Category Archives: Stock markets

If Biden wins

If history is any guide, it will be four good years on the stock market if Biden wins on November 3. Historically, stocks have performed so much better under Democratic presidents. The question is whether history will be a guide also this time around.

Are Democratic or Republican presidents better for the stock market? To evaluate, let us recall the performance of the US stock market under Trump – a Republican – and compare it to its performance under Obama – a Democrat and Trump’s predecessor. Afterwards, let us look at the full history of the stock market under Democratic and Republican presidents. Finally, let us discuss what it implies for this election and the next four years on the US stock market.

Obama vs. Trump

This graphs shows the cumulative return to USD 1 invested in respective January 2009 (Obama 1st term), January 2013 (Obama 2nd term), and January 2017 (Trump). I show real returns, i.e. returns after inflation:

Cumulative real returns to US large-cap stocks under Obama and Trump. Own calculations.
Data source: http://www.econ.yale.edu/~shiller/data.htm

A couple of months remain, but during most of Trump’s presidency, the stock market has performed worse than under Obama. The exceptions are the first few months of Obama’s first term and the beginning of this year, right before the corona crisis.

In numbers, one US dollar invested in the US stock market in January 2009, when Barack Obama – a Democratic president – was inaugurated, had turned into 2.68 USD in December 2016 (when Obama’s second term ended) in real terms, given reinvestments of dividends. This is a total accumulated real return of 168 percent over eight years, or an average annual return of 13%.

One US dollar invested in the US stock market in January 2017, when Donald Trump – a Republican president – was inaugurated, had turned into 1.46 USD in September this year (in real terms). This is a total accumulated return of 46 percent over four years, or an annual average real return of 10% (there are still three months to go of Trump’s presidency, so the numbers might change a little in the end).

Some extraordinary events influenced the stock market under both Obama and Trump.

Early 2009, the stock market was still suffering from the financial crisis of 2008. Obama was inaugurated in January 2009. A few months later (in March 2009), the stock market turned around. Following March 2009, many great years on the stock market followed.

This year, 2020, has seen the fastest bear market in history (in March; link), caused by the corona crisis, hurting the stock market’s performance during Trump’s presidency.

The financial crisis of 2009 and the corona crisis were very unusual events. Perhaps the stock market’s performance under Trump and Obama was unusual.

It turns out that the picture painted above – that the stock market performs better under Democratic presidents – is robust. In fact, the US stock market has historically performed much better under Democrats.

The Presidential Puzzle

Pedro Santa-Clara and Rossen Valkanov published in 2003 a paper (link) entitled ”The Presidential Puzzle”. They documented an intriguing stylized fact: Over the 1927-1999 period, the excess return on the US stock market has been nine percentage points higher under Democratic than Republican presidencies. The average excess returns under Democratic presidencies, they showed, was 11 percent versus 2 percent only under Republican presidents. A nine-percentage point difference is enormous. For instance, it exceeds the excess return on the stock market in general, i.e. the return stocks provide over and above the return on risk-free assets.

Santa-Clara and Valkanov took great care in investigating potential reasons for this stylized fact. The most obvious explanation, financial economists would suggest, is that this is simply a compensation for risk, i.e. that risks have been higher under Democratic presidents. It turns out that this is not the case. In the end, their conclusion was:

”There is no difference in the riskiness of the stock market across presidencies that could justify a risk premium. The difference in returns through the political cycle is therefore a puzzle. ”

Pastor and Veronesi (link) update the results of Santa-Clara and Valkanov. They add app. twenty years of data (until 2015, i.e. their sample runs from 1927 through 2015). Pastor and Veronesi find even stronger results. In their extended sample, they find that the average return under Democratic presidents is eleven percentage points higher than the average return under Republican presidents.

Pastor and Veronesi have this figure with average annual excess returns under each president:

Average excess returns during individual presidencies.
Source: Pastor and Veronesi (2020).

The figure shows that the only Democratic presidency that delivered returns significantly below the average return over the whole period (the dotted line) was Roosevelt’s second term (1937-41). In contrast, a number of Republican presidents have delivered subpar returns (Nixon, first Reagan term, Bush Jr.). My small calculation in the beginning of this post, that returns have been higher under Obama than Trump, strengthens this conclusion.

Pastor and Veronesi show that this finding is robust during subsamples, for instance if excluding the large negative and positive returns during the 1930s. They also show that it is particularly the first year of the presidency that drives these differences. During the first year in office, Democrat presidents have experienced a 37%-points (!) larger return than Republican presidents have:

Difference between average excess returns in the returns during the presidents’ early years in office.
Source: Pastor and Veronesi (2020).

(If you are interested, here is a detailed account of the stock market’s performance under every single president since Truman: link).

There is some discussion whether this finding (that the stock market does better under leftwing presidents) holds internationally. Pastor and Veronesi show in the (114 pages…) appendix to their article that it holds internationally while others claim that it does not (link). We leave this aside here.

Democratic presidents are elected when times are bad

Pastor and Veronesi develop an interesting explanation of this intriguing pattern of the data. They argue that the reason for the difference between the stock market’s performance under Democratic and Republican presidents has nothing to do with economic policies during presidencies but everything to do with the economic situation when new presidents are elected.

Pastor and Veronesi argue that Democratic presidents are elected at points in time when risk aversion is high. Remember, for instance, the election of Obama in autumn 2008. This was right in the middle of the financial crisis. The worst financial and economic crisis since the 1930s. Everybody was afraid and uncertain how things would evolve. Risk aversion was high. When risk aversion is high, investors demand high compensation for taking on risks in the stock market. Subsequently, investors get compensated by high average returns.

So, the story of Pastor and Veronesi is that Democratic presidents get elected when times are bad. When times are bad, voters have a tendency to vote for left-wing candidates, as voters demand more social insurance during hard times. An important implication of this theory is that Democrat presidents do not cause higher stock returns (and Republican presidents do not cause lower stock returns). Instead, Democratic presidents are elected when the economy is suffering and risk aversion is high, causing high expected returns and subsequent high average returns.

Implications for this election

If (and I write if) it is correct that Democratic presidents get elected when risk aversion is high, and that good returns subsequently follow, what does this imply for this election and the next four years on the stock market?

Pastor and Veronesi suggest a number of proxies for risk aversion. To illustrate, let us look at two of them. The first is unemployment. The idea is straightforward: when unemployment is high, people are afraid of taking on risk on the stock market. Risk aversion is high and so are expected returns.

Here is unemployment in the US since 1947:

US unemployment rate.
Source: FRED.

Unemployment is currently high, at 7.9% in September (latest figure at the time of writing). This is more than two percentage points above the historical average rate of unemployment of 5.8%. Unemployment is coming down, though, and fast. Also, there are still two weeks to go until the election. Nothing is for sure. But, as it looks now, this indicates high risk aversion, and thus high expected returns.

Another measure of risk aversion is the habit-persistence idea of Campbell and Cochrane (link). If your consumption is low today, in relation to your past consumption, you feel that times are bad. If you are used to go on holiday a couple of times per year, but now you don’t dare because you are afraid of losing your job, you also become afraid of taking on risk in the stock market. Your risk aversion is high. You require high expected returns if you should be convinced to nevertheless invest in stocks.

Let me present a simple illustration here, inspired by Atanasov, Moeller, and Priestley: link. I take consumption (real per capita) and divide by habit. I approximate habit by the average of the past three years of consumption (this is a blog, so this should be OK), i.e. the habit ratio is here: C(t)/(AVG[C(t-1)+(C(t-2)+…..+C(t-12]), where C(t) is consumption in period t and AVG is the average. I do this calculation for every quarter since 1950. The result is the following time series:

Consumption habit ratio. Own calculations.
Data source: FRED.

When an entry in the figure is above one, consumption during that quarter is higher than its past three-year average, and times are good. When the habit-ratio is low, times are bad. The habit ratio (current consumption to habit) thus has a tendency to drop around recessions (1980, 2008, etc.), as, during recessions, people cut consumption in relation to past their consumption.

The lower is the habit ratio, the higher is risk aversion and thus expected returns. Currently, due to the enormous drop in consumption resulting from the corona-crisis, the habit-ratio is historically low. Times are bad. Consumption is low. Biden should win (according to this theory). Risk aversion is high. Expected returns should be high. The next four years on the stock market should be good.

There is uncertainty, of course

Many things can happen until November 3 and the next four years. And, for sure, this has been a really weird campaign. Nothing is for sure.

Some reservations:

My figure with the habit-ratio is based on quarterly data (consumption is quarterly). The last entry is Q2 2020. Since Q2, the stock market has been sprinting ahead, implying that the potential for future returns is, all else equal, lower now than in Q2.

Also, financial markets have been pricing in an enormous amount of event risk surrounding this election. The uncertainty surrounding this election is high. Protection against event risk is expensive (link, link, and link).

At the same time, the stock market has been doing really well since March 23 (link). This is unlike recessions in general. During normal recessions, the stock market tanks. This stock market rebound since spring, everything else equal, reduces the potential for future returns as of now.

