Tobin's q as an estimator

Research on Safe Withdrawal Rates

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JWR1945
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Tobin's q as an estimator

Post by JWR1945 »

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 The amount withdrawn varied.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.
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Post by JWR1945 »

Years from 1921-1980 ordered by Tobin's q and Historical Database Rates for 50% stocks and for 80% stocks. (Asterisks identify years with sharp dividend cuts within two or three years and which affect the dividend approach for designing portfolios for high levels of safety.)

The twenty most favorable years of valuations:
Year Tobin's q HDBR (50%) HDBR (80%)
1948 0.3352 7.6% 10.8%
1921 0.3469 9.6% 11.6%
1941*** 0.3538 5.0% 7.0%
1949 0.3566 7.8% 11.0%
1974 0.3618 5.6% 5.8%
1978 0.3634 8.0% 9.2%
1947 0.3662 6.8% 9.4%
1942*** 0.3732 6.0% 9.0%
1979 0.3755 8.6% 9.6%
1953 0.3777 6.6% 8.6%
1977 0.3925 6.8% 7.4%
1950 0.3966 7.2% 10.2%
1952 0.3987 6.8% 9.0%
1923 0.3988 7.6% 9.0%
1922 0.4003 8.4% 10.2%
1951 0.4216 7.0% 9.4%
1980 0.4275 9.4% 10.4%
1932*** 0.4303 6.0% 8.0%
1943 0.4354 6.6% 9.2%
1946 0.4406 5.2% 6.8%


The twenty years with middle levels of valuation.
Year Tobin's q HDBR (50%) HDBR (80%)
1975 0.4472 7.0% 8.2%
1931 *** 0.4507 5.0% 5.6%
1924 0.4582 7.8% 9.4%
1944 0.4764 6.0% 8.6%
1940 *** 0.4905 4.6% 6.0%
1976 0.4925 6.6% 7.2%
1954 0.4957 6.8% 9.0%
1957 0.5004 5.2% 6.0%
1945 0.5470 5.8% 8.2%
1937 *** 0.56354 3.8% 4.6%
1925 0.56357 7.2% 8.4%
1934 0.5717 4.8% 6.2%
1955 0.5752 5.8% 6.8%
1956 0.5755 5.2% 5.8%
1926 0.5847 6.8% 7.6%
1933 *** 0.6097 5.8% 8.4%
1939 0.6322 4.6% 6.0%
1973 0.6450 4.6% 4.6%
1958 0.6466 5.8% 7.0%
1938 *** 0.6572 4.8% 6.6%


The twenty years with the least favorable valuations.
Year Tobin's q HDBR (50%) HDBR (80%)
1960 0.6956 5.0% 5.2%
1959 0.6963 5.0% 5.4%
1930 0.7294 5.0% 4.8%
1927 0.7398 6.6% 7.2%
1970 0.7480 4.8% 4.8%
1962 0.7608 4.6% 4.8%
1935 0.7816 5.2% 7.6%
1966 0.7965 4.2% 4.0%
1971 0.8067 4.8% 6.8%
1961 0.8095 5.0% 5.2%
1969 0.8109 4.2% 4.2%
1963 0.8109 4.8% 5.0%
1964 0.9082 4.6% 4.6%
1972 0.9228 4.8% 4.8%
1967 0.9647 4.4% 4.4%
1928 0.9729 5.6% 5.8%
1965 0.9743 4.2% 4.2%
1936 0.9791 4.4% 5.4%
1968 1.0556 4.2% 4.2%
1929 1.3521 4.6% 4.2%
Last edited by JWR1945 on Thu Aug 21, 2003 7:59 am, edited 1 time in total.
JWR1945
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Post by JWR1945 »

Looking for a 1900 to 1920 Anomaly with Tobin's q

The years are ordered according to Tobin's q. The table shows successes (S) and failures (F) along with the year when failure occurs (relative to the starting year). Withdrawal rates are 5% or 6% of the portfolio's initial balance and stock allocations are 50% or 80%, as indicated.

