Do Dividends Affect Firm Value?

The Impact of Dividend on Stock Prices — a Regression Analysis

 Question:   Do firms that pay dividends have a higher stock price than firms that don’t pay dividend after accounting for earnings per share and sales per share?

Motivation:   The issue of whether dividends impact the value of the firm is a central discussion for students of finance. (My Ph.D. dissertation was on this topic.)

Modigliani and Miller found that if capital markets are perfect dividend policy will not impact the value of the firm.  More recent work indicates that dividends can influence firm value when capital markets are imperfect and insiders have better information than outsiders.

Dividend payments are unlikely to increase share value for older firms or firms with fewer growth opportunities.  By contrast, high fliers like Amazon and Netflix do not pay dividends.

Dividends can be associated with either higher or lower share prices.   The results can differ across industries and across samples of firms.

The Data:   The analysis is based on a single cross section of 67 firms.  The data was collected in mid-September 2018 after the close of market on a weekend.  Roughly half of the firms are large-cap growth firms and the other half are large cap value firms.

The data used in the regression analysis is described in the table below.

Description of Data in Regression Model
Mean Std. Err.
earnings per share 6.43 1.04
sales per share 160.29 91.41
Positive dividend dummy 0.87 0.04
price of a share 196.51 41.51


The Regression Results:



Regression Results for Share Price Equation
  Coeff. t-stat
Earnings Per Share 10.5 2.36
Sales Per Share 0.2 3.63
Dividend Dummy -331.0 -4.27
_cons 385.6 4.92
R2 0.66
N 67.0


Discussion of Regression Results

All three variables – earnings, sales and dividend dummy – are significantly related to price per share.

The dividend coefficient is negative suggesting that dividend payments are associated with lower share prices.

Why are dividend payments reducing share value in this sample?

The sample includes some growth names – Facebook, Amazon, Google, Netflix – which do not pay dividends.   The sample also includes some more established firms – GE, IBM, Coke, Pepsi and Bank of America – which are not growing fast but do pay dividends.

In this sample, growth prospects appear to have a larger impact on stock price than the promise of dividends.

Traditionally, firm earnings has been considered the more important determinant of stock price.  However, the sales coefficient has a larger t-statistic than the earnings coefficient.


The model is built with cross-sectional data.  Cross-sectional models often do not explain the change in stock prices over time.

The dividend variable could be an endogenous variable.  A second equation that predicts dividend behavior and the level of dividends could be added.

A larger model might include information on capital expenditures and share buybacks.




Are Dividend Payments Sustainable?


Contingency Tables of Dividend Yields vs Dividend Payout

Issue:  Contingency table of dividend yield versus dividend payout for 35 growth stocks and 35 value stocks are used to analyze the sustainability of dividend payouts.

Contingency tables for the two portfolios are presented below.


Contingency Table for Dividend Yields vs Payout Ratios –

 Growth Firms

Dividend Yield
Dividend Payout 0 >0  & <=2 >2 & <4 >=4 Total
0 9 0 0 0 9
<=50 0 13 1 0 14
>50 & <=90 0 2 5 0 7
>90 or <0 0 0 4 1 5
Total 9 15 10 1



Contingency Table for Dividend Yields vs Payouts –

Value Firms

Dividend Payout 0 >0  & <=2 >2 & <4 >=4 Total
0 1 0 0 0 1
<=50 0 5 5 2 12
>50 & <=90 0 2 5 0 7
>90 or <0 0 3 10 2 15
Total 1 10 20 4 35

Comments on the Construction of the Contingency Tables:

The columns of the table are based on the dividend yield defined as annual dividend payments as a percent of the current stock price. The dividend yield measures the generosity of a firm’s dividend.

The dividend yield categories are – yield = 0, yield > 0 &yield <2, yield >=2 and yield <4, and yield >=4.

The rows of the table are based on the dividend payout ratio defined as dividend as a percent of income.   The dividend payout ratio measures the ability of a firm to maintain dividends in the future.

