Tontines: Could they help the economy?

Summary

- Even before the COVID-19 pandemic, the global economy was experiencing a slowdown. One important reason behind this slowdown has been the aging of the world population.

- Seniors tend to be savers. Therefore, as seniors become a larger part of the global population, this puts downward pressure on global consumer spending.

- Tontines are financial plans that combine elements of retirement annuities and lotteries. The longer a tontine member lives, the greater is the potential for an outsized return on his or her initial investment.

- By definition, individuals cannot outlive their initial contribution to a tontine.

- One possible advantage of tontines is that they could stimulate spending among seniors.

The problem

Even before the COVID-19 pandemic, the global economy was experiencing a slowdown. One important reason behind this downward economic trend has been the aging of the world population. (). There have been increasingly more seniors as a percentage of the population of most countries, particularly in developed countries.

Seniors tend to be savers. Therefore, as seniors become a larger part of the global population, this puts downward pressure on worldwide consumer spending. And consumer spending drives the global economy. Adding to this is the fact that, with fixed income returns going down, the economic environment is increasingly hostile to savers. Returns are depressed, which can lead to a propensity to save even more.

What are tontines?

Tontines are financial plans that combine elements of retirement annuities and lotteries. They were popular in the 1700s and 1800s. Many different variations are possible (), with various contribution and distribution rules. The following items give an idea of what a tontine could look like from a financial perspective:

- Each of a group of seniors makes an initial contribution to the tontine.

- The tontine members start receiving distributions.

- As tontine members die, their distributions are made to the surviving members.

- A small number of survivors receive a final lump-sum payment.

The longer a tontine member lives, the greater is the potential for an outsized (or asymmetric) return on his or her initial investment. In the basic simulation below, one could receive payments for a number of years, and nevertheless end up with a lump-sum payment that is 10 times the person’s initial investment.

A basic simulation

Let us assume that we have a tontine with 1,000 members, each contributing 100 thousand dollars by the time they reach age 65 (see table below). When they reach that age, they start receiving 4% yearly dividends. The total assets under management here would then be 100 million dollars.

We are assuming that the tontine would be managed by an organization that would be able to pay the 4% in dividends to the tontine members and still make a profit. This organization would have to not only manage the funds but also make sure that no fraud is committed. For example, deaths would have to be properly logged.

Also, we are assuming in this simulation a bell-shaped (i.e., normal) life expectancy distribution centered at age 80, with a standard deviation of 10 years. This means that, of the initial 1,000 individuals, approximately 16% would have died after 5 years (age 70). And, approximately 50% would have died after 15 years (age 80).

Still consistently with a normal distribution, after 25 years (age 90), approximately 16% of the original tontine members would still be alive. Soon after that, when only 10% of the remaining tontine members were still alive, each would receive a lump-sum payment of 1 million dollars.

As you can see, the dividend received by each surviving tontine member goes up over time, growing exponentially over time. This is highlighted in the figure below. If the members of a tontine had slightly different ages, which is likely, their distributions could be adjusted accordingly without affecting this exponential growth.

Currently there are a number of legal obstacles to the establishment of tontines. Among them are insurance and gambling laws at the local and federal levels. It would probably take targeted legislation at the federal level to overcome all of the obstacles to nationwide tontines, which would probably be preferable to local tontines (e.g., tontines where all members are from the same city).

How can this help the economy?

One possible advantage of tontines is that they could stimulate spending among seniors. As noted earlier, the trend for the future is a growing percentage of seniors in the population of most countries, and seniors tend to be savers. Since consumer spending is a major component of most national economies, this spells trouble for most countries’ finances and the global economy.

Seniors tend to be savers in part because they fear outliving their savings – this is one of their main fears (). That is, the prospect of living a long life is a major source of financial stress, which may shorten that life. With a tontine, the longer one lives the more income one gets, with a nice payout waiting for the oldest surviving members.

By definition, individuals cannot outlive their initial contribution to a typical tontine. As the world population ages, tontines could significantly increase consumer spending, even if that extra spending in restricted to the tontine’s annual distribution.

Understanding the price of bitcoin: Data from early 2019 to mid-2020

Summary

- We conducted a multivariate analysis of the price of bitcoin with financial data from early 2019 to mid-2020.

- Our main conclusion is that bitcoin should do well in what we could call a “nervous bull market”.

