Tobin's q as an estimator
Posted: Tue Aug 19, 2003 1:02 pm
Tobin's q as an estimator of Historical Database Rates
Background
wanderer has suggested that Tobin's q may be a better estimator of value than P/E10. He identified several good reasons why that might be so. He provided a link to a data source as well. See this post on the FIRE board:
http://nofeeboards.com/boards/viewtopic ... 133#p10133
This is the data source: http://www.valuingwallstreet.com/updates.shtml
Test Conditions
I used the same methodology as I did on the Safe Withdrawal Rate versus P/E10 Data study. I ordered the years from 1921-1980 according to Tobin's q and I listed the Historical Database Rates for the same portfolios as before. I have listed the results in the attached tables. The tables show the highest withdrawal rates that have no failures. They are in increments of 0.2%. (This is different from before. In the earlier post, I listed withdrawal amounts at which the first failure occurred. The numbers in these tables are 0.2% lower. Also, I had incorrectly identified Historical Database Rates as Safe Withdrawal Rates.)
As before I determined the Historical Database Rates using the FIRECalc historical sequence calculator. My inputs were to have an initial balance of $1000, a portfolio life span of 30 years, a portfolio of stocks and commercial paper, inflation adjustments according to the CPI and expenses at 0.20% of the portfolio balance. The amount withdrawn varied. The stock allocations were 50% and 80%.
Results
I have listed the results in the attached tables. My initial conclusion is that Tobin's q does not estimate Historical Database Rates as well as P/E10. In these tables the Historical Database Rates with 80% stocks range from 5.8% to 11.6% at the twenty most favorable valuations, from 4.6% to 9.4% for the middle twenty valuations and from 4.0% to 7.6% for the twenty least favorable valuations.
The comparable results using P/E10 (using the proper term, Historical Database Rates) were 7.2% to 11.6% for the twenty most favorable valuations, 5.6% to 9.4% for the middle twenty valuations and 4.0% to 5.8% for the twenty least favorable valuations.
The 1881-1920 Anomaly
I looked at the Tobin's q data to see if the same anomaly exists with it as does for P/E10. The data for Tobin's q extend only to 1900 so that there are only 21 years to examine. With P/E10 there was a distinct safe area at the middle range of valuations. Danger zones were at both higher and lower valuations. These data are consistent with such an anomaly but they are not as dramatic, possibly because of the limited number of historical sequences examined. They are not sufficient by themselves to establish the stronger conclusion that an anomaly definitely exists.
I have attached a table that shows when portfolios would have been safe (S) or when they would have failed (F). I have indicated when failures occurred after the start. That is, F24 means that there was a failure in year number 24.
I examined portfolios of 50% and 80% stocks along with commercial paper, a portfolio life span of 30 years, withdrawal rates of 5% and 6%, inflation adjustments to match the CPI, expenses of 0.20% of the portfolio balance and annual re-balancing at no cost. Once again, I made my runs on FIRECalc.
Conclusions
I am not familiar with the details of Tobin's q. It is possible that others can identify a tighter relationship with Historical Database Rates than I have. I would not rule out that possibility.
It should be kept in mind that these comparisons are made with the intention of estimating Historical Database Rates and applying that information later on to calculate Safe Withdrawal Rates. That is quite different from many alternative uses for measures of value.
Data Sources
I used the dory36 FIRECalc retirement calculator at http://capn-bill.com/fire/ .
I have extracted P/E10 numbers from Yale Professor Shiller's website at http://www.econ.yale.edu/~shiller/. I have extracted Tobin's q values from the site listed above: http://www.valuingwallstreet.com/updates.shtml
Have fun.
John R.
Background
wanderer has suggested that Tobin's q may be a better estimator of value than P/E10. He identified several good reasons why that might be so. He provided a link to a data source as well. See this post on the FIRE board:
http://nofeeboards.com/boards/viewtopic ... 133#p10133
This is the data source: http://www.valuingwallstreet.com/updates.shtml
Test Conditions
I used the same methodology as I did on the Safe Withdrawal Rate versus P/E10 Data study. I ordered the years from 1921-1980 according to Tobin's q and I listed the Historical Database Rates for the same portfolios as before. I have listed the results in the attached tables. The tables show the highest withdrawal rates that have no failures. They are in increments of 0.2%. (This is different from before. In the earlier post, I listed withdrawal amounts at which the first failure occurred. The numbers in these tables are 0.2% lower. Also, I had incorrectly identified Historical Database Rates as Safe Withdrawal Rates.)
As before I determined the Historical Database Rates using the FIRECalc historical sequence calculator. My inputs were to have an initial balance of $1000, a portfolio life span of 30 years, a portfolio of stocks and commercial paper, inflation adjustments according to the CPI and expenses at 0.20% of the portfolio balance. The amount withdrawn varied. The stock allocations were 50% and 80%.
Results
I have listed the results in the attached tables. My initial conclusion is that Tobin's q does not estimate Historical Database Rates as well as P/E10. In these tables the Historical Database Rates with 80% stocks range from 5.8% to 11.6% at the twenty most favorable valuations, from 4.6% to 9.4% for the middle twenty valuations and from 4.0% to 7.6% for the twenty least favorable valuations.
The comparable results using P/E10 (using the proper term, Historical Database Rates) were 7.2% to 11.6% for the twenty most favorable valuations, 5.6% to 9.4% for the middle twenty valuations and 4.0% to 5.8% for the twenty least favorable valuations.
The 1881-1920 Anomaly
I looked at the Tobin's q data to see if the same anomaly exists with it as does for P/E10. The data for Tobin's q extend only to 1900 so that there are only 21 years to examine. With P/E10 there was a distinct safe area at the middle range of valuations. Danger zones were at both higher and lower valuations. These data are consistent with such an anomaly but they are not as dramatic, possibly because of the limited number of historical sequences examined. They are not sufficient by themselves to establish the stronger conclusion that an anomaly definitely exists.
I have attached a table that shows when portfolios would have been safe (S) or when they would have failed (F). I have indicated when failures occurred after the start. That is, F24 means that there was a failure in year number 24.
I examined portfolios of 50% and 80% stocks along with commercial paper, a portfolio life span of 30 years, withdrawal rates of 5% and 6%, inflation adjustments to match the CPI, expenses of 0.20% of the portfolio balance and annual re-balancing at no cost. Once again, I made my runs on FIRECalc.
Conclusions
I am not familiar with the details of Tobin's q. It is possible that others can identify a tighter relationship with Historical Database Rates than I have. I would not rule out that possibility.
It should be kept in mind that these comparisons are made with the intention of estimating Historical Database Rates and applying that information later on to calculate Safe Withdrawal Rates. That is quite different from many alternative uses for measures of value.
Data Sources
I used the dory36 FIRECalc retirement calculator at http://capn-bill.com/fire/ .
I have extracted P/E10 numbers from Yale Professor Shiller's website at http://www.econ.yale.edu/~shiller/. I have extracted Tobin's q values from the site listed above: http://www.valuingwallstreet.com/updates.shtml
Have fun.
John R.