On the other hand, at least right now, the polls seem to offer some support for the story. We are in a big downturn (corona crisis). In downturns, people have a tendency to vote left-wing. As we all know, Biden leads the polls at the time of writing:

Poll average. October 16, 2020.
Source: www.realclearpolitics.com.

Conclusion

The stock market has performed worse under Trump than under Obama. This is not an outlier. Historically, the US stock market has performed much better under Democratic presidents.

One explanation why the stock market performs well under Democratic presidents is that Democratic presidents get elected during bad times, when risk aversion is high.

Currently, we are in the midst of a terrible situation (corona crisis). Supporting this theory, Biden leads the polls. If history is any guide, this indicates good years ahead on the stock market. Not necessarily because Biden – if he wins – implements policies that support the stock market (perhaps he does, but this is not the point of the theory), but because risk aversion is high right now, at the time of the election.

Of course, so many things can happen. This certainly has been a strange (and, at least for many Europeans, myself included, a very weird and scary) campaign to follow from the sideline. The performance of the stock market during this recession has also been weird. It is important to recognize that the stock market rebound since March reduces the potential for future returns as of now. And, in general, so many things can happen during the next four years. Perhaps the situation will thus play out differently this time around. We will know how the election turns out in two weeks, and we will know how the stock market performs during the next presidency in four years and three months. It will be interesting to follow.

The Fed’s “Whatever it takes” moment. Or, how the Fed saved equity and credit markets

Facing a looming recession and financial market panics, the Fed intervened heavily in late-February/early-March, lowering the Fed Funds Rate to zero and expanding its balance sheet dramatically. In spite of this, markets kept on panicking. Then, suddenly, on March 23, everything changed. Stock markets started their rally. This was not because the Fed lowered the rate or expanded its asset purchases even further, nor because the economic data improved. What happened? The Fed made an announcement. Nothing else. It is a fascinating illustration of how expectations can change everything on financial markets.  

Much has been written about the massive interventions of the Fed during February and early March. In my previous post (link), I list Fed interventions as one of the reasons why the stock market is back to pre-crisis highs. In this post, I dig one step deeper and explain the fascinating story of how the Fed said something and thereby rescued markets.

Asset purchases and rate reductions did not save markets in February/March

Let us start by illustrating how the actual Fed interventions (interest rate changes and asset purchases) did not save markets in March. The Fed lowered the (lower range of the) Fed Funds Target Range to 1% from 1.5% on March 2 and then again to 0% less than two weeks later, on March 14. At the same time, it bought Treasuries and mortgage-backed securities to the tune of USD 600bn per week. These interventions succeeded in lowering yields on government and mortgage-backed bonds, but did not cheer up stock markets.

This graph shows how Treasury yields came down significantly in February/March, by basically 1.5%-point (from close to 2% to close to 0.5%; I show yields on 10-year Treasuries in this graph), as a result of reductions in the policy rate (the Fed Funds Rate) and asset purchases by the Fed.

SP500 and yield on 10-year Treasuries. Daily data.
Source: Fed St. Louis Database

The graph also shows that the SP500 continued falling throughout February/March. In other words, the massive interventions by the Fed in late-February/early-March (and these interventions really were massive – buying for USD 600 bn per week and lowering rates to zero is indeed a massive intervention) did not convince stock markets that the situation was under control. And, remember, these were not minor stock-market adjustments. It was the fastest bear market ever (link).

What turned the tide?

On March 23, the SP500 reached its low of 2237, a drop of 31% compared to its January 1 value. Since then, everything has been turned upside down and markets have been cheering, as the above graph makes clear.

What happened on March 23? The Fed had its finest hour. It did not do anything. It merely said something. A true “Whatever it takes” moment.

As you remember, a “Whatever it takes” moment refers to the July 26, 2012 speech by then ECB-president Mario Draghi (link). The speech was given at the peak of the Eurozone debt crisis. The debt crisis pushed yields on Italian and Spanish sovereign bonds to unsustainable levels. Italy was too big to fail, but also too big to save. The pressure on Italy was a pressure on the Eurozone construction. Mario Draghi explained the situation and said the by-now famous words:

But there is another message I want to tell you. Within our mandate, the ECB is ready to do whatever it takes to preserve the euro. And believe me, it will be enough.

Investors understood that the ECB would be ready to buy sovereign bonds to save the Euro. Markets calmed down. Italian and Spanish yields fell. And this – and this is the point here – without the ECB actually intervening, i.e. without the ECB buying Italian or Spanish bonds. The announcement that the ECB would intervene was enough to calm down investors.

Why is this relevant here? Because on March 23 the Fed sent out a press release, announcing that:

“…the Federal Reserve is using its full range of authorities to provide powerful support for the flow of credit to American families and businesses.”

And, then, as one of the new features announced the:

Establishment of two facilities to support credit to large employers – the Primary Market Corporate Credit  Facility (PMCCF) for new bond and loan issuance and the Secondary Market Corporate Credit Facility (SMCCF) to provide liquidity for outstanding corporate bonds.

This statement turned everything upside down. The important thing is that this turn of events happened without the Fed using any money at all. It was a “Whatever it takes” moment (though, perhaps not as Dirty-Harry dramatic as Mario Draghi’s “And believe me, it will be enough”): The Fed announced what they would do, investors believed the Fed, and markets started cheering. It is a prime example of how investor expectations influence financial markets.

What are the PMCCF and SMCCFs, why did the Fed announce them, and why were their effects so dramatic?

The lowering of the Fed Funds Rate and the purchasing of Treasuries succeeded in lowering yields on safe assets, such as Treasury bonds, as explained above, but did not lower yields on corporate bonds. In fact, during the turmoil in late-February/early-March, credit spreads (the spread between yields on corporate bonds and safe bonds) widened dramatically. When yields on corporate bonds rise, it becomes more expensive for corporations to finance their operations. And, when yields rise a lot, as in February/March, investors get nervous about the profitability and survival of firms.

This graphs shows how yields on both the least risky corporate bonds (Triple A) and speculative grade bonds (Single B) rose dramatically in relation to 3-month Treasury Bills, with yields on lower-rated bonds (Single-B) naturally rising more than yields on higher-rated (Triple-A) bonds.

Difference between yields on ICE BofA AAA US Corporate Index and 3-month Treasuries as well as the difference between yields on ICE BofA Single-B US High Yield Index and 3-month Treasuries. Daily data.
Source: Fed St. Louis Database

The important point in the picture is that the spreads continued rising throughout late-February/March, in spite of the intensive interventions described above, i.e. in spite of Fed purchases of government and mortgage bonds. The Fed was happy that safe yields fell, but was concerned that credit spreads kept on rising. Volatility in corporate bonds markets also rose (link), making the whole thing even worse.

More or less all firms saw their funding costs increase, even when there were differences across firms in different industries, with firms in the Mining, Oil, and Gas, Arts and Entertainment, and Hotel and Restaurant sector hit the hardest, and firms in Retail and Utilities sectors less affected (link). The Fed became nervous because higher funding costs for firms affect firms negatively, causing them to cut jobs, reduce investments, etc.

The Fed decided to act. It announced on March 23 that it would launch two new programs, PMCCF and SMCCFs. The PMCCF is the ’Primary Market Corporate Credit Facility and the SMCCF the Secondary Market Corporate Credit Facility. Primary markets are where firms initially sell their newly issued bonds. The PMCCF should thus ease the issuance of newly issued corporate bonds, i.e. help firms raise funds. Secondary markets are where bonds are traded afterwards, i.e. the SMCCF should ease the trading (liquidity) of already existing corporate bonds.

The effect on equity and credit markets of the announcement of the PMCCF and SMCCFs was immediate and spectacular. Immediately after the announcement, credit spreads narrowed (see, e.g., link, link, and link).

Interestingly, stock markets reacted immediately, too. The stock market, thus, did not react to the lowering of the Fed Funds Rate and the extensive expansion of the Fed balance sheet in late-February/early-March, but reacted strongly to the announcement that the Fed would buy corporate bonds on March 23.

This (supercool, I think 🙂 ) graph shows developments on corporate bond and equity markets. The graph shows the spread between yields on AAA-rated corporate bonds and 3-month Treasury Bills and the stock market inverted, both normalized to one on January 1. The graph for the inverted stock market means that when the SP500 is at 1.45 on the y-axis on March 23, the stock price at January 1 was 45% higher than it was on March 23.

Difference between yields on ICE BofA AAA US Corporate Index and 3-month Treasuries (Left hand axis) as well as the SP500 inverted (Right hand axis). Both series normalized to one on January 2, 2020. Vertical line indicates March 23.
Source: Fed St. Louis Database

The parallel movements in equity and credit markets are striking. Equity and credit markets moved in parallel during January, when stock markets rose and credit spreads narrowed, in late-February/early-March when credit spreads widened dramatically and stock markets fell like a stone, as well as after March 23, when both credit spreads and stock markets improved spectacularly. Since then, stock markets have continued to rise and credit spreads have continued to narrow.

The correlation between the two series is an astonishing 0.93 for the January 2 through May 31 period.

