Exploring P/E (009.0)

Summary: A look into the quality of the AAII data and the need for some recalculation.

The price to earnings ratio (P/E or PE) is a popular characteristic for measuring the value of a stock. It measures the number of dollars required to buy $1 worth of earnings. Unfortuneately, earnings can be zero which causes the ratio to be undefined and negative earnings cause the ratio to lose meaning. There is a simple adjustment which is to calculate the E/P also know as earnings yield as a stock price does not reach zero.

We will pick the first period in our data which is 20030103. We filter our universe of 8558 companies to those with prices >=$5 and a market cap >=$250MM which reduces to a sample of 2696. The first thing we note is that there are a lot of missing (NA) P/E values. There are 555 (20.6%) missing values. By calculating E/P. The percent of missing values drops to 2.1%.

A closer examination reveals a puzzle that suggests the data is not perfectly clean. I wanted to check that our calculation of E/P was consistent with the P/E supplied by AAII. Any stock with a P/E should have a P and an E. However, not all do. It appears that all the companies with P/E but missing earnings are ADRs. I would guess that either AAII uses a different E for the calculation or is supplied a PE from a different source.

It appears that calculating E/P is better than using the supplied P/E because we will get more information. In addition, for those companies where our E is missing, but we have P/E we can use 1/(P/E) to find E/P. This means we need to go back an calculate a lot of variables.

##                        Company Ticker    PE EP EPS  Price
## 36            AEGON N.V. (ADR)    AEG  28.3 NA  NA 13.580
## 82         Amcor Limited (ADS)   AMCR   7.8 NA  NA 19.850
## 213      Banco Itau S.A. (ADR)    ITU  11.2 NA  NA 26.130
## 239      BBVA Banco BHIF (ADR)     BB  22.6 NA  NA 13.350
## 296  Brilliance China Automoti    CBA   6.7 NA  NA 20.200
## 337          CSR Limited (ADR)  CSRLY  11.0 NA  NA 14.350
## 384   Cemex S.A. de C.V. (ADR)     CX   6.6 NA  NA 22.260
## 415  China Southern Airlines L    ZNH  18.4 NA  NA 14.200
## 428   Ciba Specialty Chemicals    CSB   8.8 NA  NA 36.000
## 455  Coca-Cola FEMSA, S.A. (AD    KOF  12.1 NA  NA 18.020
## 482  Companhia de Bebidas Amer    ABV  22.4 NA  NA 15.690
## 483  Compania Anonima Nacional    VNT  29.1 NA  NA 12.500
## 527  Cristalerias de Chile S.A    CGW  22.5 NA  NA 18.920
## 560   Desc, S.A. de C.V. (ADR)    DES  31.4 NA  NA  6.900
## 638  Embraer-Empresa Brasileir    ERJ   7.8 NA  NA 16.050
## 818          Gerdau S.A. (ADR)    GGB   7.1 NA  NA  9.850
## 851  Grupo Televisa, S.A. (ADR     TV  33.9 NA  NA 29.800
## 854  Grupo Aeroportuario Del S    ASR  12.8 NA  NA 12.200
## 974      Industrias Bachoco SA    IBA   3.6 NA  NA  8.650
## 1086  Konami Corporation (ADR)    KNM  30.5 NA  NA 22.850
## 1087        Kookmin Bank (ADR)     KB  10.6 NA  NA 36.060
## 1246 Millea Holdings, Inc. (AD   MLEA  18.0 NA  NA 36.560
## 1543 Randgold Resources Ltd.(A   GOLD  30.5 NA  NA 31.771
## 1570    Repsol YPF, S.A. (ADR)    REP  15.8 NA  NA 13.310
## 1644   Sanofi-Synthelabo (ADR)    SNY  17.5 NA  NA 29.900
## 1647  Sanyo Electric Co., Ltd.  SANYY 223.0 NA  NA 13.380
## 1765 Stet Hellas Telecomm. S.A  STHLY  13.9 NA  NA  6.970
## 1821     Tate & Lyle PLC (ADR)  TATYY  12.6 NA  NA 20.000
## 1839      TeliaSonera AB (ADR)   TLSN  22.3 NA  NA 19.400
## 2009 Wal-Mart de Mexico S.A. (  WMMVY  26.2 NA  NA 23.600

For good, measure for each company with a supplied P/E we calculate P/E by taking 1/(E/P). The largest difference is 0.05 which is rounding error given that P/E is given to one decimal place.

