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Forecasting US stock market returns by the aggressive
stock-selection opportunity
Yan Li , Chao Liang , Toan Luu Duc Huynh
PII: S1544-6123(22)00502-5
DOI: https://doi.org/10.1016/j.frl.2022.103323
Reference: FRL 103323
To appear in: Finance Research Letters
Received date: 28 July 2022
Revised date: 6 September 2022
Accepted date: 8 September 2022
Please cite this article as: Yan Li , Chao Liang , Toan Luu Duc Huynh , Forecasting US stock mar-
ket returns by the aggressive stock-selection opportunity, Finance Research Letters (2022), doi:
https://doi.org/10.1016/j.frl.2022.103323
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© 2022 Elsevier Inc. All rights reserved.
- 1 -
Highlights
The aggressive stock-selection opportunity is defined by the average of
cross-sectional stocks’ positive alphas plus idiosyncratic volatilities.
The change of aggressive stock-selection opportunity ( ) can
significantly and negatively predict stock market returns.
The aggressive stock-selection opportunities in the market have stronger
predictive information rather than the moderate stock-selection opportunities.
The predictive role of is not induced by the potential predictive
power of the average of positive alphas and the average of idiosyncratic
volatilities.
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Forecasting US stock market returns by the aggressive
stock-selection opportunity
Yan Li
a
, Chao Liang
a,*
, Toan Luu Duc Huynh
b
a
School of Economics & Management, Southwest Jiaotong University, Chengdu, China
b
University of Economics Ho Chi Minh City, Vietnam
Abstract
We propose a measurement of aggressive stock-selection opportunity based on
positive alphas and idiosyncratic volatilities of cross-section stocks, and examine the
role of aggressive stock-selection opportunity in predicting stock market returns. For
the US stock market, we find that the change of aggressive stock-selection
opportunity has a significant and negative coefficient for predicting future one-month
market returns. The out-of-sample results also show the change of aggressive
stock-selection opportunity improves the return forecasting performance and increases
investors’ economic values. In particular, the predictive information of the change of
aggressive stock-selection opportunity is independent of traditional macroeconomic
predictors. The economic channel evidence shows that the change of aggressive
stock-selection opportunity increases future market volatility and then results in lower
* Corresponding author. Address: No. 111, North 1st Section, 2nd Ring Road, Chengdu, China. Zip code: 610031.
E-mail addresses: liangchaoswjt@163.com (Chao Liang)
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market returns.
Keywords: Stock-selection opportunity; aggressive stock-selection opportunity; Stock
market returns; Forecasting returns
JEL classification: G12, G14, G23
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1. Introduction
Investigating return predictability has important theoretical and practical
significance, and a number of studies on predicting stock market returns are
documented in the literature (Goyal & Welch 2003; Campbell & Vuolteenaho 2004;
Lewellen 2004; Guo 2006; Welch & Goyal 2008; Bollerslev et al. 2014; Neely et al.
2014; Liu et al. 2015; Baker et al. 2016; Chen et al. 2017; Byun et al. 2018; Wang
2020; Dai et al. 2021; He et al. 2021). This paper examines the role of aggressive
stock-selection opportunities on the predictability of stock market returns.
Motivated by Jiang et al. (2021) who proposed a stock-selection opportunity
measurement, we introduce a measure of aggressive stock-selection opportunity
(ASSO) that contains the information of both stocks’ alphas and idiosyncratic
volatilities on the cross-section. Jiang et al. (2021) mainly investigate the ability of
mutual fund managers in stock-selection timing. Different from the investigating
perspective of Jiang et al. (2021), we explore whether the stock-selection opportunity
can be used to predict market returns, in particular, from a novel perspective of the
aggressive investment opportunity.
We mainly censor the predictive ability of the change of ASSO ( ) in
market returns with the consideration of removing the trend term in ASSO. The data
sample period for the US stock market spans from 1963-09 to 2021-12. We find that
has a significant and negative coefficient for predicting future one-month
market returns. Among and traditional macroeconomic predictors, the
univariate model based on shows the highest R-squared of 1.248%. The
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results of the bivariate models that regress market excess returns on and
one of the popular predictors further show that maintains its significant
impact on future market returns for all 14 models. This evidence identifies that the
predictive information of is independent of these macroeconomic predictors.
Our out-of-sample findings confirm the predictive ability of from the
perspectives of predictive accuracy and economic value.
Additionally, we discuss the potential economic channel for the predictive role of
, and find that the volatility channel is supported. We also demonstrate the
unique predictive role of by excluding the potential predictive power of the
average of positive alphas and the average of idiosyncratic volatilities.
We contribute to the literature by proposing a new return predictor, an aggressive
stock-selection opportunity measurement based on cross-section positive alphas and
idiosyncratic volatilities. The main measurement of stock-selection opportunity in
Jiang et al. (2021) only considers the information of stocks’ positive alphas. Moreover,
we show the change of aggressive stock-selection opportunity has a significant
predictive role in stock market returns but Jiang et al. (2021)’s measurement does not.
Additionally, we also show the economic channel for the predictive performance of
the change of aggressive stock-selection opportunity, where stock market volatility is
the possible intermediate variable.