- In this scenario, we would see the market generally going up, with some expectation of inflation in the future, all of this against a bearish backdrop.

The analysis

We used WarpPLS () to create several second-order indices (as composites of first-order index funds) and link them in an exploratory model to help us understand what has been driving the price of bitcoin from early 2019 to mid-2020.

The period from early 2019 to mid-2020 was used because prior to it bitcoin was generally perceived as a cash-like currency that could be used for day-to-day transactions among individuals and organizations. From early 2019 onwards, the perception shifted to one of a store of value; something akin to “digital gold”.

We collected and analyzed daily data from various funds. More specifically, the price of one share of each fund at each day’s close was used. In terms of WarpPLS settings, the outer model analysis algorithm used was “PLS Regression”, and the default inner model analysis algorithm was “Linear”. The composite variables were made up of the following funds.

- FIN, reflecting a bullish view of financial institutions, was made up of the iShares U.S. Regional Banks ETF (IAT), and the Financial Select Sector SPDR Fund (XLF).

- HDG, reflecting a bearish view of the market (intention to hedge), was made up of the iShares Silver Trust (SLV), the SPDR Gold Shares (GLD), and the iShares 20+ Year Treasury Bond ETF (TLT).

- MKT, reflecting a bullish view of the market, was made up of the SPDR S&P 500 ETF Trust (SPY), and the Invesco QQQ Trust (QQQ).

- GBTC, reflecting the price of bitcoin, was measured through a single indicator, namely the Grayscale Bitcoin Trust (GBTC).

The Grayscale Bitcoin Trust (GBTC) provides one of the most straightforward ways for investors to own bitcoin. It is generally available to retail investors through various online brokers.

The results

The figure below shows our model with the main results. The iGBTC variable is an instrumental variable that controls for the effect of “time” on the results; to account for autoregression, or the fact that the variable GBTC is influenced by its own values back in time. The instrument used was a numeric variable generated based on the date associated with each data point. In a previous analysis published on this blog, based on the same data, we did not employ this type of control, which led to slightly different results.

The path coefficients (indicated as beta coefficients) reflect the strength of the relationships; they are a bit like standard univariate (or Pearson) correlation coefficients, except that they take into consideration multivariate relationships (they control for competing effects). A positive beta means that an increase in a variable is associated with an increase in the variable that it points to.

The P values indicate the statistical significance of the relationship; a P lower than 0.05 means a significant relationship (95 percent or higher likelihood that the relationship is “real”). The R-squared value reflects the percentage of explained variance for the variable in question; the higher it is, the better the model fit with the data.

I should note that the P values have been calculated using a nonparametric technique, which does not require the assumption that the data is normally distributed to be met. This is good, because I checked the data, and it does not look like it is normally distributed. 

So, what does the model above tell us? It tells us that: 

- As a bullish view of financial institutions (FIN) increases, the price of bitcoin (GBTC) also increases, in a statistically significant way (beta=0.13; P below .01). This is not normally what one would expect, if we assume that bitcoin’s success means the failure of financial institutions.

- As a bearish view of the market (HDG) increases, the price of bitcoin (GBTC) also increases, in a statistically significant way (beta=0.42; P below .01). This is what one would expect, if we assume that bitcoin is used as a hedge against a drop in the market. Note that this effect is the strongest in the model, by far.

- As a bullish view of the market (MKT) increases, the price of bitcoin (GBTC) also increases, in a statistically significant way (beta=0.17; P below .01). Again, this is not normally what one would expect, if we assume that bitcoin’s success means that a bear market is under way.

The three predictors above (i.e., FIN, HDG, and MKT) explain 33 percent of the variance in the variable GBTC (R-squared=0.33). This essentially means that the model is incomplete, although it does explain enough of the variance in GBTC to be useful in an exploration of major influences on the price of bitcoin.

Main conclusion

While the results above may look contradictory, they in fact suggest that bitcoin should do well in what we could call a “nervous bull market”. Here we would see the market generally going up, with some expectation of inflation in the future (which tends to be good for financials), all of this against a generally bearish backdrop.

Disclosure

The author does not own bitcoin at the time of this writing.

Does yield curve flattening hurt US bank stocks?

Summary

- US banks derive part of their income from borrowing funds and investing them, with interest rates paid and earned being correlated with the short and long ends of the Treasuries yield curve.

