Are we already in a recession?

2022 Q1 GDP growth was already negative.  And, 2022 Q2 may very well be [negative] when the released data comes out. 

 

The majority of the financial media believes we are already in a recession because of the stubbornly high inflation (due to supply chain bottlenecks) and the Federal Reserve aggressive monetary policy to fight inflation.  The policy includes a rapid rise in short-term rates, and a reversing of the Quantitative Easing bond purchase program (reducing the Fed’s balance sheet and taking liquidity & credit out of the financial system).  The Bearish stock market also suggests we are currently in a recession. 

 

On the other hand, Government authorities including the President, the Secretary of the Treasury (Janet Yellen), and the Federal Reserve all believe that the US economy can achieve a “soft landing” with a declining inflation rate, while maintaining positive economic growth.  

 

The linked presentations include two explanatory models to attempt to predict recessions.  

 

Recessions at Slideshare.net 

Recessions at SlidesFinder  

 

The first one is a logistic regression.  The second one is a deep neural network (DNN).  Both use the same set of independent variables: the velocity of money, inflation, the yield curve, and the stock market.  

 

A copy of one of the slides describes the Logistic Regression model below.

 

A foundational equality: Price x Quantity = Money x Velocity of money

 

The logistic regression to predict regression includes Price (cpi) and Velocity (velo).  As the CPI goes up, the probability of a recession increases and vice versa.  As the velocity of money goes up the probability of a recession decreases and vice versa. 

 

This model also includes the yield curve, a well established variable to predict recession.  Notice that this variable is not quite statistically significant (p-value 0.14).  But, the sign of the coefficient is correct.  It does inform and improve the model.  And, is well supported by economic theory.  When the yield curve widens the probability of a recession goes down and vice versa.

The model includes the stock market (S&P 500) that is by nature forward looking in terms of economic outlook.  This makes it a most relevant variable to include in a regression model to predict recessions.  When the stock market goes up, the probability of a recession goes down and vice versa. 

The deep neural network (DNN) model is described below.

 The DNN model uses the same explanatory variable inputs.  

The DNN model has two hidden layers with 3 neurons in the first one, and 2 neurons in the second one. 

Number of neurons is nearly predetermined as hidden layers must have fewer neurons than the input layer and more neurons than the output layer. 

 

The activation function is Sigmoid, which is the same as a Logistic Regression.  And, the output function is also Sigmoid.  This makes this DNN consistent with the Logistic Regression model.  

 

I noticed that when using the entire data (from 1960 to the present using quarterly data), ROC curves and Kolmogorov - Smirnov plots did not differentiate between the two models.  I am just showing the KS plots below.  The two plots are very similar, not allowing you to clearly rank the models. 

 

The next set of plots more clearly differentiate between the two models.  

On the plots above, the recessionary quarters are shown in green, and the others are shown in red.  You can see that the DNN generates nearly ideal probabilities that are very close to 1 during a recession, and very close to Zero otherwise.  The Logistic Regression model generates a much more continuous set of probabilities within the 0 to 1 boundaries.  Notice that both models do make a few mistakes with green dots (indicating recessions), when they should be red.  

The graph above displays how much more certain the DNN model is.  

All of the above visual data was generated using the entire data set.  Next, we will briefly explore how the models fared when predicting several recessionary periods treated as Hold Out or out-of-sample if you will. 

Let's start with the Great Recession. 

 

 

 

As shown above, during the Great Recession period, the Logistic Regression was a lot better at capturing the actual recessionary quarters.  It captured 4 out of 5 of them vs. only 2 out of 5 for the DNN. 

Next, let's look at the COVID Recession period. 

 

The above shows a rather rare occurrence in econometrics modeling, a perfect prediction.  Indeed, both models with much certainty predicted all 6 quarters of this COVID Recession period correctly.  And, as a reminder, these 6 quarters were indeed treated out-of-sample. 

Next, we will use a frequentist Bayesian representation of both models when combining all the recession periods we tested (on an out-of-sample basis).

