants, there will be growth, but that growth will come from investments that earn returns equal to the cost of equity. The problem with both assumptions is that they are in conflict with the data. First, the earnings on the S&P 500 companies has increased 6.58% a year between 2000 and 2024, making the no-growth assumption a non-started. Second, the return on equity for the S&P 500 companies was 20.61% in 2023, and has averaged 16.38% since 2000, both numbers well in excess of the cost of equity.     So, what is the alternative? Starting 30 years ago, I began estimating a more complete expected return on stocks, using the S&P 500, with the level of the index standing in for the price you pay for stocks, and expected earnings and cash flows, based upon consensus estimates of earnings and cash payout ratios. I solve for an internal rate of return for stocks, based upon these expected cash flows: The expected return from this approach will be different from the earnings to price ratio because it incorporate expected growth and changes in cash flow patterns. The critique that this approach requires assumptions about the future (growth and cash flows) is disingenuous, since the earnings yield approach makes assumptions about both as well (no growth or no excess returns), and I will wager that the full ERP approach is on more defensible ground than the earning yield approach.      Using this approach at the start of 2025 to the S&P 500, I back out an implied expect return of 8.91% for the index, and an implied equity risk premium of 4.33% (obtained by netting out the ten-year bond rate on Jan 1, 2025, of 4.58%): Implied ERP calculation in 2025 You are welcome to take issue with the number that I use there, lowering the growth rates for the future or changing the assumptions about payout. That is a healthy debate, and one that provides far more room for nuance that looking at the earnings yield.         How does an implied equity risk premium play out in market level arguments? Every argument about markets (from them being in a bubble to basement level bargains) can be restated in terms of the equity risk premium. If you believe that the equity risk premium today (4.33%) is too low, you are, in effect, stating that stocks are overvalued, and if you view it as too high, you are taking the opposite position. If you are not in the market timing business, you take the current premium as a fair premium, and move on. To provide perspective on the ERP at the start of 2025, take a look at this graph, that lists implied ERP at the start of each year going back to 1960: Historical implied ERP There is something here for almost point of view. If you are sanguine about stock market levels, you could point to the current premium (4.33%) being close to the historical average across the entire time period (4.25%). If you believe that stocks are over priced, you may base that on the current premium being lower than the average since 2005. I will not hide behind the "one hand, other hand" dance that so many strategists do. I think that we face significant volatility (inflation, tariffs, war) in the year to come, and I would be more comfortable with a higher ERP. At the same time, I don't fall into the bubble crowd, since the ERP is not 2%, as it was at the end of 1999.  Valuation Questions     Pulling together the disparate strands that are part of this post, I valued the index at the start of 2025, using the earnings expectations from analysts as the forecasted earnings for 2025 and 2026, before lowering growth rates to match the risk free rate in 2029. As the growth rates changes, I also adjust the payout ratios, given the return on equity for the S&P 500 companies: Download spreadsheet With the assumption that the equity risk premium will climb back to 4.5%, higher than the average for the 1960-2024 period, but lower than the post-2008 average, the value that I get for the index is about 5260, about 12% lower than the index at the start of the year. Note that this is a value for the index today, and if you wanted to adopt the market strategist approach of forecasting where the index will be a year from now, you would have to grow the value at the price appreciation portion (about 7.5%) of the expected return (which is 9.08%).     As I see it, there are two major dangers that lurk, with the first being higher inflation (translating into higher treasury rates) and the second being a market crisis that will push up the equity risk premium, since with those pieces in play, the index becomes much more significantly over valued. From an earnings perspective, the risk is that future earnings will come in well below expectations, either because the economy slows or because of trade frictions. Rather than wring my hands about these uncertainties, I fell back on a tool that I use when confronted with change, which is a simulation: Crystal Ball used for simulations While the base case conclusion that the market is overvalued stays intact, not surprising since my distributions for the input variables were centered on my base assumptions, there is a far richer set of output. Put simply, at today's price levels, there is an 80% chance that stocks are overvalued and only a 20% chance that they are undervalued. That said, though, if you are bullish, I can see a pathway to getting to a higher value, with higher earnings, lower interest rates and a continued decline in the equity risk premium. Conversely, you are bearish, I understand your point of view, especially if you see earnings shocks (from a recession or a tariff war), rising inflation or a market crisis coming up.     I don't dish out market advice, and as one whose market timing skills are questionable, you should not take my (or anyone else's) assessments at face value, especially heading into a year, where change will be the byword. It is possible that lower taxes and less regulation may cause to come in higher than expected, and that global investment fund flows will keep interest rates and equity risk premiums low. My advice is that you download the valuation spreadsheet, change the inputs to reflect your views of the world, and value the index yourself. Good investing requires taking ownership of the decisions and judgments you make, and I am glad to provide tools that help you in that process. YouTube Video Data Updates for 2025 Data Update 1 for 2025: The Draw (and Danger) of Data! Data Update 2 for 2025: The Party continued for US Equities Datasets Historical returns on stocks: https://pages.stern.nyu.edu/~adamodar/pc/datasets/histretSP.xlsx Historical implied ERP: https://pages.stern.nyu.edu/~adamodar/pc/datasets/histimpl.xls  PE ratios for the S&P 500: https://pages.stern.nyu.edu/~adamodar/pc/PEforS&P500updatedJan25.xlsx Spreadsheets  Implied ERP at the start of 2025: https://pages.stern.nyu.edu/~adamodar/pc/implprem/ERPJan25.xlsx Valuation of the index on Jan 1, 2025: https://pages.stern.nyu.edu/~adamodar/pc/blog/S&PValueJan25.xlsx