The announcement effect

The Fed has experience with and a mandate to buy mortgage-backed securities and Treasuries. It had no such experience when it comes to purchases of corporate bonds and corporate bond ETFs. This means that the Fed could not start buying corporate bonds on March 23, it needed an institutional set-up. It created an SPV with capital injections from the Treasury and leverage from the New York Fed, it asked a financial firm (Blackrock) to help them purchase the bonds, etc. These things take time. The Fed only started buying corporate bond ETFs in mid-May and corporate bonds in mid-June.

Given that the Fed only started buying bonds and ETFs in May/June, the spectacular turnaround on March 23 really was due to the announcement only.

In slightly more detail, it played out as follows. The March 23 announcement primarily dealt with higher-rated corporate bonds (Investment Grade), and spreads narrowed immediately. On April 9, the Fed announced that they would expand “the size and scope of the Primary and Secondary Market Corporate Credit Facilities (PMCCF and SMCCF)”, buying bonds that were Investment Grade on March 22 but had been downgraded since then as well as corporate bond ETF. High-yield spreads tightened even more (link). Today, the Fed explains that the programs allow the Fed to buy “investment grade U.S. companies or certain U.S. companies that were investment grade as of March 22, 2020, and remain rated at least BB-/Ba3 rated at the time of purchase, as well as U.S.-listed exchange-traded funds whose investment objective is to provide broad exposure to the market for U.S. corporate bonds.”

The actual purchases began in May/June, several months after the announcement. Interestingly, the purchases themselves have had a modest impact only. First, the amounts of corporate bonds and corporate bond ETFs bought pale in comparison with the amounts of mortgage-backed securities (MBS) and Treasuries bought. The Fed has bought MBS and Treasuries to the tune of USD 3,000bn this year. It has “only” bought corporate bonds and ETFs for around USD 12bn. The amount used to buy corporate bonds thus corresponds to less than 0.5% of the amount used to buy MBS and Treasuries. This graphs shows the daily purchases. Using the latest figures from August 10, the Fed has basically stopped buying corporates.

Daily Fed purchases of corporate bonds and corporate bond ETFs. Daily data.
Source: Fed webpage. Thanks to Fabrice Tourre for collecting and sharing the data.

So, the Fed has not bought a lot of corporate debt. It has, however, the power to buy a lot. The PMCCF and SMCCF set-up is such that the Treasury has committed to make an USD 75bn investment in the SPV that buys the assets (USD 50bn toward the PMCCF and USD 25bn toward the SMCCF). The New York Fed then has the ability to level this up by a factor of ten, i.e. the Fed can buy corporate debt for up to USD 750bn. This is a sizeable fraction of the total US corporate bond market. This, that the Fed can potentially buy a lot, helps making the program credible and thus helps explaining its powerful impact.

Dilemmas

Given the success of the PMCCF and SMCCFs, commentators have started arguing that the Fed should be allowed to buy corporate bonds as part of its standard toolkit (link). This might be relevant, but purchases of corporate bonds by central banks raise a number of dilemmas:

  • Keeping zombie firms alive. By easing up stresses in corporate bond markets, the Fed calmed down markets. This was the intention of the PMCCF and SMCCF announcements and it worked. It eased access to funding for firms, and firms have raised a lot of cash as a consequence (link). It is positive that malfunctioning markets are stabilized, but if central bank intervention makes markets too cheerful it may allow firms that in principle should not receive funding to nevertheless get it. And, thereby, to keep firms alive for too long, and increase firm leverage too much. Basically, the fear is that programs such as the PMCCF and SMCCFs create too many zombie firms. My CBS colleague Fabrice Tourre and his co-author Nicolas Crouzet has an interesting paper that examines this (link). Fabrice and Nicolas find that when financial markets work perfectly (no disruptions), Fed intervention might be detrimental to economic growth. On the other hand, if markets are disrupted, Fed intervention might prevent a too large wave of liquidations. One thus needs to determine when markets are disrupted “enough” to rationalize interventions in credit markets. This is no straightforward task.
  • Distributional aspects. By buying some bonds but not others, the Fed exposes itself to the critique that it helps some firms at the advantage of other. To alleviate such criticism, the Fed has been very transparent and publishes a lot of information about the bonds it buys, the prices at which it buys the bonds, etc. (link). Nevertheless, it is easy to imagine that some firms at some point will start saying ‘Why did you buy the bonds of my competitor, but not my bonds’?
  • The Fed put. The more the Fed intervenes when troubles arise, the more investors get reassured that the Fed will also come to the rescue next time around. When the Fed saves markets, it is sometimes called the Fed exercises the “Fed Put”. The potential problem here is that if investors believe that the Fed will exercise the Fed put, investors will be tempted to take on even more risk. Those of us concerned about systemic risks get nervous.

So, in the end, the announcement of the PMCCF and SMCCFs was crucial during this crisis. There are, however, important dilemmas that need to be addressed when evaluating whether such programs should be part of the standard toolbox. I am not saying they should not. I am saying that one needs to be careful.

Conclusion

The Fed launched massive “traditional” interventions in late-February/early March, lowering the Fed Funds Rate and buying mortgage and government bonds. In spite of these very large interventions, equity and credit markets kept on tail spinning. When firms struggle, it hurts economic activity and employment. The Fed got nervous.

The Fed announced – and this is the whole point here; they only announced – that they would start buying corporate bonds. Markets turned upside down. Credit markets stabilized, credit spreads narrowed, corporate bond-market liquidity improved, and stock markets cheered. And, all these things without the Fed spending a single dime until several months after the fact. Even today, the Fed has spent very little (some might say that USD 12bn is a lot, but compared to asset purchases of USD 3,000bn, it pales).

It was a “Whatever it takes” moment. It illustrates how managing investor expectations can be crucial. Understanding this announcement is thus important for understanding the behavior of financial markets during this pandemic.

The weird stock market. Part II: Potential explanations

The behavior of the stock market during this recession raises three main questions: (i) why did stock markets fall so spectacularly during February/March, (ii) why did stocks rebound so spectacularly during April/May, and (iii) why is the stock market currently at its pre-crisis level? My previous post (link) presented the stylized facts and addressed stories that cannot explain the facts. In this post, I provide some potential explanations.

I my previous post (link), I mentioned that the rebound in the stock market since its low in March cannot be explained by (i) revisions to the economic outlook – in fact, economic forecasts were revised down during spring, (ii) a preference for just a few (FAANG) stocks, as the rebound has been international and broad based, even when large-cap stocks have done particularly well, (iii) a hypothesis that this recession is not particularly bad – in fact, at least in the short run, this recession is much worse than the 2008 recession, or (iv) the fact that markets also recovered after 2008 – markets always recover, i.e. this is not an explanation.

What can explain it, then? First, a warning: I do not want to raise expectations too much (sorry). I will not be able to offer a full explanation of these puzzles in an app. 1,900 words blog post. Also, as you will see, puzzles remain, even if we can explain some things. Finally, I have not seen a good explanation of these puzzling stylized facts (though Gavyn Davies’ piece in the FT is a good place to continue after reading this post; link). Hence, it would not be serious nor academic if I claimed that I could explain everything. What I can do, though, is to provide some hints at what might be relevant parts of an explanation.

Explanations that contain elements of truth

Earnings suffered more in 2008               

In the end, earnings and not economic activity (GDP) determine stock prices. In the long run, there is a strong relation between earnings and economic activity, which is why we focus on economic developments when we try to understand stock markets. The relation is not one-to-one, though, in particular in the short run. Hence, let us discuss earnings.

Earnings suffered dramatically in 2008. Often, we look at 12-month earnings, as quarterly earnings are volatile. 12-month reported earnings per share for the S&P500 came in at 6.86 in Q1 2009, which is app. 10% of 12-month reported earnings in Q1 2008. I.e., earnings fell by a mind-blowing 90% during the financial crisis of 2008.

Earnings fell in Q1 2020, too, but much less: From USD 139 per share in Q4 2019 to USD 116 (12 month reported earnings), i.e. by 17%. At the time of writing, around 90% of companies in the S&P500 have reported earnings for Q2 2020. Earnings (12-month reported) seem to be coming in at close to USD 96 per share, which is a drop of 17%, too, compared with Q1. Earnings have thus dropped by 17% during each of two consecutive quarters. But, and this is the main thing, these drops pale in comparison with autumn 2008. In autumn 2008, earnings dropped by 68% from Q3 to Q4 and then again by 54% from Q4 2008 to Q1 2009. This figure shows the quarterly percentage changes in 12-month reported earnings of the S&P500 in 2008 versus 2020. “0” on the x-axis is Q2 2020, respectively Q4 2008. The drop in earnings was just so much larger in 2008.

Quarterly changes in 12-month reported earnings per share, S&P500. “0” is Q2 2020, respectively Q4 2008. For Q3, 2020 and forward, these are expected earnings.
Source: https://www.spglobal.com

“1” on the x-axis in the figure is thus Q1 2009 and Q3 2020, i.e. firms’ expected earnings in Q3 2020 (and actual earnings in Q1 2009). If these expectations hold true, earnings are expected to do relatively fine going forward.

