Forecasting Long-Term Portfolio Returns: The Efficient Valuation Hypothesis

Summary

• The study seeks to demonstrate that much of the long-term (20-year rolling periods) variability in stocks can be explained by the beginning-of-period earnings yield.
• Much of the previous financial research suggests either forecasting future returns a futile exercise because returns are random, or that asset class performance tends to display mean reversion.
• We aim to illustrate that starting earnings yields are similarly predictive of the future returns in an equity portfolio, over 20-year investment periods.

By Niall J. Gannon and Scott B. Seibert, CFA

Forecasting long-term asset class returns with reliability is an important component for matching a portfolio’s performance with its future liabilities. Whether one is an individual investor or a public pension fund, a reliable estimate of an asset’s minimum expected return is critical for financial planning purposes. Using the United States public pension system as an example, the use of inflated return expectations has perpetuated a growing deficit. According to Moody’s, in 2017, US public pension plans had unfunded liabilities of over $4 trillion. A deficit this massive can only be rectified by either cutting previously promised benefits for current participants or having future generations pick up the difference through higher contributions, sacrificing their standard of living. Most investors have an understanding that inception yield is predictive of the future returns of a fixed-income (bond) portfolio. We aim to illustrate that starting earnings yields are similarly predictive of the future returns in an equity portfolio, over 20-year investment periods.

Much of the previous financial research suggests either that forecasting future returns a futile exercise because returns are random, or that asset class performance tends to display a reversion to the mean of its historical observations. Eugene Fama, known for developing the Efficient Market Hypothesis, famously stated:

Most simply the theory of random walks implies that a series of stock price changes has no memory-the past history of the series cannot be used to predict the future in any meaningful way. The future path of the price level of a security is no more predictable than the path of a series of cumulated random numbers.

- Random Walks in Stock-Market Prices, Eugene Fama (1965)

Among those who adhere to the theory of mean reversion, Jeremy Siegel wrote in Stocks for the Long Run (2007) that stock returns “cling” to a statistical trend line. In reality, for the first 18 years of the 21st century, the total return on the S&P 500 index (with dividends reinvested) was only 5.34%, approximately 50% lower than its often-quoted long-term average of 10%. Was this dramatic underperformance of stocks for such an extended period truly a function of randomness? Does the degree of this underperformance weaken the theory of reversion to the mean? Our analysis seeks to narrow the gap between an investor’s equity return expectations and the actual future returns received. We aim to illustrate, utilizing 20-year rolling periods, that equity returns and portfolio performance over the long run do not perform randomly, but rather, are remarkably predictable.

Hypothesis

The study seeks to demonstrate that much of the long-term (20-year rolling periods) variability in stocks can be explained by the beginning-of-period earnings yield (the inverse of the starting price-to-earnings ratio). If our hypothesis is correct, investors can plan for the future using a forecasted minimum expected return to be realized over a 20-year investment horizon.

Method Description

A typical 20-year investment horizon includes multiple business cycles, possibly comprised of unexpected economic events, which have the potential to add or subtract from investment returns over the analysis period. According to the National Bureau of Economic Research (NBER), the United States has experienced 11 business cycles during the modern era, 1945-2009. The average cycle length, whether measured from trough from previous trough or peak from previous peak, is roughly 69 months, or 5.75 years. We seek to neutralize the impact of outsized returns derived from a single business cycle by focusing on 20-year rolling periods. In choosing the beginning-of-period price-to-earnings ratio as the starting point for our analysis, we have selected a measure of valuation that is widely available and well understood by investors.

Time Period

A total of 42 rolling full calendar year 20-year periods exist in the analysis period, which begins at the inception date of the S&P 500 on January 1, 1957 and ends December 31, 2017 (1957-2017). Each rolling 20-year period has its own annualized return.

Annualized Returns

The 20-year annualized rolling returns from the S&P 500 are presented. The returns are displayed as a pre-tax and pre-liquidation return of the S&P 500 over each 20-year period.

P/E

The price-to-earnings ratio is presented as of January 1 of the beginning year of each 20-year period.

Earnings Yield

The earnings yield of the index is derived from taking the inverse of the price-to-earnings ratio at the beginning of each period (January 1).

