**Measures of Stock Market Valuation**

**A. Background**

1. I chose to use the price to earnings ratio P/E10 of the SP500 for stock market valuation in my recent post:

**Price Adjusted Safe Withdrawal Rates: Overview.**

2. The price to earnings ratio has long been known as a good indicator of value. Lower P/E ratios are usually better. The definition that I use, P/E10, is non-standard.

3. I have looked at several alternative measures of valuation. I looked at an adjustment for inflation, an adjustment according to whether the P/E10 is rising or falling and a comparison to interest rates. One often hears about similar comparisons by those who favor stocks in today's market.

4. In all cases the unadjusted P/E10 was better.

5. I have also identified a change detector that is worth examining further.

**B. Definition**

1. I use the definition of the price to earnings ratio that Professor Shiller uses for his database that he posts on his website, P/E10. The price P is the current value of the SP500 index. The term E is the average of the previous ten years of earnings.

2. All values include adjustments for inflation. This adjustment affects all of the components of the earnings term E. The latest earnings term in the ten-year average has the same inflation index as the price term P. But the other earnings terms in the ten-year average have their own, different inflation index values.

**C. Alternative measures of valuation**

1. One alternative is to adjust the price to earnings ratio P/E10 for inflation. This is based on the premise that lower inflation supports higher P/E10 ratios. I multiplied the basic price to earnings ratio P/E10 by the ratio of the latest two CPI (consumer price index) values. This product is an effective P/E10 ratio that is lower during times of disinflation (i.e., a decreasing rate of inflation) and higher when inflation is increasing. When you order each year according to its SP500 P/E10 ratios, the order changes slightly.

2. Another alternative is to multiply the current year's P/E10 by a ratio of the current year's P/E10 to the average of the latest five-year's P/E10s. The current year's price to earnings ratio is multiplied by itself (i.e., squared) and then divided by the average price to earnings ratios of the latest five years. This adjustment increases the effective price to earnings ratio P/E10 when the most recent value is higher than normal. The effective P/E10 decreases when the most recent value is lower than normal. The choice of five years is somewhat arbitrary. It is long enough to reduce short-term fluctuations. It is short enough to indicate recent trends.

3. The third alternative is to multiply the SP500 P/E10 ratio by the short-term interest rate. The inverse of the price to earnings ratio is called the earnings yield. The product of the SP500 P/E10 ratio and interest rates is the same as the ratio of interest rates to the SP500 earnings yield. The lower that this product is, the more attractive stocks become relative to cash. This is similar to the Federal Reserve's indicator for measuring relative valuations. The Federal Reserve uses ten-year bond yields. Their analysis is based on post World War 2 data. I did not have bond data for the years before World War 2. My data comes from Professor Shiller's website. It covers the entire period from 1871 to 1999. It is based primarily on the rates of commercial paper.

**D. Comparisons**

1. I made four lists covering the years of 1881 to 2000. In each list I ordered the years according to its measure of valuation. I then filled in each list with the results from the

**dory36**calculator FIRECalc for 5%, 6%, 7%, 8% and 9% withdrawal rates. My inputs to the

**dory36**calculator were 80% stocks, 20% commercial paper, a 0.20% expense ratio, a 30-year withdrawal period and the CPI for inflation adjustments. I did not use the results for a 4% withdrawal rate because it showed a failure in only one year (1966).

2. I found it useful to group the outputs from the

**dory36**calculator in three ways. The first group includes portfolios that last for the entire 30 years. The second group includes those portfolios that last from 21 to 30 years. The final group consists of those portfolios that fail in year 20 or sooner.

3. As a practical matter, I did not draw any conclusions from the data corresponding to 8% and 9% withdrawal rates. There were too many failures and they came too soon to be meaningful. Also, the results from the 7% withdrawal rates simply reinforced conclusions from the 5% and 6% rates. I do not present them here.

4. I examined start years 1881 through 1980. There are no price to earnings P/E10 numbers before 1881 since the earnings component requires ten years of data. The last start year that covers a full 30-year period is 1970. However, I included the decade of the 1970s because there are many failures in portfolios started in those years.

