A Deeper Statistical Look at the Performance of P/E Ratio's in Factor Analysis

I needed a bit of a project to test out the features of the PerformanceAnalytics package for R that looks really good. One of the things I have been working on lately is quantile bucketed factor backtests, so I thought I would use the features of the package to take a closer look at the performance of a simple one-factor backtest.

One of the traditional value based metrics that has been shown in academic papers and by some very successful practitioners is the trailing price-earnings ratio. It is very logical that you should purchase shares in companies that trade at a lower price-earnings valuation, but what does the data show. So using data from Portfolio123.com, I performed a factor backtest on P/E Ratios using the parameters below.

Parameters

Period of Test: 1999-01-02 to 2013-11-23
Re-balancing Frequency: Monthly
Ranking Method: Percentile into 5 buckets (0 to 20% (Lowest P/E), 20% to 40%, etc)
Stock Universe: Russell 3000
Factor: Trailing 12M P/E Ratioi ex Extraordinary Items

Additionally, the long/short strategy is created by going long the lowest P/E ratio shares (0 to 20) and going short the highest P/E shares (80 to 100).

Annualized Return Statistics

Re-balancing monthly on data from 1999, there is a nice upward sloping return and Sharpe ratio performance as you move to lower P/E ratio buckets. For example, the 80+ percentile (highest) P/E ratios had a compounded annualized growth rate (CAGR) of 3.06% and a Sharp ratio of 0.09, while the <20+ percentile (lowest) P/E ratios had a CAGR of 12.79% and a Sharpe ratio of 0.58.

Strategy Return (%) Std Dev (%) Sharpe
SP500 3.05 17.86 0.1708
80 to 100 3.06 30.97 0.0989
60 to 80 6.65 20.86 0.3187
40 to 60 8.23 19.15 0.4298
20 to 40 8.97 18.22 0.492
0 to 20 12.79 21.89 0.5841
Long/Short 5.12 18.02 0.2843
PE Factor Backtest: Annualized Return Barplot

Cumulative Return

On a cumulative basis the lowest P/E shares (0 to 20) had the highest wealth index of 6 since 1999 but with a significant drawdown in 2008 during the Lehman collapse. The long/short portfolio has a less volatile wealth curve but only finishes with wealth index of a little over 1 since 1999.

PE Factor Backtest: Historical Cummulative Returns
PE Factor Backtest: Rolling 12 Month Performance Chart

Relative Performance Statistics

What pops out from the first graph is the two pronounced periods of out-performance of the long/short strategy during the 2002-2003 and 2008 market downturns.

PE Factor Backtest: Rolling 12 Month Relative Performance Chart

In the table you can see that the long/short strategy has a negative overall (Beta), up (Beta+) and down (Beta-) market beta versus the S&P 500 as well as a negative correlation and low R-squared.

Strategy vs S&P 500 80 to 100 to SP500 60 to 80 to SP500 40 to 60 to SP500 20 to 40 to SP500 0 to 20 to SP500 Long/Short to SP500
Alpha (%) 0.06 0.29 0.43 0.5 0.8 0.74
Beta 1.5691 1.112 1.0143 0.9343 1.0742 -0.4949
Beta+ 1.5136 0.9969 0.9593 0.9221 1.1614 -0.3522
Beta- 1.4676 1.1163 1.0888 0.9888 1.0751 -0.3925
R-squared 0.819 0.9064 0.8948 0.8386 0.7685 0.2407
Annualized Alpha (%) 0.69 3.59 5.24 6.15 10 9.26
Correlation 0.905 0.952 0.9459 0.9157 0.8766 -0.4906
Information Ratio 7e-04 0.538 0.8332 0.7976 0.9171 0.0668
PE Factor Backtest: Rolling 12 Month Alpha/Beta Regression Chart
The low beta and low R-squared of the long/short strategy, particularly during the market downturn in 2008.
PE Factor Backtest: Annualized Return_and_Risk Scatterplot
The long/short portfolio has a higher annualized return with the same annualized risk. Additionally, buying low P/E shares significantly increases annualized return with a small increase in annualized risk.


Correlations Statistics

This table shows the correlations of each of the strategies to the S&P 500, including there p-value and confidence intervals.

Strategy Correlation p-value Lower CI Upper CI
80 to 100 to SP500 0.91 0 0.88 0.93
60 to 80 to SP500 0.95 0 0.94 0.96
40 to 60 to SP500 0.95 0 0.93 0.96
20 to 40 to SP500 0.92 0 0.89 0.94
0 to 20 to SP500 0.88 0 0.84 0.91
Long/Short to SP500 -0.49 0 -0.59 -0.38


Risk Metrics Statistics

Across almost all of the metrics the long/short portfolio decreases risk.

  • Tighter dispersion of monthly returns in the monthly returns box plot
  • Lower loss deviation than any strategy and largest gain deviation (lower bad risk, higher good risk).
  • Lower downside deviation.
  • Lower historical VaR and historical expected shortfall.

Additionally, the low P/E strategy doesn’t materially increase risk versus the S&P 500 or other strategies other than long/short.

PE Factor Backtest: Annualized Return Barplot

Risk Metrics (%) SP500 80 to 100 60 to 80 40 to 60 20 to 40 0 to 20 Long/Short
Semi Deviation 3.95 6.67 4.65 4.27 4.03 4.71 3.38
Gain Deviation 2.84 5.16 3.08 3.02 2.93 3.96 4.46
Loss Deviation 4.02 6.44 4.50 4.44 4.16 4.95 3.49
Downside Deviation (MAR=10%) 4.17 6.76 4.70 4.28 4.02 4.53 3.53
Downside Deviation (Rf=0%) 3.76 6.34 4.29 3.89 3.64 4.16 3.13
Downside Deviation (0%) 3.76 6.34 4.29 3.89 3.64 4.16 3.13
Maximum Drawdown 51.51 77.29 52.56 48.56 50.89 58.06 53.29
Historical VaR (95%) -8.40 -13.69 -9.43 -7.86 -7.90 -8.36 -7.31
Historical ES (95%) -12.19 -19.85 -13.02 -12.48 -11.86 -13.64 -11.00
Modified VaR (95%) -8.81 -14.78 -10.20 -9.23 -8.54 -9.62 -6.33
Modified ES (95%) -14.91 -22.45 -16.69 -17.13 -17.05 -20.16 -6.33


Overall, the P/E ratio seems to be a useful factor for inclusion in multi-factor models since both outright (buying low P/E shares) and long/short strategies performed well. Whether you use it alone or as part of a long/short strategy depends on what type of return profile and correlation to the S&P 500 you are looking for.


By Jon Eickmeier | November 26, 2013 | analysis markets quantitative factor backtest

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