Showing posts with label Price of Risk. Show all posts
Showing posts with label Price of Risk. Show all posts

Wednesday, April 1, 2026

Oil, War and the Global Economy: The Market's Narrative in March 2026

    Markets play an expectations game, and in March 2026, we saw the process play out, with all of its upsides and downsides. The month started with a war in the Middle East, which quickly percolated into soaring oil prices and dropping stock prices, but the overwhelming factor was uncertainty about almost every dimension of the war - how long it would last, what permanent changes to oil prices would emerge as a consequence and how global governments and economies would respond to these changes. As we reach the end of the month, rather than getting answers, we face more questions, and not surprisingly, markets are volatile, not just on a day-to-day basis, but in intraday trading, driven as much by rumors and conjecture, as by facts. In keeping with my view that it is during periods of maximal uncertainty that you need perspective and to back to basics, I will focus my attention on market behavior in March, and what we can learn from that behavior, as a precursor for the months to come. 

The Market Narrative in March
    We live in an age of commentary, as self-proclaimed experts offer prognostications, half-baked or otherwise, about what is to come, and the Iran war, with its mix of politics, economics and religion baked in,, has drawn a large and extremely diverse set of expert forecasts. Given the strong priors (about Iran and Trump) that many of these experts bring to the game, it should not be surprising that their views about how the war will play out and the effect on markets is driven by those priors. It is up to markets to reconcile these contradictory perspectives, and come to consensus, and I will try to extract from market behavior what the market narrative is, leading into April 2026, with the recognition that it could be wrong and change overnight in good and bad ways. That said, over the last decade, I have learned that the market is far better at making sense of complexity and uncertainty than experts are, and it behooves us therefore to listen to what it is saying.

The Oil Price Shock
    As with almost every event in the middle east, the effects of the Iran War played out first in oil prices, and oil has been the lead player in March, surging and volatile, but with disparate impacts even within that market. In the graph below, I look at spot prices on Brent Crude and West Texas Intermediate (WTI) during March:


Both Brent and WTI crude oil saw prices increase in March, but with the price of Brent rising 49.9% and WTI rising 48.6% during March, the difference between the two almost doubled during the second half of the month. That divergence reflects the two-fold effect of the war on oil supply, with the first being the shuttering of oil production in the Gulf States and the second being the effecting throttling of ship traffic through the Strait of Hormuz, a key passageway for Middle Eastern oil to Asia and Europe. While both factors push up oil prices, oil and gas production in the US, the largest oil producer in 2025 (producing 13.58 million barrels or 16% of the total), was less affected by the Hormuz closing and supply chain issues, explaining the increasing price divergence mid-month.
    There was another tea leaf to read, and it came from watching oil futures prices. In the graph below, I compare the spot prices to Brent crude to June and December futures contracts prices:


While spot and futures prices have both risen in March, the latter have gone up less, indicating that, at least for the moment, the market sees the interruptions in oil supply as more temporary than permanent, though the market does see a lasting impact even in that optimistic scenario, with December futures up almost 25% over the pre-war level.

Inflation, Interest Rates and the Economy
    The creation of OPEC and the oil price embargo in the 1970s and the subsequent inflation spiral in the 1970s is now part of market legend, and the interlude in 2022, when the Russian invasion of Ukraine, and the subsequent sanctioning of Russian oil, caused a spike in inflation rates, has made investors wary. While the effects on gasoline prices are in the news, it is one item in the inflation basket, and it is unclear still how much higher oil prices will affect inflation for the rest of the year and perhaps into next year. While we wait for the actual inflation numbers to come out, markets don't have that luxury and the early and perhaps best indicator of market expectations on inflation are showing up in interest rates. The graph below looks at 3-month and 10-year US treasuries over the course of March 2026:


The 3-month treasury bill rate has barely budged over the month, moving from 3.67% on February 27, 2026 to 3.70% on March 31, 2026, but the ten-year bond rate saw a much bigger increase from 3.97% on February 27, 2026, to 4.30% on March 31, 2026. The biggest increases in rates are in the intermediate maturities, with the 2-year and 5-year rates rising by 0.41% over the course of the month. If you view interest rates, as I do, as driven by expected inflation and expected real growth, the most plausible reading is that the market sees an increase in inflation that is persistent. If you are a Fed-watcher, though, your reading may be that the rise in oil prices has tied the hands of the Fed, lowering the likelihood that the Fed Funds rate will be cut in the coming months, but that would leave you with a puzzle to resolve. Since the Fed Funds rate, an overnight bank borrowing rate, has its biggest impact on the short end of the maturity spectrum, how do you explain the fact that short term rates have not changed much?
    The increase in interest rates is not just specific to the US, with rises in rates across other currencies, as you can see in this graph of ten-year Euro, Yen and Yuan rates:

The Japanese Yen and Euro rates are up significantly over the month, but the Yuan rate has seen no change in March 2026. Staying with the market narrative, this indicates higher inflation across countries and currencies.
    While there are many who are speculating on what higher inflation and oil prices will do to the economy, and investment banks and data services (See Moody'sGoldman Sachs) have been rushing to update their forecasts for the US economy, the market has not been in as much of a rush to make the judgment. The economy was showing signs of fatigue coming into March 2026, with anemic growth and employment numbers, and it is possible that the oil price shock will tip it over into a recession.