Earnings do fall from Q1 to Q2 this year. Earnings surprises matter, too, though, i.e. whether actual earnings are higher (or lower) than expected. At the time of writing, around 80% of companies have reported positive earnings surprises for Q2. This, that actual Q2 2020 earnings are better than expected, helps explaining why stock prices rise currently.

If investors primarily look at earnings, this helps explaining why stock prices fell considerably more in 2008 than they have done during this recession and why the stock-market recovery took longer in 2008. Earnings have simply not suffered so much this time around. For that reason, stock prices have not suffered so much this time around either.

Monetary and fiscal policies have been aggressive

Another factor that helps explaining why stock prices today are at pre-crisis levels, in spite of the severity of the recession, is that policy interventions have been aggressive. Immediately, at the onset of the crisis, monetary policy turned very expansionary. This can be illustrated by the weekly changes in the Fed balance sheet, as in this graph:

Weekly changes in the Fed balance sheet. USD mio.
Data source: Fed St. Louis Database

The figure plots the weekly changes in the Fed balance sheet due to purchases of financial assets, in millions of USD. The Fed balance sheet changes when the Fed buys/sells financial assets. During March this year, there were weeks when the Fed intervened to the tune of USD 600bn. This is an enormous amount of money. It is, by way of comparison, more than twice the weekly amounts spent during the financial crisis of 2008, the figure also shows.

At the same time, yields are very low. This forces investors to buy risky assets if they want some kind of return, supporting stocks.

In addition to very aggressive monetary policy, fiscal policy has also been very aggressive.

Why did stock prices fall during February/March?

OK, so earnings have not fallen as much as in 2008, earnings for Q2 2020 have surprised positively, monetary and fiscal policies have been very aggressive, central banks pump liquidity into the system, and interest rates are very low, implying that investors need to invest their money in risky assets if they want a positive expected return. These features help explaining why stock prices today are not much lower than in the beginning of the year. But, if this is the story, why did stock markets drop so dramatically in March?

Changes to expectations to earnings

Earnings have dropped in Q1 and Q2, even if considerably less than in 2008. Perhaps the stock-price drop in February/March was simply due to a downward revision in expected earnings. Alas, this is not the case. Landier & Thesmar (link) have an interesting analysis where they look at analysts’ expectations to the earnings of S&P500 companies during Q1 and Q2 2020. They find that analysts cut their expectations to earnings of S&P500 firms, but not so much that it can account for the drop in stock prices during February/March. In other words, the drop in stock prices in February/March cannot be explained by analysts reducing their earnings forecasts.

If the drop in expected earnings cannot account for the drop in stock prices in February/March, what happened then? Financial economists have a straightforward way of explaining this. Stock prices are discounted cash-flows. To understand stock price movements, we must understand cash-flow and discount rate movements. When the fall in expected earnings is not large enough to account for the drop in stock prices, discount rates must have increased in February/March. In other words, during February/March investors required a higher expected return if they should invest in stocks. This is also the conclusion in Landier & Thesmar and in Gormsen & Koijen (link). Basically, this is the conclusion in most empirical asset-pricing literature: stock prices move too much to be justified by movements in cash-flows. Discount rate variation is the reason, the literature concludes.

When stock prices move, and it cannot be because of cash-flow movements, it must be discount-rate movements. This is fine, but it is also somewhat tautological: If A = B + C, and A moves but B does not, then it must be because C moves.  A more difficult question is what makes discount rates move in the first place? I.e., what is the deeper economic explanation? Perhaps/probably risk aversion spiked, when investors in February suddenly realized the severity of the virus. Perhaps/probably some market participants faced funding constraints. And so on. In other words, I agree that discount rates most likely spiked during March, but I am not 100% sure why and I do not know if the increase in risk aversion is large enough to account for the increase in discount rates, and thus account for the drop in stock prices.

Lingering doubts

So, a potential reason why stock markets have done better than in 2008 is that earnings have not suffered as much as in 2008 and central banks have flooded the market with liquidity (and yields are at zero). The reason why we saw a massive fall in stock prices in February/March, and an unprecedented rebound during April/May/June, then probably is that discount rates increased during the early phase of the crisis, and then stabilized. This is a story that somehow makes sense.

Two things are still strange (to me at least), though.

First, if stock prices are at their right levels now, why did they have to fall so much in March? OK, because risk aversion increased and funding conditions tightened. But, if risk aversion increased in February because investors understood that a recession was looming, why would investors turn less risk averse three weeks later, when economic forecasts just kept on deteriorating? Probably the Fed and the Treasury (via monetary policy and fiscal policy) eliminated the spike in risk aversion via aggressive policy interventions, but it is still not 100% clear how to reconcile these features of the data.

Second, the behavior of earnings has been surprising. During recessions, earnings normally contract much more than economic activity. So, when economic activity in 2020 contracts much more than in, as an example, 2008, a reasonable hypothesis is that earnings in 2020 would contract much more than in 2008. This has not happened.

To some extent, this graph summarizes both the explanation of the relatively mild response of the stock market to this recession and the remaining puzzle:

Percentage changes in US real GDP and earnings of S^P 500 firms from Q3 to Q4 2008 and from Q1 to Q2 2020.

The figure shows how earnings dropped 68% from Q3 to Q4 2008 but seems to drop only 17% from Q1 to Q2 this year. This explains why the stock market has performed considerably better during this recession compared to its performance in 2008, for instance. On the other hand, the figure also shows that GDP dropped by 10% from Q1 to Q2 this year and only by 2% from Q3 to Q4 2008, i.e. the fall in economic activity is five times larger during this recession. It is puzzling that earnings drop so much less during this recession when economic activity contracts so much more.

So, the relatively modest contraction in earnings helps explaining the relatively fine performance of the stock market during this recession, but it is difficult to understand why earnings have behaved reasonably well. Perhaps this is because banks were suffering in 2008, but are able to help firms getting through this recession. Perhaps it is because firms have been able to adapt better this time. We do not really know. From an academic asset-pricing perspective, it is interesting that the stock market has behaved so differently this time around, compared to how it normally behaves. From an investor perspective, we can only hope that the stock market will keep on behaving in a different way than it usually does, as, otherwise, stock prices will fall going forward.

Conclusion

The facts that earnings have done better than in 2008 and that monetary policy has been very aggressive help us understand why the stock market has done well during this recession. Some puzzles still remain, though. For instance, why have earnings done so reasonably well, given the severity of the recession, and why did risk aversion increase so dramatically in February only to normalize few weeks later, in spite of the worsening recession. Perhaps the sensible answer is that this recession has been unusual in many dimensions, and some things will remain difficult to understand.

The weird stock market. Part I: Facts and wrong explanations

The behavior of the stock market during this recession has been perplexingly. To understand it, we need to answer three main questions: (i) why did stock markets fall so spectacularly during February/March, (ii) why did stocks rebound so spectacularly during April/May, and (iii) why is the stock market currently at its pre-crisis level? This blog post explains why these stylized facts are so difficult to understand jointly. In my next blog post (link), I will offer my interpretation of the evens.

Observing the stock market during this recession has been a like watching a roller coaster. The fall in late-February/early-March was the fastest bear market in history, the rebound has been historically fast, too, and – in spite of the worst recession ever – the stock market is currently back at pre-recession levels. Somebody leaving for the moon in January and returning now would not be able to see any trace in the stock market of the worst recession ever. This is in stark contrast to normal recessions. People interested in financial markets and the economy should be puzzled.

The problem – in a nutshell – is that if you claim that you understand why stocks are currently at pre-recession levels, then you face a challenge explaining why we needed to go through the fastest bear market ever during February/March. On the other hand, if you claim that the fast fall and rise in markets was just a short-lived technical blip (perhaps due to funding squeezes and fear), then you face a challenge explaining why that technical blip should result in a loss to the tune of USD 20 trillion (link). Finally, if you claim that you understand why markets fell so fast in February/March (perhaps because we were facing the worst recession ever – which, by the way, is a good explanation), then you face a challenge explaining why markets recovered so strongly in April/May/June, as the recovery cannot be explained by a brighter economic outlook. In fact, we have seen continuous downgrades of the economic outlook. E.g., the IMF WEO in June lowered its April forecasts for global economic output to –4.9%, from –3.0%. A huge downgrade. Strange that stocks recover in spite of this.

In this post, I describe the facts. I also review a couple of suggested, but wrong, explanations. In my next post (that I will publish next week), I will offer my view on what has been going on.

The facts

Here is an updated version of a graph that I have presented earlier. It shows the Danish, US, emerging market, and world stock markets (MSCI), normalized to one on January 1, 2020:

Stock markets since January 1, 2020. MSCI indices.
Data source: Thomson Reuter Datastream via Eikon.

Stock markets reached a temporary peak on February 19, after which they tanked dramatically. As mentioned here (link), it was the fastest US bear market in history.

The rebound has been equally spectacular. The US stock market is already back at its January 1 level. World and emerging markets are still a few percentages behind, but, basically, they have also recovered from the crisis.