A dividend paying firm with negative earnings (or an undefined dividend payout ratio) is not likely to be able to continue paying dividends.

The four dividend payout ratios considered here are payout =0, payout<=50, payout>50 & payout<=90 and payout >90 or payout<0.

Note I have placed firms with negative earning that are currently paying dividends and firms with dividend payout ratios greater than 90 in the same high dividend payout category.   This makes sense because firms with high dividend payout ratios and firms paying dividends even though they have negative earnings will have trouble sustaining dividend payments unless earnings grow.

Note also by definition of yield and payout all firms with dividend yield equal to 0 also have dividend payout equal to 0.

Observations about dividend payments and sustainability of payments for growth and value firms:

 Growth firms pay less in terms of dividends than value firms.   There are 9 of 35 growth firms with a 0% yield compared to 1 of 35 value firm that pays no dividends.

A substantial percent of value firms may not be able to sustain their current dividend level.   15 value firms have a dividend payout over 90 or under 0 compared to only 5 of 35 growth firms.

Concluding Remarks:    The tech sector and growth ETFs have led the market upwards over the past couple of years.   A lot of analysts believe that the market can continue upwards through a rotation to value stocks.

I don’t see this happening.   Over 40 percent of my sample of dividend paying value firms has a payout ratio over 90 or negative earnings.   Their current dividend yield while attractive may not be sustainable.

A previous analysis of PE ratios indicated that many analysts are understating the overvaluation of value firms by ignoring firms with undefined PE ratios.


Valuation of Growth and Value Stocks with PE Ratios

Question:   The chart below contains the frequency distribution for trailing and forward PE ratios for 33 growth firms and 31 value firms.  The data was collected from the top 35 positions from two ETFs – VUG Vanguard large cap growth and VTV Vanguard large cap Value funds. Two growth stocks and four value stocks were omitted from the analysis because of negative earnings, which leads to an undefined PE ratio.

What can we learn about the relative valuations of growth and value firms from this chart?  How did the omission of firms with negative earnings impact our conclusions?  How do conclusions based on trailing PE and forward PE ratios differ?  What are the economic implications of large differences between trailing and forward PE ratios?

The Data:

Trailing PE Ratios
Growth Stocks Value Stocks
Freq. Percent Freq. Percent
Under 15 5 15.15 6 19.35
15 to 25 10 30.3 11 35.48
Over 25 18 54.55 14 45.16
Total 33 100 31 100
<=75 28 84.85 25 80.65
>75 5 15.15 6 19.35
Total 33 100 31 100
Forward PE Ratios
Freq. Percent Freq. Percent
Growth Stocks Value Stocks
Under 15 5 15.15 25 80.65
15 to 25 19 57.58 6 19.35
Over 25 9 27.27 0 0
Total 33 100 31 100
<=75 31 93.94 31 100
>75 2 6.06 0 0
Total 33 100 31 100

Short Answer:  Analysts on television routinely discuss PE ratios when talking about the valuation of the market.   Their analysis does not specify how PE ratios are assigned to firms with negative earnings or whether these firms are omitted from the sample.   The analyst often fails to state whether his analysis is based on trailing or forward PE ratios. Many analysts routinely present statistics, which understate the extent stocks are overvalued.

Observations about Growth and Value Firm PE Ratios

54 percent of growth firms and 45 percent of value firms report a trailing PE ratio greater than 25.

27 percent of growth firms and 0 percent of value firms report a forward PE ratio greater than 25.

15 percent of growth firms and 19 percent of value firms report a PE ratio greater than 75.

6 percent of value firms and 0 percent of growth firms report a forward PE ratio greater than 75.

Discussion of Growth and Value PE Ratios

I have not reported mean PE ratios because of outliers.  The max PE ratio for value firms in our sample was 272 for growth firms and 2352 for value firms.