The Price of Risk
    The heightened uncertainty generated by war and its consequences has played its way out not just in oil prices and treasury rates, but in the prices that investors charge for risk. In a month where the clash between greed and risk took front stage, with the balance shifting often on a minute-by-minute basis during the trading day, we also see increases in the price that investors charge for taking risk in both equity and bond markets. In the equity market, that price of risk is the equity risk premium, a topic that I talked about extensively in this post and paper, with the argument that a good measure of this risk premium will be forward-looking and dynamic. My implied equity risk premium estimates tried to capture the changes in equity risk premiums on a daily basis, and completing the assessments for the entire month, here is what the equity risk premiums looked like in March 2026:


The surprise here is not that the equity risk premium rose over the course of the month, expected given what was happening in the Middle East, but that it rose so modestly. In fact, over the course of March, the implied equity risk premium for the S&P 500 rose from 4.37% on February 27, 2026, to 4.77%  at close of trading on March 31, 2026, an increase of 0.40% for the month.
    In the bond market, the price of risk is the bond default spread, and in the graph below, I look at default spreads for seven bond ratings classes from AAA to C (& below):


Here again, the spreads increased over the month, but only modestly, even at the lowest ratings classes. Thus, the BBB default spread over the 10-year treasury rose only 0.08% during the month, from 1.07% on February 27, 2026, to 1.15%on March 31, 2026, and the high yield spread (for CCC and below) increased from 9.50% at the start of March 2026 to 10.10% at the end of the month.
    The third proxy for risk is the volatility index (the VIX) for US equities, and that measure rose during the course of March 2026:


During March 2026, the VIX rose from19.86 at the start of the month to 25.25 by the end of the month, an increase much smaller than the increases we saw in March 2020 (COVID) or in the first week of April 2025 (Tariff week).
    With the caveat that this is still mid-narrative, the bottom line from the movement in all of these risk measures is that while the market had a bad month, much of the marking down in equity values can be attributed to real concerns about higher inflation and economic damage, and is not the result of panic selling, at least in the aggregate. To back this up, I took a look at two collectibles - gold, which has a history of holding its value or even increasing during crises and panics in financial markets, and bitcoin, which has not had that history so far, but is marketed by its advocates as a potential hedge:

Gold was down 10.42% during March 2026, uncommon for a crisis month, but bitcoin was up 3.30% during the month, and it is entirely in keeping with bitcoin investors marching to their own music, though it will be interesting to see how this dynamic plays out, as this repricing continues.

Effect across Geographies
    The war is in the Middle East, but there is no place to hide from its effects. To see how the war has played out in different regions, I looked at the change in aggregate market cap, in US dollar terms, in March 2026:

You may be surprised to see Africa & the Middle East and Eastern Europe & Russia show up as the best performing markets, with about 2% decreases in market capitalization, but it reflects the dual impact of the war. While it has wreaked havoc across the Middle East, the higher oil prices that it has brought with it are providing upside for oil producers that offsets some of the damage.
    Since these dollar returns reflect local market performance as well as the strength/weaknesses of their currencies against the dollar, I looked at the US dollar's performance in March 2026:

I know that I am piling on at this stage, but I do compute equity risk premiums for other countries twice a year, once at the start and once mid-year. Given how much March has shaken up the status quo, I will make an exception and re-estimate equity risk premiums, by country, updating both my mature market premium (which I estimate from the S&P 500) as well as the country ratings, default spreads and country equity risk premiums for other countries. 
Download spreadsheet with country ERPs

It is worth noting that these equity risk premiums are computed based upon sovereign ratings, which are slow to change, as the world convulses. That has been an issue with my ERP computations for Russia and Ukraine, since 2022, with the rating for the former withdrawn and the rating for the latter frozen at Ca (Moody's); I have use a country risk score from PRS for the last two years to update Russia's equity risk premium, an have done the same for the Ukraine in this update. You can see the same issues now, with the war in Iran rocking the boat, and at least for the Middle East, there is reason to believe that the ratings may understate country risk. While none of the countries in the war zone have seen their sovereign rating change (yet), these countries have market estimates of sovereign default risk in the form of sovereign CDS spreads, I looked at the movement in those spreads during the course of the month:

Not surprisingly, market measures of default risk are more sensitive to war effects, and have risen for much of the Middle East, as worries have mounted, with bigger increases in Qatar, the UAE and Turkey than in Saudi Arabia and Kuwait. The United States has also seen a surge in its sovereign CDS spread, and the global sovereign CDS spreads have risen about 12% in the first quarter of 2026. Using these sovereign CDS spreads as measures of default spreads for this part of the world may yield more realistic equity risk premiums.

What now?
    I noted at the start of this post that the uncertainties that manifested during March 2026 about the direction, duration and effects of war are still unresolved and perhaps even grown as we start April. As investors try to navigate their way through this period, here are the questions that you will need to answer to decide where you fall in the continuum between complacency to full-blown panic:
In the complacency scenario, the war ends quickly (in days or weeks, rather than months), the damaged  infrastructure  is repaired quickly and the new regime in Iran is viewed favorably by the rest of the world, allowing the sanctions on the country to be removed, it is likely that oil prices will drop, perhaps even to below pre-war levels, as Russian and Iranian oil is freely bought and sold. In the full-scale panic scenario, the war continues for months, with lasting damage to infrastructure and supply chains and Iran's new government stays sanctioned, oil prices are likely to stay high and perhaps even go higher, the global economy will be kneecapped and parts of the Middle East (Dubai and Abu Dhabi) that had created a business and tourist friendly setting will struggle to find their balance. 
    In either case, the war has shaken up the status quo, and I see lasting consequences that go well beyond oil. The capital flows from the oil rich countries which has flowed generously to everything from AI start ups to Premier League clubs will shrink, creating down-market effects.  That money, and the funds that were set aside to build vanity projects, from ski resorts in the deserts to state-of-the-art cities will be redirected to building pipelines and securing the flow of oil. Global politics has also been roiled, and even if the war ends quickly,  there is damage that has been done to partnerships and security agreements that cannot be undone. 

