Tobin q Backup Material

This is a numerical summary.

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.

Errors

1923-1980 Data: Prediction Errors versus Returns, x=returns:

Returns at Year 10
If y is the error from a prediction based on 100E10/P: y=-0.617x+3.8643. R-squared=0.617.
If y is the error from a prediction based on qefm: y=-0.5949x+3.7256. R-squared=0.5949.
If y is the error from a prediction based on 1/qefm: y=-0.579x+3.626. R-squared=0.579.

Returns at Year 15
If y is the error from a prediction based on 100E10/P: y=-0.4613x+2.9238. R-squared=0.4613.
If y is the error from a prediction based on qefm: y=-0.3754x+2.3798. R-squared=0.3754.
If y is the error from a prediction based on 1/qefm: y=-0.3302x+2.0933. R-squared=0.3302.

Returns at Year 20
If y is the error from a prediction based on 100E10/P: y=-0.4409x+2.9271. R-squared=0.4409.
If y is the error from a prediction based on q, q=0.5: y=-0.2865x+1.9027. R-squared=0.2865.
If y is the error from a prediction based on q, q=2: y=-0.3081x+2.0457. R-squared=0.3081.
If y is the error from a prediction based on 1/q, q=0.5: y=-0.3168x+2.103. R-squared=0.3168.
If y is the error from a prediction based on 1/q, q=2: y=-0.3027x+2.0095. R-squared=0.3027.

1923-1980 Data: Prediction Error Magnitudes versus Returns, x=returns:

Returns at Year 10
If y is the error magnitude from a prediction based on 100E10/P: y=0.0709x+2.9735. R-squared=0.0305.
If y is the error magnitude from a prediction based on qefm: y=-0.0443x+3.6236. R-squared=0.0122.
If y is the error magnitude from a prediction based on 1/qefm: y=-0.0238x+3.4908. R-squared=0.0039.

Returns at Year 15
If y is the error magnitude from a prediction based on 100E10/P: y=0.1603x+1.4452. R-squared=0.2313.
If y is the error magnitude from a prediction based on qefm: y=-0.0192x+2.2631. R-squared=0.0033.
If y is the error magnitude from a prediction based on 1/qefm: y=0.0169x+1.9045. R-squared=0.003.

Returns at Year 20
If y is the error magnitude from a prediction based on 100E10/P: y=0.1026x+1.1841. R-squared=0.0757.
If y is the error magnitude from a prediction based on q, q=0.5: y=0.0259x+1.2867. R-squared=0.0066.
If y is the error magnitude from a prediction based on q, q=2: y=0.0062x+1.4966. R-squared=0.0004.
If y is the error magnitude from a prediction based on 1/q, q=0.5: y=0.0557x+1.1228. R-squared=0.0251.
If y is the error magnitude from a prediction based on 1/q, q=2: y=0.0244x+1.2817. R-squared=0.0049.

Have fun.

John Walter Russell
August 13, 2006