Forecasting Earnings, The P/E Multiple, And The S&P 500

Aug. 4.14 | About: SPDR S&P (SPY)

Summary

We have developed a model that predicts the P/E multiple of the S&P 500 based on future levels of the ratio of Federal Spending to GDP and interest rates.

We have also developed a model of the earnings on the S&P 500 based on GDP, unit labor costs and the growth in real GDP.

Combining the P/E multiple of the S&P 500 and the earnings gives forecasts of the S&P 500 under various scenarios.

There are various different measures of the earnings on the S&P 500 and different ways to calculate it.

Measures of the S&P500 (NYSEARCA:SPY) and the price-earnings ratio are neither as simple nor as uniform as one might expect. For example, the same analyst on different occasions may use coincident earnings and prices to derive a market multiple, and then in the next breath use forward or trailing earnings against the current index to derive a multiple that is obviously different. The waters can be further muddied by even longer term backward looking earnings histories to generate a multiple or forward looking earnings estimates that reflect varying time periods. What is worse, very often the precise timing of the earnings measure is not even specified, leaving the reader/investor guessing what exactly is being measured and its consistency with others' benchmarks.

Aside from the issue of trailing versus coincident versus forward earnings, there is the issue of alternative definitions of earnings. There are measures using earnings as stated by reporting companies. This measure is in accord with GAAP (Generally Accepted Accounting Principles) reporting requirements. This is the most commonly used measure but there are also measures of operating earnings; earnings excluding extraordinary factors or onetime events etc. which cause differentiation in earnings measures for identical periods of time.

The two most popularly published measures of the S&P index are one that is published by the NYU Stern School in conjunction with S&P, and one that is published by Yale professor Robert Shiller. The NYU measure is the one we use in our forecasting models, and it is a measure of reported earnings that are in accord with GAAP requirements. The Shiller calculation is not as clearly defined but its history differs from the NYU measure. While not particularly relevant for our purposes, Shiller publishes a monthly earnings series which he interpolates from quarterly data. This allows him to match monthly earnings with a monthly average of daily closes on the S&P index to derive a cyclically adjusted price-to-earnings ratio.

To be clear, in our modeling, see: The Market Multiple On The S&P 500 Can Be Explained: P/E Ratios Are Inversely Related To Future Federal Spending, we use annual earnings data as reported by NYU and S&P. And for the index we use its year-end value. To estimate earnings we use a four year average of labor cost in manufacturing and the relation between this and earnings is inverse. We also use the growth rate of inflation-adjusted GDP and a smoothed linear measure of nominal GDP. These two variables are directly related to earnings meaning that the stronger they are, the stronger the positive impact on earnings. This formulation covers more than 50 years of history and it explains about 96% of the variation in S&P reported earnings. See: Updating The Market Multiple On The S&P 500 Can Be Explained: P/E Ratios Are Inversely Related To Future Federal Spending.

To estimate the market multiple that corresponds to the index, we match coincident year-end values of the multiple against an annual average of the yield on the Ten year Treasury note and a four year forward ratio of federal government spending to GDP. The relationships are inverse for both variables in that lower interest rates and a lower spending ratio imply higher levels of the market multiple. Obviously innumerable factors go into the formulation of the amount investors are willing to pay for a given dollar of earnings in any period. But this formulation has the attraction of a quantitative history and a plethora of forecasts of interest rates and the role of government. The formulation explains more than 60% of the historical variation of the multiple.

The accompanying table shows updated forecasts for our input variables and for earnings, the index, and the multiple through 2015. Back testing our model for 2013 showed positive results. Indeed our original 2013 forecast for earnings (made in 2012) was about $105 and the actual came in at $107. Our model estimate of the market multiple was 18.4 which gave us an index value of 1839 versus the actual year-end close of 1849. At the time, even we were skeptical that the multiple would rise as sharply as it did last year but then again we were certainly not in a minority in doubting such a sharp increase.

The accompanying table sketches a base, best, and worst case scenario for the input variables we use in our models. We think these are reasonable but they obviously can be adjusted to reflect one's own bias. The base case is our most realistic economic scenario characterized by continued low and stable long-term interest rates with economic growth and inflation i.e. nominal GDP averaging about 4% this year and in 2015. This would somewhat lower than current consensus forecast for interest rates and the economy. In this scenario, S&P earnings would be about $116 this year with a multiple of 18.1 yielding a year-end target of 2100 for the index. Next year would show earnings rising to $125 with a multiple that is slightly lower and an index value of 2213.

Our best case scenario for equities is characterized by stronger economic growth, slightly higher inflation, and a continued downward bias to interest rates. This could be viewed as inconsistent in that stronger growth and inflation might be incompatible with lower interest rates, but it is a best case for equities and recent history has shown that economic performance and interest rates have diverged for various reasons. Whatever, our model forecasts would be $118 of earnings this year; and 18 multiple and thus a year-end S&P target of 2148. The S&P index would rise further to 2366 in 2015.

Finally, our worst case for equities is a scenario approximating stagflation. We show weaker economic growth than our base case but with higher inflation and higher interest rates. Earnings would be $110 this year with the implication being a much weaker performance in the second half than current consensus expectations) a multiple of 17.8 and an index value of 1958 or very close to the current level. For 2015 earnings would stagnate and the multiple would fall such that 2015 would be a negative one for equities as the index would fall to 1782.

S&P 500 Model Predictions

2012 actual

2013 actual

2013 model

2014

2015

Base Case

Real GDP %

2.8

1.9

1.9

2.2

2.7

inflation %

1.8

2.1

2.1

1.5

1.5

unit labor costs/mfg %

0

-1.3

-1.3

1.2

1.2

10-year treasury %

1.8

2.35

2.35

2.5

3.8

S&P Earnings

96.82

107.45

105.4

116

125

P/E multiple

14.7

17.2

18.4

18.1

17.7

S&P Index

1426.19

1848.36

1939

2100

2213

Worst Case

Real GDP %

2.8

1.9

1.9

1.5

1

inflation %

1.8

2.1

2.1

2.5

3

unit labor costs/mfg %

0

-1.3

-1.3

2.5

3.8

10-year treasury %

1.8

2.35

2.35

2.8

3.5

S&P Earnings

96.82

107.45

105.4

110

110

P/E multiple

14.7

17.2

18.4

17.8

16.2

S&P Index

1426.19

1848.36

1939

1958

1782

Best Case

Real GDP %

2.8

1.9

1.9

2.5

3.2

inflation %

1.8

2.1

2.1

2

2

unit labor costs/mfg %

0

-1.3

-1.3

2.5

3.8

10-year treasury %

1.8

2.35

2.35

2.5

2.8

S&P Earnings

96.82

107.45

105.4

118

130

P/E multiple

14.7

17.2

18.4

18.2

18.2

S&P Index

1426.19

1848.36

1939

2148

2366

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Disclosure: The author has no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. The author wrote this article themselves, and it expresses their own opinions. The author is not receiving compensation for it (other than from Seeking Alpha). The author has no business relationship with any company whose stock is mentioned in this article.

Additional disclosure: Please note that this article was written by Dr. Vincent J. Malanga and Dr. Lance Brofman with sponsorship by BEACH INVESTMENT COUNSEL, INC. and is used with the permission of both.