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2. Variable and methodology
2.1. Aggressive stock-selection opportunity
In Jiang et al. (2021), a stock-selection opportunity measurement is given by the
average of cross-sectional positive alphas. The alpha of a stock is estimated by
the CAPM model:
, = + (, − ,) + ,, (1)
where , − , is the market returns in excess of the risk-free interest rates. The
daily returns for each month are used to estimate the above parameters. Drawing on
the setting of Jiang et al. (2021), we further introduce an aggressive stock-selection
opportunity (ASSO) measure. When investors capture investment opportunities by the
positive alphas of stocks, aggressive investors among them may be more concerned
with an upper limit of investment opportunities. Therefore, considering the positive
alpha plus the idiosyncratic volatility is a potential way to capture an aggressive
opportunity. Specifically, if stock has a positive alpha, an aggressive investment
opportunity for stock is given by its alpha plus its idiosyncratic volatility, where the
idiosyncratic volatility is the standard deviation of the residual term , in equation
(1). Thus, the ASSO for the whole market is the average of the aggressive investment
opportunities of individual stocks. Compared with the average positive alpha of
individual stocks of Jiang et al. (2021), our ASSO is also calculated based on the
same stocks with a positive alpha, but using an aggressive opportunity. To remove the
trend term of ASSO, we perform first-order difference processing on ASSO, that is,
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the change in aggressive stock-selection opportunity ( ) is
= − −1. (2)
In particular, the average of the idiosyncratic volatility of individual stocks is an
alternative proxy for the stock-selection opportunity in Jiang et al. (2021). We also
discuss the unique role of in predicting stock market returns.
Stock sector indices provide a good overview of stock-selection opportunities in
the market. We use the data of 49 industry portfolios and market factors from the
website of Kenneth R. French
1
to calculate the alphas and idiosyncratic volatilities of
individual industries, then calculate market-level . In addition, 14 traditional
predictive variables of Welch and Goyal (2008) are also introduced for predicting
market returns.
2.2. Methodology
The univariate and bivariate predictive regressions are
+1 = + ·x + +1, (3)
+1 = + · + ·, + +1, (4)
respectively, where is stock market excess returns, is a predictor of interest
including , , is one of the macro predictors, and +1 is the residual
term. The independent variables are standardized, and the market return is annualized
by multiplying by 12. The direction and significance of the estimated show the
predictor’s impact and predictive power. The corresponding t-values are adjusted by
1
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
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the Newey and West (1987) method.
The out-of-sample evaluation is necessary to examine the predictive performance
of predictors (Wang et al. 2016; Wang et al. 2019a). We conduct the recursive
estimation window method to yield forecasts (Campbell & Thompson 2008), and the
initial M months for estimating the first batch of parameters is 240 (Wang et al.
2019b). The sample period spans from 1963-09 to 2021-12, and there are 700
observations. The out-of-sample spans from 1983-09 to 2021-12.
We evaluate the out-of-sample performance of models by the out-of-sample
R-squared, where the benchmark model is the historical average of stock returns
(Campbell & Thompson 2008), specifically:
2 = 1 −
∑ (̂−)
2
=+1
∑ (̅−))2
=+1
, (5)
where ̂, , and ̅ are the model forecast, true market return, and historical return
average, respectively. The MSFE-adjusted statistic of Clark and West (2007) is used
to evaluate the significance of
2 .
Furthermore, from the perspective of economic value, referring to Campbell and
Thompson (2008), the return of the optimal portfolio with two assets (stock index and
risk-free asset) in a mean-variance utility framework is
̂,+1 =
∗ ⋅ r+1 + r,+1, (6)
where the optimal weight
∗ of holding risk asset is
̂+1
̂+1
2 , ̂+1 is the forecast of
market excess return, ̂+1
2 is the variance of returns over the past 60 months (Wang
et al. 2019b), and is a risk aversion factor set by 3 (Rapach et al. 2010). Due to the
short-selling restrictions,
∗ is constrained between 0 and 1.5 (Neely et al. 2014;
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Wang et al. 2019b). Following Wang et al. (2019b), we further evaluate the
performance of portfolios by the certainty equivalent return (CER) and Sharpe ratio
(SR) are introduced. And the CER and SR gains are the difference between the CER
and SR of the portfolio of interest and the CER and SR of the portfolio based on the
average of historical returns, respectively2.
3. Empirical results
We forecast monthly excess returns of the S&P 500 index. We obtain predictors
and index returns from the website of Amit Goyal
3
, and obtain the data of industry
portfolios and market factors from the website of Kenneth R. French
4
, where the
period of market factors data starts from 1963-07. Considering all available data, the
entire sample period for the empirical analysis is from 1963-09 to 2021-12 with 700
observations. Descriptive statistics of our variables are shown in Table 1.
Insert Table 1 about here
Insert Figure 1 about here
3.1. In-sample estimations
The estimation results of univariate models are shown in Table 2, and we find that
has a significant and negative coefficient of -0.058 for the next-month
2
The annualized economic values are SR and CER gains multiplied by √12 and 1200.
3
http://www.hec.unil.ch/agoyal/
4
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
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market returns. The negative coefficient indicates that the aggressive stock-selection
opportunity negatively results in future market returns. A potential reason is that when
investors capture this aggressive opportunity, they may overreact to it and then their
aggressive trading activities result in high market uncertainty and high illiquidity.
