Current Research J: Tobin’s q
Updated: August 14, 2006.
Current Research Index
Here is an index with links to my previous Current Research efforts.
Current Research Index
Current Research J: Tobin’s q
I found out about Rational Pessimism: Predicting Equity Returns using Tobin's q and Price/Earnings Ratios only in the last few days. I am impressed.
In this review, I show how this fits into my own research. As a result, I am opening up this new section, Current Research J: Tobin’s q.
Rational Pessimism and Tobin’s q
Tobin q Survey
Here are my initial findings about Tobin’s q using Smithers and Co. Ltd. data.
I am still screening. This analysis is almost entirely based on numbers alone.
Tobin q Survey
I have copied the Analysis section below.
1923-1980 Data: Returns
The values of R-squared for q and 1/q returns are similar. This is consistent with an exponential representation: exp(q)=1+q approximately when q is small. This is consistent with plots that compare P/E10 with the natural logarithm of q.
The best choice of q varies with the time period being projected. At 5 years, none were especially good, but qefm and 1/qefm were best. At 10 years, qefm and 1/qefm were best. At 15 years, all values of q and 1/q were excellent. At 20 years, all values of q and 1/q except qefm and 1/qefm were excellent.
The percentage earnings yield 100E10/P was best at year 5, comparable to qefm and 1/qefm at year 10, a laggard at year 15 and a laggard in most cases at year 20. It did better than qefm and 1/qefm (slightly) at year 20.
1900-1990 Data: Returns
Extending the data to include 90 start years indicates a possible anomaly associated with Tobin’s q. If so, it would be similar to the P/E10 anomaly, which was most noticeable in the first decade of the twentieth century.
Judging from R-squared: qefm does much better than 1/qefm at 5 years. The opposite is true at 10. They do almost the same at 15 years.
Judging from R-squared: it is better to use the abbreviated 1923-1980 data set than 1900-1990.
1923-1980 Data
30-Year Historical Surviving Withdrawal Rates
The percentage earnings yield 100E10/P was the best choice for both portfolios (HSWR50 and HSWR80).
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.
Tobin q Survey Follow-On
Tobin q 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 Errors
Tobin q Backup Material
Turning Points
History verifies that the stock market rises higher than expected and falls lower than expected. Our investigations of Tobin’s q and stock market returns tell us more. They tell us about the turning points.
Turning Points