**E. Details**

1. My standard for comparison was the ordering according to the unadjusted price to earnings ratio P/E10. At a 5% withdrawal rate, the first year with a portfolio that lasts less than the full duration is 1916. Its order is 33 out of the 100 data samples. The first year with a portfolio that lasts 20 years or less is 1973. The year 1973 is number 81 (out of 100). For a 6% withdrawal rate, 1915 is the first start year in the list with a portfolio failure. Its order is 19 (out of 100). The year 1919 is the first start year with a failure at year 20 or earlier. Its order is 33 (out of 100).

2. When I examined the results of weighting by inflation, they were very close to those of the unadjusted price to earnings P/E10. In fact, the years that made up the first thirty-four entries are almost identical except for their order. At a 5% withdrawal rate, all of the portfolios of all the start years in both lists last a full 30 years except for one. That year is 1916. A portfolio started in 1916 would have failed in year 28. For an unadjusted price to earnings ratio P/E10, it is number 33 on a list of 100. On the inflation-adjusted list it is number 34 of 100. At a 6% withdrawal rate, it is also the first start year which would have produced a portfolio failure at year 20 or earlier.

3. Up to this point it is difficult to separate the two lists except for a very slight preference for the one with an inflation adjustment.

4. However, portfolios that started in 1908, 1914, 1915 and 1917 would have failed in years 21 to 30 with a 6% withdrawal rate. Those four years are on both lists. They are ranked 30, 28, 19 and 21 respectively on the unadjusted price to earnings list. They are ranked 22, 26, 16 and 30 respectively on the inflation adjusted listed. These differences favor the unadjusted list.

5. The unadjusted price to earnings ratio P/E10 list includes the years 1947 and 1952 among its first 34 entries. The inflation-adjusted list includes years 1885 and 1886. All of the other entries among those 34 are the same except for their order. Portfolios starting in the years 1947 and 1952 all last the entire thirty years for withdrawal rates of 5%, 6%, 7% and 8%. Portfolios begun in 1885 fail at an 8% withdrawal rate. Portfolios began in 1886 fail at both 7% and 8% withdrawal rates. This comparison favors the unadjusted price to earnings ratio P/E.

6. In any event both the unadjusted price to earnings ratio P/E10 and the inflation adjusted price to earnings ratio P/E10 produce almost identical results. I do not have a strong preference. The unadjusted P/E10 is easier to calculate.

7. The second alternative measure produces similar comparisons although the arguments against using it are stronger. This is the measure that multiples the current price to earnings P/E10 number by its ratio to the average P/E10 of the last five years. At a 5% withdrawal rate the first two failures occur in 1913 at position number 34 (out of 100) and in 1916 in position 39 (out of 100). With the unadjusted price to earnings ratio P/E10, failures occur for the same two start years. But 1913 occurs at position 38 (out of 100) and 1916 occurs in position 33 (out of 100). Again, it is the portfolio failures at the 6% withdrawal rate that cause us to choose the unadjusted number. At a 6% withdrawal rate, portfolios that start in 1908, 1914, 1915, 1917 and 1974 fail. They are among the first 30 entries on the list. Their positions are 13, 22, 14, 23 and 27 respectfully. Using the unadjusted price to earnings ratio, the portfolios that start in 1908, 1914, 1915 and 1917 - but not 1974 - fail among the first 30 entries (out of 100). Their positions are 30, 28, 19 and 21 respectfully.

8. The third alternative measure of valuation multiplies the current price to earnings ratio by the short-term interest rate. This turns out to be a poor indicator. It strongly favors the years 1933 through 1950 because short-term interest rates were exceedingly low during those years. The highest rate during that period was 1.58% in 1949. The lowest was 0.53% in 1941. Again, the 5% comparisons are similar. The 6% data show the differences. At a 6% withdrawal rate, portfolios started in 1936 and 1937 would have failed on year 20 or sooner. Those years appear as entries 13 (out of 100) and 18 (out of 100) respectively. This is far worse than the results of ordering by the unadjusted price to earnings ratio P/E10. That ordering shows failures initially in 1913 and 1916 at positions 38 out of 100 and 33 out of 100 respectively.