Moreover, explains the most variance of future market returns among
all 15 predictors supported by the highest in-sample R-squared 1.248%. Among 14
macroeconomic variables, only 5 predictors show a significant predictive impact on
stock market returns, including TBL, LTY, TMS, LTR, and INFL. These estimations
simply illustrate the powerful predictive role of in the predictability of
stock market returns.
Insert Table 2 about here
To further identify the unique predictive information of , Table 3
presents the in-sample results of bivariate models conducted by two regressors of
and one of the macro predictors. The results show that still
possesses significantly negative coefficients in all bivariate models, consistent with
the findings of the univariate model of . Moreover, these coefficients of
are very stable around -0.058 with little deviation, which directly
demonstrates the predictive information obtained from is independent of
that of the 14 macroeconomic variables. In addition, the bivariate model based on
and TBL has an in-sample R-squared of 2.151%, which is the highest
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among all 14 bivariate models.
Overall, the in-sample results show has unique predictive information
in forecasting stock market returns.
Insert Table 3 about here
3.2. Out-of-sample performance
In Panel A of Table 4, we present the out-of-sample forecasting results. The
univariate predictive model based on has a significant and positive oos
2 of
0.890%, a positive CER gain of 2.494 and SR gain of 0.277, which are the highest
economic values among these univariate models. For the other predictors, only TBL
and LTY yield significant oos
2 . In Panel B, almost all of these bivariate models with
bring significant oos
2 values and positive economic values.
Comprehensively summarizing the results of Table 4, we find that introducing
improves the forecasting performance of predictive models.
Insert Table 4 about here
To test the independent predictive information of , we compare a
forecast combination of bivariate models with and a combination of
univariate models without . We have 4 forecasting combination models
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(Zhang et al. 2020): Equal-weighted combination (EWC), trimmed mean combination
(TMC), and two combination models based on the discounted MSPE (DMSPE) of
Stock and Watson (2004), that is, DMSPE models with discount ratios of 1 and 0.9.
Table 5 presents the out-of-sample results for forecasting combinations. Across the
four combination methods, the forecasting combination of bivariate models with
show significantly positive oos
2 and positive economic values but the
forecasting combination of univariate models without does not.
In short, the unique predictive information obtained from is supported
from the out-of-sample perspective.
Insert Table 5 about here
4. Robustness check
4.1. Economic constraint
Campbell and Thompson (2008) document that many predictors in the literature
cannot beat the historical mean of returns. The CT truncation rule of Campbell and
Thompson (2008) limits the return forecasts to be greater than zero. We also apply the
CT truncation rule to our forecasts and further test the forecasting accuracy of the
model based on .
In Table 6, we report the oos
2 of the forecasts based on the CT truncation rule
for 15 univariate models and 14 bivariate models. The CT forecasts of the univariate
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model based on obtain a significantly positive oos
2 of 1.587% which is
even higher than the oos
2 by the raw forecasts without truncation. Most of the
bivariate models have significant oos
2 excluding the model based on and
SVAR that still has improvement in forecasting performance beyond the univariate
model of SVAR. On the whole, applying the CT rule does not affect the significance
of the forecasting performance of but enhance the predictive accuracy.
Insert Table 6 about here
4.2. Trading cost
One may concern about the effect of transaction cost on the profits of investment
strategies. Following Anderson et al. (2012) and Byun et al. (2018), we examine the
impact of the transaction cost. Two trading cost ratios are considered: c = 0.1% (Byun
et al. 2018), and c = 0.2%. We report the economic values of portfolios in Table 7.
The results further shed light on the predictive performance of under the
actual situation with trading costs.
Insert Table 7 about here
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5. Discussion
5.1. The potential economic channel for the predictive role of
The aggressive stock-selection opportunities capture investors' aggressive trading
behavior that may lead to excess trading volume or increase market volatility, then
affect market returns. To address this issue, we perform the following regressions:
SVAR = + ∑ 1 ⋅ SVAR−
1
=1 + + −1 + , (7)
= + ⋅ SVAR + , (8)
and
AVOL = + ∑ 1 ⋅ AVOL−
2
=1 + + −1 + , (9)
= + ⋅ AVOL + , (10)
where SVARt is short-term market volatility, AVOLt is the abnormal trading volume
of the S&P 500 index by the current trading volume divided by the average trading
volume over the past 12 months, and is the residual term. The lag terms are
determined by the AIC rule, specifically, 3 lags for SVAR and 1 lag for AVOL.
We show the regression results in Table 8, and the risk channel is supported and
the trading channel is half successful. Specifically, both the contemporaneous and
lagged have a significant impact on SVAR. Moreover, the relation between
SVAR and market return over the same period is significant and negative which is
consistent with previous studies regarding the complex volatility-return relation, such
as Glosten et al. (1993), Bekaert and Wu (2000), and Jin (2017). These impact
directions are consistent, that is, the positive -SVAR predictive relation and
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the negative SVAR-return contemporaneous relation result in the negative
-return predictive relation. From the market volatility perspective, the evidence
shows the potential transitive relationship among the three items of , market
volatility, and market returns.
For the trading activities channel, although the does significantly
increase market trading volume, the latter does not have a significant impact on
market returns over the same period.
In short, our evidence supports the risk channel for the predictive role of
, that is, the change in the aggressive stock-selection opportunities increases
future stock market volatility and then negatively impacts future market returns.