 

We can consider that recession is like a disease.  And, given a disease prevalence, a given test sensitivity and specificity, we can map out the actual accuracy of a positive test or a negative test.  Below we are doing the exact same thing treating recession as a disease.  

 

Here is the mentioned representation for the Logistic Regression.

 

As shown above, during the cumulative combined periods there were 13 recessionary quarters out of a total of 30 quarters.  And, the Logistic Regression model correctly predicted 10 out of the 13 recessionary quarters. 

 And, now the same representation for the DNN.

 

   A table of these accuracy measures is shown below.

 

When you use the entire data set, the DNN is marginally more accurate.  When you focus on the recessionary periods on an out-of-sample basis, the two models are very much tied.

 

So, can these models predict the current prospective recession? 

 

No, they can’t.  That is for a couple of reasons: 

 

First, both models have already missed out 2022 Q1 as a recessionary quarter.  Even using the historical data (not true testing), the Logistic Regression model assigned a probability of a recession of only 6% for 2022 Q1; and the DNN assigned a probability of 0%.  Remember, the DNN is always far more deterministic in its probability assessments.  So, when it is wrong, it is far more off than the Logistic Regression model. 

 

Second, for the models to be able to forecast accurately going forward, you would need to have a crystal ball to accurately forecast the 4 independent variables.  And, that is a general shortcoming of all econometrics models. 

  

  

 

 

Inequality in the United States

I used the data provided by the US Government Survey of Consumer Finance (SCF) that publishes its data set every 3 years ranging from 1989 to 2019. 

Using this data I explored trends in inequality along several dimensions including: education, work status, and ethnicity.  I did not study gender because the SCF data is aggregated at the families level (similar to households).  

You can see the complete study at the following links: 

Inequality at Slideshare.net 

Inequality at Slidesfinder

I looked at several different variables to identify inequality including: net worth, pre-tax income, and stock holdings.

And, I measured inequality between different groups by looking at their difference at the median level.  I focused on the median, instead of the mean, in order to factor out the net worth of billionaires and other high-net worth families, that skew the mean or average value.  I call this phenomenon the Elon Musk effect.  And, I wanted to be sure to factor it out when dealing with between-differences. 

For instance, comparing the net worth of college grads vs. high school grads, I compared their respective median net worth as shown below. 

 

Notice how on an inflation adjusted basis, the net worth of high school graduate families remained under $75K in 1989 and 2019.  

Next, I graphed the multiple between the median net worth of college grads divided by the median net worth of high school grads.  And, I observed the trend over time of this multiple as shown below. 

 

The graph above indicates that this between-difference has increased since 1995.  It peaked in 2013.  And, it has somewhat mean-reverted to around 4 times, where it has been since 2001.  

The above gives us a pretty good take on inequality or between-difference between college grads and high school grads families in term of their respective net worth. 

But, how about inequality within a group.  For that, I looked at the within-difference for college grads (in this example).  And, now I focus on the multiple between the average or the mean divided by the median.  Now, I do want to include the Elon Musk effect because I want to measure the inequality within a group.    So, let's look at the data. 

Next, let's visualize this college grad's net worth Mean/Median multiple over time. 

 

As shown, this within-difference Mean/Median multiple has fairly much steadily risen over time.  One may think that this trend is pretty much due to the rising long term trend in the stock market.  It actually is not.  The two do not track closely (the two diverge markedly from 1989 to 2001; from 2007 to 2010; from 2016 to 2019). 

The linked studies cover inequality in a similar fashion for ethnicity, work status; and along net worth, pre-tax income, and stock holdings.  I expected the inequality trends in stock holdings to be closely related to stock market movements.  And, for the most part, they really were not.  

As an additional information gathering, the SCF data allowed me to evaluate the financial readiness for retirement of 55 - 64 year old families.  Here we focused on families retirement funds.   

Currently, a 60 year old is expected to have a remaining life expectancy of 21 years.  Given that, the 55 - 64 year old families retirement funds, whether you focus on the mean or the median, seem grossly inadequate to support a comfortable and secure retirement.  This is a stealthy fiscal nationwide crisis that remains unaddressed.  It is unclear what the solution is given the fiscal pressures at all levels of Government.    