From AAII’s SIP documentation:

Also called the price multiple, the price-earnings ratio is the most popular price multiple. Calculated by dividing the current stock price by diluted earnings per share from continuing operations for the last four quarters (trailing 12 months). The PE ratio embodies the market’s expectations regarding a company’s growth prospects and risk. High PE ratios generally represent the market’s belief that that the company has strong future growth prospects and that it will achieve this growth, while a low price-earnings ratio represents the market’s low earnings growth expectations for the firm or the high risk or uncertainty of the firm actually achieving growth. The usefulness of this ratio is limited to those firms that have positive earnings. In addition, earnings are more subject to management assumptions and manipulation than other income statement items such as sales. Price to Earnings = Price / EPS Diluted Continuing 12m

The Performance of 10,000 Monkeys

Is the performance of a stock mutual fund (or manager or model) better than chance? How could we decide? What follows is a simple description of a method even non-statisticians can appreciate. We’ll also learn something about portfolio weighting. Turns out we can learn a lot from “monkeys”.

Imagine teaching 10,000 monkeys each to throw 50 darts at a list of all the stocks in our universe which is about 3,000 stocks all with prices of at least $5/share and a market capitalization of $250 million. We don’t have that many monkeys but a computer can randomly pick stocks which is as good and faster. This gives us a set of 10,000 portfolios of 50 stocks created by chance. If our fund is in the top 5% of the universe, one interpretation of that would be that there is a 5% chance that through just luck we could have ended up with such a portfolio.

One crucial caveat is that this logic applies to the evaluation of one portfolio. While an individual fund may have a 5% chance of such performance, if we create 1000 portfolios or look at 1,000 funds, there’s a much higher probability that the best of the 1,000 will. So we must be careful. Across the many funds out there, the laws of chance dictate some will do well.

There’s another interesting question that we address as we create this universe. Once one of our virtual monkeys picks 50 stocks, how should we weight them? We’re going to look at three weighting schemes: equal weighted, weighted by market capitalization, and weighted by the inverse of the risk as measured by price volatility over the last three years.

The following table and chart show the distribution of the 10000 returns for the three weighting methods.

       Min. 1st Qu. Median Mean 3rd Qu.  Max.
Equal  1.26    6.99   8.02 8.03    9.03 14.49
Cap   -3.55    4.74   6.50 6.47    8.17 16.06
Risk   2.52    6.88   7.73 7.74    8.58 13.52

The best average returns are generated by equal weighting. The best minimumn returns are produced by risk weighting. The worst minimumn returns and best maximum returns are produced by the capitalization weighting. In other words, cap-weighting has the greatest dispersion, and risk-weighting has the least.

It may seem odd that giving more weighting to large companies, generally thought to be less risky, seems riskier. The explanation for this is that in a randomly chosen 50 stock portfolio we may be giving a lot of weight to a few companies, thereby increasing risk.

The following chart shows the same data in a different form to help us decide if one weighting scheme is preferable. We order the returns of the three sets of 10000 returns from best to worst. The green line is the capitalization weighted portfolios. While it has the single highest return, there’s only about a 10% chance it will be the best and about an 80% chance it will be the worst. The red is the risk-weighted. It has the best of the worst returns. But this is only useful 1 in 10000 observations. Most of the time the (blue) equal weighted portfolio can be expected to outperform the others. It may be that larger companies have less risk and thus risk weighting tends to weight larger companies more.

Returning to the original issue of considering the chance of performance being due to luck or skill, we consider one more chart. Each point in the gray cloud represents the performance of one monkey. We add various indices. The boxplots along the axes show the dispersion. Comparing performance against the universe gives a fair idea of how lucky a manager would have to be to achieve his or her results by chance. In this case, there is a 5% chance of returning 10.58% which is 2.55% above the average of 8.03%.

The returns used in this analysis are price-only returns from January 2003 to October 2015.