Insert Table 8 about here
5.2. Comparing stock-selection opportunity measurements: The
success of comes from its aggressive angle
One may concern whether the original SSO measurement of Jiang et al. (2021)
has a predictive role on stock market returns. In Table 9, our in-sample results show
the raw SSO cannot significantly affect market returns and the change of SSO
( ) has a weak significant and negative coefficient. Here we also report how
the ASSO affects the subsequent market returns, and we find the absence of a
significant coefficient for ASSO. The result indicates that , the detrended
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measurement, is more suitable and sensitive to predicting market returns than the raw
form of ASSO. Comparing the results between and , we find that
the aggressive stock-selection opportunities in the market have stronger predictive
information for market returns rather than the moderate stock-selection opportunities
(e.g. SSO).
Furthermore, our is constructed by the information of positive alphas
and idiosyncratic volatilities (residual volatilities) of individual stocks. A direct
conjecture to one is that the predictive information could be due to the idiosyncratic
volatilities of stocks. In Jiang et al. (2021), the average of idiosyncratic volatilities
( ) of individual stocks also could be suitable as a proxy for stock-selection
opportunities. We also examine the impacts of and the change form
on future market returns. Our results show there are no significant coefficients and
small in-sample R-squared values close to zero for these two measurements. In short,
we demonstrate the unique predictive role of by excluding the potential
predictive power of the average of positive alphas and the average of idiosyncratic
volatilities.
Insert Table 9 about here
6. Conclusion
We define a measurement of aggressive stock-selection opportunity (ASSO) and
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find that the change of aggressive stock-selection opportunity ( ) has powerful
and unique predictive information for stock market returns. Compared with the
original measure of stock-selection opportunity (SSO) by the average positive alphas
in Jiang et al. (2021), our ASSO is the average of the positive alphas plus the
idiosyncratic volatilities of cross-sectional individual stocks. Our empirical evidence
in the US stock market supports the unique role of in predicting stock
market returns. Moreover, the predictive impact of is not due to the
individual predictive impacts of the average of positive alphas and the average of
idiosyncratic volatilities. This indicates the effectiveness of the distinctive definition
in . Our study is helpful for investors to improve their trading strategies and
portfolio management. In our future work, we will further study the stock-selection
issues, such as the impact of stock-selection risk on stock market returns, and how
investors trade-off between stock-selection risk and opportunity.
Conflict of Interest
We declare that there is not conflict of interest.
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References
1) Anderson, R.M., Bianchi, S.W., Goldberg, L.R., 2012. Will My Risk Parity
Strategy Outperform? Financial Analysts Journal 68, 75-93
2) Baker, S.R., Bloom, N., Davis, S.J., 2016. Measuring economic policy
uncertainty. Quarterly Journal of Economics 131, 1593-1636
3) Bekaert, G., Wu, G., 2000. Asymmetric Volatility and Risk in Equity Markets.
The Review of Financial Studies 13, 1-42
4) Bollerslev, T., Marrone, J., Xu, L., Zhou, H., 2014. Stock return predictability and
variance risk premia: Statistical inference and international evidence. Journal of
Financial and Quantitative Analysis 49, 633-661
5) Byun, S.J., Frijns, B., Roh, T.Y., 2018. A comprehensive look at the return
predictability of variance risk premia. Journal of Futures Markets 38, 425-445
6) Campbell, J.Y., Thompson, S.B., 2008. Predicting excess stock returns out of
sample: Can anything beat the historical average? Review of Financial Studies 21,
1509-1531
7) Campbell, J.Y., Vuolteenaho, T., 2004. Bad beta, good beta. American Economic
Review 94, 1249-1275
8) Chen, J., Jiang, F.W., Tong, G.S., 2017. Economic policy uncertainty in China
and stock market expected returns. Accounting and Finance 57, 1265-1286
9) Clark, T.E., West, K.D., 2007. Approximately normal tests for equal predictive
accuracy in nested models. Journal of Econometrics 138, 291-311
10) Dai, Z.F., Zhou, H.T., Kang, J., Wen, F.H., 2021. The skewness of oil price
returns and equity premium predictability. Energy Economics 94
11) Glosten, L.R., Jagannathan, R., Runkle, D.E., 1993. On the Relation between the
Expected Value and the Volatility of the Nominal Excess Return on Stocks. The
Journal of Finance 48, 1779-1801
12) Goyal, A., Welch, I., 2003. Predicting the equity premium with dividend ratios.
Management Science 49, 639-654
13) Guo, H., 2006. Time-varying risk premia and the cross section of stock returns.
- 19 -
Journal of Banking & Finance 30, 2087-2107
14) He, M.X., Zhang, Y.J., Wen, D.Y., Wang, Y.D., 2021. Forecasting crude oil prices:
A scaled PCA approach. Energy Economics 97
15) Jiang, G.J., Zaynutdinova, G.R., Zhang, H., 2021. Stock-selection timing. Journal
of Banking & Finance 125, 106089
16) Jin, X., 2017. Time-varying return-volatility relation in international stock
markets. International Review of Economics & Finance 51, 157-173
17) Lewellen, J., 2004. Predicting returns with financial ratios. Journal of Financial
Economics 74, 209-235
18) Liu, L., Ma, F., Wang, Y.D., 2015. Forecasting excess stock returns with crude oil
market data. Energy Economics 48, 316-324
19) Neely, C.J., Rapach, D.E., Tu, J., Zhou, G.F., 2014. Forecasting the Equity Risk
Premium: The Role of Technical Indicators. Management Science 60, 1772-1791
20) Newey, W.K., West, K.D., 1987. A Simple, Positive Semi-definite,
Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.