The exclusion of firms with negative PE ratios makes it very difficult to measure and compare valuations.   Many analysts top-code firms with large or negative PE ratios.  One way to deal with this issue is to look at the earnings to price ratio (the reciprocal of the PE ratio) or to use techniques mentioned in a previous blog.

This analysis substantially understates the current overvaluation of value firms.  Why do I say that?

  • First, more value firms than growth firms have negative earnings and have been excluded from the sample. The excluded negative earnings firms are arguably more overvalued than firms with low positive earnings and a high PE ratio.
  • Second, as noted the PE outlier is larger for the large cap value sector than the large cap growth firms.

A valuation analysis based on PE ratios does not always result in a larger bias for value firms than growth firm.   A comparison of small cap growth to small cap value firms might find more growth firms with negative or astronomic PE ratios than presented here for the comparison of the two large-cap portfolios.

The lower forward portfolio PE ratios are the consequence of an optimistic assumption on earnings growth.   As shown in a previous post one estimate of projected earnings growth is 100*(PET/PEF)-1 where PET is trailing PE and PEF is forward PE.

Projected Growth Rate in Earnings from the Comparison of

Trailing and Forward PE Ratios

Growth Stocks Value Stocks
Min -45.1 -51.6
Max 1,615.9 16,146.5

The comparison of trailing and forward PE ratios implies substantial dispersion in projected earnings growth.

It is very easy for an optimistic analyst or an analyst who wants to sell stock to juice forward earnings and make valuations seem more reasonable than they are.

Concluding Remark:

PE ratios are often imprecise measures of firm valuation, especially when earnings are low.   Analysts are using forward earnings estimate to obtain a more optimistic picture of the overall market valuation.  But are these estimates valid or reasonable?





Are Tech Firms Overvalued

Question:  The chart below has information on the trailing PE ratio, the forward PE ratio, the PEG ratio and 2014 and 2017 gross income figures for 9 tech firms.

How do the trailing and forward PE ratios differ for these 9 firms?

What is the implied growth rate in earnings from the trailing PE ratios and the PEG ratio?  How do these implied earning growth rates compare to actual earing growth rates?

What is the implied growth rate in earnings based on the forward PE ratio and the PEG ratio? How do these implied earning growth rates compare to actual earing growth rates?

Financial Statistics for Nine Tech Firms
Trailing PE Forward PE PEG Gross Income December 2017 Gross Income December 2014
AAPL 20.35 16.56 1.46 88.2 70.5
AMZN 159.84 79.55 2.51 65.9 26.2
MSFT 52.8 22.91 2.07 72 60.5
FB 27.73 21.49 1.1 35.2 10.3
NFLX 169.65 85.72 2.19 4.03 1.75
GOOG 53.96 26.03 1.75 65.27 40.69
NVDA 40.83 35.11 2.17 5.82 2.6
EA 52.57 20.61 1.68 3.87 3.09
TXN 26.17 18.41 1.41 9.61 7.43


Below is information on the trailing and forward PE ratios for the 9 tech firms.

Comparing Trailing & Forward PE Ratios
Trailing PE Forward PE Diff.
AAPL 20.35 16.56 3.79
AMZN 159.84 79.55 80.29
MSFT 52.8 22.91 29.89
FB 27.73 21.49 6.24
NFLX 169.65 85.72 83.93
GOOG 53.96 26.03 27.93
NVDA 40.83 35.11 5.72
EA 52.57 20.61 31.96
TXN 26.17 18.41 7.76
Average 30.83
Paired t test 0.018

The trailing PE ratio is larger than the forward PE ratio for all 9 firms.

This occurs because analysts are optimistic that forward earnings will exceed past earnings.

The paired t-test indicates we should reject the null hypothesis that the mean difference between the trailing and forward PE ratio is zero.

Note:   The implied earnings growth forecast used in a PEG ratio can be obtained by dividing the PE ratio by the PEG ratio.   The definition of a PEG Ratio is PE/G.   This means PE/PEG or PE/(PE/G) is equal to G.