Return - EY

The beginning of period earnings yield is compared to the actual 20-year annualized return produced during the 20-year period. The difference between the actual annualized return and the earnings yield is displayed.

Exhibit 1

Results

Using the earnings yield as a minimum expected return, the hypothesis was successful at a rate of 95%. Over the 42 periods, only two scenarios had a realized annualized return less than the beginning-of-year earnings yield “forecast”. The two periods that didn’t meet the minimum expected return were 1958-1977 and 1989-2008. For 1958-1977, an annualized return of 7.79% was realized versus an earnings yield forecast of 8.40%, which resulted in a missed forecast of -.62%. In 1989-2008, an annualized return of 8.34% was realized versus an earnings yield forecast of 8.70%, which resulted in a missed forecast of -.35%. A couple of similarities exist with the two periods that didn’t meet the forecasted earnings yield. First, both of the earnings yields fell in the 75th percentile of all starting earnings yields. Also, in both scenarios, the last year of the analysis period was a negative total return year for the S&P 500. The total return was -6.76% in 1977 and -36.12% in 2008. The combination of a high earnings yield forecast plus a negative return in the final year of the analysis partially contributed to the missed forecasts.

Exhibit 2

In Exhibit 2, we have plotted the annualized 20-year returns versus earnings yield from the 42 periods that were observed in the analysis. The correlation of the data sets as shown in Exhibit 1 is .83, representing a strong linear correlation. In analyzing the data further, through a regression analysis, we calculate that the R2, the coefficient of determination, was 68%. Therefore, 68% of the variation in 20-year annualized returns is explained by beginning year earnings yield. The equation of the line of best fit is: 20-year annualized return = 1.02*(Earnings Yield) + .0307.

Observations of extreme high/low points of historical returns and earnings yields:

• The highest observed earnings yield of 13.7%, in 1975, produced a 14.33% annualized return.
• The lowest observed earnings yield of 4.54%, in 1998, produced a 7.11% annualized return.
• The highest observed 20-year portfolio return of 17.56% (1980-1999) began with an earnings yield of 13.51%.
• The lowest observed 20-year portfolio return of 6.42% (1959-1978) began with an earnings yield of 5.24%.
• Analyzing 2000-2017 (18 years): The beginning earnings yield in 2000 was 3.52%, and the annualized return, over 18 years, is currently tracking at 5.34%. The 2000 vintage portfolio is on pace to produce a lower annualized return than any other vintage since 1957. Also, the 2000 vintage portfolio has the lowest starting earnings yield of any observed year since 1957.

Conclusions

Our conclusions from the analysis:

• A strong correlation exists between 20-year annualized returns of the S&P 500 and the beginning-of-period earnings yield.
• Much of the variation in 20-year annualized returns can be explained by beginning-of-period earnings yield.
• Beginning-of-period earnings yield provides a useful estimate of minimum expected return that investors can expect over a long-term horizon, specifically a 20-year investment period.
• Excess return above starting earnings yield is unexplained in this study when only using historical data available to an investor at the beginning of each period. We strongly suspect that forward earnings growth and/or inflation is the driver of the unexplained portion of the forward expected return.
• Long-term portfolio forecasting includes the mandate for investors to consider real (net of inflation) returns. The nominal returns observed in this study provide a baseline from which investors can model for various forward-looking inflation scenarios.

Investors should use the earnings yield to approximate a minimum expected return for future financial planning. This conservative estimate of future returns could help reduce the unfunded liabilities that have accumulated in public pension plans due to poor forecasting. For individual investors, it should provide confidence that a minimum expected return can be achieved, even with unforeseen events, when investing over long time horizons. In the practice of setting asset allocation policy, the use of earnings yield as a minimum expected return produces a more informed comparison of the future return potential of equities versus fixed income than the application of the theory of mean reversion or the Efficient Market Hypothesis.

References:

Fama, E.F. “Random Walks in Stock-Market Prices.” Financial Analysts Journal, Vol. 21, No.5 (1965), pp. 55-59.