YouTube Video

Datasets

Sunday, March 15, 2026

The Price of Risk: An Equity Risk Premium Monologue!

   I start my valuation classes with a question of whether valuation is an art or a science, and I argue that it is neither; it does not have the precision that characterizes a science and unlike an art, it does come with principles that constrain you on what you can and cannot do. I describe valuation as a craft, where you learn as you value companies, and in the process, there are times where you question how it is practiced, and try to find ways to do it better. I have learned my share of lessons in the four decades that I have practiced valuation, and I have often abandoned standard practices, in the hope of developing better ones. There is no input in valuation where I have found myself questioning existing practices more than in estimating the price of risk in equity markets, i.e., the equity risk premium, and I have wrestled with ways of coming up with alternatives. That endeavor was pushed into high gear by the 2008 market crisis, when I started to pay more attention to how markets price risk, what causes that price of risk to change over time and the limitations in the ways that we estimate that price of risk in financial analysis.

Status Quo and Standard Practice
    Leading into 2008, I had long been skeptical about how we approached the estimation of equity risk premiums,  essential ingredients in hurdle rates in corporate finance and discount rates in valuation. It was (and still remains) standard practice to look at historical data, almost entirely from the US, on what stocks had earned over treasuries, and use that historical equity risk premium as the best estimate of the equity risk premium for the future, That approach would have yielded an equity risk premiums of between 5.5% to 14.5%, at the start of 2026, depending on the time period used, the way we compute averages and what we use as the riskfree rate.


These historical equity risk premiums are not only backward-looking and very noisy (see the standard errors), but they allow bias to easily creep in, through the choice of equity risk premiums, with bullish (bearish) analysts picking lower (higher) numbers.  Disconcertingly, they also move in the wrong direction, falling during crises (as historical returns get updates) and rising during good times.

A Forward-Looking Alternative
    To counter the problems that I saw with historical risk premiums, I started estimating forward-looking equity risk premiums, by essentially backing out from stock prices and expected cash flows, the expected return (internal rate of returns) that markets were pricing into stocks. 


That approach yields forward-looking equity risk premiums, and while there is estimation error in the expected earnings growth and payout numbers, it yields vastly more precise estimates that are also model-agnostic. Using this approach, the equity risk premium at the start of 2026 was 4.23% (over the US treasury bond rate):
Note that this estimation is model-agnostic, and is simply a measure of what markets are pricing in, given expected cash flows at the moment.

ERP Estimation during Crises
    Unlike historical equity risk premiums, these implied premiums are sensitive to market gauges of fear and greed, and change, as those change. In fact, I computed the ERP, by day, during the 2008 market crisis, and you can see the shifts during that 14-week period below:


Note that the crisis started with the equity risk premiums at 4.2% on September 12, 2008m but almost doubled over the next two months, as stocks went into free fall. To me, these implied equity risk premiums made far more intuitive sense, rising as market fears about banks and the economy rose.
    I have continued with the practice of estimating equity risk premiums, by day, during market crises (real or perceived). Here, for instance, is my assessment of the UK market in 2016 in the weeks leading up to the Brexit vote, the market reaction to COVID and the global economic shutdown in 2020, and how the tariffs roiled markets last year. In fact, as we wrestle with an war and oil price induced market shock in March 2026, I started my daily estimates for the ERP on March 1 and will report on how that price has changed over the last two weeks, in the next section.

Equity Risk Premiums - Lessons Learned
        The process of estimating implied equity risk premiums on a continuing basis is driven less by intellectual curiosity and more by my need for these numbers, when I value companies. That process has taught me three lessons about equity risk premiums, and I have responded by altering my practices.
    
1. The equity risk premium is a dynamic and shifting number, and a good estimate of the premium should reflect this volatility. Using an equity risk premium that is different from the implied equity risk premium makes every valuation a joint judgment on what you think about the company and what you think about the market. Put simply, sticking with a 4% equity risk premium during a crisis, when the implied risk premium has surged to 6% will lead you to find most companies to be undervalued, almost entirely because you think that the market is undervalued (not the company). In my view, a company valuation should be market-neutral, and the only way you can get there is by using a current implied equity premium.
My response: Rather than compute the implied equity risk premium at the start of every year, and using that premium over the course of the year, I shifted to computing the equity risk premium for the S&P 500 at the start of every month, in September 2008.  I report those numbers on my entry page to my website (damodaran.com) and use them to value companies during the course of the month. You can find these monthly equity risk premium estimates by going to this link
2. The implied equity risk premium is a consolidated metric for market pricing, and every debate or discussion about whether the market is under or over priced can be reframed as a debate about whether the implied equity risk premium is too low (over pricing), just right (fairly priced) or too high (under pricing). Since the implied ERP incorporates the level of interest rates, expected growth and cash payout, it is a more complete assessment of the market than looking at dividend yields and earnings yields (or variants of PE ratios), two widely used proxies for market pricing. In this post, I took an extended look at how these different measures of equity risk premiums measure up, in terms of predicting future equity returns.
My response: I have been open about my discomfort with timing markets, but when I am asked what I think of the overall market (Is it too high? Is it a bubble?), I first measure the current equity risk premium and then assess it against history. I used this technique to assess US equities at the start of this year in a post, with the accompanying graph: 