The actual annual growth rate of earnings between 2014 and 2017 is ((E17/E15)(1/3) -1.

Below is the comparison of implied growth rates from reported trailing PE and PEG ratios to actual earnings growth rates.

Implied vs. Actual Growth Rates
Trailing PE Ratio PEG


Implied Growth Rate Actual Average Annual Rate of Growth in Gross Profits 2014 to 2017
AAPL 20.35 1.46 13.9% 7.8%
AMZN 159.84 2.51 63.7% 36.0%
MSFT 52.8 2.07 25.5% 6.0%
FB 27.73 1.1 25.2% 50.6%
NFLX 169.65 2.19 77.5% 32.1%
GOOG 53.96 1.75 30.8% 17.1%
NVDA 40.83 2.17 18.8% 30.8%
EA 52.57 1.68 31.3% 7.8%
TXN 26.17 1.41 18.6% 9.0%

Implied growth rate based on trailing PE ratios.

For 8 of the 9 companies the implied growth rate from trailing PE ratio and reported PEG is larger than the actual growth rate in gross earnings.

Only NVDA had an implied growth rate lower than its actual growth rate.

Below is the comparison of the implied growth rates from reported forward PE ratios and PEG ratios to actual earnings growth rates

Implied vs Actual Growth Rates
Forward PE PEG Implied Growth Rate Actual Average Annual Rate of Growth in Gross Profits 2014 to 2017
AAPL 16.56 1.46 11.3% 7.8%
AMZN 79.55 2.51 31.7% 36.0%
MSFT 22.91 2.07 11.1% 6.0%
FB 21.49 1.1 19.5% 50.6%
NFLX 85.72 2.19 39.1% 32.1%
GOOG 26.03 1.75 14.9% 17.1%
NVDIA 35.11 2.17 16.2% 30.8%
EA 20.61 1.68 12.3% 7.8%
TSN 18.41 1.41 13.1% 9.0%

Implied Growth Rate based on forward PE ratios

For 5 of the 9 firms the implied growth rate based on forward PE ratio is larger than the actual growth rate.

The other 4 firms have higher actual growth rates than implied growth rates


 Are these tech stocks overvalued?

My view is there is a lot of unjustified optimism about these stocks.

Many of these firms had high actual growth rates 2014 to 2017.   This actual growth rate may be unsustainable.

Many of the implied growth rates calculated here are even higher than current unsustainable growth rates.

Perhaps analysts are using the growth rate of net taxes in their PEG estimates but tax cuts result in a one-time shift in earnings growth.  Soon the tax cut will define net earnings in the bae year of the earnings growth calculation.   This should decrease growth rates and cause the PEG ratio to rise.

Impact of Gender on Annuity Payments

Impact of Gender on Annuity Payments

 Introduction Females have longer life expectancy than males in virtually all countries.   Gender related differences in life expectancy make it more likely that females will out-live their retirement resources than will males. Females, because of their longer life expectancy, might choose to purchase a longer-term annuity.

Question:   A 75-year old person has $100,000 to spend on an annuity., which makes monthly payments for a fixed period.  She or he wants to reduce the probability of outliving the annuity to below 10 percent.

What annuity term would accomplish this goal for a male and for a female?

How does the longer life expectancy of the female affect the size of the monthly annuity payment?

Data Source: This analysis is based on the United States Life Tables, 2008 published on September 24, 2012 by the National Center for Health Statistics of the Centers for Disease Control and Prevention

Table Two of the report has life statistics for males and Table Three of the report has life statistics for females.   Both tables can be downloaded directly into an EXCEL Spreadsheet.The data in the Table below is from the CDC life tables. 