In the US, it was the fastest bear market ever, as mentioned. In this graph, I document that it has also been one of the fastest recoveries. I calculate rolling 11-week gains/losses in the SP500 during the last 50 years.

S&P 500, 11-week percentage changes.
Data source: Fed St. Louis Database

As you can see from the encircled peak on the right-hand-side of the graph, from its bottom on March 23, the SP500 gained app. 45% until June 8. The graphs shows that no other 11-week period since 1970 has witnessed such a large gain (I cherry-pick the 11-week period, but the main message is that the rebound has been spectacular, and this message is robust).

Wrong explanations

You hear/read many explanations. Some of them are just not correct.

It all boils down to FAANG

Some claim that it is not the overall stock market (typically these people refer to the SP500) that has recovered. Instead, some argue, it is all due to FAANG (Facebook, Apple, Amazon, Netflix, and Alphabet’s Google). It is true that the behavior of FAANG has been impressive and has driven a significant part of the SP500’s recovery, but this is not the whole story. As you see from the first graph above, emerging markets have recovered, too. This is obviously not due to FAANG. Also, some markets, such as the Danish, have recovered even more spectacularly than the US market. Not FAANG either. Even US small-cap stock have recovered. Not fully, but significantly. The Wilshire US Small-Cap Index gained an astonishing 57% during the March 23 through June 6 period. True, small-cap stocks are still (early August) 12% below their January 1 level, but when small-cap stocks have rebounded spectacularly, too, it emphasizes that this is not all about all FAANG, even when FAANG stocks have done very well.

Markets also recovered after the 2008 financial crisis

This is a no-brainer: Markets always recover. The point here is that this rebound has just been amazingly strong. In this graph, I compare the behavior of the SP500 during autumn 2008 and the corona crisis. “0” in the figure is September 19, 2008, respectively February 21, 2020:

S&P 500, daily closing prices. Normalized to “1” 25 days before September 19, 2008, respectively February 21, 2020. September 19, 2008 and February 21, 2020 marked by vertical line.
Data source: Fed St. Louis Database

During the first couple of weeks of this spring’s crash, it looked like autumn 2008. The pain was short-lived, though. Stock markets fell for a couple of weeks and then rebounded. In 2008, stocks just continued falling.

It has taken a couple of months to recover this time around. After the financial crisis of 2008, it took more than two years. This figure shows that the US stock market was back at its summer-2008 level in early 2011 only, and the world stock market later still.

Stock markets since January 1, 2020. MSCI indices.
Data source: Thomson Reuter Datastream via Eikon.

This recession is not as bad as 2008

It should be obvious by now that this argument is very wrong indeed. I have argued myself that there is hope that, when we get a vaccine and economic activity picks up again, the economic rebound will be stronger than in 2008, the reason being that we entered this recession with a more “balanced” economy than in 2008 (in 2008, we had a housing bubble, a weak financial sector, etc.). Nevertheless, the short-run loss this time around is just so much larger than in 2008.

Last week, we got figures for GDP in the US and Europe. This graph compares the cumulative falls in real GDP in the Eurozone and the US in Q3+Q4 2008 with the cumulative drops during the first two quarters of this year.

Cumulative change in real GDP in the US and the Eurozone. “2008” is Q3+Q4 2008 and “2020” is Q1+Q2 2020.
Data source: Fed St. Louis Database

US real GDP fell by more than three percent in Q3 and Q4 2008, whereas Eurozone real GDP dropped by five percent in autumn 2008. It was a severe recession in 2008. Nevertheless, it pales compared to this recession. This time around, US GDP has fallen by more than ten percent already and Eurozone GDP is down by a staggering 15% during the first two quarters of 2020.

What about the length of the recovery? After 2008, it took around two years before economic activity had reached its pre-crisis level. This figure shows for, e.g., the Eurozone that it will last more or less equally long this time (expectations for 2020 and 2021 are from the EU Commission, Spring 2020).

Development in real GDP for the Eurozone as of Q2 2008 and as of Q4 2019. Developments after Q2 2020, i.e. after 2 quarters in 2020, are expectations from the EU commission.
Data source: EU commission.

The figure shows that Eurozone GDP was 5% lower in Q4 2008 compared to Q2 2008 whereas it is 15% down in Q2 2020 compared with Q4 2019. After eight quarters, GDP is basically back at its pre-crisis level. This means that the recovery is expected to be stronger, but this recession is just very deep.

In other words, this recession is much deeper – one can multiply the drop in 2008 by a factor of three or so to get the drop this time – and it will take several years before economic activity is back at pre-crisis levels. This means that the short-run cost to society is bigger this time around (a deeper fall stretched over the same period).

And, in spite of this very strong recession, stocks are doing fine. That is perplexing.

Above, I have presented stories that cannot explain what has been going on. In my next post (link), I will offer my view on this.

Expected returns

The Council for Return Expectations published its forecasts of expected returns last week. There is a wide dispersion across asset classes. Returns on “safe” assets (government bonds) are expected to be very low, even negative, on the short horizon, whereas emerging markets equities are expected to return close to ten percent per year. The Council also publishes forecasts for standard deviations, correlations, and inflation.

As one of my external activities, I chair the Council for Return Expectations (link). The Council estimates expected returns, standard deviations, and correlations on ten broad asset classes. The estimates are widely used in the Danish financial sector and public discussions. Danish pension funds use the estimates when they calculate pension projections for their customers and banks use them when they make projections for how outside-pension savings can be expected to develop. Newspapers also write about them, too.

I will argue that the Danish financial sector has been a front-runner in designing a way to make such independent return assumptions. I hope the set-up helps improving the credibility of the projections banks and pension funds make.

In this blog post, I present the latest estimates from the Council. As it is the first time I present these estimates on this blog, I start out describing why the Council was established, how the Council works, and the procedure we use in the Council to find expected returns. Afterwards, I present the forecasts.

Background: The Council for Return Expectations

The Council was established (under a slightly different name) two years ago. The background was as follows.

Danes have large pension savings. Together with the Netherlands, Denmark has the largest pension savings in the world relative to GDP (We have a paper describing some of the key features of the Danish pension system here; link). Historically, pension savings have been guaranteed, meaning that pension holders were guaranteed a minimum average annual return on their pension savings. Because of low interest rates, longer life-expectancies, etc., Danish pension funds have shifted into so-called market-based pension products during the last decade or so. In these products, there is no minimum guaranteed return. This allows the pension funds to invest more freely, hopefully enabling them to secure higher risk-adjusted returns. Basically, you go from a constrained to an unconstrained (or at least less constrained) maximization problem, which should lead to a better outcome. However, when a pension holder is not guaranteed a minimum return, the expected pension payouts during retirement will obviously become more uncertain. The assumed expected returns and risks on the different assets that pension funds invest in thus become even more important (compared to a guaranteed pension product) for an individual’s expected pension payments during retirement.

A couple of years ago, I was approached by the Danish pension industry and asked whether I would help them design a set-up that could be used to generate expected returns on pension funds’ investments. The result was the following: based on inputs from international financial institutions, present expected returns over the next ten years on ten different asset classes, as well as long-run (> 10 years) expectations on two assets classes (stocks and bonds), and update these forecasts annually. The pension industry judged that an independent committee should specify and regularly update the return expectations, in order to secure arms-length. They asked me if I would chair this committee. The Committee is now called the Council for Return Expectations

Last year, banks in Denmark asked whether we (The Council) would be able to expand the set of return assumptions. The background was – probably fair to say – a scandal in the largest bank in Denmark. Danske Bank had advised some of its customers to invest in an investment product that the bank itself expected would yield a lower return than a bank deposit. I.e., the bank had advised its customers to invest in a suboptimal product, given expected returns. It led to the resignation of the interim Danske Bank CEO (link). The Danish banking sector concluded that arms-length was needed in determining return expectations used for investments outside pension savings. They asked the Council if we could include return expectations for a shorter horizon (1-5 years, in addition to the 1-10 years horizon) and a more frequent update of the return assumptions (twice a year, instead of annually). These forecasts were published last week.

Procedure for determining expected returns

We provide forecasts for nominal returns on ten broad asset classes. Having done extensive research on the determinants of expected returns myself, I know that even within a precisely defined asset class, forecasters can disagree substantially on the outlook for the asset class. When designing the set-up, I thus suggested that return expectations should be based on an arms-length principle and take estimation uncertainty into account. We do this by basing our expectations on inputs from several international investment houses.

We (The Council) receive inputs from Blackrock, J.P. Morgan, Mercer, and State Street. We are truly thankful for their help.

Blackrock, J.P. Morgan, Mercer, and State Street provide their estimates of expected returns, standard deviations, and correlations on each of the ten asset classes for each of the different horizons to the Council. The ten asset classes for which we provide expected returns are:

  • Government and Mortgage Bonds
  • Investment-grade bonds
  • High-yield bonds
  • Emerging market sovereign bonds
  • Global equity (developed markets)
  • Emerging markets equity
  • Private equity
  • Infrastructure
  • Real estate
  • Hedge funds

The horizons are:

  • 1-5 years.
  • 6-10 years.
  • 1-10 years.