Overfitting with Deep Neural Network (DNN) models

 I developed a set of models to explain, estimate, and predict home prices.  My second modeling objective was to benchmark the accuracy in testing (prediction) of simple OLS regression models vs. more complex DNN model structures.  

I won't spend any time describing in much detail the data, the explanatory variables, etc.  For that you can look at the complete study at the following links.  The study is pretty short (about 20 slides). 

Housing Price models at Slideshare

Housing Price models at Slidesfinder 

Just to cover the basics, the dependent variable is home prices in April 2022 defined as the median county zestimate from Zillow, that I just call zillow within the models.  The models use 7 explanatory variables that capture income, education, innovation, commute time, etc.  All variables are standardized.  But, final output is translated back into nominal dollars using a scale of $000.

The models use data for over 2,500 counties. 

I developed four models:

1. A streamlined OLS regression (OLS Short) that uses only three explanatory variables.  It worked as well as any of the other models in testing/predicting; 

2. An OLS regression with all 7 explanatory variables (OLS Long).  It tested & predicted with about the same level of accuracy as OLS Short.  But, as specified it was far more explanatory (due to using 7 explanatory variables, instead of just 3); 

3. A DNN model using the smooth rectified linear unit activation function.  I called it DNN Soft Plus.  This model structure had real challenge converging towards a solution.  Its testing/predicting performance was not any better than the OLS regressions; 

4.  A DNN model using the Sigmoid activation function (DNN Logit).  And, this model will be the main focus of our analysis regarding overfitting with DNNs.   

The DNN Logit was structured as shown below: 

I purposefully structured the above DNN to be fairly streamlined in order to facilitate convergence towards a solution.  Nevertheless, this structure was already too much for the DNN Soft Plus (where I had to prune down the hidden layers to (3, 2) in order to reach mediocre convergence (I also had to rise the error level threshold).  

When using the entire data set, the Goodness-of-fit measures indicate that the DNN Logit model is the clear winner. 

You can also observe the superiority of the DNN Logit visually on the scatter plots below. 

On the scatter plot matrix above, check out the one for the DNN Logit at the bottom right; and focus on how well it fits all the home prices > $1 million (look at rectangle defined by the dashed red and green lines).  As shown, the DNN Logit model fits those perfectly.  Meanwhile, the 3 other models struggle in fitting any of the data points > $1 million. 

However, when we move on to testing by creating new data (splitting the data between a train sample and a test sample), the DNN Logit performance is mediocre. 

 As shown above when using or creating new data and focusing on model prediction on such data, the DNN Logit predicting performance is rather poor.  It is actually weaker than a simple OLS regression using just 3 independent variables.  

Next, let's focus on what happened to the DNN Logit model by looking how it fit the "train 50%" data (using 50% of the data to train the model and fit zestimates) vs. how it predicted on the "test 50%" data (using the other half of the data to test the model's prediction). 

As shown in training, the DNN Logit model perfectly fit the home prices > $1 million.  At such stage, this model gives you the illusion that its DNN structure was able to leverage non linear relationships that OLS regressions can't.  

However, these non linear relationships uncovered during training were entirely spurious.  We can see that because in the testing the DNN Logit model was unable to predict other home prices > $1 million within the test 50% data.   

The two scatter plots above represent a perfect image of model overfitting.  

Is the Market Rigged (Part II)?

 This is a follow up to my earlier blog post on the subject a few days ago.  To remind ourselves, our starting point was the following chart from the Bespoke Investment Group that indicated that the entire accrued value of the S&P 500 since 1992 was captured by After Hours traders (who bought the S&P 500 after the Close the previous day and sold it at the Open on the following day), and that the "during regular hours traders" (who bought the S&P 500 at the Open and sold it at the Close of the market on a daily basis), did not capture any of the upward movement in the S&P 500 since 1992. 

