spx ey-10y stoch Earnings Yield – 10 Year Treasury Yield Versus Next 12 Months Change S&P 500 1953-2000

Earnings Yield – 10 Year Treasury Yield Versus Next 12 Months Change S&P 500:

Data: April, 1953 – November, 2000, S&P 500, trailing 12 month earnings, 10 year Treasury bond yield.

Source: www.federalreserve.gov, Barrons, spx Monthly Data.xls, Earnings yield.xls

x: Earnings yield – 10 year Treasury Bond yield.

y: subsequent 12 month total return in the S&P 500 (dividends included).

Summary: The earnings yield minus the 10 year yield is not very helpful per se. Although the subsequent 12 month S&P 500 return was very high (27.4%) at the extreme (90^th percentile and above: 4.3-7.8% difference), the market also performed well when this difference was between the 10^th and 25^th percentile (17.1% average S&P 500 change).

Statistics: The difference between the earnings yield and the 10 year Treasury yield ranged from a minimum of –4.2% to a maximum of 7.8% with an average over the 560 months in the sample of 0.4%. In other words, if the earnings yield is 0.4% greater than the 10 year Treasury yield, the market is of average historical value; a difference less than this indicates relative overvaluation. A difference below this indicates undervaluation. The median, however, is –0.2%, indicating distortion by very large high values.

	Summary Statistics:
		x:	y :
	n :	560	560
	Max:	7.8%	61.0%
	Min:	-4.2%	-38.8%
	Average:	0.4%	14.2%
	Median:	-0.2%	14.4%

It is clear from the finely sliced data that the relationship if any is not simple. The worst 12 month returns are found after earnings yield differences of between –0.2% and 1.8% (50^th to 75^th percentiles).

Sliced data:
		n :	From:	To:	y :
	Min-10%	56	-4.2%	-2.5%	10.2%
	10-25%	84	-2.5%	-1.5%	17.1%
	25-50%	140	-1.5%	-0.2%	14.2%
	50-75%	140	-0.2%	1.8%	6.0%
	75-90%	84	1.8%	4.3%	15.4%
	90-Max	56	4.3%	7.8%	27.4%
		560

In fourths:
		N :	From:	To:	y:
	Min-25%	140	-4.2%	-1.5%	14.4%
	25-50%	140	-1.5%	-0.2%	16.1%
	50-75%	140	-0.2%	1.8%	6.0%
	75-Max	140	1.8%	7.8%	20.2%
		560

In the most robust division – into thirds – the relationship virtually disappeared, with the middle third performing the worst, and the bottom and top thirds performing about equal.

In thirds:
		n:	From:	To:	y:
	Bottom	185	-4.2%	-1.1%	16.1%
	Middle	184	-1.1%	1.2%	8.5%
	Top	191	1.2%	7.8%	17.7%
		560

36 Month Stochastic of (Earnings Yield – 10 Year Treasury Yield) Versus Next 12 Months Change S&P 500:

Data: May, 1956 – November, 2000, S&P 500, trailing 12 month earnings, 10 year Treasury bond yield.

Source: www.federalreserve.gov, Barrons, spx Monthly Data.xls, Earnings yield.xls

x: Stochastic( Earnings yield – 10 year Treasury Bond yield, 36 months)

y: subsequent 12 month total return in the S&P 500 (dividends included).

Summary: The stochastic on the earnings yield minus the 10 year yield (hereafter referred to as earnings yield stochastic) is much more helpful than the difference between the earnings yield and the 10 year Treasury yield alone. The stochastic normalizes this difference, adjusting for recent values.

The stochastic ranged from 0 to 100%, as expected; the average value was 41% with a median of 33.2%. This is interesting, meaning that the difference between the earnings yield and the 10 year Treasury yield must pop up periodically, then drop down and spend much of the next 3 years in the lower end of its range.

The subsequent 12-month performance of the S&P 500 ranged from a loss of 38.8% to a gain of 71.7% with a median gain of 13.7% (including dividends).

	Summary Statistics:
		x:	y:
	n:	535	535
	Max:	100.0%	71.7%
	Min:	0.0%	-38.8%
	Average:	41.0%	13.5%
	Median:	33.2%	13.7%

Analysis of the data reveals an almost stepwise linear relationship, at least in the lower strata. The market only returned 3.9% when the earnings yield stochastic was in the lowest 10 percentile (0%)

Sliced data:
		n:	From:	To:	y:
	Min-10%	61	0.0%	0.0%	3.9%
	10-25%	73	0.0%	10.6%	5.3%
	25-50%	133	10.6%	33.2%	13.5%
	50-75%	134	33.2%	71.8%	17.8%
	75-90%	80	71.8%	92.9%	15.9%
	90-Max	54	92.9%	100.0%	17.3%
		535
In fourths:
		n:	From:	To:	y:
	Min-25%	134	0.0%	10.6%	4.7%
	25-50%	133	10.6%	33.2%	15.0%
	50-75%	134	33.2%	71.8%	17.8%
	75-Max	134	71.8%	100.0%	16.4%
		535
In thirds:
		n:	From:	To:	y:
	Bottom	177	0.0%	17.5%	6.0%
	Middle	176	17.5%	56.4%	17.5%
	Top	182	56.4%	100.0%	16.8%
		535

Non-Overlapping 12-Month Periods

I next used this 36-month stochastic of the difference between the S&P 500 earnings yield (trailing 12 months) and the 10 year Treasury yield, and excluded all overlapping readings. I then looked at subsequent 12-month S&P 500 index change (not including dividends).

There were 10 non-overlapping cases since 1953 (when my Treasury yield data set began) in which there was a 100% stochastic of this variable. The average advance was 14.3%, the median advance was 20.0% (the mean was dragged down by 1973 and 1974 which skewed the sample). 80% of the subsequent years were up.

On the flip-side, if you look at cases where the market was very richly valued (earnings relative to Treasury yield normalized for past 36 month action) or 0% stochastic, the average subsequent 12 month S&P 500 return was 1.5%. The median was –2.7%. 50% of the time, the market declined. This, in one of the greatest bull markets in history!

I find this encouraging and interesting with one caveat: in the 1973-74 market meltdown the market by this parameter went from undervalued to ridiculously undervalued. An additional filter is needed.

Trading System

A simple system can be developed from these data: buy the S&P 500 when the stochastic of the (SPX E yield - 10 year yield) is less than 25%; sell and move to cash when it is greater than 75%. The results from 4/1/56 to 2000 follow:

Buy:	Sell:	Profit/ Loss:	System: Buy when Stochastic of (Earnings Yield – 10 Year Treasury Yield) <> 75%:	Buy & Hold:
48.38	48.38	0%	10.000	10.000
39.99	47.19	18%	11.800	9.754
54.75	89.11	63%	19.206	18.419
86.13	90.64	5%	20.212	18.735
94.23	116.03	23%	24.888	23.983
104.95	100.86	-4%	23.918	20.847
89.25	114.16	28%	30.594	23.597
238.90	290.10	21%	37.150	59.963
230.30	367.07	59%	59.213	75.872
443.38	669.12	51%	89.360	138.305
1328.92	1328.92	0%	89.360	274.684

The strategy performed very well during the early years, but very poorly (relative to buy and hold) later. Cash dividends were not included, nor were dividends on invested capital. Nevertheless, the results are intriguing since this is one of the few value indicators that would not have had you in the side lines during one of the greatest bull markets in history.