My conclusion, at the start of 2026, was that while stocks were richly priced using almost every conventional metric (high PE ratios, low dividend yields), the implied equity risk premium was in line with what US stocks have generated over the last 65 years. That said, I did note that 2025 was a tumultuous year, with tariffs making the news and the post-war dollar-centric global economic system starting to fray, and argued that the market seems to be too sanguine about catastrophic risk. Almost on cue, two weeks ago, bombs started falling in the Middle East, and US equities and bonds have been struggling to price in the effects of higher oil prices. In keeping with my practice of estimating equity risk daily, during troubled times, I did compute the implied ERP for the S&P 500 every day, during the last two weeks (Feb 27- March 13):

Oil is up to over a hundred dollars a barrel and the S&P 500 is down, but so far, the market is not behaving as if it is in crisis mode. The equity risk premium, which started March at 4.37% has risen, but only to 4.51%, over the two weeks. In fact, it is the ten-year US treasury bond that has had the bigger surge, up from 3.97% at close of trading, on February 27, to 4.28% at close of trading, on March 13, indicating inflation fears are trumping other market concerns right now. All of this could change next week or the week after, and I will continue to track the equity risk premiums, by day, until the market settles in.
3. The equity risk premium is an essential ingredient into almost every part of financial analysis, incorporated into hurdle rates in corporate finance, discount rates in valuation and in expected returns on equity in financial planning. Given this centrality, I was surprised how little attention it has received from both academics and practitioners, when I looked for references. There is very little usable academic research on equity risk premiums specifically, though there is a great deal on asset pricing and risk. As for practitioners, they have, for the most part, relied on historical risk premiums, and often obtain these premiums from services that summarize the historical data. When I took my first finance class, the historical risk premiums came from data from Ibbotson Associates, that contained annual return data on stocks, bonds and bills. That data was acquired by Duff and Phelps, where it became part of a voluminous book on cost of capital, but much of what that book had to say about equity risk premiums reflected slicing and dicing the historical data, hoping to get further insights, and for the most part failing, because of the noisiness in the data. The US historical data is now in the hands of Kroll, but there is little of value that be extracted by doing deeper and deeper mining expeditions on historical return data. In fact, if you are a fan of historical equity risk premiums (I am not, as you can guess), my suggestion would be to use the Credit Suisse Yearbook, which looks at historical equity risk premiums in 20 markets over more than a hundred years, and does not suffer from the selection bias of focusing on just US data.
My response: I am a practitioner and I decided, for my own understanding, to pull together everything I knew about equity risk premiums into a paper that I wrote in early 2009, and shared online that year. Practitioners seemed to find it useful, and I have updated that paper every year since, at the start of the year. It has grown over time, as I have sought to pull together new findings on equity risk premiums and incorporate changes in markets, and my seventeenth annual update is now ready. I have to confess that at this point, much of the change is data-driven, with tables and graphs updated to include the most recent year's data, but I hope you still find it useful. The paper resides on the social science research network (SSRN), an Elsevier-run platform for working papers in the social sciences. Unlike most of the other papers on that platform, I have no interest is ever publishing this paper, but you are welcome to download not just the paper, but all of the data that goes with the paper. 

Equity Risk Premiums - The 2026 Edition
    If you do get a chance to download the paper, I should warn you ahead of time that it long (153 pages), unexciting and entirely directed at practitioners. It is modular, though, and it is broadly broken down into the following sections:
1. The Determinants of Equity Risk Premiums: Given that equity risk premiums represent the price of risk in the market, it should come as no surprise that almost everything that happens in the market, political or economic, affect its level. The picture below summarizes the determinants, and you can find more details in the paper:
As you can see, all of these variables can and will change over time, explaining why the ERP should be a volatile number.

2. Historical Equity Risk Premiums (and spin offs): I spend a section of the paper discussing historical equity risk premiums, examining the statistical properties that make it a faulty approach, and why a belief in mean reversion has made it the status quo. While most of the historical equity risk premiums that you see reported in practice come from the US and are based upon the Ibbotson data going back to 1926, I also look at historical data that goes back further (to 1871) as well as historical premiums in the rest of the world. The historical data on returns in the US has also been mined by services to extract premiums that have been earned by subsets of stocks, and since these premiums often get used by practitioners, I look at the efficacy of these premiums. I specifically look at the small cap premium, a widely used add on in valuation, and not that not only has it been noisy over the entire time period (1926-2025), but that it has disappeared since 1981:

The fact that the small cap premium endures in practice is a testimonial to how once bad practices become embedded in valuation, they never leave.

3. Equity Risk Premiums, by country: While I do have a companion paper that explores country risk in detail, that I update in the middle of the year, I describe my process for estimating equity risk premiums, by country, starting with a mature market premium, and then adding on additional premiums, based on country default risk spreads (based on ratings and sovereign CDS spreads).


4. Implied Equity Risk Premiums and Alternatives: In this section, I start with a description of an intrinsic value model for the market, and use that model to illustrate what you would need to assume for the dividends yield or earnings yield to become reasonable proxies for the equity risk premiums; for the latter, for instance, you have to assume either that there is no earnings growth or that if there is growth, it is value neutral. I then use the full version of the model, allowing for higher growth and cash payout that includes buybacks, to derive my implied equity risk premium estimates. I also look at how my implied equity risk premium estimates relate to other risk proxies (default spreads on bonds, VIX etc.) and how they change over time, as the riskfree rate changes.