Returns are nominal. Estimates are for the arithmetic average annual return per year during the different horizons.

Returns are hedged into euros, i.e. are euro returns, except from emerging market equities and local currency emerging market debt that are unhedged (emerging market debt is 50%/50% local/hard currency). The Danish kroner is pegged to the euro, i.e. euro returns are basically also Danish Kroner returns. Returns are before fees, expect from the last four asset classes (private equity, Infrastructure, real estate, and hedge funds) that are after fees to the funds that manage these types of investments, but before the fees to the Danish pension/mutual fund that in turn invests in the private equity funds, hedge funds, etc.

In addition, we provide forecasts for Danish inflation based on inputs from a number of Danish forecasters (the Danish central bank, ministry of finance, etc.).

The Council consists of three people: Torben M. Andersen (professor of economics, University of Aarhus; link), Peter Engberg Jensen (former CEO of Nykredit and current chairman of Financial Stabilitet; link ), and myself as Chairman. Our job in the Council is to specify the relevant asset classes and their characteristics, choose methods used to weight the inputs together, come up with reasonable forecasts, communicate these to the public, etc.

Forecasts of expected returns

The following table presents our forecasts of expected annual returns for the next five years, the next ten years, and years six through ten:

Source: Council for Return Expectations.

Over the next five years, we expect “safe” investments (government bonds and Danish mortgage bonds) to return a negative 0.3% per year on a pre-fees, pre-taxes, and pre-inflation basis. This is a low return. On a net-of-fees, after-tax, and real-terms basis, it is even lower. In the Danish media, much was written about this number (-0.3%). For finance professors and professionals, the number is no big surprise given low interest rates, but for ordinary investors, the publication of numbers such as these from trustworthy sources helps communicating the message that it is difficult to earn a decent return these days without taking on risk.

On a more technical term, the return on this asset class is the return to a bond portfolio consisting of 50% Danish mortgage bonds (that are triple-A rated, as you probably know), 20% Danish government bonds, and 30% Euro government bonds, with a duration of five years.

There is a wide dispersion across the different asset classes. For instance, we expect emerging market equity to yield 9.5% per year. There is thus an almost ten-percentage point difference between the expected return on the safest asset class and the asset class yielding the highest expected return.

Notice also that we generally expect higher returns after five years. We expect higher interest rates, causing capital losses and thus low returns during the first five years, but then higher returns later on. This in itself helps raising expected returns on other asset classes.

Standard deviations

In the Council, we want to stress that estimates of expected returns are surrounded by uncertainty. To the finance professionals, this is obvious (though, one might sometimes have the impression that even professionals tend to forget this), but to the ordinary investor, this is even more important to emphasize. The ordinary investor might otherwise conclude that when expected returns on emerging markets is 9.5% per annum, but government bonds are expected to yield a negative 0.3% per annum, I better put all my money in emerging market equity. We want to stress that this is a risky strategy. This ambition has guided us when it comes to our estimation of standard deviations.

The expected returns we present are constructed as simple unweighted averages of the expected returns of Blackrock, J.P. Morgan, Mercer, and State Street, asset-class by asset-class. They also provide us with their expected standard deviations. We do not use the simple averages of these as our estimates of expected returns, though. Instead, we regress the standard deviations we receive from the investment houses on the expected returns received from the same investment houses. The standard deviations the Council presents are then the fitted values from this regression. The main objective we achieve by following this procedure is that we make sure that there is a clear relation between risks and returns.

The standard deviations surrounding the estimates of expected returns are here:

Source: Council for Return Expectations.

We expect a 3.5% standard deviation of government and mortgage bonds (over the next ten years) whereas we expect a 29.6% standard deviation surrounding the estimated returns to emerging markets equity. There is thus a clear relation between expected risks and returns. This clear relation also appears from this graph that plots risks on the ten asset classes against their returns (1-10 years horizon):

Source: Council for Return Expectations.

One might say that the price we pay from estimating standard deviations in this way is that some of the individual estimates of standard deviations might differ slightly from market consensus. As an example, our estimate of the standard deviation of global equity is around 14%. Market consensus probably is that this is a little higher, at 16%-17%. On the other hand, the advantage we obtain from proceeding in this way, as mentioned, is that we secure a clear relation between risk and returns.

Correlations

We also present correlations between expected returns. Here they are for the first ten years:

Source: Council for Return Expectations

Correlations are simple averages of the correlations we receive from Blackrock, J.P. Morgan, Mercer, and State Street, asset-class by asset-class. The main thing to notice probably is that we expect all correlations to be positive. This is bad news for investors, one might argue, but we saw this during the March turmoil. In March, bonds and stocks both lost in value, i.e. bonds did not hedge the risk of stocks. Our correlations reflect this.

The correlations and standard deviations are used by the pension funds to calculate confidence intervals surrounding the individual’s expected pension income. I want to stress that it is advanced – and good! – that pension holders in Denmark not only learn about their expected pension income but also the uncertainty surrounding this expectation.

Inflation

We expect the Danish rate of inflation to be 1.2% over the next five years and 1.4% over the next ten years.

All the numbers

All the numbers – means, standard deviations, correlations, for all the horizons, etc. – are available on the webpage of the Council (link). On this webpage, addition information about the Council can be found as well.

Conclusions

We live in low-interest times. Investors might be tempted to invest more risky in order to generate a decent return. But what are decent returns? And how much extra risk do investors incur when investing more risky? In most countries, you get one set of answers when you visit one pension fund/bank/financial advisor, but another set of answers when you visit a different pension fund/bank/financial advisor. This makes investors uncertain and do not help building trust between the financial sector and investors. The financial sector in Denmark has found a cool way of presenting independent/arms-length forecasts. I hope that other countries might be inspired from this way of addressing this important issue.

—————————————————————————-

PS. In my last post (link), I wrote about a new paper I have written on the financial stability in the Nordics. The journal where the paper is published is now available (link). It contains my own article and articles on the banking union, bail-in debts, household debts, and macroprudential policy, as well as a number of enlightening discussions.

Zero-probability events that happened

Some of the events we have seen during this crisis are so unlikely that we need tricks to calculate their probabilities. This is a journey into the world of very small probabilities and very large numbers. I admit it is somewhat surreal. But it is important as these small-probability events can have long-lasting effects on economic activity.

The defining characteristic of this recession is the speed with which markets and economies started freefalling. From one day to the next, economies were shut down. Economic activity came to a complete sudden stop in some sectors. In different blogposts, I have used words such as “unprecedented”, “completely crazy”, “horrifying”, “tremendous”, etc. to describe what happened.

Using words like these is adequate, I think (I admit I was shocked by what happened), but I have come to a point where I want to be more precise. As economists, we want to put numbers on things. I want to calculate the probability of the events. This turned out to be more complicated than I had first imagined.

The probability of a 121-sigma event

On Monday, April 20, the oil price (West Texas Intermediate) closed at USD -38 for a barrel of oil. I describe this here (link). This was a drop of 306% relative to the closing price the previous trading day. Based on daily data since 1983, the average percentage change in the oil price is 0.03% and the standard deviation 2.5%. I called the event “completely crazy”, which I still believe is a fair description. Now, I want to know “how crazy” it was. What was the probability that it would happen?

The happy-go-lucky Professor of Finance, i.e. me, opens his Excel spreadsheet and enters the command used to find the probability that an event of -306 happens when data are normally distributed with mean 0.03 and standard deviation 2.5.

I press “Enter”. Excel returns “0”. The Professor of Finance thinks this look strange and increases the number of decimal places. Excel just shows “0.000….”. According to Excel, this is a zero-probability event. It could not happen.

But it did happen. I start remembering the statistic classes many years ago, and recall the discussions on low-probability events.

Luckily, I have helpful colleagues. I write CBS Professor of Statistics Søren Feodor Nielsen. He tells me that the probability I am looking for is below the “machine precision”. He also tells me that the probability itself might be extreme, but the logarithm to the probability is probably not. We calculate the log-probability (using a different statistical package than Excel). It is -7495.137, i.e. the likelihood is exp(-7495.137). This is, unfortunately, such a low number that a computer cannot calculate this either.

We then calculate the log base 10 probability. Now we have the result. The probability is 0.799 x 10^(-3255).

This is a zero followed by 3255 zeroes, and then 799. Practically zero, but not exactly zero. The event happened, but it is extremely unlikely. We can call it “completely crazy”, but we can also say that the probability is 0.799 x 10^(-3255).

There is another way to illustrate how unlikely this event was. When the probability is 0.799 x 10^(-3255), we should see this event happen every 1.2516 x 10^(3255) days. I.e., a number with 3255 numbers before the decimal place. I simply do not know what such a number is called (link). This is where it starts getting surreal.

How precise is this? We have calculated it, but Søren tells me we should not put too much faith in its precision. Tail-probabilities in the normal distribution are calculated by numerical approximations, and it is questionable how precise they are when we are that far out in tail. Admittedly, the question is of course also how important it is that it is precise that far out in the tail. The probability is unbelievably small. That is the main thing. Exactly how small is perhaps not that important.

