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.
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|
|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|
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|
|Annualized Alpha (%)||0.69||3.59||5.24||6.15||10||9.26|
The low beta and low R-squared of the long/short strategy, particularly during the market downturn in 2008.
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|
|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|
|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.