Code: Select all

Year Tobin's q  5%(80/20 %)  6%(80/20%)  5%(50/50%)
1920   0.2706   S     S     S
1918   0.3330   S     S     S
1919   0.3356   S     S     S
1917   0.3362   S     F25   S
1907   0.6410   F27   F19   F27
1916   0.6468   S     F20   F28
1914   0.6649   S     F24   S
1903   0.7726   S     F23   S
1913   0.7847   F40   F20   F28
1900   0.8012   S     S     S
1915   0.8114   S     F30   S
1911   0.8665   F28   F18   F25
1910   0.8707   F29   F19   S
1912   0.8842   F27   F18   F25
1908   0.9111   S     F29   S
1901   0.9396   S     F25   S
1909   0.9917   F28   F18   F26
1902   0.9964   S     F21   F29
1906   1.0215   F24   F18   F25
1904   1.0245   S     S     S
1905   1.1177   S     F21   F30
Last edited by JWR1945 on Sat Aug 23, 2003 10:51 am, edited 1 time in total.
peteyperson
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Post by peteyperson »

Hi John,

This is on my reading list, but I have to say in advance that I am somewhat dubious of any new way to value stocks. New and financial measurements don't seem to go well together. However, I am open minded enough to buy the book and see what it says though it is low down on the list currently.

Petey
JWR1945 wrote: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

<snip>

Have fun.

John R
JWR1945
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Location: Crestview, Florida

Post by JWR1945 »

To peteyperson:

I have not yet found an advantage to using Tobin's q.

wanderer provided a data source and some reasons that he prefers to use Tobin's Q as a measure of valuation.
http://nofeeboards.com/boards/viewtopic ... 133#p10133

I am hindered somewhat because I am unfamiliar with it and I am not really sure what it is supposed to predict. Knowing that might help me find explanations as to why it has failed so far. There are quite a few ways to modify the indicator that might help us improve its utility. Doing so is not likely to be easy.

We are in much better shape with P/E10. Professor Shiller did the heavy lifting for us, so to speak. He followed Benjamin Graham's suggestion and averaged ten years of earnings to come up with P/E10. P/E10 turns out to be a much better predictor of portfolio safety than the normal P/E based upon a single year. It may be that something similar can be done with Tobin's q.

I have the impression that Tobin's q is really an economic indicator and not a stock market indicator. There is a distinction between the two. In addition, I see no reason to believe that Tobin's q is calculated any better than P/E10 or even P/E. wanderer thinks otherwise. It may be that he is unduly forgiving of the problems in calculating Tobin's q because he is intimately aware of the problems associated with reported earnings by major corporations.

Again, I am not familiar with this indicator, Tobin's q.

Have fun.

John R.
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Post by JWR1945 »

I have tried taking the product of PE10 and Tobin's q. It still has problems, but it looks promising. It seems to improve estimates in the middle ranges of valuations. There are only two years, 1971 and 1974, which seem to produce anomalous results.

The Historical Database Rates of sequences starting in years with the twenty lowest PE10*q products range from 5.8% to 11.6%. Excluding the single year 1974, the range is from 7.0% to 11.6%. The Hardware Database Rates of sequences starting in years with the middle twenty PE10*q products range from 5.6% to 9.0%. The Hardware Database Rates of sequences starting in years with the highest PE10*q products range from 4.0% to 6.8%. Excluding the single year 1971, the PE10*q products range from 4.0% to 5.8%.

For PE10 alone, the orderings are 7.2% to 11.6%, 5.6% to 9.4% and 4.0% to 5.8%.

The Historical Database Rates are given for an 80% stock portfolio with 20% commercial paper designed to last for 30 years. The expense ratio is 0.20%. Withdrawals are matched inflation as measured by the CPI. I used the FIRECalc to obtain my results.

See the next few posts for my results (raw data in tabular form).

If I understand correctly, Tobin's q is similar to a price to book ratio (it uses market capitalization for price but it uses replacement cost instead of book value). PE10 is similar to the price to earnings ratio, but it uses the average of ten years of earnings to smooth out year-to-year fluctuations in earnings.

Have fun.

John R.
Last edited by JWR1945 on Tue Nov 11, 2003 8:11 am, edited 1 time in total.
JWR1945
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Post by JWR1945 »

Historical Database Rates (with 80% stocks) as ordered by the product of PE10 and Tobin's q. These are the start years with the twenty lowest product values.