Econometrica 55, 703-708
21) Rapach, D.E., Strauss, J.K., Zhou, G., 2010. Out-of-sample equity premium
prediction: Combination forecasts and links to the real economy. Review of
Financial Studies 23, 821-862
22) Stock, J.H., Watson, M.W., 2004. Combination forecasts of output growth in a
seven-country data set. Journal of Forecasting 23, 405-430
23) Wang, X., 2020. Frequency dynamics of volatility spillovers among crude oil and
international stock markets: The role of the interest rate. Energy Economics 91,
104900
24) Wang, Y., Diao, X., Pan, Z., Wu, C., 2019a. Heterogeneous beliefs and aggregate
market volatility revisited: New evidence from China. Pacific-Basin Finance
Journal 55, 127-141
25) Wang, Y.D., Ma, F., Wei, Y., Wu, C.F., 2016. Forecasting realized volatility in a
changing world: A dynamic model averaging approach. Journal of Banking &
Finance 64, 136-149
- 20 -
26) Wang, Y.D., Pan, Z.Y., Liu, L., Wu, C.F., 2019b. Oil price increases and the
predictability of equity premium. Journal of Banking & Finance 102, 43-58
27) Welch, I., Goyal, A., 2008. A comprehensive look at the empirical performance of
equity premium prediction. Review of Financial Studies 21, 1455-1508
28) Zhang, Y., Ma, F., Liao, Y., 2020. Forecasting global equity market volatilities.
International Journal of Forecasting 36, 1454-1475
- 21 -
Tables and Figures
Table 1. Descriptive statistics
Variables Mean. Std Skewness Kurtosis
0.325% 4.295% -0.452 1.826
0.112% 22.197% 0.394 3.417
DP 2.863% 1.161% 0.664 -0.340
DY 2.880% 1.166% 0.668 -0.329
EP 6.229% 2.704% 1.093 0.835
DE -3.366% 1.789% -0.669 1.373
SVAR 0.225% 0.509% 10.134 124.375
BM 0.477 0.263 0.887 -0.205
NTIS 0.888% 1.996% -0.507 -0.048
TBL 4.505% 3.263% 0.649 0.631
LTY 6.285% 2.878% 0.499 0.008
TMS -1.780% 1.470% 0.263 -0.288
LTR 0.614% 2.988% 0.411 2.328
DFY 1.025% 0.443% 1.733 4.388
DFR 0.025% 1.532% -0.680 7.377
INFL 0.316% 0.359% -0.039 3.066
Notes: is the market returns excessed the risk-free interest. The sample period spans from
1963-09 to 2021-12 with 700 observations.
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Table 2. Univariate models: +1 = + ·x + +1
Model t-stat
2( )
-0.058** -2.513 1.248
DP -0.002 -0.100 0.002
DY -0.001 -0.044 0.000
EP -0.004 -0.163 0.005
DE 0.004 0.177 0.007
SVAR -0.011 -0.234 0.042
BM -0.017 -0.768 0.108
NTIS -0.022 -0.932 0.179
TBL -0.049** -2.446 0.920
LTY -0.038* -1.894 0.556
TMS -0.034* -1.706 0.448
LTR 0.047** 2.244 0.825
DFY 0.020 0.732 0.147
DFR 0.024 0.777 0.223
INFL -0.043* -1.875 0.699
Notes: The sample period spans from 1963-09 to 2021-12 with 700 observations.
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Table 3. Bivariate models: +1 = + · + · + +1
Model t-stat t-stat
2( )
& -0.058** -2.515 -0.003 -0.118 1.250
& -0.058** -2.515 -0.001 -0.068 1.249
& -0.058** -2.510 -0.003 -0.151 1.252
& -0.057** -2.507 0.004 0.150 1.253
& -0.059*** -2.958 0.006 0.133 1.260
& -0.058** -2.520 -0.017 -0.789 1.360
& -0.058** -2.513 -0.022 -0.990 1.437
& -0.057** -2.498 -0.049** -2.450 2.151
& -0.058** -2.540 -0.039* -1.920 1.811
& -0.057** -2.450 -0.033* -1.659 1.657
& -0.058** -2.550 0.047** 2.267 2.089
& -0.057** -2.474 0.018 0.676 1.375
& -0.056** -2.506 0.019 0.615 1.385
& -0.057** -2.487 -0.043* -1.888 1.942
Notes: T The sample period spans from 1963-09 to 2021-12 with 700 observations.