Moody’s Investors Service. "State and local government - US: Pension burdens to rise through 2020, even in positive investment scenario." June 2017 (Source)

The National Bureau of Economic Research. “US Business Cycle Expansions and Contractions.” 2017

Siegel, Jeremy. Stocks for the Long Run: The Definitive Guide to Financial Market Returns and Long-Term Investment Strategies (4th Edition). New York: McGraw-Hill, 2007. Print.

Silverblatt, H. “S&P 500, Ticker: SPX.” S&P Dow Jones Indices. 2017

Analyst’s Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.

Comments

[Bruce Talen]

Notwithstanding the comments that suggest this hasn't worked recently for John Hussman or is not useful for one to five year periods, it seems this would be an excellent tool for longer term planning, particularly for investors who are managing to a goal or against a set of liabilities (as opposed to a benchmark). Would be interesting to see what might have happened to all the underfunded state and local pension plans during various time periods, in terms of contributions and asset allocation, if they had used this approach to return assumptions instead of the historic 8% forever. Well done!

[flyingcircus]

it begs the question what "did not work"? Hussman has been bearishly pounding the table about overvaluation for years - and stayed mostly out of the stock market. And lost because of it. So he has been wrong (in hindsight). If the market suddenly tanks >20%, he will have the opportunity to say he was right; but even a stopped clock is right twice a day.

Nothing about this research says the stock market can not become even more overvalued. All it is saying is to expect lower forward returns, and by implication, this isn't a great time to invest new cash in US stocks from a "buy low" perspective.

If you have high credit card debt, paying it off is a better option - at the moment.
If you are interested in more stable returns, buying short to intermediate term corporate bond/bond funds is a better option - at the moment (assuming interest rates don't triple in the next couple of years).

[Learner16]

Thank you, Mr Gannon, As joesmith323 says, this is very similar analysis to Hussman's. Can you explain to us why the results would be different in this case, please?

It looks like it should work in theory, but it did not work for Hussman in practice. Do you happen to know why?

[flyingcircus]

Really solid, concise article. Thanks!

[chrisA23]

Without comparing the 20 year periods to interest rates and inflation we have only part of the picture. There is some real useful data in the article but without interest rates there is less than half a tale being told.

Could we please have an article that shows the 10 year treasury yield besides the earnings yield.
We can not assume the current 20 year period will be having low returns in a growing GDP environment with little competition from bond rates.

If you look at around 6% in the 90s for 10 year treasury rates and sometimes P/E higher or lower, it makes our times look like a good time to invest.
Though I am a bull I think demographics matter and aging in japan and other countries has to be balanced with the problem of aging workers but better workers in developing countries vs a generation ago. When I lived in India decades ago the workers were almost all terrible, but nice. Now they can usually speak English and kids use computers.

The world is always changing and in recent decades changing faster . "This time is different" applies in both positive and negative ways. Few articles begin to address the complex issues most investors have barely considered if at all. Thank you for this one. Overall I am long.

[Niall Gannon]

Chris, thank you for the question. I am going to refer you to the reader supplement for my first book: Investing Strategies for the High Net Worth Investor in which you will be able to see the 20 year treasury rates for each year back to 1957. The data goes through yr. end 2015 but will be updated shortly http://bit.ly/2DejzfI

So you know our thinking: the initial research stemmed from a Journal of Wealth Management paper in 2006 studying the after-tax returns of equities versus bonds. For that paper, we used the Bond Buyer GO index (a 20 year duration index) as it had a data set going back to 1957. It was in reviewing and updating that research that we found a remarkable correlation at the 20 year period and chose to add the 20 year treasury for application to non-taxable investors.

The inflation question is one that must be dealt with for both stock and bond investors, but you will see from the early 1980s data points, the bond market compensated investors for more than the inflation that they would ultimately receive. In 1981, for example you’ll see that the 20 year treasury traded at a yield of 13.29% and the S&P traded at an earnings yield of 10.99% (a P/E ratio of 9.1x). At the end of the 20 years, the buyer of a 20 year treasury strip earned exactly 13.29% and the equity portfolio produced 15.42%. Here we observe that there was indeed a tight correlation between the two.

