The Defect in Price/Earnings Ratios – Part 2

Wednesday, November 18, 2009

614682_damn_mathYesterday we saw the challenge in using price/earnings ratios (P/Es) to analyze individual stocks. Today, we turn to the added difficulties in combining multiple company P/Es into a usable average P/E for portfolios and indexes…

Developing composite measures is important for understanding portfolio and index characteristics. Some information is straightforward to calculate, such as dividend yield. A “weighted average” is all we need.  Simply multiply each stock’s characteristic by the stock’s proportion of the portfolio, then add.

Some ratios are tricky, however, and the weighted average can produce misleading results. This is the problem with P/Es. The non-linear distribution we saw yesterday skews the average. Ways of dealing with this problem vary, leading to the differing average P/E numbers being reported. Based on yesterday’s closing prices, the S&P 500’s weighted average P/E is 16.1 times, excluding negative earnings forecasts.

One solution is to substitute median for average. Simply rank the individual P/Es from high to low, then pick the middle one: currently this is 14.9 times. A possible adjustment: define “middle” as the point where 50% of the portfolio weight is reached: 14.4 times.

Another solution is to bypass company P/Es altogether. Rather, sum all the stock values and divide by total earnings. This method treats the index as a big conglomerate. It gives us 14.3 times.

And another solution is to use earnings yields (E/Ps). As we saw yesterday, they have a linear relationship, so we can use a weighted average. The result is an earnings yield of 7.0%. We don’t give up anything compared to the P/E approaches. The 7.0% reciprocal is 14.3 times, mathematically identical to the conglomerate approach.

I prefer this earnings yield approach because it meshes with the individual company calculations allowing direct comparisons. Also, its more normal distribution allows other statistical calculations to be made. You can see the difference in the P/E and E/P distributions below. Clearly, P/E is skewed and E/P is fairly normal.

G-H PE

G-H EP

So, be wary of the average P/Es being reported, and look at the methodology being used. For your portfolio or funds, using the earnings yield approach provides accuracy and understanding.

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