At the time, I was skeptical  that the After Hours traders would reap 100% or more of the gains in the S&P 500.  And, I replicated this graph using data from Yahoo Finance.  And, I uncovered that the Bespoke Investment Group (BIG)  simply confused one variable for another.  And, after making the appropriate correction, the World still made sense.  And, contrary to what BIG disclosed, the vast majority of the gains were actually captured to the traders during market hours as one would expect as shown on my chart below. 

Readers of the first blog post on the subject a few days ago invited me to give the data a second and more detailed look at the data.  When I did that, I uncovered that there is a divergent period from September 2016 to the present, when the majority of the gains actually do flow to the After Hours traders.  And, the chart below reflecting this visual data looks very similar to the original BIG chart (but using a truncated time period). 

In the chart above, over the reviewed period, even after using accurate data the vast majority of the gains in the S&P 500 do accrue to the After Hours traders.  I find that rather dismaying.  And, after doing a bit of research based on hypotheses generated by readers, I could find an explanation.  There are a lot of breaking news during the After Hours period.  Companies are allowed to release quarterly earnings after the market Close and before the market Open.  Similarly, the majority of economic indicators releases are disclosed by the Government before the market Open.  Given that, it makes much sense that the After Hours traders would reap the gains.  

Now, is the market rigged?  I find this question really uncomfortable because I find it rather challenging to answer this question in the negative.  The timing of breaking news disclosure favors the large institutional investors over the retail investors that trade mainly during regular trading hours.

However, I have no explanation why this phenomenon (advantage of institutional investors trading After Hours) kicked in only since September 2016.  

Yet, I am concerned that once this advantage has been captured by institutional investors, it will propagate going forward forever. 

On the other hand, I am still comforted that a simple Buy & Hold strategy still performs a lot better than the daily After Hours strategy, as shown on the chart below. 

 The simple Buy & Hold strategy holds several "efficient" advantages over the After Hours trading, including: 

1) Operating efficiency.  Buy & Hold foregoes having to make 506 trades a year (253 trading days times 2 trades per day); 

2) Buy & Hold value accretion is not impaired by bid-ask spreads.  The latter materially affects the After Hours traders' value accretion, that is not shown on this graph (absence of data); and 

3) Tax efficiency.  The After Hours traders gains are 100% taxable as ordinary income.  The Buy & Hold traders have unrealized capital gains that are not taxable.  And, they will be taxable only when realized at much lower capital gains tax rates.  

More often than not, the Buy & Hold strategy over a long period of time will perform better than After Hours trading; that is because Buy & Hold gains = After Trading Hours gains + Regular Hours gains + compounding effect.  For instance, since September of 2016, when After Trading Hours performed well, it captured 80% of the gains of the Buy & Hold strategy.  During Regular Hours trading captured 10%.  And, the compounding effect captured the remaining 10%.  

Is the Market rigged?

 A friend of mine recently shared this arresting chart.

The above chart suggests that since the beginning of 1993, some large institutional investors extracted all the gains out of the S&P 500 by simply buying it at the Close of the previous day and selling it at the Open of the following day.  Meanwhile, many retail investors (day-traders types) who would simply buy the S&P 500 at the Open and sell it at the Close during regular trading hours would have reaped no gain whatsoever going back to 1992!  

The chart above was created by the Bespoke Investment Group.  You can review their website at the link below.

Bespoke Investment Group  

For a better understanding of After Hours Trading, please refer to the following link. 

After Hours Trading explanation

The above chart left me baffled.  So, I extracted the relevant data from Yahoo Finance.  And, I replicated this chart.  And, all of a sudden the World still made sense.  And, the Market is not rigged (at least on this one count).  

As you can see on my chart above, the gains in the S&P 500 accrue to the ones who simply bought it at the Open and sold it at the Close during the regular trading hours.  Meanwhile, the ones who would have traded after hours, overall did not reap any gain whatsoever.  My chart looks very much like the one from Bespoke, except that in my chart the gains are associated with the regular trading hours.  I gather, Bespoke simply confused the time series for After Hours Trading vs. Regular Hours Trading.  

Next, I just added an extra time series to see how those strategies would compare vs. simply a Buy & Hold strategy.  

As shown above, you can see that from beginning to end point, the Buy & Hold strategy is way ahead. 

