Abstract
We compare the relative contribution of conditional mean and conditional volatility terms in vector autoregression–exponential generalized autoregression conditional heteroskedasticity models of bivariate returns to international stock indices. Conditional mean terms are relatively unimportant for bivariate returns to country pairs that trade synchronously such as Australia/Japan, where they account for only 8% of the increase in log-likelihood over an unconditional model, on average. They are more important in nonsynchronous domestic/world-ex-domestic series such as Japan/world-ex-Japan, where they account for 24% of the increase in log-likelihood over an unconditional model, on average. Despite their increased prominence in the domestic/world-ex-domestic series, conditional mean terms detract from residual behaviours in these series. They also detract from some out-of-sample return and volatility predictions in both synchronous and nonsynchronous series.
Notes
1 Long-horizon (weekly or longer) return predictability has been found using publicly available information variables including lagged returns (Fama and French, Citation1988a), short-term T-bill rates (Fama and Schwert, Citation1977), dividend (Fama and French, Citation1988b) and earnings yields (Campbell and Schiller, Citation1988; Ang and Bekaert, Citation2007), term (Campbell, Citation1987) and default premiums (Fama and French, Citation1989), aggregate consumption-wealth ratios (Lettau and Ludvigson, Citation2001), liquidity (Avramov et al., Citation2006) and aggregate and idiosyncratic volatilities (Ang et al., Citation2006; Guo and Savickas, Citation2006). These findings are controversial for several reasons. First, the predictive relation varies across samples and is unstable over time (Goyal and Welch, Citation2003). This in turn raises concerns about the out-of-sample performance of these predictors, with significant predictive performance being claimed by some authors (Sullivan et al., Citation1999; Guo, Citation2006) and refuted by others (Bossaerts and Hillion, Citation1999; Cooper et al., Citation2005; Goyal and Welch, Citation2008). Return predictability is confounded by persistence in the return predictors, which implies persistence in expected returns as well (Paye and Timmermann, Citation2006; Boudoukh et al., Citation2008). In contrast to long-horizon return predictions, short-horizon (i.e. daily) volatility predictions typically rely on the historical time series.
Fama
,
EF
and
French
,
KR
.
1988a
.
Permanent and transitory components of stock prices
.
Journal of Political Economy
,
96
:
246
–
73
.
Fama
,
EF
and
Schwert
,
GW
.
1977
.
Asset returns and inflation
.
Journal of Financial Economics
,
5
:
115
–
46
.
Fama
,
EF
and
French
,
KR
.
1988b
.
Dividend yields and expected stock returns
.
Journal of Financial Economics
,
22
:
3
–
25
.
Campbell
,
JY
and
Schiller
,
RJ
.
1988
.
Stock prices, earnings and expected dividends
.
Review of Financial Studies
,
1
:
661
–
76
.
Ang
,
A
and
Bekaert
,
G
.
2007
.
Stock return predictability: is it there?
.
Review of Financial Studies
,
20
:
651
–
707
.
Campbell
,
JY
.
1987
.
Stock returns and the term structure
.
Journal of Financial Economics
,
18
:
373
–
99
.
Fama
,
EF
and
French
,
KR
.
1989
.
Business conditions and expected returns on stocks and bonds
.
Journal of Financial Economics
,
25
:
23
–
49
.
Lettau
,
M
and
Ludvigson
,
S
.
2001
.
Consumption, aggregate wealth, and expected stock returns
.
Journal of Finance
,
56
:
815
–
49
.
Avramov
,
D
,
Chordia
,
T
and
Goyal
,
A
.
2006
.
Liquidity and autocorrelations in individual stock returns
.
Journal of Finance
,
61
:
2365
–
94
.
Ang
,
A
,
Hodrick
,
RJ
,
Xing
,
Y
and
Zhang
,
X
.
2006
.
The cross-section of volatility and expected returns
.
Journal of Finance
,
61
:
259
–
99
.
Guo
,
H
and
Savickas
,
R
.
2006
.
Idiosyncratic volatility, stock market volatility, and expected stock returns
.
Journal of Business and Economic Statistics
,
24
:
43
–
56
.
Goyal
,
A
and
Welch
,
I
.
2003
.
Predicting the equity premium with dividend ratios
.
Management Science
,
49
:
639
–
54
.
Sullivan
,
R
,
Timmermann
,
A
and
White
,
H
.
1999
.
Data-snooping, technical trading rule performance, and the bootstrap
.
Journal of Finance
,
54
:
1647
–
91
.
Guo
,
H
.
2006
.
On the out-of-sample predictability of stock market returns
.
Journal of Business
,
79
:
645
–
70
.
Bossaerts
,
P
and
Hillion
,
P
.
1999
.
Implementing statistical criteria to select return forecasting models: what do we learn?
.
Review of Financial Studies
,
12
:
405
–
28
.
Cooper
,
M
,
Gutierrez
,
RC
and
Marcum
,
W
.
2005
.
On the predictability of stock returns in real time
.
Journal of Business
,
78
:
469
–
99
.
Goyal
,
A
and
Welch
,
I
.
2008
.
A comprehensive look at the empirical performance of equity premium prediction
.
Review of Financial Studies
,
21
:
1455
–
508
.
Paye
,
BS
and
Timmermann
,
A
.
2006
.
Instability of return prediction models
.
Journal of Empirical Finance
,
13
:
274
–
315
.
Boudoukh
,
J
,
Richardson
,
MP
and
Whitelaw
,
RF
.
2008
.
The myth of long-horizon predictability
.
Review of Financial Studies
,
21
:
1577
–
605
.