- 24 -
Table 4. Out-of-sample results
Model R
2 ( ) CER gain SR gain
Panel A. Univariate models: +1 = + ∙ + +1
0.890** 2.494 0.277
DP -0.790 -0.334 -0.076
DY -0.818 -0.279 -0.069
EP -0.297 0.119 0.015
DE -0.259 -0.065 -0.007
SVAR -3.884 -0.110 -0.014
BM -0.365 -0.669 -0.026
NTIS -0.695 -1.667 -0.049
TBL 0.540** -0.006 0.099
LTY 0.521** 0.372 0.087
TMS -0.989 -2.652 -0.121
LTR -0.709 -0.551 0.026
DFY -1.018 -1.953 -0.207
DFR -0.487 0.932 0.131
INFL -0.116 0.231 0.104
Panel A. Bivariate models: +1 = + · + · + +1
& 0.128* 1.492 0.184
& 0.077* 1.379 0.172
& 0.600** 1.884 0.220
& 0.631** 1.989 0.228
& -3.170 1.594 0.191
& 0.557** 2.365 0.260
& 0.201** 2.022 0.227
& 1.405*** 3.925 0.369
& 1.423*** 3.545 0.354
& -0.152** 0.623 0.132
& 0.320** 1.581 0.191
& -0.119* 1.800 0.210
& 0.251* 2.316 0.261
& 0.713*** 3.599 0.346
Notes: The significance of the out-of-sample R
2 is based on Clark & West's (2007)
MSFE-adjusted statistic. The sample period spans from 1963-09 to 2021-12 with 700 observations.
The out-of-sample period is from 1983-09 to 2021-12.
- 25 -
Table 5. Forecast combination results
2 ( ) CER gain SR gain
Panel A. The combination of univariate models without A
U-EWC 0.000 -0.717 -0.067
U-TMC 0.014 -1.077 -0.093
U-DMSPE (1) 0.007 -0.743 -0.069
U-DMSPE (0.9) 0.013 -0.725 -0.067
Panel B. The combination of bivariate models with A
B-EWC 0.836** 2.691 0.290
B-TMC 0.890** 2.721 0.291
B-DMSPE (1) 0.838** 2.704 0.291
B-DMSPE (0.9) 0.837** 2.690 0.289
Notes: The significance of the out-of-sample R
2 is based on Clark & West's (2007)
MSFE-adjusted statistic. The sample period spans from 1963-09 to 2021-12 with 700 observations.
The out-of-sample period is from 1983-09 to 2021-12.
- 26 -
Table 6. Robustness checks: Forecasts based on the CT truncation rule
Univariate models R
2 ( ) Bivariate models R
2 ( )
1.587***
DP -0.231 & 1.174**
DY -0.241 & 1.103**
EP 0.014 & 1.465***
DE 0.004 & 1.463***
SVAR -1.450 & -0.470
BM 0.058 & 1.491***
NTIS -0.306 & 1.211***
TBL 0.714** & 1.661***
LTY 0.706** & 1.894***
TMS -0.813 & 0.373**
LTR -0.128 & 1.023**
DFY -0.400 & 0.894**
DFR -0.035 & 1.112**
INFL -0.104 & 1.273***
Notes: The significance of the out-of-sample R
2 is based on Clark & West's (2007)
MSFE-adjusted statistic. The sample period spans from 1963-09 to 2021-12 with 700 observations.
The out-of-sample period is from 1983-09 to 2021-12.
- 27 -
Table 7. Robustness checks: Trading cost
Models c = 0.1% c = 0.2%
CER gain SR gain CER gain SR gain
1.979 0.229 1.463 0.180
DP -0.333 -0.077 -0.332 -0.077
DY -0.279 -0.070 -0.279 -0.071
EP 0.117 0.015 0.115 0.014
DE -0.068 -0.008 -0.071 -0.008
SVAR -0.177 -0.024 -0.245 -0.033
BM -0.692 -0.027 -0.714 -0.028
NTIS -1.721 -0.052 -1.775 -0.055
TBL -0.044 0.097 -0.082 0.096
LTY 0.353 0.086 0.335 0.086
TMS -2.744 -0.127 -2.836 -0.133
LTR -0.961 -0.005 -1.373 -0.036
DFY -1.975 -0.209 -1.996 -0.211
DFR 0.751 0.106 0.568 0.082
INFL -0.072 0.084 -0.375 0.064
& 1.094 0.143 0.695 0.102
& 0.983 0.131 0.585 0.090
& 1.398 0.173 0.910 0.126
& 1.472 0.180 0.954 0.131
& 1.096 0.144 0.596 0.096
& 1.858 0.215 1.348 0.169
& 1.522 0.190 1.021 0.154
& 3.323 0.325 2.720 0.281
& 3.015 0.311 2.483 0.267
& 0.048 0.093 -0.529 0.053
& 0.992 0.145 0.400 0.099
& 1.357 0.169 0.912 0.127
& 1.808 0.213 1.298 0.164
& 2.977 0.300 2.352 0.253
Notes: The sample period spans from 1963-09 to 2021-12. The out-of-sample period is from
1983-09 to 2021-12.
- 28 -
Table 8. Discussion results: The economic channel for the predictive role of
Intercept 0.039** 0.225*** 0.039** 1.055***
t-stat (2.127) (14.611) (1.981) (267.471)
-0.157***
t-stat (-6.186)
−1 0.154**
t-stat (2.556)
−2 0.085***
t-stat (3.024)
−3 0.051***
t-stat (3.358)
0.024
t-stat (0.840)
−1 0.102***
t-stat (22.916)
0.222*** 0.071***
t-stat (2.735) (11.525)
−1 0.118** 0.012**
t-stat (2.423) (2.248)
2( ) 9.251 32.835 0.226 52.768
Notes: The sample period spans from 1963-09 to 2021-12.
