The figure below shows the adjusted three-month moving average of the national unemployment rate in the U.S. for the past 12 months, with the minimum and current values indicated at the bottom-left and top-right areas. This is known as the Sahm Recession Indicator, which signals the start of a recession when the it rises by 0.50 percentage points or more relative to its minimum value in the previous 12 months. The Sahm Recession Indicator has been named after economist Claudia Sahm.
If the adjusted three-month moving average of the national unemployment rate, or the the Sahm Recession Indicator, continues rising at the same rate, we should either be in recession right now in August 2024, or enter a recession within the next few months – according to the Sahm Rule, which is based on the Indicator. The video linked below provides a brief discussion on this a few other related issues.
This blog is about data analytics, statistics, economics, and investment issues. The "Warp" in the title refers to the nonlinear nature of investment instrument variations.
Thursday, August 29, 2024
Thursday, July 25, 2024
A simulation-based valuation of the S&P 500: July 2024
The figure below shows two simulation-based valuations of the S&P 500. They assume a fair price-to-earnings (PE) ratio for the S&P 500 that is the inverse of half of the 10-year U.S. Treasury yield. The price (at the top) is the most recent top value of the S&P 500.
The numbers on the left consider a more benign scenario: S&P 500 earnings in 2024 are up by 12.10% from the previous year, and the 10-year U.S. Treasury yield is at 4.28%. The numbers on the right refer to a less positive scenario: S&P 500 earnings are up by 9.90%, and the 10-year U.S. Treasury yield is at 4.28%.
The second scenario takes us to a fair price for the S&P 500 of 2,843.17, which is 49.37% down from the most recent high. The video linked below discusses these simulations, some of the most recent values for the simulation inputs, and a few other things.
The numbers on the left consider a more benign scenario: S&P 500 earnings in 2024 are up by 12.10% from the previous year, and the 10-year U.S. Treasury yield is at 4.28%. The numbers on the right refer to a less positive scenario: S&P 500 earnings are up by 9.90%, and the 10-year U.S. Treasury yield is at 4.28%.
The second scenario takes us to a fair price for the S&P 500 of 2,843.17, which is 49.37% down from the most recent high. The video linked below discusses these simulations, some of the most recent values for the simulation inputs, and a few other things.
Wednesday, May 29, 2024
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.
Sunday, April 28, 2024
Estimating the time decay of inverse leveraged funds
The figure below shows the performance of two funds: the iShares Russell 2000 ETF (IWM), and the Direxion Daily Small Cap Bear 3X Shares (TZA). The TZA is expected to return 3 times the inverse of the IWM within very short time frames. As you can see, over 6 months the IWM drops -15.41% and the TZA gains 30.63%.
Three times the inverse of -15.41% is 46.23%. Since the TZA gained only 30.63%, the difference of 15.60% (46.23% minus 30.63% = 15.60%) is the decay associated with the 6-month period.
You can do similar estimations for other inverse leveraged funds. The video linked below discusses this and a few other options.
Three times the inverse of -15.41% is 46.23%. Since the TZA gained only 30.63%, the difference of 15.60% (46.23% minus 30.63% = 15.60%) is the decay associated with the 6-month period.
You can do similar estimations for other inverse leveraged funds. The video linked below discusses this and a few other options.
Thursday, February 29, 2024
Is a PE ratio of 12 attractive? A simulation-based view of company valuation
Summary
- The price/earnings (PE) ratio is one of the most widely used measures of company valuation.
- Through a simulation, we show that if growth is expected to slow down, then PE ratios are likely to go down, possibly in a dramatic fashion.
- For example, if earnings are expected to grow only 2% per year, then an attractive PE ratio would be 7.95. This is much lower than the PE ratio of 12, which is generally seen as attractive.
- For a PE ratio of 12 to be attractive, the expected earnings growth has to be at least 10.18% per year.
The PE ratio
The price/earnings (PE) ratio is one of the most widely used measures of company valuation (). It is calculated by dividing a company's share price by its earnings per share. Essentially, the PE ratio reflects a company’s value, as seen by the stock market, divided by its net profits.
What is an attractive PE ratio?
From early 2009 to early 2019 the SPY exchange-traded fund (ETF) has gone up in value approximately 222.72%. The SPY is an index fund, which tracks the S&P 500 index (, ). It had a relatively low net expense ratio of 0.09% at the time of this writing. The SPY has also paid dividends during this period. In early 2019 the dividend was a little less than 2%.
