The Price Earnings Ratio of a Portfolio Where Some
Firms Have Negative Earnings
Issue: How does one create an accurate measure of
price in relation to earnings for a portfolio of stocks when some firms in the
portfolio have negative earnings?
Question: A person owns three stocks Apple, Microsoft,
and Twitter. The stock price and
earnings per share for the three stocks are listed below.
Earnings Per Share and Price Per Share of Three Stocks


AAPL

MSFT

TWTR


E

8.52

2.27

0.62

P

153.61

69.96

18.23

A person invests 40 percent
of her funds in Apple, 40 percent in Microsoft and 20 percent in Twitter. What is the PE ratio of this portfolio?
Background: In a previous post I explain that negative
PE ratios have no economic meaning. Firms
with negative earnings generally have a lot in common with high PE startups
that have small current earnings and high expectations for future
earnings. Moreover, a firm with
negative earnings that is close to zero will have a lower PE ratio than a firm
with huge losses.
Some analysts appear to
average all firms (both firms with negative and positive earnings) to get a portfolio
PE. This approach is nonsense.
Other analysts simply omit
information on PE ratios for firms with negative earnings. This approach ignores important information
by understating the deviation between perceived value of stocks measured by
price and earnings for the current year.
How does one create an
accurate measure of price in relation to earnings for a portfolio of stocks
when some firms in the portfolio have negative earnings?
My Solution: My solution is based on the statistic (PE)/P. The advantage of the (PE)/P statistic
compared to the P/E statistic is that it has the same economic meaning for
firms with positive and negative earnings.
This statistic compares the amount the value of the price of stock
exceeds earnings for one year. This
difference represents future expected earnings, liquidation value or some
combination of the two.
When earnings are negative as
in the case of Twitter (1P)/P will exceed 1.0.
Using algebra, it is easy to
show that there is a one to one relationship between (PE)/P and P/E. Denote (PE)/P as f. Use algebra (shown in appendix below) to show
P/E=1/(1f)
My procedure for finding the
P/E of the portfolio involves three steps:
· Find (PE)/P for all three stocks
· Take weighted average of (PE)/P for all three stocks
· Plug weighted average of (PE)/P into formula for P/E
shown above to get portfolio P/E.
Step One:
The value of (PE)/P for the
three stocks are presented below.
Earnings Per Share and Price Per Share of Three Stocks


AAPL

MSFT

TWTR


E

8.52

2.27

0.62

P

153.61

69.96

18.23

(PE)/P

0.94

0.97

1.03

1/(1(PE)/P)

18.03

30.82

29.40

P/E

18.03

30.82

29.40

Note the correspondence between
(PE)/P and P/E is correct.
Step Two:
Find weighted average of
(PE)/P where weights are 0.40 of Apple, 0.40 for Microsoft, and 0.20 for
Twitter. This can be done with the
SUMPRODUCT function in Excel.
The SUMPRODUCT of the (PE)/P
vector with the portfolio share vector (0.40,0.40,0.20) is 0.971637.
Step Three: Transform the weighted average of (PE)/P to
a P/E ratio.
1/(10.971637) or 35.25.
Concluding Thoughts: Many analysts citing PE
ratios for Tech stock ETFs claim that Tech stocks are not overvalued. The analysis presented here suggests this
claim is incorrect. I suspect these
analysts are overvaluing the Tech sector by failing to accurately incorporate
information about firms with negative earnings in their calculation of Tech
Sector PE ratios.
My finance post discusses the
literature on PE ratios and looks at the frequency distribution of the PE
ratios in Vanguard Tech fund VGT.
I am concerned that we have
entered a bubble that will not end nicely.
A Note: When firms are near bankruptcy (PE)/P could
be quite large because earnings are a very large negative number. The PE of this firm might not have a large
impact on the P/E ratio because the low share price of a firm near bankruptcy
will lead to a portfolio share near zero.
However, if portfolio share estimates are not up to date the inclusion
of firms near bankruptcy in the PE calculation might overstate financial risk
because the investor cannot lose more than the value of the outstanding shares.
The Tech firms in VGT have
negative earnings with high stock prices that have risen in future months. These highflying firms need to be included
when assessing portfolio risk.
Appendix: Show
that P/E = 1/(1f) where f is (PE)/P using P and E data for Microsoft. The algebra is shown below.
0.94453 = (PE)/P
Rearrange this equation to
solve for P/E.
(10.94453)*P =E
or
P/E= 1/(10.94453)
The more direct way to get
P/E is simply divide P by E. Confirm
that both statistics equals to 18.029 for Microsoft.
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