Age Total number of females alive at age x Proportion of 75-year-old females who survive to age X Total number of Males Alive at age X Proportion of 75-year Males surviving until age X
75 73,974 61,980
76 71,973 97.3% 59,531 96.0%
77 69,831 94.4% 56,962 91.9%
78 67,539 91.3% 54,268 87.6%
79 65,080 88.0% 51,437 83.0%
80 62,448 84.4% 48,469 78.2%
81 59,647 80.6% 45,390 73.2%
82 56,688 76.6% 42,227 68.1%
83 53,563 72.4% 38,994 62.9%
84 50,253 67.9% 35,694 57.6%
85 46,782 63.2% 32,360 52.2%
86 43,166 58.4% 28,996 46.8%
87 39,414 53.3% 25,650 41.4%
88 35,567 48.1% 22,372 36.1%
89 31,677 42.8% 19,213 31.0%
90 27,805 37.6% 16,223 26.2%
91 24,017 32.5% 13,448 21.7%
92 20,380 27.6% 10,928 17.6%
93 16,962 22.9% 8,691 14.0%
94 13,821 18.7% 6,754 10.9%
95 11,006 14.9% 5,122 8.3%
96 8,549 11.6% 3,783 6.1%
97 6,467 8.7% 2,719 4.4%
98 4,754 6.4% 1,898 3.1%
99 3,392 4.6% 1,286 2.1%
100 2,345 3.2% 844 1.4%


 Calculation the Annuity Term:

Based on this cohort of 100,000 females, 73,974 females have survived to page 75.   Around 90% of these females are still alive until somewhere between age 95 and 96.

In a cohort of 100,000 men 61,980 are still alive at age 75 and the 90% survival mark for these 75-year olds is reached somewhere between age 94 and 95.

Let’s interpolate to get an exact number of months for our annuity formula.

For females we get 96-75 (21) years plus (11.6-10)/(11.6-8.7) x 12 or (7) months.  The 75-year old female must buy an annuity of 259 months  to reduce the probability that she will outlive the annuity to 10 percent.

For males we get 94-75 (19) years plus (10.9-10)/(10.9-8.3) x 12 or 5 months (I am rounding up to fulfill the contract.)   The 75-year old male must buy an annuity of 233 months to reduce the probability that he will outlive the annuity to 10 percent.

Calculating the Impact on Annity Payments:

So now we calculate the annuity payments for the female and the male with the PMT function.   The only input that differs is the duration of the contract – 259 months for females and 233 months for males.

The annuity payment calculations were obtained from the PMT function in Excel.


Female Male
Rate 0% 0 0
Rate 3% 0.03 0.03
Rate 6% 0.06 0.06
NPER 259 233
PV $100,000 $100,000
PMT rate=0 $386.10 $429.18 ($43.08) -11.2%
PMT rate =3% $524.96 $566.77 ($41.81) -8.0%
PMT rate=6% $689.45 $727.62 ($38.17) -5.5%


Conclusions:   Females must buy a longer-term annuity to obtain the same reduction in longevity risk as a male.   This reduces their monthly annuity payment.

This annuity calculator on the web confirms that females receive lower annuity payments and or pay higher prices for a comparable annuity.  I am not familiar with the specific formulas used by this calculator or the product that it pertains to.   My sole interest here is to provide some insight on how gender determines longevity risk.







Survivor Bias and Stock Market Risk


Survivor Bias and Stock Market Risk


Shortly after the large stock price decline of Facebook on July 26,2018, CNBC posted an article with a chart of other large market-cap declines of U.S. stocks.   Every single company in the chart still exists as an ongoing company.   It appears as the chart was compiled from a database that only contain companies that are still listed.

What no longer actively traded companies might have made a list of the largest declines in equity value for large-cap companies?

Why does the exclusion of these companies from the chart create a misleading picture of the risk of investing in equity?

The chart lists three companies with large cap declines in 2018?  Why is the occurrence of so many recent large declines in big-cap equity a concern?

