Linear Regression

The other day my co-worker and fellow investor enthusiast asked me this simple question “Why are some companies trading at 10 times earnings and others at 30 times earnings?” His question was based on the assumption that in an efficient market, trading multiples should be equal for all companies. How can AAPL trade at 30 x times’ earnings and not be overvalued while MSFT is trading at 14 times and not be considered undervalued? After all the average P/E multiple is historically around 18. Does this disparity not prove the inefficiency of the Market?

I replied that companies trading at higher multiples do so because they deserve to be traded at higher levels. Their higher real profits combined with higher growth expectations warrant higher multiples. Companies trading at low multiples, trade so because the Market sees less value in their current earnings and little growth potential

“Prove it”, the challenge appeared without hesitation.

Finding some reasonable basis to support my statements turned out to be much more complicated. How can I show the correlation between the two variables? How do I show that higher earnings also mean higher trading multiples? The very first statement of correlation between variables, as expressed numerous times by my University Professors back in Copenhagen, immediately came back to haunt me: “Correlation between two variables do not imply causation” they stated, and “Only linear regression may prove cause and effect”

Linear regression analysis…… Let X equal earnings and Y equal trading multiples; let’s use a performance metric that would be under company control and then find its corresponding wealth metric; but how to find the ratios?

The answer lies in Economic Value Added or EVA. This performance metric is the most effective measurement of pure economic profit as it indicates a company’s returns on its invested capital minus its cost of capital.

The X ratio could then be expressed as ROIC/WACC (Return on Invested Capital divided by Weighted Average Cost of Capital) and Y ratio could be expressed as Market Cap divided by Invested Capital. This method would use Invested Capital to find both its return and its corresponding Market multiples.

There is much academic discussion about what exactly constitutes ROIC, but I believe the method utilized to obtain ROIC was less important than showing consistency between measurements. To find Returns, I used NOPAT which is Net Operating Profits after adjustments for taxes. I found Invested Capital by subtracting Accounts Payable + Other current Liabilities from Total Assets. In all cases latest annual statements were used.

To obtain WACC, I used the Modigliani-Miller method that increases a company’s capital cost based on its debt to equity ratio. The formula is as follows: COE + (COE less Cost of Debt) multiplied by D/E ratio. To keep my calculations simple, COE was found using the standard CAPM: Risk Free Rate + Premium * Beta. I kept risk free rate at 3.5% and Market Premium at 4%. For cost of debt I used current AAA bond rates less tax rates. Again, there may be better methods, but the intent was to use the same formula across the board for consistency.

The Y ratio was much easier to find; simply divide the current Market Cap by Invested Capital.

To select a random set of companies I decided to use Standard and Poor’s latest Five Star stock recommendations. The list is comprised of about 100 “Strong Buy” companies spread across different sectors, surely I would be able to show a correlation between increased profits and increased market multiples. Full disclosure, I removed all financial sector stocks, as EVA is not a suitable performance metric for financial companies




Now let’s create a scatter graph to show the relationship between the two ratios. Again X is ROIC/WACC and Y is Market Cap/Invested Capital.

Clearly the results would indicate that companies that have relative higher profits also trade at higher market multiples.

Secondly, we can demonstrate the there is proof of a somewhat efficient market; in a non-efficient market we would have expected the scatter graph not to show a linear correlation between the two variables.

Third, as an interest to value investors, we may use this linear regression analysis to see where value traps may be at play. Companies right of the Best Fit Line (least squared method) could be interpreted as being undervalued, while companies trading to the left of the best fit line may be currently overvalued. Value traps could be companies that are trading at low multiples and less than 1 on their corresponding profit ratio, because effectively < 1 ratio would mean a company is actually not making any real profit. (Its return on invested capital is less than its cost of capital)

Four, the linear regression would also explain why P/E multiples change during different economic periods. When company profits are squeezed it puts downwards pressure on the market multiples. As an example companies showing a 2:1 real profit ratio should trade at approx 3.5 times their Invested Capital. Easy to see when companies real profits fall during recessionary times, that their corresponding market values have to be decreased. This regression analysis also proves that earnings actual drive markets, there is logic in market caps increasing as companies profits increase. Furthermore the scatter graph could visually illustrate possible ‘bubble’ scenarios where market caps are far out of line with actual earnings.

Fifth, more analysis needs to be done to see the effect of growth expectations and market caps. Companies with real economic profit and with high growth expectations should be located to the left of the Best Fit Line, not because they are necessarily overvalued but because the market emphasizes potential growth over current earnings. Investors who look for possible ‘shorts’ should focus on companies to the left of the Best Fit Line, certainly in cases where these companies miss street expectations, there would be an immediate expected correction to its market price as the companies are not supported by current earnings only, but much more on expected growth.