NTU Conference

1

• based on the joint work with
• Devraj Basu
• EDHEC Business School

Anomaly Timing Daniel Chi-Hsiou Hung Durham
Business School Durham University http//www.dur.a
c.uk/d.c.hung
2
Introduction
overview
literature
results
extensions
theory
synopsis
objectives

• in this paper
• we construct timing strategies
• based on the lagged return on the market
• time the portfolios of asset-pricing anomalies
• achieve higher Sharpe ratios
• with lower volatility
• positive and significant model alphas

• develop timing strategies
• use the state of the market as a timing signal
• use size, book-to-market and momentum portfolios
  as primitive assets
• investigate their performance
• an upside risk factor

3
Introduction
overview
literature
results
extensions
theory
Motivation
Asset-pricing anomalies

• Zero net-worth portfolios which buy and sell
  short on equity securities with some
  firm-characteristics generate profits
• The effect of size (market capitalization of
  equity) Banz, 1981
• The effect of value (book-to-market equity ratio)
  Fama and French, 1993
• The effect of momentum (past returns) Jegadeesh
  and Titman (1993 and 2001)

Chi-Hsiou Hung
4
Introduction
overview
literature
results
extensions
theory
Motivations
the returns on the anomalies portfolios and
trading activities are correlated with the states
of the market

• momentum profits follow positive market returns
  (Cooper, Gutierrez and Hameed, JF, 2004 )
• momentum loses follow negative market returns
  (Cooper, Gutierrez and Hameed, JF, 2004)
• small size stocks, value stocks, and past return
  losers exhibit greater correlation asymmetries
  with the aggregate U.S. market (Ang and Chen,
  JFE, 2002)
• trading volume is positively related to lagged
  market returns (Statman, Thorley and Vorkink,
  RFS, 2006)

Chi-Hsiou Hung
5
Introduction
overview
literature
results
extensions
theory
Our investigations
the state of the market may be a timing signal

• We construct simple timing strategies that invest
  in the primitive assets of the size,
  book-to-market and momentum portfolios
• The objectives are to capture the upside returns
  and avoid the downside losses on these portfolios
• the type I and type II timing strategies
• These strategies are long only
• and are easy to implement

Chi-Hsiou Hung
6
Introduction
literature
theory
results
extensions
data
Our investigations
Timing strategies

• Type I
• invest in the primitive assets in a given month
  if the return on the CRSP Value Weighted index in
  the previous month is positive
• otherwise invest in the 1 month Treasury bills
• Type II
• invest in the primitive assets in a given month
  if the return on the CRSP Value Weighted index in
  the previous month is greater than 2
• otherwise invest in the 1 month Treasury bills

7
Introduction
literature
theory
results
extensions
data
Our investigations
Evaluation of the economic and statistical
significance of the returns

• timing strategies outperform the primitive assets
  in terms of
• Higher Sharpe ratio
• considerably lower volatility
• use asset-pricing models
• that explain the returns on the primitive
  portfolios
• find positive, often significant, alphas relative
  to these models
• We augment the models with an upside factor
• which is the maximum of the market return and
  zero
• most of the alphas become negative
• none of the positive alphas are significant
• positive and significant loading on the upside
  factor

8
Introduction
overview
literature
results
extensions
methodology
What is the type I timing strategy?

• The strategy switches in and out of the risky
  assets

return of the strategy
the timing signal
9
Introduction
overview
literature
results
extensions
methodology
What is the type II timing strategy?

• The strategy switches in and out of the risky
  assets

return of the strategy
the timing signal
Chi-Hsiou Hung
10
Introduction
overview
literature
extensions
theory
empirical tests
Data

• We use all monthly equity data of the NYSE, AMEX
  and NASDAQ files from the Center for Research in
  Security Price (CRSP) between January 1926 and
  December 2006.

Chi-Hsiou Hung
11
Introduction
overview
literature
extensions
theory
empirical tests
Primitive assets

• two sets of equally weighted portfolios
• The top and bottom decile portfolios
• Stock portfolios of the top and bottom 30 of the
  sorting criteria
• momentum winner and loser portfolios (returns
  over months t-2 to t-12)
• book-to-market ratio (value) portfolios
• equity market capital (size) portfolios
• long-term winner and loser portfolios (reversal)
  returns over months t-13 to t-60

Chi-Hsiou Hung
12
Introduction
overview
literature
extensions
theory
analysis
risk and return profiles of the primitive
portfolios
Chi-Hsiou Hung
13
Introduction
overview
literature
extensions
theory
results
risk and return profiles of the type I strategies
14
Introduction
overview
literature
extensions
theory
results
risk and return profiles of the type I strategies

• All the average returns of the strategies are
  positive
• The Bonferroni adjusted probabilities for
  observing the p-values are all highly significant
  
• the type I strategies based on for all primitive
  assets but the winner portfolios improve the risk
  adjusted performance (Sharpe ratio)

15
Introduction
overview
literature
extensions
theory
results
risk and return profiles of the type II strategies
16
Introduction
overview
literature
extensions
theory
results
risk and return profiles of the type II strategies

• the type II strategies further improve the risk
  reward profiles for all but the strategy based on
  the loser portfolios
• The type II timing strategies considerably reduce
  both total volatility and downside volatility

17
Introduction
overview
literature
extensions
theory
results
Extreme up and down moves ratios

• Extreme up moves
• a monthly gain of more than 5
• Extreme down moves
• a monthly loss of more than 5
• We compute the ratio of extreme up (down) moves
  of a timing strategy to that of the primitive
  portfolio
• A high ratio of extreme up moves indicates the
  ability of the strategy in capturing the extreme
  upside returns of the primitive portfolio
• A low ratio of extreme down moves indicates that
  the strategy avoids much of the extreme downside
  losses

18
Introduction
overview
literature
extensions
theory
results
Extreme up and down moves ratios
19
Introduction
overview
literature
extensions
theory
results
Extreme up and down moves ratios

• the type I strategies
• capture between 57 and 79 of the extreme up
  moves of the primitive assets,
• reduce the extreme down moves to between 38 and
  59
• the type II strategies
• capture between 37 and 57 of the extreme up
  moves
• reduce the extreme down moves to between 10 and
  33

20
Introduction
overview
literature
extensions
theory
analysis
Evaluation using unconditional asset-pricing
models

• an unconditional K-factor model

the MKT, SMB, HML and UMD
plus an upside market factor
21
Introduction
overview
literature
extensions
theory
results
Evaluation using asset-pricing models
22
Introduction
overview
literature
extensions
theory
results
Evaluation using unconditional pricing models for
type I
23
Introduction
overview
literature
extensions
theory
results
Evaluation using unconditional pricing models for
type II
24
Introduction
overview
literature
extensions
theory
analysis
Evaluation using conditional asset-pricing
models

• a conditional K-factor model

the MKT, SMB, HML and UMD
plus a dummy variable
Instruments of 1 month T-bill rate, the term
spread and the default spread
25
Introduction
overview
literature
extensions
theory
results
Evaluation using conditional pricing models for
type I
26
Introduction
overview
literature
extensions
theory
results
Evaluation using conditional pricing models for
type II
27
Introduction
overview
literature
conclusions
theory
results
Conclusions

• Simple timing strategies successfully capture the
  upside returns on the size, book-to-market and
  momentum portfolios
• and avoid their downside losses
• They remain profitable after accounting for
  relatively high levels of transaction costs
• the variation in returns on the timing strategies
  is better explained by dynamic factor betas

Chi-Hsiou Hung