Code: Select all

Year         PE10  Tobin's q  PE10*q   HDBR (80%)
1921          5.1   0.3469   1.769   11.6%
1922          6.2   0.4003   2.481   10.2%
1923          8.1   0.3988   3.230   9.0%
1978          9.2   0.3634   3.343   9.2%
1979          9.2   0.3755   3.454   9.6%
1948         10.4   0.3352   3.486   10.8%
1949         10.2   0.3566   3.637   11.0%
1924          8.0   0.4582   3.665   9.4%
1980          8.8   0.4275   3.762   10.4%
1942*        10.1   0.3732   3.769   9.0%
1975          8.9   0.4472   3.980   8.2%
1932*         9.3   0.4303   4.001   8.0%
1947         11.4   0.3662   4.174   9.4%
1950         10.7   0.3966   4.243   10.2%
1943         10.1   0.4354   4.397   9.2%
1977         11.4   0.3925   4.474   7.4%
1974         13.5   0.3618   4.884   5.8%
1953         13.0   0.3777   4.910   8.6%
1941*        13.9   0.3538   4.917   7.0%
1951         11.8   0.4216   4.974   9.4%
* indicates that dividends were cut substantially within the next two or three years.

Have fun.

John R.
Last edited by JWR1945 on Tue Nov 11, 2003 8:12 am, edited 1 time in total.
JWR1945
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Post by JWR1945 »

Historical Database Rates (with 80% stocks) as ordered by the product of PE10 and Tobin's q. These are the start years with the twenty middle product values.

Code: Select all

Year   PE10   Tobin's q   PE10*q   HDBR (80%)
1952   12.5   0.3987   4.983   9.0%
1944   11.0   0.4764   5.240   8.6%
1933*   8.7   0.6097   5.304   8.4%
1925    9.6   0.56357  5.410   8.4%
1976   11.1   0.4925   5.466   7.2%
1954   12.0   0.4957   5.948   9.0%
1945   11.9   0.5470   6.509   8.2%
1926   11.3   0.5847   6.607   7.6%
1946   15.6   0.4406   6.873   6.8%
1934   13.0   0.5717   7.432   6.2%
1931*  16.7   0.4507   7.526   5.6%
1940*  16.3   0.4905   7.995   6.0%
1957   16.7   0.5004   8.356   6.0%
1958   13.7   0.6466   8.858   7.0%
1938*  13.5   0.6572   8.872   6.6%
1935   11.4   0.7816   8.910   7.6%
1955   15.9   0.5752   9.145   6.8%
1927   13.1   0.7398   9.691   7.2%
1939   15.5   0.6322   9.799   6.0%
1956   18.2   0.5755  10.474   5.8%
* indicates that dividends were cut substantially within the next two or three years.

Have fun.

John R.
Last edited by JWR1945 on Tue Nov 11, 2003 8:13 am, edited 1 time in total.
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Post by JWR1945 »

Historical Database Rates (with 80% stocks) as ordered by the product of PE10 and Tobin's q. These are the start years with the twenty highest product values.

Code: Select all

Year   PE10   Tobin's q   PE10*q   HDBR (80%)
1973   18.7   0.6450   12.061   4.6%
1937*  21.6   0.56354  12.172   4.6%
1959   17.9   0.6963   12.463   5.4%
1970   17.0   0.7480   12.716   4.8%
1960   18.3   0.6956   12.729   5.2%
1971   16.4   0.8067   13.229   6.8%
1961   18.4   0.8095   14.894   5.2%
1963   19.2   0.8109   15.569   5.0%
1972   17.2   0.9228   15.872   4.8%
1962   21.1   0.7608   16.052   4.8%
1930   22.3   0.7294   16.265   4.8%
1936   17.0   0.9791   16.644   5.4%
1969   21.1   0.8109   17.109   4.2%
1928   18.8   0.9729   18.290   5.8%
1966   24.0   0.7965   19.116   4.0%
1964   21.6   0.9082   19.617   4.6%
1967   20.4   0.9647   19.679   4.4%
1965   23.2   0.9743   22.603   4.2%
1968   21.6   1.0556   22.800   4.2%
1929   27.0   1.3521   36.506   4.2%
* indicates that dividends were cut substantially within the next two or three years.

Have fun.

John R.
Last edited by JWR1945 on Tue Nov 11, 2003 8:14 am, edited 1 time in total.
JWR1945
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Post by JWR1945 »

Looking for a 1900 to 1920 Anomaly with the product of P/E10 and Tobin's q

The years are ordered according to the product P/E10*q. The table shows successes (S) and failures (F) along with the year when failure occurs (relative to the starting year). Withdrawal rates are 5% or 6% of the portfolio's initial balance and stock allocations are 50% or 80%, as indicated.