**F. Excursions**

1. I made three excursions. The first is to multiply the product of the P/E10 and the interest rate once more by the P/E10 ratio. I have no good rationale for doing so except that it has the form of a weighted P/E10 ratio. That is, the product of the P/E and the interest rate indicates the relative attractiveness between stocks and cash. Higher P/E ratios make stocks less attractive because their earnings yields (the inverse of P/E) are low. Higher interest rates make cash more attractive. The product is high when cash is attractive. It is low when stocks are attractive. The final product is the P/E squared times the interest rate.

2. The ordering that this produces is much better than I had expected. Once again, the 6% withdrawal rate results favor using the unadjusted P/E10 ratio. With the adjusted P/E10 ratio portfolios that start in 1939 and 1940 fail to last the entire thirty years. But they appear in positions 9 and 10. With the unadjusted P/E10, the first two failures occur in positions 19 and 21. At a 5% rate of withdrawal the comparison is not nearly as dramatic. The first two failures correspond to positions 31 and 37 for the adjusted P/E10 ratios and positions 33 and 38 for the unadjusted P/E10 ratios.

3. The other excursions examine a couple of change detectors. The first is simply to take the difference of the current year's P/E10 ratio and the previous year's P/E10 ratio. The other starts by dividing the current year's P/E10 ratio by the average of the last five years of P/E10 ratios. That was for me easy to do. I had already calculated the ratio of the current year's P/E10 to the average P/E10 from the last five years. Then I took the difference between the current year and the previous year. I called it DELTA. I multiplied DELTA by the current year's P/E10. Bigger positive numbers would indicate a change for the worse. Negative numbers, especially those with large absolute values, would indicate a change for the better.

4. I only performed a cursory evaluation of the change detectors. I rated each year from 1886 through 1910 as being better than, the same as or worse than the year before. I began with 1886 since my most complex indicator required five years of P/E10 data. An ordering by P/E10 alone actually provides a little bit of an indication. If a particular year has a very high P/E10, it is likely to be worse than (i.e., not as safe as) the year before. In a sense this could be likened to comparing the current P/E10 to an average. Taking the difference between the current year's P/E10 and the previous is better. It uses an actual comparison. The most complex measure is best. The highest position for which it indicates that the current year will be worse than the year before is 13 (out of 25). There are 9 such cases. The lowest rank that indicates an improvement is 17 out of 25. There are 6 such cases. Years that are predicted to be the same rank between 9 to 23. There are 10 such cases.

5. My examination of change detectors has been quite limited. I only looked at 25 years of data. The change detector with the most promise is also the most complex. In addition, the words "better, same and worse"Â are poorly defined.

**G. Conclusions**

1. I selected the unadjusted price to earnings ratio that Professor Shiller provides at his website. It is at least as good as the alternatives that I examined.

2. So far, my more complex change detector shows promise. But I have only looked at it under very limited conditions. My tentative opinions about it may be wrong.

3. It will be worthwhile to look at additional inflation adjustments. My adjustment takes the ratio of this year's CPI and divides it by last year's CPI. It may be better to divide by the CPI from three or four years ago. That would average out the effects of inflation over several years.

**H. References**

1. I found all of my data sources initially from posts by

**intercst**on the Retire Early Home Page discussion board. In addition, I recommend that you read everything on his web site www.retireearlyhomepage.com. It includes a free version of his Retire Early Safe Withdrawal Rate Study. I recommend that you download the full report. It only costs $5.00.

2. The

**dory36**calculator FIRECalc is available at http://capn-bill.com/fire/.

3. Dr. Shiller's website is www.econ.yale.edu/~shiller/. You can go directly to his historical SP500 data by using www.econ.yale.edu/~shiller/data/ie_data.xls. He has also posted an insightful (but somewhat technical) paper date 7-21-96 with the title "Price-Earnings Ratios as Forecasters of Returns: The Stock Market Outlook in 1996."Â

Have fun.

John R.