S&P 500

This graph shows daily percentage changes in the S&P 500 throughout the last 50 years.

S&P 500. Daily data. May 1970 – May 2020.
Data source: Thomson Reuter Datastream via Eikon.

On March 13, the S&P 500 fell 12%. The average daily percentage change in the S&P 500 (calculated up until March 12) is 0.03% and the standard deviation is 1.05%.

The likelihood that we will see a 12% drop in the S&P 500 on a daily basis, given the behavior of the S&P 500 during the last 50 years, is very small, but not so small that it cannot be calculated in Excel. Excel says it is 1.0827 x 10^(-29).

These are daily data. If we assume 250 trading days per year, we should see this event happen every 3.69 x  10^(27) = 3,694,454,429,465,560,000,000,000,000 year. I.e., every 3.694 octillion year.

This is also somewhat surreal.

There are many caveats. We are again so far out in the tail that we should not put too much emphasis on the exact number of decimals and the exact number after all the zeroes. Also, all these calculations are based on the assumption of normally distributed data. Given that we saw a 21% fall in the S&P 500 on Black Monday, October 19, 1987, we have seen two very unlikely crashes within the last three decades. According to these calculations, they should happen much more seldom. We use the normal distribution, but data might follow a different distribution. For most practical purposes, however, it is not necessary to know the exact distribution of these extreme events. The important thing to know is that the likelihood is very small.

Other numbers

In this post (link), I describe how the initial jobless claims soared, confidence indicators fell, GDP dropped, etc. As an example, the likelihood that we should see almost 7 million people filing for jobless claims on March 28, given the complete previous history of jobless weekly claims, is 0.97 x 10^(-841). This is again such a small probability that Excel cannot even calculate it.

Economic effects

There is a broader point to these discussions. Events like those described above might have long-lasting consequences for economic activity.

When events are unlikely, we assign low probability to their occurrence. One hypothesis is that we keep on assigning low probabilities to their occurrence. In this case, future investment decisions of firms and future consumption decisions of households are unaltered by the events we have been going through. It was a temporary shock. It has very low probability. It will not influence how we form expectations going forward.

An alternative hypothesis is that we have become so scared by the event that it will haunt us for years to come. We update our beliefs disproportionally much.

Which of the two scenarios play out is important for the recovery from this recession. Will we start consuming when economies open up or will we hold back because we have become scared?

Kozlowski, Veldkamp and Venkateswaran (2020) have an important paper on this (link). Their main point is that events like those studied above, i.e. events that are very unlikely but have large impacts, will have persistent effects on beliefs. They write that “tail events trigger larger belief revisions” and that “because it will take many more observations of non-tail events to convince someone that the tail event really is unlikely, changes in tail beliefs are particularly persistent”. This is an important insight. If this is how we form expectations, it will slow down the recovery from this recession. Kozlowski et al. also show, however, how government interventions can reduce the effect, but not eliminate it.

Conclusion

These weeks we are seeing infection rates declining in many countries and economies opening up again. These are very good news. Let us hope we can start returning to some kind of normality. It will take time before we are back to where we came from, though. Some things might even have changed for good. One thing is for sure: we will not get back as fast as economies and markets fell in March. What happened was very unlikely. But it did happen.

Is the stock market too optimistic? Or, is the market always right?

The rebound in stock markets has been spectacular. One may wonder whether it is sustainable.

What does it actually mean that the stock market is “too optimistic”? Doesn’t the stock price always reflect the average expectation of all investors? True, and, in this sense, the market cannot be “too optimistic”. On the one hand, the market is always right.

On the other hand, the legendary economist Paul Samuelson famously noticed that the “stock market has predicted nine of the last five recessions”. Stock markets also appear “excessively volatile”, as Shiller showed already in 1981. I.e., the stock market might always be right, but perhaps we are going through a period of excessive volatility where markets were overly pessimistic in March and are overly optimistic now.

In any case, if the stock market is always right, so is the futures market. Investors in the futures market expect huge drops in dividends over the next year. If stock prices behave as they usually do during recessions, stock prices should drop even more, that is dropping even more than dividends.

Market developments

Before we start this attempt to explain things and look ahead, let us review the facts. This graph shows developments in the Danish, the US, the world (MSCI All countries), and the emerging stock markets since the start of the year, all MSCI indices (Danish index is in Danish kroner, the rest in USD):

Stock markets since January 1, 2020. MSCI indices.
Data source: Theomson Reuter Datastream via Eikon.

Stock markets did well in the beginning of the year, fell dramatically from mid-February through mid-March, and have rebounded spectacularly since then. Today, the Danish stock market is above its January 1 value, the US market is 10% down, the world market is 15% down, and emerging markets are 20% down.

What could explain current stock prices?

Stock prices are by definition discounted future cash-flows. That is easy to say. The difficult part is to find the expected future cash-flows and the appropriate discount rate.

Let us start with a positive view on markets and see what is needed to support this.

To begin with, let us keep the discount rate fixed. Let us also, as a starter, assume that valuation ratios are constant. For instance, let us assume that stock prices closely follow developments in real economic activity. Under these assumptions, we would, largely, be able to understand recent market movements. These assumptions would also support a rosy view of the future. Afterwards, we discuss if this is a likely scenario.

Forecasts for economic activity in light of the corona crisis start coming in. Late April, we got the WEO from the IMF and forecasts for the US from the CBO, and this week we got forecasts for Europe from the EU-commission. This figure shows the expected path of real GDP in the US and EU:

Expected developments in EU and US real GDP. The CBO does not provide quarterly growth rates for 2021, so I assume linear growth during 2021, accumulating to the CBO forecast of 2.8% for 2021 .
Data source: EU commission and CBO.

This recession is enormous. GDP is expected to fall by 15% in Q2 this year, compared to late 2019. Luckily, economies are expected to rebound sharply after this quarter, too. The EU commission expects a strong recovery in the EU in 2021, with 6.1% growth in 2021. The CBO expects 2.8% growth in 2021 in the US. Whether this difference is realistic, I do not want to discuss here.

The economy drops by 15% in Q2. If stock prices follow GDP, as we assume for now, stock prices should have dropped by 15% in Q2. This is almost spot-on.

This theory would also predict that we have a great year in front of us. Economic activity should improve by something like 15-20% until late 2021. If stock prices follow, stock prices should also increase with something like 15-20% from here.

What about the huge drop in March? This we can also explain, I think. Basically, it had little to do with underlying economic fundamentals. Some leveraged hedge funds got squeezed, they received margin calls, they dumped everything to raise cash, there was panic, spreads widened, and markets feared a replay of 2008 (I comment on it here and John Cochrane has a nice and more detailed explanation here). Stress on markets almost reached 2008 levels, as, for instance, the St. Louis Fed Financial Stress index indicates:

St Louis Fed Financial Stress Index.
Data source: St. Louis Fed.

Central banks intervened and provided liquidity. Markets calmed down. The stress index is still somewhat elevated, but much lower than in March. Markets started looking at economic fundamentals again. With lots of liquidity around, and low yields, investors bought stocks. This was a temporary crash.

The intermediate conclusion is that if stock prices follow GDP, stock prices should drop by something like 15% during Q2, only to rebound afterwards. And, as of today, stock prices have in fact fallen by something like 15% since the start of the year, with a bumper on the road in March. If we stop here, everything would be fine and we should expect substantial stock market gains going forward. Under these assumptions, markets are expected to rebound by something like 15-20% until late 2021.

Cash-flows do not always follow economic activity

Unfortunately, we cannot stop here. We need to go back to the definition of stock prices: Discounted cash-flows. I truly believe that cash-flows relate to economic activity in the long run (I have research demonstrating this), but I also believe that there are temporary business-cycle deviations between cash-flows and economic activity. And these deviations can be substantial.

We have expectations to economic activity from IMF, CBO, EU, and so on, but how do we find expectations to cash-flows? Niels Joachim Gormsen from the University of Chicago, a smart former Ph.D. student at Copenhagen Business School, has, together with Chicago Professor Ralph Koijen, developed a method that can be used to back out expected changes in dividends from dividend futures. They also estimate a relation between dividend growth and GDP growth, such that they can back out expected GDP growth, too.

Their latest estimates are from April 20. Compared to January 1, 2020, Gormsen and Koijen estimate that US GDP will be 3.8% lower over the next year (precisely, Niels tells me, they compare expected growth from April 1, 2020 through April 1, 2021, to expected growth from January 1, 2020 through January 1, 2021). This is not far from what the CBO expects (the figure above shows that GDP will be something like 5% lower ultimo 2020 compared to primo 2020).

The scary thing is that Gormsen and Koijen show that markets expect dividends to be 18% lower over the next 12 months, i.e. drop by 13%-points more than GDP. An 18% drop in dividends is a very large drop in historical terms.

This graph shows how investors update their expectations to future dividend growth rates during the corona crisis:

Data source: Gormsen and Koijen (2020).

