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DGTW Return Adjustment with Characteristic-Sorted Benchmarks

Article Quant Q&A · Author: Martin
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Summary

The document outlines the Daniel, Grinblatt, Titman, and Wermers approach to evaluating stock strategies or funds against characteristic-matched benchmarks. It describes forming 125 portfolios sorted by size, book-to-market, and momentum, then assigning stocks to portfolios using lagged characteristics. Characteristic selectivity aggregates holdings-weighted stock returns in excess of their matched benchmarks.

It also sketches characteristic timing, based on changes in benchmark portfolio performance and the strategy’s exposure to those portfolios, and average style, based on benchmark performance weighted by prior holdings. The construction described requires stock data from two years earlier, uses industry averages for book-to-market, and measures momentum from past returns excluding the latest month. The text raises, but does not resolve, questions about new stocks, short positions, applying the method to other factors, and industry use; it is a summary of the method rather than a complete specification.

Key ideas

  • DGTW benchmarks match stocks on size, book-to-market, and momentum characteristics.
  • Characteristic selectivity measures holdings-weighted returns relative to matched benchmark portfolios.
  • Characteristic timing and average style capture additional benchmark exposure and performance components.
  • The described portfolio construction relies on historical stock data and lagged characteristics.
  • The document leaves implementation questions about IPOs, short positions, and new factors unanswered.

Tags

EquitiesFactor investingBacktestingPortfolio constructionStatistics
Full text
# DGTW return adjustment


# DGTW return adjustment












DGTW refers to the 1997 Daniel, Grinblatt, Titman, and Wermers paper available on Wermers' personal website.

The general idea from what I have understood (please correct me if you think I'm wrong!) is to adjust the returns of a strategy. There are three main measures:

First, the characteristic selectivity:

- You form 5^3 = 125 conditional sorted quintile benchmark portfolios on (1) size, (2) book-to-market, and (3) momentum.

- For each stock that's in the strategy or fund that you're evaluating, you subtract the same-period performance of that benchmark portfolio that we formed that the respective stock fell into a month earlier. So we get an excess return of the stock pick relative to the "characteristic" portfolio. (eq. 1 in the paper)

- You calculate a weighted sum of these excess returns according to the strategy's (or fund's) weights. This is the "characteristic selectivity" (CS) measure.

Second, the characteristic timing:

- Use the same 125 benchmark portfolios as before.

- We calculate the benchmark portfolio minus the same benchmark portfolio 12 months earlier, each weighted by how much the strategy/fund was invested in stocks that belong to these benchmark portfolios. (eq. 2 in the paper)

- The sum of these is the "characteristic timing" (CT) measure.

Third, the average style:

- Same benchmark portfolios.

- We calculate the performance of the weights times respective benchmark portfolios 12 month earilier. (eq. 3 in the paper)

The construction of the benchmark portfolios is described in the paper's appendix.

- Requires data for each stock to be available 2 years earlier.

- For the book-to-market sorting we first industry average.

- Momentum sorting based on 12 month past returns excluding the very last month.

My questions:

- When we say DGTW adjusted returns do we normally refer to the CS? Is CT and AS less important?

- How would we handle new stocks? Like what if we want to evaluate a fund that focuses on recent IPO'd stocks? We don't know what benchmark portfolio they fall into.

- Does it make sense to DGTW adjust other sorting strategies? Like let's take another sorting factor we come up with, does it make sense to calculate DGTW adjusted returns? Is this done? Is there a better way to see if the new factor bring new information? Of course we can regress the returns in a factor model, but is there a better way?

- Does it make sense to DGTW adjust returns with short positions?

- Is DGTW used in the industry like at Morningstar or other fund evaluation firms?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.