However, most of that advantage occurred in the past couple of years since the beginning of 2020 (blue line spikes upward much above the red line).  During this period, the After Hours traders made some marginal gains (the Market on the next day at the Open was at times marginally higher than the Close of the previous day).  And, those small gains compounded on a larger accrued value for the Buy & Hold strategy, allowed it to zoom passed the regular trading hour strategy. 

The reverse was true during a long period from the end of 2006 to end of 2014, when the Buy & Hold strategy was hindered by the small losses in the S&P 500 between the Close of the previous day and the Open of the following day.  During that period, you can see the red line (regular trading) steadily above the blue line (Buy & Hold).  Afterwards, the two lines start to converge. 

From the end of 1992 till the end of 2006, there was virtually no difference between Buy & Hold and Regular Trading hours (the blue and red lines overlap, so you just see the blue one).  This entails that throughout that period, the S&P 500 opened the next day at the exact same value as the Close on the previous day. 

Once you convey the S&P 500 data accurately, there is nothing that suggests that institutional investors who trade after hours extract any rent-profits from the Market.  

Although this was not the main topic of this post, you have to note the superior efficiency of the Buy & Hold strategy on several counts.  And, the "efficiency" has several dimensions.  

First, from an operational standpoint, the Buy & Hold strategy allows you to avoid 506 trades per year (253 trading days x 2 trades per day).  

Second, it is a lot more tax efficient.  All the accrued value represents not taxed unrealized capital gains.  Meanwhile, all gains under the other two strategies would be taxed as short-term gains at ordinary income tax rates.  

Global Aging & Africa's Divergence

I recently completed an analysis focused on population aging, population age categories in % (age pyramids), and overall population growth.  It looks at various geographic units (countries, continents, regions, World) from 1950 to the Present (2019 & 2020).  And, it looks at projections out to 2100.  

 

I used data sourced from the UN Population Division.   

 

The main takeaway is that Africa is an outlier to the overall global aging; its population growth (historical & projected) is far faster than for other major regions. 

 

You can read the complete study at the following link: 

Global Aging at Slideshare 

 

... or a slightly shorter version at the following link:

Global Aging at Slidesfinder 

 

The above study consists of a Powerpoint with close to 60 slides.  It is very visual, and easy to digest.  But, as an intro to the whole thing, I will share a few highlights below by illustrating some of the key slides.  

First, let's disclose the three types of age pyramids.  Age pyramids are an aesthetic way of visualizing the population age profile of a country.  

 

A young population has a sharp looking pyramid with a large foundation (large youth base associated with high fertility) and a very sharp top (few elderly, short life expectancy). 

We can articulate an explanatory model that describes the process of global aging.  As women get more educated, they participate in the labor force.  And, fertility drops, life expectancy increases, population growth slows down, and population ages.

Within the full presentation, I share a ton of visual data that supports many of the variables' relationships defined in the model. 

This model explains how a population pyramid evolves from looking like a pyramid (young) to a urn (old), as shown below. 

 

The graph below compares the age pyramid of Nigeria, Brazil, and Japan in 1950 and in 2019. 

 

Back in 1950, the three countries' respective age pyramids looked nearly identical.  But, in 2019 they look radically different.  Nigeria's age pyramid has not changed since 1950.  It is still depicting a very young population.  Meanwhile, in 2019 Brazil's population pyramid looks very mature; and, Japan's looks very old. 

 

The population of Nigeria has grown from 37.9 million in 1950 to 206.1 million in 2020; and is projected to reach 793.9 million by 2100!

This historical and projected explosive population growth is true not only for Nigeria but for the whole of Africa.  Africa's population has grown from 0.23 billion in 1950 to 1.34 billion in 2020; and is projected to reach 4.47 billion in 2100!

 

Africa's continued explosive population growth is truly divergent when compared with any other large region. 

 

By comparison, see how Europe's population has already peaked by 2020, and is projected to decline out to 2100.  This is a picture of ongoing population aging.   

Population aging is even more pronounced for China.  Its population is expected to peak before 2040, and decline rapidly out to 2100. 

