Tobin q Survey Follow-On

From my Tobin q Survey:

“The next obvious steps are (a)to compare the percentage earnings yield 100E10/P and qefm and 1/qefm results in depth at years 10 and 15 and (b)to compare the percentage earnings yield 100E10/P and q and 1/q with q=0.5 in 1871 and with q=2 in 1871 at year 20.”

Returns

1923-1980 Data: Returns

Returns at Year 10
If x=100E10/P: y=1.3564x-3.8223. R-squared=0.383.
If x=qefm: y=-14.568x+15.111. R-squared=0.4051.
If x=1/qefm: y=5.4397x-3.8278. R-squared=0.421.

Returns at Year 15
If x=100E10/P: y=1.3165x-3.4499. R-squared=0.5387.
If x=qefm: y=-14.804x+15.331. R-squared=0.6247.
If x=1/qefm: y=5.615x-4.0768. R-squared=0.6698.

Returns at Year 20
If x=100E10/P: y=1.0946x-1.5004. R-squared=0.5591.
If x=q, q=0.5: y=-14.163x+14.055. R-squared=0.7135.
If x=q, q=2: y=-11.356x+14.383. R-squared=0.6918.
If x=1/q, q=0.5: y=3.6291x-1.3287. R-squared=0.6832.
If x=1/q, q=2: y=5.0404x-1.7373. R-squared=0.6973.

Confidence Limits

At Year 10

When x=100E10/P: The confidence interval is minus 5% to plus 5%. The low return outlier is minus 7% on the downside and plus 6% on the upside. The high return outlier is minus 6% on the downside and plus 8% on the upside.

When x=qefm: The confidence interval is minus 6% to plus 4%. The low return outlier is minus 7% on the downside and plus 7% on the upside. The high return outlier is minus 8% on the downside and plus 7% on the upside.

When x=1/qefm: The confidence interval is minus 5% to plus 5%. The low return outlier is minus 6% on the downside and plus 8% on the upside. The high return outlier is minus 10% on the downside and plus 5% on the upside.

At Year 15

When x=100E10/P: The confidence interval is minus 4% to plus 5%. The low return outlier is minus 4% on the downside and plus 4% on the upside. The high return outlier is minus 6% on the downside and plus 5% on the upside.

When x=qefm: The confidence interval is minus 4% to plus 4%. The low return outlier is minus 4% on the downside and plus 7% on the upside. The high return outlier is minus 5% on the downside and plus 5% on the upside.

When x=1/qefm: The confidence interval is minus 3% to plus 4%. The low return outlier is minus 4% on the downside and plus 3% on the upside. The high return outlier is minus 7% on the downside and plus 5% on the upside.

At Year 20

When x=100E10/P: The confidence interval is minus 2.5% to plus 3.0%. The low return outlier is minus 2.5% on the downside and plus 3.5% on the upside. The high return outlier is minus 5.0% on the downside and plus 3.5% on the upside.

When x=q, q=0.5: The confidence interval is minus 3.0% to plus 2.0%. The low return outlier is minus 3.5% on the downside and plus 2.0% on the upside. The high return outlier is minus 5.0% on the downside and plus 3.5% on the upside.

When x=q, q=2: The confidence interval is minus 3.0% to plus 3.0%. The low return outlier is minus 3.5% on the downside and plus 3.5% on the upside. The high return outlier is minus 4.0% on the downside and plus 3.5% on the upside.

When x=1/q, q=0.5: The confidence interval is minus 2.0% to plus 2.5%. The low return outlier is minus 3.0% on the downside and plus 3.5% on the upside. The high return outlier is minus 5.0% on the downside and plus 3.5% on the upside.

When x=1/q, q=2: The confidence interval is minus 2.0% to plus 2.5%. The low return outlier is minus 3.5% on the downside and plus 4.5% on the upside. The high return outlier is minus 5.0% on the downside and plus 3.0% on the upside.

Sharpened Focus

This sharpens our focus. Tobin’s q can improve our estimates, but it may have problems with outliers. The next step is to look more closely at historical prediction errors.

Have fun.

John Walter Russell
August 12, 2006