“... and the Cross-Section of Expected Returns” Harvey, R. Campbell, Yan Liu, and Heqing Zhu

Question 1

What is the main idea?

Answer 1

Authors test what significance level/t-statistic should be used to consider a factor significant in explaining returns.

Question 2

What is the problem with trying to explain the cross-section of expected returns?

Answer 2

At least 316 factors have been tested to explain cross-section of expected returns (most proposed in the last 10y)

Paper argues, that it is a mistake to use the usual statistical significance cutoffs (e.g., a t-statistic exceeding 2.0) in asset pricing tests
o Many historically discovered factors may be significant by chance (too many factors, inevitable data mining)

Question 3

What kind of testing do authors use, what is the problem with it and how is it solved?

Answer 3

• Use multiple testing
• Problem: Type I error increases (False positive)
• Solution:
  1. Out-of-sample test (can’t be used in real time)
  2. Statistical framework – Require lower p-value = higher t-statistic = more significance; But increases Type II errors (false negative)

Question 4

Why do authors use multiple testing?

Answer 4

Sample: 313 articles that propose and test new factors

The sample is likely to underestimate the actual factor population —> use multiple testing framework

Question 5

Why may the new proposed t-statistic still be too low?

Answer 5

316 different factors, which likely underrepresent the factor population and therefore t-statistic threshold of 3.0 might be too low, because:

o Only consider top journals
o Selective in choosing only a few working papers
o Sometimes many variants of the same characteristic, they only include most representative ones
o Should be measuring the number of factors tested (which is unobservable, bc of failed/insignificant/unpublished factors)

Question 6

Why do authors’ threshold cutoffs increase through time?

Answer 6

Authors’ threshold cutoffs increase through time as more factors are data mined.

REASONS:
 The easiest-to-find factors are already been found
 Limited amount of data
 Cost of data mining has dramatically decreased (easier to do “p-hacking” – try a lot of stuff until you find something, by chance, you are gonna find smth anyway)

Question 7

What t-statistic should a newly discovered factor have today?

Answer 7

T-statistic that exceeds 3.0, however it might be too low.

Nevertheless, a t-statistic of 1.96 is no longer appropriate – even for factors that are derived from theory.

Question 8

What are the limitations to authors’ framework?

Answer 8

o All factor discoveries should not be treated equally, factor derived from economic theory should have lower threshold for significance than the ones founded empirically

o Tests focus on unconditional tests, which consider factor marginals (The factor may be important in certain economic environments and not important in others)

Question 9

Which 3 popular p-value adjustment types do authors look at?

Answer 9

o Bonferroni’s adjustment
o Holm’s adjustment
o Benjamini, Hochberg, and Yekutieli’s adjustment

Question 10

Which 5 factors survive all three adjustments?

Answer 10

1. HML - book-to-market
2. MOM - momentum
3. DCG - durable consumption goods
4. SRV - short-run volatility
5. MRT - market beta