The article:

The Chart:

Market Cap Losses in Big Cap Stock


Date Decrease In Equity ($B)


Jul 26 2018 $114.50


sep 22 2000



Apr 3 2000


Apple Jan 24 2016


Exxon Mobile

Oct 15 2008


General Electric

Apr 11 2008



Feb 2 2018


Bank of America

Oct 7 2008



Apr 2,2018


Wells Fargo

Feb 5 2018



Jul 23 2002


JP Morgan Chase Sep 29 2008




What no longer actively traded companies might have made a list of the largest declines in equity value for large-cap companies?

Companies no longer actively traded, which experienced large one-day drops in equity value include   — Enron, Worldcom, the old General Motors, Lehman Brothers, Bear Stearns, and Merill Lynch.   There are probably many more.

Why does the exclusion of these companies from the chart create a misleading picture of the risk of investing in equity?

 First, this list suggests large drops in equity values occur less frequently than a chart composed from all firms that ever existed.

Second, a list of large declines composed of stocks that survived understates the potential loss of wealth from buying and holding stocks after a large decline.   In fact, all the stocks on the CNBC list have recovered nicely.

Third, an anaysis of risk, which includes bankrupt firms would encourage investors to seek greater diversification in terms of number of equity holdings, sector, and asset classes.

The chart lists three companies with large cap declines in 2018?  Why is the occurrence of so many recent large declines in big-cap equity a concern?

Facebook, Alphabet, and Amazon all had their large declines in 2018.   These are three of the four FANG stocks.   The smallest FANG company also has had a recent large percentage decline.

The most popular trendy sector of the stock market is now realizing extremely large one-day changes.   This appears to be happening with greater frequency.

The disproportionate number of 2018 large-cap declines in this chart convinces me that people who have made a lot of money in FANG and in other high-tech stocks need to take some money off the table when the stock prices reach new highs.

Of course, in the case of Facebook  this advise was more valuable prior to July 26.

The volatility of FANG names and other Tech stocks does not mean this is a good time to buy value stocks because the pending  increase in interest rates might hurt value stocks more than growth stocks

I would be alarmed by the large number of 2018 events even if the chart contained firms that were no longer actively traded.

Holdings of Ten Emerging Market Funds

Holdings of Ten Emerging Market Funds

This post started with a list of emerging market funds found at the site below.

I examine and describe the holding and recent returns on the 10 largest of these funds.

I comment on the holdings of these funds, the risk of these funds and the risk of some of the holdings.

List of Funds, Discussion of Geographic Diversifications, and YTD returns:

Some Information on Ten Emerging Market Funds
Symbol Fund Geographic Concentration YTD Returns
VWO Vangarud FTSE Emerging Market 7 of top ten holdings are in China -7.32%
IEMG I Shares Core MSCI Emerging Market 7 of top ten holdings are in China -6.95%
EEM I Shares MSCI Fund 7 of top ten holdings are in China -7.44%
SCHE Schwab Emerging Markets Fund 6 of top ten holdings are in China -7.34%
FNDE Schwab Fundamental Large  Firm Emerging Market Index Largest holding is from Korea and second and third largest holding are Russian.  Top 10 holdings also include companies from China, Brazil and Taiwan -6.71%
DEM Wisdom Tree Emerging Markets Equity Income Fund Top two holdings are Russian.   Most other top ten holdings are form China or Taiwan. -4.54%
RSX Van  Eck Vectors Russia ETF All holdings appear to be in Russia. 4.36%
GEM Goldman Sachs ActiveBeta Emerging Markets Equity ETF 7 of top ten holdings are in China -6.75%
SPEM SPDR Portfolio Emerging Markets ETF 6 of top 10 holdings are in China -6.54%
DGS Wisdom Tree Emerging Markets Small Cap ETF Top 10 holdings are less than 9 percent of all holdings.   Highly diversified, smaller companies. -7.34%


Some Observations:

Many of the funds have a very large share of their funds in China.   In fact, some of the emerging market funds could accurately be called China plays.