For the EU, Gormsen and Koijen expect GDP, respectively dividends, to drop by 6.3%, respectively 28%. The market is always right, right?

Unfortunately, we cannot stop here either.

Stock prices react excessively to cash-flows during recessions

We need to talk about the last part of the definition of stock prices: discount rates. Research shows that discount rates move counter-cyclically, increasing in bad times and dropping in good. From our definition of stock prices, this means that stock prices should fall by more than dividends in bad times, if discount rates increase in bad times.

Tim Kroencke from the Univeristy of Neuchatel has an interesting paper that studies how stock prices move in relation to dividends during recessions. The central graph in the paper is this one:

Data source: Kroencke (2020)

The graphs shows how dividends (and earnings) fall during recessions and how stock prices fall even more (there are two stock price indices. Read Tim’s paper to get the explanation for the difference. The point is that stock prices fall more than dividends.)

The figure shows that US dividends drop by 10% and US stock prices drop by ten percentage-points more, i.e. 20%, on average during US recessions. It also shows that stock prices do not drop ahead of the drop in dividends, but alongside. This is not good news.

Gormsen and Koijen’s estimates say that we should expect dividends to drop by 18% for the US and 28% for the EU over the next year. Kroencke says that on average stock prices drop by 10%-points more. This means that stock prices should drop by close to 30% in the US. If we use the 10% drop in the price-dividend ratio for EU data, EU stock prices should drop by close to 40%. Today, stock prices are down 15% globally.

Conclusion

We might hope that this recession plays out in a different way than recessions usually do. We might also hope that stock markets react in a different way than they usually do. We might hope that everybody starts spending when economies open up, companies start producing, and earnings and dividends do not suffer. In this case, the drop in dividends might not be that large. And, we might hope that stock markets do not fall by more than dividends, in contrast to what they normally do. This could for instance be because central banks are marginal investors in many markets now, driving asset prices away from what they would have been if prices were solely determined by private market participants. This is what markets hope. And, of course, this might turn out to be the case.

We might also fear, however, that companies will start facing problems given the severity of the crisis, i.e. this turns from a liquidity crisis to a solvency crisis. Should this happen, earnings and dividends will drop. The market is always right. The futures market expects dividends to drop by something like 20% for the US and 30% for Europe. If stock prices react as they normally do during recessions, stock prices should drop even more. The 15% drop since early 2020 seems small in this light.

———————————————————————————-

PS. Did you by the way notice the German Constitutional Court ruling this week? Given last week’s post on the Italian situation, I might just inform you that the Italian yield spread to Germany widened as a consequence. Not a lot – 15 basis points or so – but in the wrong direction.

The stock market and more horrifying figures

A couple of weeks ago, I collected some graphs revealing how deep this recession is (Link). Two weeks have passed. New data have arrived. They are still horrifying.

We now have aggregate numbers for Europe. In the first quarter of 2020, Eurozone GDP dropped more than it did during the worst quarter of the financial crisis of 2008:

Quarterly growth rate of Eurozone real GDP.
Data source: ECB.

GDP figures are aggregate data. They show how total economic activity has developed. That’s why they are important. They are, however, also a snapshot of the level of economic activity, collected with a lag. The latest figures deal with the first quarter of 2020. So what about asking firms and households how they feel and how confident they are? If people and firms think this will be a short-lived recession, they should be confident. The EU commission publishes confidence indices for firms in the industrial sector, the services sector, and for households in the EU. Confidence indices drop, as we have never seen before.

Monthly changes in confidence indices.
Data source: EU commission.

The industry, the service sector, and households all have no confidence in the economy.

Next, I collect trailing averages of initial jobless claims in the US during the preceding six weeks. During the past six weeks, more than thirty million Americans have lost their jobs. It is not just a historical record. It is very sad.

Initial jobless claims in the US. Rolling six-week averages.
Data source: St. Louis Fed.

Most likely the unemployment rate will come in at close to 20%.

Behind all these numbers and figures, there are real firms and real people. Firms will be forced to close. Individuals will lose their jobs. Households will struggle.

So, how does the stock market do? Given the scale of the recession, you would expect it to suffer tremendously. It does, however, great.

From its temporary trough on March 23, the SP 500 has gained 32%. It tanked heavily in late February and early March, but it is today (May 1) “only” 13% below its peak on February 19. I write “only” as the stock market often losses something like 50% in a recession (Link). This recession is unprecedented, as shown above, so you would expect unprecedented losses on the stock market. This is not what we see.

It is not unusual that the stock market starts rising before the end of the recession . And the stock market did fall very fast early in the recession. In the US, it was the fastest bear market ever (Link). But given the depths of the recession, stock markets have rebounded surprisingly fast.

True, not all stock markets have rebounded. The Spanish stock market (MSCI Spain) is 30% below its peak on February 19. So is the Italian. And, the Argentine is down 31%.

So, some stock markets have rebounded strongly, but others have not. Let us try to get an overall picture.

This is a global recession. The aggregate value of global stocks markets is USD 44 trillion on April 29 (FTSE All World Index). On February 19, it was USD 52 trillion. At the bottom on March 23, it was USD 35 trillion.

World stock market capitalization. FT All World Index. USD bn.
Data source: Thomson Reuter Datastream via Eikon

This means that 20,000 billion USD(!) was lost on the stock market from February 19 through March 23, globally. It also means, however, that almost 10,000 billion USD have been gained during the last month or so.

Given the severity of this recession, it is – frankly speaking – somewhat surprising that global stock markets have not lost more than something like 15% since mid-February. Stock markets seem disconnected from the real economy. Why?

Of course, stock markets are forward looking and all that. And, yes, luckily, it seems that the corona virus is on retreat. These are very good news and give some hope. But, given the depth of the recession, I think it will leave scars. It will take time before unemployment in the US reaches 4% again, as an example.

The reason why stock markets in many countries have done great during the last month, when economy activity has suffered like never before, is actually rather simple. Central banks exercised the “central bank put”.

Central banks were every fast to enact even very large rescue packages. They started doing so in mid-March. This helped stabilize financial markets, depress yields, and flooded markets with liquidity. The goal, of course, was to support the real economy. It saved stock markets, too. Shortly after the announcement of all these comprehensive measures, the stock market started rising.

With lots of liquidity around, and low yields everywhere, markets convinced themselves that central banks would save the world. Markets bought stocks, and stock markets surged.

This is what I believe explains it. Otherwise, I cannot make sense of the fast rebound in the stock market. But I do believe markets have thereby become somewhat disconnected from the real economy. And this is strange to witness.

V, U, W, or L? The stock market votes “V”.

How will this recession play out and how will the recovery look? Will we get a short recession with a fast rebound (V), will we get a longer recession before the recovery (U), will we get a new lockdown in autumn resulting from a second wave of the Corona virus (W), or will economies remain depressed for a long time (L)?

Nobody knows, particularly this time around when the shape of the recovery will be determined by a virus and how this develops.

Supporting the V-shaped recovery, this recession is not caused by economic imbalances, such as an overvalued housing sector, too much debt, a fragile banking sector, or the like. Also, we know from history that recessions last longer and are deeper if they are caused by financial crises. This is also not the case this time around, in contrast to 2008, for instance. This means there is hope for a reasonably fast rebound, if we manage to get the virus under control.

On the other hand, if we get a second outbreak, e.g., in autumn, and economies are shut down again, the path of economic activity will probably take the shape of something like a W.

What we do know is that the depths of the recession is unprecedented. The fall in economic activity and the increase in unemployment is mind-blowing, and very scary (link).

This makes one fear that the recession could drag out. When economies open up, it will take time to find jobs for those who get unemployed during the recession. Firms will probably be reluctant making new investments until we have a vaccine. Consumers want to go to restaurants, cinemas, on vacation etc., but will probably hold back until they feel on safe ground, too. Uncertainty abounds.

In this environment, one would imagine that the stock market suffers tremendously. With a recession impeding, and with so much uncertain surrounding the future path of economic activity, one would imagined that stock markets, like economic activity, would be in freefall. This is not the case.

In the beginning of the lockdown, the stock market tanked. It was the fastest bear market ever (link). It reminded us very much about the dark days of autumn 2008. This graph shows the SP500 on a daily basis during the 2008 financial crisis and this crisis. “0” in the figure is September 19, 2008, respectively February 21, 2020.

S&P 500, daily closing prices. Normalized to “1” 25 days before September 19, 2008, respectively February 21, 2020.
Data source: Fed St. Louis Database.

Financial markets were in stress in mid-March, when even yields on safe assets increased (link). Fearing a replay of 2008, central banks and governments came to the rescue, and the stock market started its recovery. Since the bottom on March 23, the S&P 500 has gained an astonishing 28%. This is remarkable, given all the uncertainties and the depth of the recession. The contrast to the autumn of 2008 is stark. The stock market kept on falling throughout 2008 and early 2009, only to start its recovery in March 2009.

The stock market seemingly believes this recession will result in a V-shaped recovery. Let’s hope it is right. One might fear that it is not.