## Friday, April 10, 2009

### Jeremy Siegel's False Logic

Jeremy Siegel has in two articles argued that the current methodology for determing the stock market P/E ratio is misleading, because profits and losses aren't weighted by the market value of the respective company. According to Siegel himself, he has convinced Robert Shiller of this argument, and Greg Mankiw says that he is increasingly convinced of it.

In his first article, he doesn't provide any example of his methodology, but he does so in his second article:

"My methodology would weight the \$45 billion earned by Exxon Mobil by 95 percent and the \$99 billion loss of AIG by 5 percent to obtain a weighted average earnings of \$39 billion for the portfolio. With a weighted average market value of AIG and Exxon Mobil of \$335 billion, this would lead to approximately a 9 P/E ratio for the portfolio, not the infinite P/E computed by Standard & Poor's."

He claims that this weighting is equal to how stock portfolio returns are calculated. However, he is simply wrong about that. It is pretty remarkable that a professor in finance doesn't understand how return is calculated.

When the return for a portfolio is calculated you do not weight the absolute gains or losses for each stock, you weight the percentage gains or losses for each stock. But Siegel weights the absolute implicit fundamental return by market cap, which is very different-and very misleading.

The reason why you weight percentage return of each stock is because the small absolute returns has been set in relationship to the small market value of that particular stock. It has in other words been divided by a small number. When you put that in to relation to total value, you need to undo that by giving it a smaller weight. But when setting the original absolute value of return to the total value, there is no justification for weighting. If you have two stocks in a \$1 million portfolio, with one constituting 90% of your portfolio and the other 10%, it doesn't matter which one of them produced a \$90,000 and which one produced a zero return. Or in other words, regardless of whether the smaller stock had a 90% gain or if the larger stock had a 10% return, the overall gain is still only 9%.

Or to use the companies discussed by Siegel: If a fund holds \$19 billion of Exxon and \$1 billion of AIG, and Exxon rises by 10% and AIG falls with 50%, then total return is of course 7% ((0.95*0.1)-(0.05*0.5)). But Siegel's methodology for weighting earnings is like weighting the \$1.9 billion Exxon gain by 95% and the \$0.5 billion AIG gain by 5%, which would produce a return of 8.9% (((0.95*1.9)-(0.05*0.5))/20). According to Siegel's logic, the return of a portfolio that rises from \$20 billion to \$21.4 billion in value is 8.9%!

Siegel's method in effect double counts the relative weighting of the percentage return. And since profit making companies are naturally valued higher than loss making companies that creates a big upward bias for earnings.

Siegel is however correct with regards to one limited point-namely that because some of the losses at some extremely unprofitable companies will be taken by creditors and/or taxpayers instead of the shareholders (who can only lose 100% of equity, so once equity is negative, they cannot lose any more), net profits available for shareholders will be underestimated because of the inclusion of companies like AIG and GM. But that problem is better addressed without the misleading double weighting of profits, by simply excluding companies like AIG and GM where we know that equity will be negative without government bailout money.

Jim Pearson said...

Of course many of America's university students are innumerate, but a Wharton professor? And the WSJ?
This is not just remarkable, but shocking. I feel very embarrassed.

1:47 PM
Kapitalist said...

I'm not at all surprised!

Logical misconceptions stream endlessly from economics professors, and through major media such as the WSJ.

When they calculate as badly as they reason, this becomes obvious even to non-Austrian economics. This is how stupid most of the mainstream economists are (or pretend to be to please higher authorites), everyday of their careers.

Just look at the Swedish Central Bank price winner (there exists no such thing as a Nobel price in economics) Paul Krugman for numerous examples!

6:01 PM