# 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 |

#### 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.

#### 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.

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 |

#### 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.

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.