- Since the short end yields (for Treasuries) tend to be lower than the long end yields, usually US banks benefit financially from the difference.

- Given this, one would expect bank stocks to be strongly and positively correlated with yield curve steepening; i.e., the opposite of flattening.

- If we look at data from the past 5 years, however, the opposite has happened. As the yield curve has flattened, bank stocks have gone up.

Yield curve flattening and US bank stocks

US banks derive part of their income from borrowing funds and investing them, with interest rates paid and earned by the banks being correlated with the short and long end of the yield curve. Since the short end yields (for Treasuries) tend to be lower than the long end yields, usually US banks benefit from the difference. Given this, one would expect bank stocks to be strongly and positively correlated with yield curve steepening; i.e., the opposite of flattening.

The figure below shows, at the top, the difference in yields for 10-year and 3-month Treasuries for the past 5 years. The two graphs at the bottom show the stock prices for two banks: JPMorgan Chase, representing multinational investment banks; and U.S. Bancorp, representing regional banks. The sources for the graphs are Yahoo Finance and the US Federal Reserve Economic Data (FRED) (, ).

As you can see, prior to COVID there seems indeed to be a correlation between US bank stocks and yield curve flattening. However, it is the opposite of what we would expect. The correlation is negative. As the curve flattens, bank stocks go up. In other words, US banks tend to do well in response to what could be seen as a major obstacle to profitability.

What is happening? Compensatory adaptation

As the yield curve flattens, US banks react in a compensatory way – e.g., by resorting to other sources of income. This is compensatory adaption theory at work (, ).

Compensatory adaptation of this type is facilitated by the size and flexibility of the US economy. This makes the environment in which US banks operate significantly different from those of Japan and Europe, where arguably banks have fared worse.

Cold weather and COVID: Compensatory adaptation may lead to unexpected results

Summary

- If COVID cases necessarily spike in cold weather, it would be reasonable to expect more lockdowns in countries, like the US, which are about to transition from warm to cold weather.

- These lockdowns would presumably have a negative economic effect, and likely a severe negative effect on equity prices.

- This post looks at data from Brazil and the US, and concludes that COVID infections may not be significantly influenced by the weather.

- The reason may be a compensatory adaption feedback loop – people adapt in a compensatory way.

- In fact, if compensatory adaptation theory is any guide, it would not be surprising to see COVID infections actually go down, as a country with growing COVID infections transitions from warm to cold weather.

Do COVID cases spike in cold weather?

If COVID cases necessarily spike in cold weather, it would be reasonable to expect more lockdowns in countries, like the US, which are about to transition from warm to cold weather. These lockdowns would have a negative economic effect, and likely a severe negative effect on equity prices. But is it inevitable that COVID cases spike in cold weather?

To answer this question, it may be instructive to look at COVID figures for Brazil and the US, because these two countries have had similar responses to the pandemic (); and have opposite weather patterns – when it is hot in the US, it is cold in Brazil, and vice-versa. This applies particularly to the most populous areas of the two countries.

COVID figures for Brazil and the US

At the time of this writing, we had the following approximate numbers for Brazil and the US. Brazil – population: 209.5 million, COVID cases: 4.12 million, and COVID deaths: 126 thousand. US – population: 328.2 million, COVID cases: 6.26 million, and COVID deaths: 188 thousand. The two graphs below show the two following ratios: cases-to-population, and deaths-to-population.

The ratios are too close to support the “spike hypothesis”

In the last several months since the pandemic hit both countries, it has been generally cold in Brazil and hot in the US. Given this, these ratios are too close to support the assumption that COVID cases spike in cold weather. So, what would be a reasonable answer to the question posed earlier: do COVID cases spike in cold weather? The answer is: probably not.

What is happening? Compensatory adaptation

This brings to mind another question: would indoor activities, such as restaurant dining and movie theater attendance, lead to spikes in COVID cases?

Well, the idea was that cold weather would lead to more indoor activities ...

While risk of infection may go up with cold weather and more indoor activities, people react in a compensatory way – e.g., by wearing masks, resorting to social distancing etc. This is compensatory adaption theory at work (,). This feedback loop may lead to unexpected results.

If we use compensatory adaptation theory as a guide here, it would not be surprising if COVID infections were to go down, as a country with growing COVID infections transitions from warm to cold weather.

