Examining Short Term Reversals in Stocks – Part 1 (Returns Data)

Introduction:

Short-term reversals, including intraday and monthly reversals, are well-known in academic literature and are observable in the markets every day. This phenomenon persists across many different asset classes, especially stocks.

There are many theories to explain this phenomenon. Some say the reversions are news-driven, in that when there is new information (e.g. Earnings or Clinical Trials), reversions occur. Others say that it’s a result of structural changes in liquidity. Some skeptics even say that short-term reversals don’t exist, because of the Efficient Market Hypothesis. And so, I have to ask: Are short-term reversals real? Exactly how real are they?

I can’t be sure of what I read thanks to #FakeNews, so I am taking matters into my own hands. In this series of posts, I will research and document factors that either prove or disprove the significance of short-term reversals.

Summary

• Testing Returns
• In Sample Results
• Out Of Sample Results
• Optimal Factors
• Building The Model
• Takeaways

Factors Affecting Short-Term Reversals

• Returns calculated as a percentage gain or loss (This post)
• Average Dollar Volume calculated simply by daily close price and volume
• Volatility calculated as standard deviation
• Macro regimes or shocks such as VIX
• News sentiment through social media
• Event Driven factors such as Earnings Announcements

Questions

1. Do short-term returns demonstrate mean reversion while long-term returns demonstrate trending properties?
2. Do Open, High, Low, Close (OHLC) prices matter when calculating factor returns?
3. Do these returns survive slippage and commissions?

Data and Tools

• Quantopian’s Backtesting Platform (Based on Zipline)
• AlphaLens for walk forward analysis
• Universe – Top 500 liquid US Equities (Q500US)
• Daily Price Data (No intraday)

Testing Vanilla Returns

Returns can be calculated using the following formula:

To comprehensively test every possibility, we can substitute the price with either Open, High, Low, or Close. Since we have two variables for both the latest price and oldest price, there are 16 different ways to substitute this formula for different results.

In addition to these replacements, there are endless look-back periods that can be used to test returns. For brevity, we will only consider periods of a single week, month, and quarter.

Although orders can be submitted anytime of the day, it’s most economical to place orders with high volume near the market open or close. Thus, we must also do walk forward analysis using both open or close prices in addition to every walk forward period. For convenience, I’ve selected periods of 5, 10 and 21 days.

As mentioned before, I am using AlphaLens to do walk forward analysis. Conveniently, I am able to extract information such as Alpha, Beta, Quantile Returns, and so on. From my experience, I tend to use the t-stat as a benchmark when comparing between factors because it helps approximate the significance of the factor.

Note: Under the hood, AlphaLens uses the Spearman Rank Correlation

To keep things clean, I have only extracted the top three t-stats for each factor and the corresponding periods.

In Sample (2004-2012) Walk Forward Analysis With Open Prices:

In Sample (2004-2012) Walk Forward Analysis With Close Prices:

 

Short-Term and Long-Term Observations

Weekly periods have extremely negative t-stats, implying that weekly returns demonstrate mean reversion properties. In contrast, monthly returns have less significant t-stats while quarterly returns have positive t-stats. This suggests quarterly returns have trending properties while weekly returns tend to revert.

In the short-term, the most consistent factors are HighToCloseReturns and CloseToLowReturns. These two factors also have high significance in both types of walk forward analysis when using open and close prices.

In the long-term, the most consistent factor is LowToOpenReturns. Other factors are not as consistent the choice of using OHLC become less significant in the long-term.

Out Of Sample Testing

So far so good. The next step is to validate these factors with out of sample data to prevent overfitting. The only differences are the start and end dates (2012 – 2018).

Out Of Sample (2012-2018) Walk Forward Analysis With Open Prices:

Out Of Sample (2012-2018) Walk Forward Analysis With Close Prices:

 

In Sample Versus Out Of Sample – Similarities

In the short-term, HighToCloseReturns consistently outperforms.
In the long-term, LowToOpenReturns consistently outperforms.
These are good signs that the factors will continually outperform in the long run.

In Sample Versus Out Of Sample – Differences

In the short-term, CloseToLowReturns no longer performs well out of sample. All other factors generally perform worse out of sample, for both short-term and long-term periods. This is likely because modern day commission costs are low, reducing the amount of alpha available. On the bright side, t-stats are still significant and the factor is worth investigating further.

For completeness, I’ve provided more details on each factor below:

HighToCloseReturns

LowToOpenReturns

Building The Model: Combining Factors

The next step is to build a single model with these two factors. We can visually see that LowToOpenReturns is less significant than HighToCloseReturns. This implies we need to weight each factor differently in order to create a better model. One way to do this is to use the absolute t-stat values to calculate a weighting for each factor.

In this case:

The final model: 76% HighToCloseReturns + 24% LowToOpenReturns

Great! Looks like there is an improvement in t-stat after combining both factors. The results are very appealing and it’s time to move to the next steps with backtesting. It’s important to note that walk forward analysis is not the same as backtesting. We did not account for commissions, slippage or order fills.

Backtesting

Based on the AlphaLens results, going long the top decile and short the bottom decile should yield an average return of about 5-6 basis points. However, the walk forward analysis assumes perfection in filling orders at the close or open prices. This is a problem since prices are extremely volatile in the market open and close auctions. 

Entry and Exit

In addition to volatile prices, it’s risky to place trades after market close because of low volume that leads to higher slippage. Thus, the more feasible option is to rebalance the portfolio one hour after market open.

Slippage, Commissions and Leverage

Thankfully, Q500US stocks are very liquid and we can generously assume a fixed slippage of five basis points. Commissions are set at the Interactive Brokers (IB) tiered rate of $0.001 per share with a minimum order of $0.35 per trade. For consistency, leverage is kept at 100% – 50% long, 50% short.

Results – $1,000,000 Starting Capital

Model – Blue, SPY – Red

Unfortunately, it looks like the model does NOT survive slippage and transaction costs. Before discarding the model entirely, there are still a few options to consider:

• Trade fewer positions
  • Instead of trading the top and bottom deciles, use the top and bottom 1%.
• Trade less frequently
  • Instead of rebalancing daily, rebalance once a week starting Monday.

Modified Results – $1,000,000 Starting Capital

Model – Blue, SPY – Red

Looks like the performance is significantly better after the modifications. However, the results are not spectacular either, at around 0.44 Sharpe. The maximum drawdown is also extremely high at 70%. The equity curve shows poor performance in 2009-2010 and 2016-2017, both times during the recovery of a market correction. Evidently, this model is unfit for trading, and there is definitely room for improvement. In upcoming blog posts, we will incrementally build on this model, and strive to develop a robust trading strategy around short-term reversals.

Takeaways

• Do short-term returns demonstrate mean reversion while long-term returns demonstrate trending properties?
  • YES, weekly returns are mean reverting while quarterly returns are trending.
• Do OHLC prices matter when calculating factor returns?
  • YES, both optimal factors rely on variations of OHLC price data.
• Do these returns survive transaction costs?
  • NO, but there are some ways to reduce slippage by trading fewer positions and less frequently.

Next Part 2 – Volume Data 

The next post will dive into volume data and the affects on short term reversals.