Tobin q Errors

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.”

From my Tobin q Survey Follow-On:

"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."

Prediction Errors

I took the equations for returns. For each year from 1923-1980, I calculated predicted returns based on the measures of valuation 100E10/P, qefm, 1/qefm, q where q=0.5 in 1871, q where q=2 in 1871, 1/q where q=0.5 in 1871 and 1/q where q=2 in 1871. I subtracted the actual return from the predicted return to calculate each year’s prediction error. I used Excel’s plotting capability to calculate regression equations between errors and returns. I also determined regression equations between the absolute value of errors and returns.

Error magnitudes (i.e., absolute values) were almost independent of actual returns. Interestingly, the smallest error magnitudes were associated with the percentage earnings yield 100E10/P.

The errors themselves had a negative correlation with actual returns. When the actual returns were small, the errors were positive and larger than normal. In such cases, the predicted returns were bigger than the actual returns. When the actual returns turned out badly, the actual returns were worse (smaller) than predicted.

When the actual returns were high, the errors were negative. When the actual returns were most favorable, the actual returns turned out better (larger) than predicted.

For a purely random error, we would not expect any such relationship. Because error magnitudes were independent, I conclude that the middle section with the bulk of the data defines the regression equations. All of the projections have problems with the extremes: the very best and worst returns.

Tobin q Backup Material

Have fun.

John Walter Russell
August 13, 2006