Interest rates and PE ratio expansion: S&P 500 going above 4100 before the end of 2020?

Summary

- Most professional investors see price/earnings (PE) ratios as inversely proportional to interest rates.

- Mathematically, this would be expressed as: PE = k / IR.

- Assuming that the interest rate on 10-year Treasuries could rise to 1%, and the k multiplier to rise to the pre-COVID level of 0.39, the expected S&P 500 PE ratio would then be 38.66.

- This would bring the S&P 500 up to 4,148. Still, not as expensive, in PE ratio terms, as in either the 2000s dot-com bubble or the Great Recession.

Interest rates and PE ratios

Most professional investors, including the late Benjamin Graham (), see PE ratios as inversely proportional to interest rates for Treasuries. Mathematically, this would be expressed as follows, where PE = the PE ratio of an equity security, IR = a relevant interest rate, and k = a multiplier.

PE = k / IR

There are a couple of key reasons for this relationship. One is that Treasuries become less attractive as an investment when interest rates go down. Since the Treasuries market is very large, a little over $21 trillion at the time of this writing, even a fraction of it moving to equities would push their PE ratios up significant.

Another key reason for the relationship above is that investing in Treasuries when interest rates are low becomes risky in terms of principal preservation. Treasury prices are inversely related to the interest they pay, or their yields. When yields are very low, the tendency is for them to go up.

Interest rates on 10-year Treasuries

The figure below shows the interest rates for the 10-year Treasury notes from January 2007 to July 2020. Those rates, which influence a number of other consumer-relevant rates (e.g., those for mortgages), go from 4.76% to 0.55% during the period.

While the interest rates have been going down over the years, they went up significantly during the recovery from the Great Recession. The same may happen during the recovery from the COVID recession. A move from 0.55% to 1% would be significant.

S&P 500 PE ratios

The figure below shows the PE ratios for the S&P 500 from January 2007 to July 2020. Note that the PE ratio for July 2020 is nowhere near the peak during the Great Recession.

The k multipliers

Finally, the figure below shows the k multipliers for the relationship between the S&P 500 PE ratios and interest rates on 10-year Treasuries from January 2007 to July 2020. An all-time low was reached for the multiplier in July 2020.

In a low interest rate environment, a high k multiplier would typically be associated with a high PE ratio. The multiplier increase, if it happens, should lag the interest rate reduction. Investors need time to be convinced that interest rates will remain subdued. 

S&P 500 above 4,100 soon?

Assuming that the interest rate on 10-year Treasuries could rise to 1%, and the k multiplier to rise to the pre-COVID level of 0.39 (which is below its historical average), the expected S&P 500 PE ratio would then be 38.66. This would bring the S&P 500 up to 4,148. Still, not as expensive, in PE ratio terms, as in either the 2000s dot-com bubble or the Great Recession.

This PE ratio expansion for the S&P 500 is already happening at the time of this writing, with the S&P 500 hitting an all-time high. Our main point in this post is that, if interest rates on Treasuries remain low, we may see more of that - even with bankruptcies among small businesses, significant  unemployment, and high volatility (including downward corrections).

The business media is missing this: The rise of the immune

Summary

- The fastest growing “demographic” in the world today are those who are immune to COVID-19.

- This is bullish for equities, because those who are immune to COVID-19 are likely less hindered as consumers than those who are not.

- The equities that should benefit the most are those for companies at the epicenter of the pandemic.

- Why is the non-immune view the prevalent one in the business media? Probably because of the average age of those speaking and writing.

- The rising immune population so far is predominantly young.

The fastest growing demographic

The fastest growing “demographic” in the world today are those who are immune to COVID-19. At the time of this writing, there were 3.3 million confirmed cases in the US alone. Assuming that the actual cases are around 10 times the confirmed cases, we have 33 million cases in US.

If we consider the death rate to be 1 percent, this means that we will have about 30 million people with immunity to COVID-19 in the US very soon. Many are already immune. Even without a vaccine and some mitigation (e.g., masks), by the end of the year the number of immune people in the US could be 100 million. In the world, this number could be 500 million.

People want the immune around them

Herd immunity is seen as a desirable goal because of the idea that the immune form a protective barrier around the non-immune (). In this sense, immune people are a better barrier than social distance. For example, if you have an immune person in between two non-immune people, that may be better than six feet of empty space. The immune person is much more lethal to the virus.

