How to beat the S&P 500 without much effort: A one-year moving average strategy

Summary

- One of the most successful strategies for long-term investment returns is to buy and hold a broad-coverage index fund.

- The SPY is an exchange-traded fund (ETF) that tracks the S&P 500, and is a good example of broad-coverage index fund.

- A simple strategy can be devised to obtain even better than buy-and-hold long-term returns, employing fast- and slow-moving averages.

- We explain and test a one-year moving average strategy that in the long term performs significantly better than buying and holding SPY.

The one-year moving average for SPY from 1995 to 2018

The graph below has been created with Yahoo Finance (). It shows the variation of the SPY exchange-traded fund (ETF) from 1995 to 2018 (in red), plus the one-year moving average during that period (in blue). The SPY tracks the S&P 500 index, and had a net expense ratio of 0.09% at the time of this writing. One of the advantages of index funds is that they have a low expense ratio compared with actively-managed mutual funds.

Note that there are two moving averages in the graph: (a) the SPY “share” price (or net asset value per share) at any given time, which is the fastest moving average possible for the fund; and (b) the SPY’s one-year moving average, which is a slow-moving simple average of the fund’s share prices. (see ).

Simple inspection would suggest that, after an initial purchase, one would do better than holding SPY by employing a simple two-step strategy: (1) sell when the SPY crosses below its one-year moving average; and (2) buy back when SPY crosses above its one-year moving average.

A test of the strategy

While on the graph the simple strategy above may look appealing, the strategy must be tested with real data and under realistic assumptions. The figure below shows part of a screen snapshot of a test of the strategy, with multiple trades on a spreadsheet. Each row of the spreadsheet corresponds to one trade. The first row corresponds to the initial buy. A conservative fee of US$ 40 per trade is assumed, in part to account for bid-ask spread losses.

The figure below shows the final rows of the simulation, the result of a comparison buy-and-hold baseline strategy, and the percentage difference. Starting with an investment of US$ 100,000 made in January 1, 1995, the simple one-year moving average strategy gets us to US$ $980,558 on January 1, 2018. The buy-and-hold baseline strategy gets us to US $611,714. That is, the simple one-year moving average strategy performs about 60 percent better.

The simulation disregards dividends and sweep account gains (whereby cash earns interest). At the time of this writing, one could easily get money market yields in sweep accounts that were comparable in value to the SPY dividend.

Is the 365 days used for the moving average optimal? Probably not, but our simulation suggests that this number is effective at limiting false positives while at the same time capturing major drops of the index (e.g., those in the two recessions in the period considered). False positives would be much more frequent with a faster moving average, such as a 50-day moving average. If too frequent, false positives can significantly increase trading-related losses, to the point of negating the benefit of the strategy.

How much do long Treasuries increase with each 1% decrease in the 10-year Treasury yield?

The figure below shows five values of the TLT exchange-traded fund, which tracks the value of Treasury bonds with maturities of 20 years or more (i.e., long Treasuries), and of the corresponding 10-year Treasury yields. The latter, 10-year Treasury yields, are highly correlated, in a lagged way, with the Federal Funds rate. This rate is set by the Fed.

As you can see from the best fitting line equation, there is an increase of approximately 19 points in the value of the TLT for each 1% decrease in the 10-year Treasury yields. So, if the Federal Funds rate us expected to go down, the gain likely to be obtained by investing in long Treasuries in quite attractive. The video linked below provides a brief discussion on this a few other related issues.

How far are we from a recession according to the Sahm Rule in August 2024?

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.

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.

PE-based valuation of companies: A five-minute strategy

The table below shows the simulation-based fair value of the price-to-earnings (PE) and price-to-earnings-to-growth (PEG) ratios associated with various annual earnings growth rates. It uses an approach discussed in this blog (). The lowest growth rate shown is minus 50 percent, which would refer to a company whose net profits are going down by 50 percent every year. The highest growth rate shown is 100 percent, for a company whose net profits are doubling every year.

Generally speaking, a PE of 12 is considered indicative of fair value, and so is a PEG of 1. As you can see, these are gross simplifications that would apply only to a company whose annual earnings growth rate is about 10 percent. By contrast, a company whose earnings are contracting at a 2 percent annual rate would be fairly valued with a PE of 6.51 and a PEG of -3.25. At the other end of the growth rate scale, a company whose earnings are growing at an annual 75 percent rate would be fairly valued with a PE of 260.47 and a PEG of 3.47.

As we can see, the relationship between the PE and PEG ratios is nonlinear. This is why valuations sometimes look odd to those thinking in terms of a PE of 12 and a PEG of 1. High growth companies, often in cutting-edge technology areas, may be fairly valued at PEs that look astronomical and PEGs that are significantly greater than 1. The video linked below discusses this in a bit more detail.

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.

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.