Three of the funds have substantial issues in Russia.  Also, most but not all, of the Russian holdings are in the oil and gas sector.  Important to research holding If concerns about corruptions and sanctions would deter you from investing in Russia.   Energy funds that are not in Russia may be preferable to Russian energy plays.

Nine of the Ten funds have negative YTD returns.  The fund that exclusively invests in Russia has a +4.36% return. This fund performed really poorly in prior years.  The YTD return on U.S. large cap stocks is around 6.0%, largely because the market has been up for the past week or so.

Can investments in emerging market ETFs provide insurance against a major downturn in the U.S. market?

 Short answer is probably not:   The downturn in emerging markets in the 2007 to 2009 crisis was larger than the downturn in large-cap U.S. stocks.

Go here for discussion of emerging market funds during the financial crisis

Thoughts on specific holding of emerging market funds:

Emerging market funds have some well know reputable holding and some firms with dubious reputations, and some firms with little name recognition.

The most successful holdings of the funds in this sector include: (1) Alibaba, (2) Tencent and (3) Baidu Inc.

Investors who want a taste of advanced emerging markets or China may be better off directly investing a small fraction of their wealth in these companies.

Emerging Markets During the Financial Crisis

Emerging Markets During the Financial Crisis

True or False:   During the 2007 financial crisis emerging market funds outperformed U.S. large Cap funds?

Answer:  False:

Evidence:   The chart below compares peak price in 2007 prior to stock market collapse and trough price in 2009 prior to the recovery.   The peak price for VLACX was on October 1, 2007.   The peak price of VWO, the largest emerging market fund, occurred a bit later, on October 22, 2007.   The trough price for both funds was realized on March 2, 2009.

U.S. Large Cap versus Emerging Market During the Financial Crisis
Funds Peak Before Crash in October 2007 Trough at End of Crash in March 2009 % Decline
VLACX U.S. Large Cap 28.1 12.6 55.3%
VWO Emerging Markets 57.5 19.0 67.0%

The collapse in the Vanguard emerging market fund was larger than the collapse in the Vanguard large-cap U.S. equity market.

Perhaps some other emerging market fund did better but I doubt it.

Review of Measuring Portfolio Valuation

My blogging ground to a halt the last few weeks because I was completing a paper “Measuring Portfolio Valuation. “  Will put link to paper here shortly.

My new paper looks at two issues.   The first issue involves correct and incorrect ways to measure the PE ratio of a portfolio of stocks.   The second issue involves the correct way to conduct statistical tests on valuation measures for groups of stocks.

The paper starts with a discussion of the limitations of the PE ratio, the most commonly used valuation measure for common stocks.   The PE ratio is undefined when earnings are negative and unstable when earnings are small. By contrast, the ratio of the difference between market cap and earnings to market cap (denoted (MC-E)/MC) has a clear economic meaning when earnings are negative and is not an outlier when earnings are low.  In addition, there is a one-to-one relationship between this ratio and the PE ratio.

Many investment firms use a weighted average of firm PE ratios to measure the PE ratio of their ETFs or mutual funds.   The firms often discard observations from firms with negative earnings and cap the PE ratio of firms with high PE ratios.   These methods are arbitrary and often tend to understate the valuation of stock prices relative to earnings.

The ratio of the sum of market caps of firms in a portfolio to the sum of earnings of firms in the portfolio is the correct way to measure the PE of a portfolio.   This measure of PE can include all firms even firms with negative earnings.  Moreover, small changes in earnings for firm with high PE ratio do not have a large impact on the overall portfolio PE ratio.

A second way to measure the PE ratio of a portfolio, which relies on the weighted average of the statistic ((MC-E)/MC) is presented and shown to be equivalent to the ratio of the sum of market cap to sum of earnings.   This result is motivated in the following blog post.

Two Ways to Calculate a Portfolio PE Ratio:

The paper contains a formal proof demonstrating the two methods of constructing a portfolio PE are identical.