5. Efficacy of ERP Estimates: The test of whether an equity risk premium estimate is a good one is in the data, since equity risk premiums measure expectations of what investors hope to earn on equities in future periods. In the last section of the paper, I examine the predictive efficacy of alternative measures of equity risk premiums, by looking at their correlation with actual stock market returns in the next year, the next five years and the next ten years:
Since a good ERP estimate should have a large positive correlation with actual returns on stocks in future years, the current implied premium does best for the five-year and ten-year return, and the historical risk premium does worst, with actual returns increasing (decreasing) when it decreases (increases). In bad news for market timers, none of the equity risk premium approaches does well at forecasting next year's actual return, and even at the longer time periods, there is significant error in predictions.

Paper




Saturday, August 5, 2023

The Price of Risk: With Equity Risk Premiums, Caveat Emptor!

    If you have been reading my posts, you know that I have an obsession with equity risk premiums, which I believe lie at the center of almost every substantive debate in markets and investing. As part of that obsession, since September 2008, I have estimated an equity risk premium for the S&P 500 at the start of each month, and not only used that premium, when valuing companies during that month, but shared my estimate on my webpage and on social media. In my last post, on country risk premiums, I used the equity risk premium of 5.00% that I estimated for the US at the start of July 2023, for the S&P 500. That said, I don't blame you, if are confused not only about how I estimate this premium, but what it measures. In fact, an article in MarketWatch earlier this year referred to the equity risk premium as an esoteric concept, a phrasing that suggested that it had little relevance to the average investor. Adding to the confusion  are the proliferation of very different numbers that you may have seen attached to the current equity risk premium, each usually quoting an expert in the field, but providing little context. Just in the last few weeks, I have seen a Wall Street Journal article put the equity risk premium at 1.1%, a Reuters report put it at 2.2%, and a bearish (and widely followed) money manager estimate the equity risk premium to be negative. How, you may ask, can equity risk premiums be that divergent, and does that imply that anything goes? In this post, I will not try to argue that my estimate is better than others, since that would be hubris, but instead focus on explaining why these ERP differences exist, and let you make your own judgment on which one you should use in your investing decisions.

ERP: Definition and Determinants

    The place to start this discussion is with an explanation of what an equity risk premium is, the determinants of that number and why it matters for investors. I will try to steer away from models and economic jargon in this section, simply because they do little to advance understanding and much to muddy the waters.

What is it?

    Investors are risk averse, at least in the aggregate, and while that risk aversion can wax and wane, they need at least the expectation of a higher return to be induced to invest in riskier investments. In short, the expected return on a risky investment can be constructed as the sum of the returns you can expect on a guaranteed investment, i.e.,  a riskfree rate, and a risk premium, which will scale up as risk increases. 

Expected Return = Risk free Rate + Risk Premium

Note that this proposition holds even if you believe that there is nothing out there that is truly risk free, which is the case when you worry about governments defaulting, though it does imply that you have cleaning up to do to get to a riskfree rate. Note also that expectations do not always pan out, and the actual returns on a risky investment can be much lower than the risk free rate, and sometimes sharply negative.

    The risk premium that you demand has different names in different markets. In the corporate bond market, it is a default spread, an augmentation to the interest rate that you demand on a bond with more default risk. In the real estate market, it is embedded in a capitalization rate, an expected return used by real estate investors to convert the income on a real estate property into a value for that property. In the equity market, it is the equity risk premium, the price of risk for investing in equities as a class.



As you can see, every asset class has a risk premium, and while those risk premiums are set by investors within each asset class, these premiums tend to move together much of the time.

Determinants

    Since the equity risk premium is a price for risk, set by demand and supply, it stands to reason that it is driven not only by economic fundamentals, but also by market mood. Equities represent the residual claim on the businesses in an economy, and it should come as no surprise that the fundamentals that determine it span the spectrum:

My equity risk premium paper

Even a cursory examination of these fundamentals should lead you to conclude that not only will equity risk premiums vary across markets, providing an underpinning for the divergence in country risk premiums in my last post, but should also vary across time, since the fundamentals themselves change over time. 

    Market prices are also driven by mood and momentum, and not surprisingly, equity risk premiums can change, as these moods shift. In particular, equity risk premiums can become too low (too high) if investors are excessively upbeat (depressed) about the future, and thus become the ultimate receptacles for market hope and fear. In fact, one symptom of a market bubble is an equity risk premium that becomes so low that it is disconnected from fundamentals, setting up for an inevitable collision with reality and a market correction.

Why it matters

    If you are a trader, an investor or a market-timer, and you are wondering why you should care about this discussion, it is worth recognizing that the equity risk premium is a central component of what you do, even if you have never explicitly estimated or used it.

  1. Market Timing: When you time markets, you are making a judgment on how an entire asset class (equities, bonds, real estate) is priced, and reallocating your money accordingly. In particular, if you believe that stocks are over priced, you will either have less of your portfolio invested in equities or, if you are aggressive, sell short on equities. Any statement about market pricing can be rephrased as a statement about equity risk premiums; if you believe that the equity risk premium, as priced in by the market, has become too low (relative to what you believe is justified, given history and fundamentals), you are arguing that stocks are over priced (and due for a correction). Conversely, if you believe that the equity risk premium has become too high, relative again to what you think is a reasonable value, you are contending that stocks are cheap, in the aggregate.  
  2. Stock Picker: When you invest in an individual stock, you are doing so because you believe that stock is trading at a price that is lower than your estimate of its value. However, to make this judgment, you have to assess value in the first place, and while we can debate growth potential and profitability, the equity risk premium becomes an input into the process, determining what you should earn as an expected return on a stock. Put simply, if you are using an equity risk premium in your company valuation that is much lower (higher) than the market-set equity risk premium, you are biasing yourself to find the company to be under (over) valued. A market-neutral valuation of a company, i.e., a valuation of the company given where the market is today, requires you to at least to try to estimate a premium that is close to what the market is pricing into equities.
  3. Corporate Finance: The role of the equity risk premium in determining the expected return on a stock makes it a key input in corporate finance, as well, because that expected return becomes the company's cost of equity. That cost of equity is then embedded in a cost of capital, and as equity risk premiums rise, all companies will see their costs of capital rise. In a post from the start of this year, I noted how the surge in equity risk premiums in 2022, combined with rising treasury bond rates, caused the cost of capital to increase dramatically during the course of the year.

