spx Bogle's Dividend Model Versus Average Next 10 Year RR S&P 500:

Bogle's Dividend Model Versus Average Next 10 Year RR S&P 500:

Data used: S&P 500 monthly close, dividend, earnings, 1945-Feb 2001.

Analysis: Bogle dividend model predicted average annual 10 year return v. actual next 10 year average annual return.

This is actually a phenomenal model. Although it uses only 1 variable – the dividend yield on the S&P 500 – it has a .71 correlation with the actual next 10 year rate of return (total) on the S&P 500, and an R2 of .504, which is huge in financial linear regression.

The linear regression line is:

Average annual rate of return next 10 years = predicted rate of return x .89 + 2%.

	Summary Statistics:
	Predicted rate of return next 10 years:	Actual rate of return next 10 years:
n:	553	553
Max:	23.4%	21.5%
Min:	5.4%	0.5%
Average:	11.4%	12.5%
Median:	10.4%	14.1%
	y = .89x + 0.02	R2 = 50.4%
	correlation:	71.0%

Sliced data:
		n:	From:	To:	y:
	Min-10%	56	5.4%	7.2%	6.2%
	10-25%	82	7.2%	8.1%	7.4%
	25-50%	139	8.1%	10.4%	12.5%
	50-75%	138	10.4%	14.2%	14.6%
	75-90%	82	14.2%	16.7%	16.3%
	90-Max	56	16.7%	23.4%	17.7%
		553

In fourths:
		n:	From:	To:	y:
	Min-25%	138	5.4%	8.1%	6.9%
	25-50%	138	8.1%	10.4%	11.8%
	50-75%	137	10.4%	14.2%	14.5%
	75-Max	139	14.2%	23.4%	16.8%
		552

In thirds:
		n:	From:	To:	y:
	Bottom	183	5.4%	8.9%	7.7%
	Middle	182	8.9%	12.6%	13.2%
	Top	188	12.6%	23.4%	16.6%
		553

Update since 1981:

Since 1981, the model has not performed nearly as well, however. The correlation dropped to .093 and the R2 was a very poor .9%.

	Summary Statistics:
	x:	y:
n:	120	120
Max:	18.0%	19.4%
Min:	5.4%	13.3%
Average:	11.0%	16.3%
Median:	10.3%	16.0%
	y = .06x + 0.16	R2 = .9%
	correlation:	9.3%

Sliced data:
		n:	From:	To:	y:
	Min-10%	12	5.4%	7.7%	15.3%
	10-25%	18	7.7%	8.9%	16.1%
	25-50%	30	8.9%	10.3%	16.3%
	50-75%	30	10.3%	12.9%	15.1%
	75-90%	18	12.9%	15.2%	15.7%
	90-Max	11	15.2%	18.0%	17.8%
		119

In fourths:
		n:	From:	To:	y:
	Min-25%	30	5.4%	8.9%	15.8%
	25-50%	30	8.9%	10.3%	17.7%
	50-75%	30	10.3%	12.9%	15.1%
	75-Max	30	12.9%	18.0%	16.6%
		120

In thirds:
		n:	From:	To:	y:
	Bottom	40	5.4%	9.2%	16.2%
	Middle	39	9.2%	12.0%	16.6%
	Top	41	12.0%	18.0%	16.1%
		120

The Vakkur Earnings Model

Data used: S&P 500 monthly close, dividend, earnings, 1945-Feb 2001.

Analysis: Vakkur earnings model model predicted average annual 10 year return v. actual next 10 year average annual return.

The model is analogous to Bogle's dividend model, but uses the earnings yield instead of the dividend yield; this switch is made because I believe there has been a paradigm shift in how investors view dividends; they are much more willing to receive their return through capital appreciation which of course is tax-deferred than through dividends. They are more trusting of the market.

This is also a solid model, although a little worse over the entire study period than the Bogle dividend model. It uses 2 variable – the earnings yield and the dividend yield on the S&P 500. It has a .688 correlation with the actual next 10 year rate of return (total) on the S&P 500, and an R2 of .473, which is very large in financial linear regression.

The linear regression line is:

Average annual rate of return next 10 years = predicted rate of return x .74 + 5%.

	Summary Statistics:
	Predicted rate of return next 10 years:	Actual rate of return next 10 years:
n:	553	553
Max:	21.9%	21.5%
Min:	3.4%	0.5%
Average:	10.5%	12.5%
Median:	9.5%	14.1%
	y = .74x + 0.05	R2 = 47.3%
	correlation:	68.8%

Sliced data:
		n:	From:	To:	y:
	Min-10%	56	3.4%	5.4%	7.5%
	10-25%	82	5.4%	6.4%	7.2%
	25-50%	139	6.4%	9.5%	12.5%
	50-75%	137	9.5%	14.2%	14.1%
	75-90%	83	14.2%	17.3%	16.1%
	90-Max	56	17.3%	21.9%	17.8%
		553
In fourths:
		n:	From:	To:	y:
	Min-25%	138	3.4%	6.4%	7.3%
	25-50%	137	6.4%	9.5%	11.8%
	50-75%	138	9.5%	14.2%	14.1%
	75-Max	139	14.2%	21.9%	16.8%
		552
In thirds:
		n:	From:	To:	y:
	Bottom	183	3.4%	7.0%	8.0%
	Middle	182	7.0%	12.4%	13.2%
	Top	188	12.4%	21.9%	16.3%
		553