- 29 -
Table 9. The predictive role of other related stock-selection opportunity variables
Univariate models t-stat
2( )
-0.033 -1.575 0.410
-0.001 -0.021 0.000
-0.027 -1.013 0.270
-0.034* -1.831 0.448
-0.014 -0.480 0.076
-0.058** -2.513 1.248
Notes: The sample period spans from 1963-09 to 2021-12 with 700 observations.
- 30 -
Figure 1. Stock market excess returns and the change of aggressive stock-selection opportunity
Forecasting US stock market returns by the aggressive
stock-selection opportunity
Yan Li , Chao Liang , Toan Luu Duc Huynh
PII: S1544-6123(22)00502-5
DOI: https://doi.org/10.1016/j.frl.2022.103323
Reference: FRL 103323
To appear in: Finance Research Letters
Received date: 28 July 2022
Revised date: 6 September 2022
Accepted date: 8 September 2022
Please cite this article as: Yan Li , Chao Liang , Toan Luu Duc Huynh , Forecasting US stock mar-
ket returns by the aggressive stock-selection opportunity, Finance Research Letters (2022), doi:
https://doi.org/10.1016/j.frl.2022.103323
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© 2022 Elsevier Inc. All rights reserved.
- 1 -
Highlights
The aggressive stock-selection opportunity is defined by the average of
cross-sectional stocks’ positive alphas plus idiosyncratic volatilities.
The change of aggressive stock-selection opportunity ( ) can
significantly and negatively predict stock market returns.
The aggressive stock-selection opportunities in the market have stronger
predictive information rather than the moderate stock-selection opportunities.
The predictive role of is not induced by the potential predictive
power of the average of positive alphas and the average of idiosyncratic
volatilities.
- 2 -
Forecasting US stock market returns by the aggressive
stock-selection opportunity
Yan Li
a
, Chao Liang
a,*
, Toan Luu Duc Huynh
b
a
School of Economics & Management, Southwest Jiaotong University, Chengdu, China
b
University of Economics Ho Chi Minh City, Vietnam
Abstract
We propose a measurement of aggressive stock-selection opportunity based on
positive alphas and idiosyncratic volatilities of cross-section stocks, and examine the
role of aggressive stock-selection opportunity in predicting stock market returns. For
the US stock market, we find that the change of aggressive stock-selection
opportunity has a significant and negative coefficient for predicting future one-month
market returns. The out-of-sample results also show the change of aggressive
stock-selection opportunity improves the return forecasting performance and increases
investors’ economic values. In particular, the predictive information of the change of
aggressive stock-selection opportunity is independent of traditional macroeconomic
predictors. The economic channel evidence shows that the change of aggressive
stock-selection opportunity increases future market volatility and then results in lower
* Corresponding author. Address: No. 111, North 1st Section, 2nd Ring Road, Chengdu, China. Zip code: 610031.
E-mail addresses: liangchaoswjt@163.com (Chao Liang)
- 3 -
market returns.
Keywords: Stock-selection opportunity; aggressive stock-selection opportunity; Stock
market returns; Forecasting returns
JEL classification: G12, G14, G23
- 4 -
1. Introduction
Investigating return predictability has important theoretical and practical
significance, and a number of studies on predicting stock market returns are
documented in the literature (Goyal & Welch 2003; Campbell & Vuolteenaho 2004;
Lewellen 2004; Guo 2006; Welch & Goyal 2008; Bollerslev et al. 2014; Neely et al.
2014; Liu et al. 2015; Baker et al. 2016; Chen et al. 2017; Byun et al. 2018; Wang
2020; Dai et al. 2021; He et al. 2021). This paper examines the role of aggressive
stock-selection opportunities on the predictability of stock market returns.
Motivated by Jiang et al. (2021) who proposed a stock-selection opportunity
measurement, we introduce a measure of aggressive stock-selection opportunity
(ASSO) that contains the information of both stocks’ alphas and idiosyncratic
volatilities on the cross-section. Jiang et al. (2021) mainly investigate the ability of
mutual fund managers in stock-selection timing. Different from the investigating
perspective of Jiang et al. (2021), we explore whether the stock-selection opportunity
can be used to predict market returns, in particular, from a novel perspective of the
aggressive investment opportunity.
We mainly censor the predictive ability of the change of ASSO ( ) in
market returns with the consideration of removing the trend term in ASSO. The data
sample period for the US stock market spans from 1963-09 to 2021-12. We find that
has a significant and negative coefficient for predicting future one-month
market returns. Among and traditional macroeconomic predictors, the
univariate model based on shows the highest R-squared of 1.248%. The
- 5 -
results of the bivariate models that regress market excess returns on and
one of the popular predictors further show that maintains its significant
impact on future market returns for all 14 models. This evidence identifies that the
predictive information of is independent of these macroeconomic predictors.
Our out-of-sample findings confirm the predictive ability of from the
perspectives of predictive accuracy and economic value.
Additionally, we discuss the potential economic channel for the predictive role of
, and find that the volatility channel is supported. We also demonstrate the
unique predictive role of by excluding the potential predictive power of the
average of positive alphas and the average of idiosyncratic volatilities.
We contribute to the literature by proposing a new return predictor, an aggressive
stock-selection opportunity measurement based on cross-section positive alphas and
idiosyncratic volatilities. The main measurement of stock-selection opportunity in
Jiang et al. (2021) only considers the information of stocks’ positive alphas. Moreover,
we show the change of aggressive stock-selection opportunity has a significant
predictive role in stock market returns but Jiang et al. (2021)’s measurement does not.