Put simply, the equity risk premiums that we estimate for markets have consequences for investors and businesses, and in the next section, I will look at ways of estimating it.

Measurement

    If the equity risk premium is a market-set number for the price of risk in equity markets, how do we go about estimating it? Unlike the bond market, where interest rates on bonds can be used to back out default spreads, equity investors are not explicit about what they are demanding as expected returns when they buy stocks. As a consequence, a range of approaches have been used to estimate the equity risk premium, and in this section, I will look at the pluses and minuses of each approach.

1. Historical Risk Premium

    While we cannot explicitly observe what investors are demanding as equity risk premiums, we can observe what they have earned historically, investing in stocks instead of something risk free (or close). In the US, that data is available for long periods, with the most widely used datasets going back to the 1920s, and that data has been sliced and diced to the point of diminishing returns. At the start of every year, I update the data to bring in the most recent year's returns on stocks, treasury bonds and treasury bills, and the start of 2023 included one of the most jarring updates in my memory:

Spreadsheet with historical data

It was an unusual year, not just because stocks were down significantly, but also because the ten-year treasury bond, a much touted safe investment, lost 18% of its value. Relative to treasury bills, stocks delivered a negative risk premium in 2022 (-20%), but it would be nonsensical to extrapolate from a single year of data. In fact, even if you stretch the time periods out to ten, fifty or close to hundred years, you will notice that your estimates of expected returns come with significant error (as can be seen in the standard errors). 
    In much of valuation, especially in the appraisal community, historical risk premiums remain the prevalent standard  for measuring equity risk premiums, and there are a few reasons. 
  • Perhaps, the fact that you can compute averages precisely gets translated into the delusion that these averages are facts, when, in fact, they are not just estimates, but very noisy ones. For instance, even if you use the entire 94-year time period (from 1928-2022), your estimate for the equity risk premium for stocks over ten-year treasury bonds is that it falls somewhere between 2.34% to 10.94%, with 95% confidence (6.64% ± 2* 2.15%). 
  • It is also true that the menu of choices that you have for historical equity risk premiums, from a low of 4.12% to a high of 13.08%, depending on then time period you look at, and what you use as a riskfree rate, gives analysts a chance to let their biases play out. After all, if your job is to come up with a low value, all you have to do is latch on to a high number in this table, claim that it is a historical risk premium and deliver on your promise. 
   When using historical equity risk premiums, you are assuming mean reversion, i.e., that returns revert  to historic norms over time, though, as you can see, those norms can be different, using different time periods. You are also assuming that the economic and market structure has not changed significantly over the estimation period, i.e., that the fundamentals that determine the risk premium have remained stable. For much of the twentieth century, historical equity risk premiums worked well as risk premium predictors in the United States, precisely because these assumptions held up. With China's rise, increased globalization and the crisis of 2008 as precipitating factors, I would argue that the case for using historical risk premiums has become much weaker.

2. Historical Returns-Based Forecasts

    The second approach to using historical returns to estimate equity risk premiums starts with the same data as the first approach, but rather than just use the averages to make the estimates, it looks for time series patterns in historical returns that can be used to forecast expected returns. Put simply, this approach brings into the estimate the correlation across time in returns:

If the correlations across time in stock returns were zero, this approach would yield results similar to just using the averages (historical risk premiums), but it they are not, it will lead to different predictions. Looking at historical returns, the correlations start off close to zero for one-year returns but they do become slightly more negative as you lengthen your time periods; the correlation in returns over 5-year time periods is -0.15, but it is not statistically significant. However, with 10-year time horizon, even that mild correlation disappears. In short, while it may be possible to coax a predictive model using only historical stock returns, that model is unlikely to yield much in actionable predictions. There are sub-periods where the correlation is higher, but I remain skeptical of any ERP prediction model built around just the time series of stock returns.

    In an extension of this approach, you could bring in a measure of the cheapness of stocks (PE ratios or earnings yields are the most common ones) into the historical return data and exploit the relationship (if any) between the two. If there is a relationship, positive or negative, between PE ratios and subsequent returns, a regression of returns against PE (or EP) ratios can be used to generate predictions of expected annual returns in the next year, next 5 years or the next decade. The figure below is the scatter plot of earnings to price ratios against stock returns in the subsequent ten years, using data from 1960 to 2022:

A regression using this data yields some of the lowest estimates of the ERP, especially for longer time horizons, because of the elevated levels of PE ratios today. In fact, at the current EP ratio of about 4%, and using the historical statistical link with long-term returns, the estimated expected annual return on stocks, over the next 10 years and based on this regression is:

  • Expected Return on Stocks, conditional on EP = .00254 + 1.4543 (.04) = .0607 or 6.07%
  • ERP based on EP-based Expected Return = 6.07% - 3.97% = 2.10%

It is worth remembering that the expected return predictions come with error, and the more appropriate use of this regression is to get a range for the expected annual return, which yields predictions ranging from 4% to 8%. Extending the regression back to 1928 increases the R-squared and results in some regressions that yield predicted stock returns that are lower than the treasury-bond rate, i.e., a negative equity risk premium, given the EP ratio today. 