If you bought US$ 10,000 in shares of a company, and had a return comparable to buying and holding the SPY in the 2009-2019 period above, the shares would be valued at approximately US$ 32,272 after 10 years. The spreadsheet section in the figure below shows a simulation where earnings are assumed to grow 2% per year over a period of 20 years. As you can see, the value of US$ 32,272 is reached at year 10. The EP percentages go up because they assume that the share prices remain constant; in reality those prices would go up, keeping the PE ratio somewhat constant. The first EP percentage is the reverse of the PE ratio.
At the top left you see the PE ratio associated with this return. It is a fairly low 7.95. This is much lower than the PE of 12, which is often seen as attractive by investors. That is, if you want to purchase shares of a company whose earnings are expected to grow only 2% per year, and obtain a return for the next 10 years that is comparable to the S&P 500 in the 2009-2019 period, then you should buy shares in a company with a PE ratio of 7.95.
The same simulation-based approach can be used to find out what growth rate would be needed for a PE ratio of 12 to be attractive. This is summarized in the spreadsheet section in the figure below. For a PE ratio of 12 to be attractive, the expected earnings growth has to be at least 10.18% per year.
The PEG ratio
Note that the PEG ratio () in the first spreadsheet section, also shown at the top left, is 3.97. The PEG ratio is the PE ratio divided by the expected annual earnings growth. This PEG ratio is much higher than 1, which is generally perceived as an attractive PEG ratio. And still, the return on the investment in 10 years will no doubt be attractive (the S&P 500 had a remarkable run in the 2009-2019 period), as long as the PE ratio is a low 7.95.
In the second spreadsheet section, the PEG ratio is 1.179, which is much closer to 1. This highlights one interesting property of the relationship between the PEG and the PE ratios - it is a nonlinear relationship. The closer the earnings growth gets to zero, the more warped it becomes, pushing the PEG ratio higher and away from 1 (assuming that the PE ratio is positive).
When growth slows down, the stock market may collapse, even without a recession
The above discussion highlights the fact that, if growth is expected to slow down, then PE ratios are also likely to go down. PE ratios may go down dramatically, leading to a severe stock market correction, even without a recession ().
In fact, as we can see from the discussion above, a severe correction may happen even without earnings going down! In other words, earnings may still keep growing, but at such a slow pace that the market is compelled to adjust PE ratios downward to match the lowered return expectations.
Tuesday, January 30, 2024
Where is the yield curve un-inversion?
The figures below show the graphs of the 10y-3m Treasury yields and 10y-2y Treasury yields. The inversion in the 10y-3m graph is the best indication of an impending recession, and that graph typically un-inverts immediately prior to a recession.
While the first graph does not show an un-inversion, the second (i.e., 10y-2y) does. And the second tends to predict the first, because the 2y yields tend to predict the 3m yields. That is where the yield curve un-inversion is, at the moment. The video linked below discusses this in a bit more detail.
While the first graph does not show an un-inversion, the second (i.e., 10y-2y) does. And the second tends to predict the first, because the 2y yields tend to predict the 3m yields. That is where the yield curve un-inversion is, at the moment. The video linked below discusses this in a bit more detail.
Sunday, December 31, 2023
Fortune favors the bold, and so does misfortune
The figure below illustrates a truth that most investors know, but tend to forget. Taking high levels of risk in the financial markets increases the tail probabilities, which are associated with massive gains and massive losses. The lure of high-risk decisions and related investment instruments often acts as a sort of tax on the statistically illiterate.
But investors can reduce the chances that they will end up at the left tail end of the probability distribution. When it comes to stock investing, paying attention to two events can help. The first is the percentage difference between 10-year and 3-month U.S. Treasury yields falling below zero, because a U.S. recession tends to occur within the next 18 months.
The second is the stock market, measured by an index such as the S&P 500, reaching a double-top within that that period of 18 months after the percentage difference between 10-year and 3-month U.S. Treasury yields falls below zero. This combination is extremely bearish. And this is where we are about now. The video linked below discusses this in a bit more detail.
But investors can reduce the chances that they will end up at the left tail end of the probability distribution. When it comes to stock investing, paying attention to two events can help. The first is the percentage difference between 10-year and 3-month U.S. Treasury yields falling below zero, because a U.S. recession tends to occur within the next 18 months.
The second is the stock market, measured by an index such as the S&P 500, reaching a double-top within that that period of 18 months after the percentage difference between 10-year and 3-month U.S. Treasury yields falls below zero. This combination is extremely bearish. And this is where we are about now. The video linked below discusses this in a bit more detail.
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