Often analysts conduct hypothesis tests on portfolio financial ratios.   Tests based on PE ratios often provide misleading results because of problems measuring the PE ratio when earnings are negative or small.   Firms with negative earnings are routinely omitted from the sample.  The standard deviation and skew of portfolio PE ratios are often large making it difficult to reject a null hypothesis.

By contrast, statistical tests based on (MC-E)/MC do not require the omission of firms with negative earnings.  Moreover, the distribution of (MC-E)/MC appears normally distributed with few outliers.    As a result, statistical tests using this ratio are more reliable than statistical tests using PE ratios.

Two Ways to Calculate a Portfolio PE Ratio

Two Ways to Calculate a Portfolio PE Ratio 

Question:  The table below contains data on the market cap and the earnings for four high-tech firms.

Market Cap and Earnings for Four Tech Firms
Market Cap

($ B)


($ B)

AAPL 892.16 46.65
MSFT 585.37 21.2
AMZN 475.37 1.92
TWTR 13.11 -0.44797


In this post, I am asking you to use two methods to calculate the PE ratio of this four-stock portfolio and to confirm that both methods provide the same answer.

Method One:

Calculate the PE ratio of this portfolio by taking the sum of the market cap numbers for the four stocks and dividing by the sum of the earnings of the four stocks.

Method Two:

Calculate the ratio of (market cap minus earnings) divided by market cap for the four stocks.

Calculate a weighted average of the values (MC-E)/MC for the four stocks with the ratio weighted by MC.  Give the name to this weighted average the letter f.

Calculate 1/(1-f).

Show that the PE ratio from method one is identical to 1/(1-f).


The straight forward way to calculate the PE ratio by taking the ratio of the sum of the market caps to the sum of the earnings is presented below.

Portfolio PE Ratio – Method One
Market Cap

($ B)


($ B)

AAPL 892.16 46.65
MSFT 585.37 21.2
AMZN 475.37 1.92
TWTR 13.11 -0.44797
Total 1966.0 69.3 28.4


This four-firm portfolio has a PE ratio of 28.4.

The PE ration calculation for method two  is presented below.


Portfolio PE Ratio — Method Two
Market Cap Earnings (MC-E)/MC Weight
AAPL 892.16 46.65 0.9477 0.4538
MSFT 585.37 21.2 0.9638 0.2977
AMZN 475.37 1.92 0.9960 0.2418
TWTR 13.11 -0.44797 1.0342 0.0067
1966.01 1.0000
f 0.9647
1/(1-f) 28.4


The second method for calculating a PE ratio gives the same result as a the first – 28.4.

Implications:   The PE ratio of a portfolio can be expressed as function of the weighted average of the ratio of the difference between market cap and earnings of the firm to market cap of the firm.    This is a very useful result.

PE ratios of firms are frequently not useful.

First, the PE ratio can become very large when earnings are very small. This means it is misleading to look at a weighted average of PE ratios because one firm can have a a very large impact. In our current example, the PE ratio of Amazon is 248 and the weighted average PE ratio for the four stocks is  77.

Second, PE ratios have no economic meaning when earnings are negative.

The PE ratio of a firm with negative earnings would reduce the weighted average of PE ratios in a portfolio.  By contrast, (MC-E)/MC will be larger than 1 if E is less than 0.

A firm with slightly negative earnings would have a negative PE ratio with a larger absolute value than a firm with very large losses.  This ranking of firms is incorrect because larger losses should be associated with lower relative valuations.   By contrast, (MC-E)/MC will always rise when E falls.

By contrast, the ratio of the difference between market cap and earnings over market cap is inversely related to the valuation of a firm.   When earnings are negative this ratio is greater than one.   When earnings are zero the ratio equals one.   When earnings are very small the ratio approaches one and is not an outlier.  The ratio of the difference between the market cap and earnings to market cap is intuitively defined for all earnings and not impacted by outliers.