 

The table below discloses the population growth (historical and projected) for Africa and a few other major regions with population of more than 1 billion in 2020.

 

 

Notice how all four regions have a fairly similar population size in 2020.  However, by 2100 Africa's population is projected to be 3 to 4 times larger than the other regions!

 

And, this is how these regions share of the World population will change over the reviewed time periods. 

 

Next, let's compare Africa vs. the remainder of the World, excluding Africa.  

 

The World's population is projected to increase from 7.79 billion in 2020 to 10.88 billion in 2100.  And, the entire growth in the World's population is due to Africa.  The remainder of the World's population is projected to remain perfectly flat at around 6.4 billion.

 

Cryptocurrencies as an asset class

We are going to analyze several of the major cryptocurrencies as an asset class.  And, we are going to address several related questions:

 

1) Do they provide diversification benefits relative to the stock market (S&P 500)?

 

2) How do their diversification benefits compare with Gold’s diversification benefit vs. the stock market? 

 

3) Do cryptocurrencies provide diversification benefits when you really need it… during market downturns?

 4) Are cryptocurrencies truly “digital Gold”?  Do they behave in a similar way given that their supply is constrained (supposedly in a similar way as Gold is)?

You can review the complete analysis at the following links:  

Crypto analysis at Slideshare

Crypto analysis at SlidesFinder 

Publicly available data on cryptocurrencies is fairly limited in terms of length of time series.  Also, many cryptocurrencies started in just the past few years.  Given that, I am focusing the first part of this analysis on monthly data from September 2015 to March 2022.  I also conducted fairly extensive analysis using daily data that you can review within the links disclosed above. 

When looking at correlations over the reviewed period as shown on the table below, we observe that both cryptocurrencies and gold have very low correlations with the stock market (S&P 500). 

 Thus, one could derive that cryptocurrencies do provide diversification benefit from equity market risk.  

However, during the one market correction (within this period), we observe that cryptocurrencies did not provide any diversification benefits.  While the S&P 500 contracted by close to - 30% between February 19 and March 16, 2020, the cryptocurrencies' respective values often contracted by more than - 50%. 

As shown earlier, cryptocurrencies have very low correlations with gold.  Thus, they can't be considered "digital gold", as they behave completely differently. 

The critical differentiating characteristic of cryptocurrencies is their volatility.  Their volatility is a high multiple higher than the stock market (S&P 500).  The graph below is focused on the volatility level-dimension that is specified as the annualized standard deviation using monthly % change.  And, the Y-axis as disclosed, when it shows a standard deviation of 7.5 ... it actually means a standard deviation of 750% (as a reference the S&P 500 annualized standard deviation over that period averaged about 14%).  Within the complete analysis, you can see details of the underlying calculations.     

As shown above, both XRP and Dodge experienced the highest volatility with both peaks for several months at or above 750%.  

When we focus our graph on the time dimension (see below), we observe that XRP experienced its peak volatility in 2018.  Meanwhile, Dodge experienced it 3 years later in 2021. 

Next, let's look at the cryptocurrencies volatility (as defined) as a multiple of the S&P 500 volatility.  As shown on the graph below, these multiples range from single digit multiple up to > 200 x.  That's pretty amazing.  It is actually hard to comprehend unless you look at the underlying data firsthand. 

As we speak, the cryptocurrencies are experiencing a severe correction (far worse than any stock market correction).  While the S&P 500 has corrected by about - 6% during this recent Winter, the cryptocurrencies have dropped between - 30% and - 80% since their most recent peak (some cryptocurrencies have been on a volatile slide since May of 2021).  This is a second instance when cryptocurrencies have provided no diversification from equity risk.

In view of the above, cryptocurrencies may be considered an asset class given that their behavior is very much different from other asset classes (at least the ones reviewed including equities and gold; and they certainly behave completely differently than bonds.  You don't need a study to assess that). 

However, as mentioned they do not provide so far any diversification benefit to protect against equities markets downturns.  And, their huge volatility renders them inappropriate for any conservative and/or long-term investor.