    Note that the results from this regression just reinforce rules of thumb for market timing, based upon PE ratios, where investors are directed to sell (buy) stocks if PE ratios move above (below) a “fair value” band. Since those rules of thumb have yielded questionable results, it pays to be skeptical about these regressions as well, and there are three limitations that those who use it have to keep in mind. 

  • First, with the longer time-period predictions, where the predictive power is strongest, the same data is counted multiple times in the regression. Thus, with 5-year returns, you match the EP ratio at the end of 1960 with returns from 1961 to 1965, and then the EP ratio at the end of 1961 with returns from 1962 to 1966, and so on. While this does not imply that you cannot run these regression, it does indicate that the statistical significance (R squared and t statistics) are overstated for the longer time horizons. In addition, the longer your time horizon, the more data you lose. With a 10-year time horizon, for instance, the last year that you can use for predictions is 2012, with the EP ratio in that year matched up to the returns from 2013-2022. 
  • Second, as is the case with the first approach (historical risk premiums), you are assuming  that the structural model is stable and that there will be mean reversion. In fact, within this time period (1928 - 2022), the predictive power is far greater between 1928 and 1960 than it is betweeen 196 and 2022.
  • Third, while these models tout high R-squared, the number that matters is the standard error of the predictions. Predicting that your annual return will be 6.07% for the next decade with a standard error of 2% yields a range that leaves you, as an investor, in suspended animation, since you face daunting questions about follow through: Does a low expected return on stocks over the next decade mean that you should pull all of your money out of equities? If yes, where should you invest that cash? And when would you get back into equities again?
Proponents of this approach are among the most bearish investors in the market today, but it is worth noting that this approach would have yielded “low return” predictions and kept you out of stocks for much of the last decade. 

3. The Fed Model: Earnings Yield and ERP

    The problem with historical returns approaches is that they are backward-looking, when equity risk premiums should be about what investors expect to earn in the future. To the extent that value is driven by expected future cash flows, you can back out an equity risk premium from current stock prices, if you are willing to make assumptions about earnings growth and cash flows in the future. In the simplest version of this approach, you start with a stable-growth dividend discount model, where the value of equity can be written as the present value of dividends, growing at a constant rate forever:


If you assume that earnings will stagnate at current levels, i.e., no earnings growth, and that companies pay out their entire earnings as dividends (payout ratio = 100%), the cost of equity can be approximated by the earnings to price ratio:

Alternatively, you can assume that there is earnings growth and that companies earn returns on equity equal to their costs of equity, you arrive at the same result:

In short, the earnings to price ratio becomes a rough proxy for what you can expect to earn as a return on stocks, if you are willing to assume no earnings growth or that firms generate no excess returns.

    This is the basis for the widely used Fed model, where the earnings yield is compared to the treasury bond rate, and the equity risk premium is the difference between the two. In the figure below, you can see the equity risk premiums over time that emerge from this comparison, on a quarterly basis, from 1988 to 2023:

Download quarterly data

As you can see, this approach yields some "strange" numbers, with negative equity risk premiums for much of the 1990s, one of the best decades for investing in stocks over the last century. It is true that the equity risk premiums have been much more positive in this century, but that is largely because the treasury bond rate dropped to historic lows, after 2008. As interest rates have risen over the last year and a half,  with stock prices surging over the same period, the equity risk premium based on this approach has dropped, standing at 0.41% at the start of August 2023. Since this is the approach used in the Wall Street Journal article, it explains the ERP being at a two-decade low, but I do find it odd that there is no mention that this approach yielded negative premiums in the 1980s and 1990s. In a variant, the Wall Street Journal article also looks at the difference between the earnings yield and the inflation-protected treasury rate, which yields a higher value for the ERP, of about 3%, but suffers from many of the same issues as the standard approach.

    My problem with the earnings yield approach to estimating equity risk premiums is that the assumptions that you need to make to justify its use are are at war with the data. First, while earnings growth for US stocks has been negative in some years, it has been positive every decade for the last century, and there are no analysts (that I am aware of) expecting it be zero (in nominal terms) in the future. Second, assuming that the return on equity is equal to the cost of equity may be easy on paper, but the actual return on equity for companies in the S&P 500 was 19.73% in 2022, 17.04% over the last decade and has been higher than the cost of equity even in the worst year in this century (9.35% in 2008). If you allow for growth in earnings and excess returns, it is clear that earnings yield will yield too low a value for the ERP, because of these omissions, and will yield negative values in many periods, making it useless as an ERP estimator for valuation.

4. Implied ERP

    I start with the same general model for value that the earnings yield approach does, which is the dividend discount model but change three components

  1. Augmented Dividends: It is undeniable that companies around the world, but especially in the US, have shifted from returning cash in the form of dividends to stock buybacks. Since two-thirds of the cash returned in 2022 was in the form of buybacks, ignoring them will lead to understating expected returns and equity risk premiums. Consequently, I add buybacks to dividends to arrive at an augmented measure of cash returned and use that as the base for my forecasts.
  2. Allow for near-term growth in Earnings: Since the objective is to estimate what investors are demanding as an expected return, given their expectations of growth, I use analyst estimates of growth in earnings for the index. To get these growth rates, I focus on analysts who estimate aggregated earnings growth the index, rather than aggregating the growth rates estimated by analysts for individual companies, where you risk double counting buybacks (since analyst estimates are often in earnings per share) and bias (since company analysts tend to over estimated growth).
  3. Excess Returns and Cashflows: I start my forecasts by assuming that companies will return the same percentage of earnings in cash flows, was they did in the most recent year, but I allow for the option of adjusting that cash return percentage over time, as a function of growth and return on equity (Sustainable cash payout = Growth rate/ Return on Equity). 
The resulting model in its generic form is below:

In August 2023, this model would have yielded an equity risk premium of 4.44% for the S&P 500, using trailing cash flows from the last twelve months as a starting point, estimating aggregate earnings for the companies from analyst estimates, for the next three years, and then scaling that growth down to the risk free rate, as a proxy for nominal growth in the economy, after year 5:
Download implied ERP spreadsheet

To reconcile my estimate of the equity risk premium with the earnings yield approach, you can set the earnings growth rate to zero and the cash payout to 100%, in this model, and you will find that the equity risk premium you get converges on the 0.41% that you get with the earnings yield approach. Adding growth and excess returns to the equation is what brings it up to 4.44%, and I believe that the data is on my side, in this debate. To the critique that my approach requires estimates of earnings growth and excess returns that may be wrong, I agree, but I am willing to wager that whatever mistakes I make on either input will be smaller than the input mistakes made by assuming no growth and no excess returns, as is the case with the earnings yield approach.

Picking an Approach
   I prefer the implied equity risk premium approach that I just described, as the best estimate of ERP,  but that may just reflect my comfort with it, developed over time. Ultimately, the test of which approach is the best one for estimating equity risk premium is not theoretical, but pragmatic, since your estimate of the equity risk premium is used to obtain predictions of returns in subsequent periods. In the figure below, I highlight  three estimates of equity risk premiums - the historical risk premium through the start of that year and the EP-based ERP (EP Ratio minus the T.Bond Rate) and the implied equity risk premiums, at the start of the year:

The historical risk premium is stable, but that stability is a reflection of a having a long tail of historical data that keeps it from changing, even after the worst of years. The implied and EP-based ERP approaches move in the same direction much of the time (as evidenced in the positive correlation between the two estimates), but the latter yields negative values for the equity risk premium in a large number of periods. 
    Ultimately, the test of whether an equity risk premium measure works lies in how well it predicts future returns on stocks, and in the table below, I try to capture that in a correlation matrix, where I look at the correlation of each ERP measure with returns in the next year, in the next 5 years and in the next 10 years:
Download data

None of the approaches yield correlations that are statistically significant, for stock returns in the next year, but the implied ERP and historical ERP are strongly correlated with returns over longer time periods, with a key difference; the former moves with stock returns in the next ten years, while the latter moves inversely. 
    While that correlation lies at the heart of why I use implied ERP in my valuations as my estimate of the price of risk in equity markets, I am averse to using it as a basis for market timing, for the same reasons that I cautioned you on using the EP ratio regression: the predictions are noisy and there is no clear pathway to converting them into investment actions. To see why, I have summarized the results of a regression of stock returns over the next decade against the implied ERP at the start of the period, using data from 1960 to 2022:
Download data

You can see, from the scatter plot, that implied ERPs move with stock returns over the subsequent decades, but that movement is accompanied by significant noise, and that noise translates into a wide range around the predicted returns for stocks. If you are a market timer, you are probably disappointed, but this type of noise and prediction errors is what you should expect to see with almost any fundamental, including EP ratios. 

Conclusion
   I hope that this post has helped to convince you that the equity risk premium is central to investing, and that even if you have never used the term, your investing actions have been driven by its gyrations. I also hope that it has given you perspective on why you see the differences in equity risk premium numbers from different sources. With that said, here are some thoughts for the road that can help you in future encounters with the ERP:
  1. There is a true, albeit unobservable, ERP: The fact that the the true equity risk premium is unobservable does not mean that it does not exist. In other words, the notion that you can get away using any equity risk premium you want, as long as you have a justification and are consistent, is absurd. So, whatever qualms you may have about the estimation approaches that I have described in this post, please keep working on your own variant to get a better estimate of the ERP, since giving up is no an option.
  2. Not all estimation approaches are created equal: While there are many approaches to estimating the equity risk premium, and they yield very different numbers, some of these approaches have more heft, because they offer better predictive power. Picking an approach, such as the historical risk premium, because its stability over time gives you a sense of control, or because everyone else uses it, makes little sense to me.
  3. Your end game matters: As I noted at the start of this post, the equity risk premium can be used in a multitude of investment settings, and you have to decide, for yourself, how you will use the ERP, and then pick an approach that  works for you. I am not a market timer and estimate an equity risk premium primarily because I need it as an input in valuation and corporate finance. That requires an approach that yields positive values (ruling out the EP-based ERP) and moves with with stock returns in subsequent periods (eliminating historical ERP). 
  4. Market timers face a more acid test: If you are using equity risk premiums or even earnings yield for market timing, recognize that having a high R-squared or correlation in past returns will not easily translate into market-timing profits, for two reasons. First, the past is not always prologue, and market and economic structures can shift, undercutting a key basis for using historical data to make predictions. Second, even if the correlations and regressions hold, you may still find it hard to profit from them, since you (and your clients, if you are a portfolio manager) may be bankrupt, before your predictions play out. Statistical noise (the standard errors on your regression predictions) can create havoc in your portfolios, even if it eventually gets averaged out.

YouTube Video

Data Links

  1. Historical returns on Stocks, Bonds and Real Estate: 1928 - 2022
  2. Earnings to Price Ratios and Dividend Yields, by Quarter: 1988 Q4- 2023 Q2
  3. Implied ERP from 1960 to 2022: Annual Data
  4. ERP and Stock Returns: 1960 to 2022

Spreadsheet

  1. Implied ERP Spreadsheet for August 2023
Papers