You correctly point out that using PAST CPI data to imply the additional forward looking return is not wise as the inflation, GDP, and political environment of the next 20 years will differ from the previous 20. For this paper, we wanted to study concrete data points that were available to the investor at the beginning of each period.

[chrave1956]

Humans certainly are pattern seeking primates.

[fishermp]

Nice work! I agree that inflation explains some of the outperformance of the stock market over the earnings yield. I would also suggest that the out performance of the stock market over earnings is due to real GDP increase. The companies that make up the stock market are worth more because of inflation and because the economy is larger. Thus for today, nominal return of entire stock market is roughly 5% earnings, plus 2% inflation plus 2% real GDP growth or ~9% a year.

[Mount Dora Capital Management, LLC]

Interesting analysis! John Hussman has also done some good research demonstrating that valuation measures are accurate predictors of returns 10-12 years into the future. But importantly, valuation tells you little about what path the market will take to get there. So in essence valuation provides no guidance about what will happen over the next 1-5 years. That is why we don't use valuation metrics in our trading models.

[scottbseibert]

The real vs nominal returns is a valid point. In order to come up with a forecast (equation) for long-term real returns, we would have to have a forecast for long-term interest rates. When I added inflation into the regression I didn't see much pick-up in the coefficient of determination. Therefore, for this analysis we determined to let individual investors apply their own inflation scenarios to forecast long-term real returns.

[joesmith323]

This is the type of analysis that John Hussman does.

It would be interesting if you had done the analysis using real rather than nominal returns.

[chrave1956]

And it hasn’t help John predict much .

[rhope2]

Thanks for the work here...very interesting read, which I'll be spending more time on.
Just a note: Prof. Siegel has an updated 5th edition (2014) of his "Stocks for the Long Run" available, which, of course, was published after the Great Recession. He added several interesting chapters- including his discussion of the financial crisis- worth a read for anyone so inclined.

[drftr]

That is extremely interesting. Have you done the exercise for other asset classes and/or other markets to test its viability?

It would have bern great to post the starting yields for 2000 and further as to get an idea of what to expect.

Thanks again...

drftr

[scottbseibert]

We have not expanded the research into other asset classes or markets. I would imagine, depending on what asset class or market you choose, that a data feed going back to 1957 would be difficult to find.

One of the observations of an extreme high/low point mentioned in the paper was the year 2000 starting EY of 3.52%. The annualized return that we have achieved over the 18 year period (2000-2017) is tracking at 5.34%. The year 2000 vintage portfolio is on pace to produce a lower annualized return than any other observed period.

Beg. of Year E/Y P/E
1999 3.60% 27.8x
2000 3.52% 28.4x
2001 4.25% 23.5x
2002 3.38% 29.6x
2003 5.23% 19.1x
2004 4.92% 20.3x
2005 5.58% 17.9x
2006 6.12% 16.3x
2007 6.18% 16.2x
2008 5.62% 17.8x
2009 5.48% 18.2x
2010 5.10% 19.6x
2011 6.66% 15.0x
2012 7.67% 13.0x
2013 6.79% 14.7x
2014 5.81% 17.2x
2015 5.49% 18.2x
2016 4.92% 20.3x
2017 4.75% 21.1x
2018 4.68% 21.4x

[crmo]

why 20 year periods instead of some multiple of your avg cycle length? how predictive is ey for forward returns on 10 year rolling basis?

[Niall Gannon]

We chose 20 year periods to allow for multiple business cycles. The correlation between earnings yield and subsequent 10 year returns went down significantly compared to the 20 year periods. Seeing the subsequent performance of the 2000 vintage portfolio (as discussed in the conclusions) strengthened our belief that the 20 year was the most reliable period, specifically since the 2000 vintage had the lowest starting earnings yield and the lowest observed subsequent performance.

[Sophocles Sophocleous]

Nice job. What P/E are you showing? GAAP? Source of data?

[scottbseibert]

We are using S&P Operating P/E's. Therefore, it is a non-GAAP P/E measure, in which the E excludes unusual (one-time) items.

The data was sourced from the S&P Dow Jones Indices website (http://bit.ly/1Ku5ObN) and Aswath Damondaran's S&P Earnings website (http://bit.ly/w4jRpw~adamodar/New_Home_Pag...