Two Ways to Calculate a Portfolio PE Ratio
Question: The table below contains data on the market cap and the earnings for four hightech firms.
Market Cap and Earnings for Four Tech Firms  
Market Cap
($ B) 
Earnings
($ 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 fourstock 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 (MCE)/MC for the four stocks with the ratio weighted by MC. Give the name to this weighted average the letter f.
Calculate 1/(1f).
Show that the PE ratio from method one is identical to 1/(1f).
Analysis:
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) 
Earnings
($ 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 fourfirm 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  (MCE)/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/(1f)  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, (MCE)/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, (MCE)/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.
In my next post, I will show that statistical tests based on samples of the ratio of the difference between the market cap and earnings to market cap are more useful than statistical tests based on PE ratios.
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