Code: Select all

Year  P/E10*q  Order  5%(80/20%)  6%(80/20%)  5%(50/50%)
1920   1.5965     1   S           S               S
1919   2.1360     2   S           S               S
1918   2.1978     3   S           S               S
1917   3.6645     4   S         F25               S
1914   7.7128     5   S         F24               S
1916   8.0850     6   S         F20             F28         
1915   8.3574     7   S         F30               S
1913  10.2795     8   F40       F20             F28
1908  10.8420     9   S         F29               S
1907  11.0252    10   F27       F19             F27
1912  12.1135    11   F27       F18             F25
1911  12.1310    12   F28       F18             F25
1910  12.6251    13   F29       F19               S
1909  14.5779    14   F28       F18             F26
1900  14.9023    15   S           S               S
1903  15.6837    16   S         F23               S
1904  16.1871    17   S           S               S
1901  19.6376    18   S         F25               S
1906  20.5321    19   F24       F18             F25
1905  20.5656    20   S         F21             F30
1902  22.2197    21   S         F21             F29
P/E10 alone showed failures at high and low valuations, but not at the middle levels. This product P/E10*q shows failures at middle valuations, but safety at high and low valuations.

Have fun.

John R.
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Post by wanderer »

I have the impression that Tobin's q is really an economic indicator and not a stock market indicator. There is a distinction between the two. In addition, I see no reason to believe that Tobin's q is calculated any better than P/E10 or even P/E. wanderer thinks otherwise. It may be that he is unduly forgiving of the problems in calculating Tobin's q because he is intimately aware of the problems associated with reported earnings by major corporations.

It is the relationship of market price to book value (adjusted for replacement cost and inflation). The market determines the numerator. Economists working independently at the fed and the BEA determine the denominator. If one can't immediately grasp the difference in quality between the numbers generated by those folks and those generated by company accountants we'll just have to agree to disagree.

One (there are others) of the shortcomings of Q is that it seems to be systematically understated. It ends up averaging about .65 (when the number should be close to, if not, 1). This problem, like the others noted previously, is dealwithable in my estimation and is what that second column of numbers does in the link I provided (that is, the 'value relative to the geometric mean of Q' column). Perhaps that will change some of the strange results of the analysis, JWR.

HTH.
regards,

wanderer

The field has eyes / the wood has ears / I will see / be silent and hear
JWR1945
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Post by JWR1945 »

wanderer
If one can't immediately grasp the difference in quality between the numbers generated by those folks and those generated by company accountants we'll just have to agree to disagree.
Yes. We will have to agree to disagree.

The two calculations are to determine two different things. I would expect that what is being calculated has the greater influence on quality, not who is doing it.
One (there are others) of the shortcomings of Q is that...Perhaps that will change some of the strange results of the analysis...
So far, only the results with the product term PE10*q have depended upon anything other than the relative order. Any kind of improvement (by taking a function of q, instead of the raw number) will be seen only when looking at such products.

Later on, there may be a curve fitting stage in which the value of q is important, not just its relative order.

I have posted a variety of tables that may yet prove useful. I have emphasized relative order. I had hoped (for example) that, when PE10 and q (or PE10 and the product PE10*q) predict results that differ greatly, it would consistently show a need to make a correction (such as lowering one's expectations). I have not found such consistency yet. I may discover something later.

Have fun.

John R.
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Post by JWR1945 »

JWR1945 wrote:Historical Database Rates (with 80% stocks) as ordered by the product of PE10 and Tobin's q. These are the start years with the twenty lowest product values.

Code: Select all

Year         PE10  Tobin's q  PE10*q   HDBR (80%)
1921          5.1   0.3469   1.769   11.6%
1922          6.2   0.4003   2.481   10.2%
1923          8.1   0.3988   3.230   9.0%
1978          9.2   0.3634   3.343   9.2%
1979          9.2   0.3755   3.454   9.6%
1948         10.4   0.3352   3.486   10.8%
1949         10.2   0.3566   3.637   11.0%
1924          8.0   0.4582   3.665   9.4%
1980          8.8   0.4275   3.762   10.4%
1942*        10.1   0.3732   3.769   9.0%
1975          8.9   0.4472   3.980   8.2%
1932*         9.3   0.4303   4.001   8.0%
1947         11.4   0.3662   4.174   9.4%
1950         10.7   0.3966   4.243   10.2%
1943         10.1   0.4354   4.397   9.2%
1977         11.4   0.3925   4.474   7.4%
1974         13.5   0.3618   4.884   5.8%
1953         13.0   0.3777   4.910   8.6%
1941*        13.9   0.3538   4.917   7.0%
1951         11.8   0.4216   4.974   9.4%

* indicates that dividends were cut substantially within the next two or three years.
Have fun.

John R.
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