# The Flaw Of Using A P/E Ratio For An Equity Index

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Includes: AAPL, AIG, AMZN, BAC, C, FMCC, FNMA, GOOG, MCD, SPY, XOM
by: Ardash Karakashian

It is common practice for financial analysts to come up with a fair or projected value for the S&P 500 and other indexes by multiplying the aggregate earnings of the 500 components by a P/E ratio (usually a historical average). For example, if the projected aggregate earnings per share of the S&P 500 are \$80, and the P/E is 16, the projected S&P 500 target is 80 x 16 = 1280. There is a major flaw in this method:

The S&P 500 is a weighted average market cap index. The weight of each component is based on its market cap. The calculation of the index would be as follows:

where

• PSP500 is the S&P500 market cap or price
• wi is the weight of component i
• Pi is the stock price of component i
• wiPi is always positive since the stock price and market cap of any company cannot go below zero.

Now, when we use the P/E ratio to calculate a fair or projected value for the index, the calculation is as follows:

• A is Historical or Fair P/E ratio
• Ei is the earnings number of component i

Rewriting the equation we get:

The market cap of component “i” in the index equals A x Ei. In the case of negative earnings, the market cap would also be negative, which is incorrect. Therefore, this method is flawed.

It is easy to think of the index as a one big company made up of its components, and to aggregate the profits and losses as you would do in a company with several divisions. While this may be relevant when assessing the state of the economy or at least the component companies involved, the PRICE of the index does not behave that way. A simple example below illustrates this point:

Assume that analysts agree that a P/E of 20 is a fair value, and that the index has only 5 components (A,B,C,D,E) with a market cap of 20B each. The market cap of the index is 100B. Each company has an expected net income of 1B, so the aggregate earnings are 5B. Multiplying by the P/E of 20, we get a fair value of 100B, which is in line with the aggregate market caps of the components. Suppose now, that the expected earnings of component E are negative1B (i.e. a loss), while there’s no change for the other components, and suppose that investors perceive a worst case scenario for component E, so its price goes down to ZERO. The new actual market cap of the index, calculated by adding up the individual market caps is 80B (loss of 20%). However, if we use the P/E ratio to project a market cap, the calculation would be 20 x (1+1+1+1-1) = 60 B (loss of 40%) which is clearly wrong.

This also applies to other cases. In any index, you have a variety of companies and individual P/E ratios. A growth company has a large P/E; a large market cap relative to its earnings. Multiplying its earnings by a standard P/E ratio understates its fair market cap in the index. In the case of value companies (low P/E), the P/E method overstates their weight in the index.

In the normal case, with hundreds of components in the index, making a reasonable return on their market values (earnings yield), the P/E method may be fairly accurate in projecting the index value. However, in extraordinary cases, the projections could be highly inaccurate, and unfortunately, this is when projections are most crucial, not when everything is going as expected! An example from the real world:

In 2008, General Motors Company (NYSE:GM) posted a net loss of \$31B while its market cap was \$2B. The worst thing that could happen is that the stock goes down to zero and the S&P500 loses 2B of its market value (about 0.02%, assuming an index market cap of 10 Trillion ). However, if we use this earnings number to compute a fair value of the index, multiplying by an overall P/E of 15 for example, GM's contribution to the index would be -465B (i.e. loss of about 4.7%, 230 times more than the worst case scenario). There were many similar examples in the financial sector; American International Group (NYSE:AIG), Citigroup (NYSE:C), Bank of America (NYSE:BAC), Fannie Mae (OTCQB:FNMA), Freddie Mac (OTCQB:FMCC), etc.

In late 2008, and early 2009 the situation was as follows:

• Many companies were experiencing abnormally large losses. Their stocks had lost more than 90% of their market values / caps, thus having very little effect on the index going forward, even if expected to post large losses.
• The S&P500 index, having lost more than half of its value (trading at less than 700 points, some analysts were still projecting a fair value in the 400 range (a further 30-40% loss!) using the naive and flawed P/E method. This may have contributed to the panic at the time.
• The earnings of many major components were mostly unaffected or even growing; Exxon Mobil Corp. (NYSE:XOM), Apple Inc. (NASDAQ:AAPL), McDonald's Corp. (NYSE:MCD), Google Inc. (NASDAQ:GOOG), Amazon.com Inc. (NASDAQ:AMZN), etc.

I believe the best way to come up with a fair value of the index is to come up with fair values of its individual components and then add the individual market caps to get to the value of the index. It's a lengthy and more costly process, but at least it does not misguide investors when they need it most.

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.