High-risk individuals, such as the elderly, are advised to isolate themselves. However, social and physical isolation could negatively affect their health in various ways unrelated to COVID-19. The real problem is interaction with the non-immune, because of the risk of infection. Interaction with the immune is fine. Maybe more than fine, because of the benefits of social interaction, not to mention needed care. People will want the immune around them.

Media naturalness theory

With current commercial technology, virtual meetings are simply not a viable alternative for a species that evolved over millions of years communicating face-to-face. The naturalness of a communication medium (i.e., how similar it is to the face-to-face medium) leads to a number of effects. For example, low naturalness reduces physiological arousal. Also, low naturalness leads to more confusion, particularly when knowledge is being communicated ().

So, face-to-face meetings will be needed, particularly when knowledge-intensive tasks must be carried out. Imagine a non-immune person being asked to attend a face-to-face meeting with 5 other people, all using masks. Would that person like the idea of the meeting more if she knows that all of the 5 other people are immune? Probably yes. Maybe not 5, but 3. The more the better. Again, people will want the immune around them.

Businesses will want the immune

Airlines are being asked to keep middle seats empty. Imagine you getting on an airplane and going to your window seat, just to find out that someone is sitting next to you, in the middle seat. You do not like it, even though the person is wearing a mask. He tells you that he is immune, and shows you the results of an immunity test. Will that make you feel better? Probably yes.

Companies that are at the epicenter of the pandemic are airlines, bars, restaurants, amusement parks, and ride-sharing companies. All of these companies have a strong incentive to have the immune as their employees, partners, and customers. Would a non-immune person favor a bar where most customers are immune? Probably yes.

Is this bullish for equities? If yes, what equities?

Arguably this is bullish for equities, because those who are immune to COVID-19 will probably be less hindered as consumers than those who are not. It stands to reason that the equities that should benefit the most from this are those for companies at the epicenter of the pandemic. Essentially, the ones that suffered the most so far.

Virtually all of the discussion in the business media nowadays is from the standpoint of the non-immune. One hears things like: “… the consumer will be cautious going forward … the risk of infection …”, “… parks will never have the same sales again …”, “… the economy will never be the same …” etc. Think about these statements assuming that you are immune – they make little sense.

And the numbers of the immune are growing fast, even without a vaccine. They will grow a lot faster with one or more effective vaccines. Also, keep in mind that the immune are not only consumers themselves, but also enablers of consumption. For the economic recovery, they are worth their weight in gold!

Why is the non-immune view the prevalent one in the business media? This may be due to the average age of those speaking and writing.

The rising immune population now is predominantly young.

Data from China suggests that economic activity could resume after initial containment and not trigger new COVID-19 cases

Summary

- A study was published in early 2020 by Ainslie and colleagues (), suggesting that, after initial containment is achieved, within-city movement (measured through a “Movement Index”) seems to be uncorrelated with new COVID-19 cases.

- Within-city movement is used in the study as a proxy for economic activity.

- Economic activity seems to have successfully resumed within approximately 2 weeks from containment, and approximately 4 weeks from the peak of new cases.

Within-city movement vs. new COVID-19 cases

The graphs below summarize key results from a study published in early 2020 by Ainslie and colleagues (). Dr. Ainslie is in the Faculty of Medicine, School of Public Health, Imperial College London. The study looked at within-city movement, as a proxy for economic activity, and how that movement has influenced the numbers of new cases of COVID-19 in various areas, after initial containment.

As you can see, after initial containment is achieved, within-city movement (measured through a “Movement Index”) seems to be uncorrelated with new COVID-19 cases; or somewhat negatively correlated, as the authors note. This rather surprising and counterintuitive outcome may be due to people becoming much more cautious about social interactions.

Time to resumption of economic activity

Note from the graphs that economic activity seems to resume within approximately 2 weeks from containment, and approximately 4 weeks from the peak of new cases.

Also note that containment has been fairly effective in China. The Chinese government has enforced it through strict lockdowns. Perhaps this is what makes people so cautious about social interactions afterwards, which we speculate might be at the source of the success of their strategy.

From an economic revival perspective, these are good news – particularly if the same approach can be replicated in other countries and regions.