Additionally, we also show the economic channel for the predictive performance of
the change of aggressive stock-selection opportunity, where stock market volatility is
the possible intermediate variable.
- 6 -
2. Variable and methodology
2.1. Aggressive stock-selection opportunity
In Jiang et al. (2021), a stock-selection opportunity measurement is given by the
average of cross-sectional positive alphas. The alpha of a stock is estimated by
the CAPM model:
, = + (, − ,) + ,, (1)
where , − , is the market returns in excess of the risk-free interest rates. The
daily returns for each month are used to estimate the above parameters. Drawing on
the setting of Jiang et al. (2021), we further introduce an aggressive stock-selection
opportunity (ASSO) measure. When investors capture investment opportunities by the
positive alphas of stocks, aggressive investors among them may be more concerned
with an upper limit of investment opportunities. Therefore, considering the positive
alpha plus the idiosyncratic volatility is a potential way to capture an aggressive
opportunity. Specifically, if stock has a positive alpha, an aggressive investment
opportunity for stock is given by its alpha plus its idiosyncratic volatility, where the
idiosyncratic volatility is the standard deviation of the residual term , in equation
(1). Thus, the ASSO for the whole market is the average of the aggressive investment
opportunities of individual stocks. Compared with the average positive alpha of
individual stocks of Jiang et al. (2021), our ASSO is also calculated based on the
same stocks with a positive alpha, but using an aggressive opportunity. To remove the
trend term of ASSO, we perform first-order difference processing on ASSO, that is,
- 7 -
the change in aggressive stock-selection opportunity ( ) is
= − −1. (2)
In particular, the average of the idiosyncratic volatility of individual stocks is an
alternative proxy for the stock-selection opportunity in Jiang et al. (2021). We also
discuss the unique role of in predicting stock market returns.
Stock sector indices provide a good overview of stock-selection opportunities in
the market. We use the data of 49 industry portfolios and market factors from the
website of Kenneth R. French
1
to calculate the alphas and idiosyncratic volatilities of
individual industries, then calculate market-level . In addition, 14 traditional
predictive variables of Welch and Goyal (2008) are also introduced for predicting
market returns.
2.2. Methodology
The univariate and bivariate predictive regressions are
+1 = + ·x + +1, (3)
+1 = + · + ·, + +1, (4)
respectively, where is stock market excess returns, is a predictor of interest
including , , is one of the macro predictors, and +1 is the residual
term. The independent variables are standardized, and the market return is annualized
by multiplying by 12. The direction and significance of the estimated show the
predictor’s impact and predictive power. The corresponding t-values are adjusted by
1
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
- 8 -
the Newey and West (1987) method.
The out-of-sample evaluation is necessary to examine the predictive performance
of predictors (Wang et al. 2016; Wang et al. 2019a). We conduct the recursive
estimation window method to yield forecasts (Campbell & Thompson 2008), and the
initial M months for estimating the first batch of parameters is 240 (Wang et al.
2019b). The sample period spans from 1963-09 to 2021-12, and there are 700
observations. The out-of-sample spans from 1983-09 to 2021-12.
We evaluate the out-of-sample performance of models by the out-of-sample
R-squared, where the benchmark model is the historical average of stock returns
(Campbell & Thompson 2008), specifically:
2 = 1 −
∑ (̂−)
2
=+1
∑ (̅−))2
=+1
, (5)
where ̂, , and ̅ are the model forecast, true market return, and historical return
average, respectively. The MSFE-adjusted statistic of Clark and West (2007) is used
to evaluate the significance of
2 .
Furthermore, from the perspective of economic value, referring to Campbell and
Thompson (2008), the return of the optimal portfolio with two assets (stock index and
risk-free asset) in a mean-variance utility framework is
̂,+1 =
∗ ⋅ r+1 + r,+1, (6)
where the optimal weight
∗ of holding risk asset is
̂+1
̂+1
2 , ̂+1 is the forecast of
market excess return, ̂+1
2 is the variance of returns over the past 60 months (Wang
et al. 2019b), and is a risk aversion factor set by 3 (Rapach et al. 2010). Due to the
short-selling restrictions,
∗ is constrained between 0 and 1.5 (Neely et al. 2014;
- 9 -
Wang et al. 2019b). Following Wang et al. (2019b), we further evaluate the
performance of portfolios by the certainty equivalent return (CER) and Sharpe ratio
(SR) are introduced. And the CER and SR gains are the difference between the CER
and SR of the portfolio of interest and the CER and SR of the portfolio based on the
average of historical returns, respectively2.
3. Empirical results
We forecast monthly excess returns of the S&P 500 index. We obtain predictors
and index returns from the website of Amit Goyal
3
, and obtain the data of industry
portfolios and market factors from the website of Kenneth R. French
4
, where the
period of market factors data starts from 1963-07. Considering all available data, the
entire sample period for the empirical analysis is from 1963-09 to 2021-12 with 700
observations. Descriptive statistics of our variables are shown in Table 1.
Insert Table 1 about here
Insert Figure 1 about here
3.1. In-sample estimations
The estimation results of univariate models are shown in Table 2, and we find that
has a significant and negative coefficient of -0.058 for the next-month
2
The annualized economic values are SR and CER gains multiplied by √12 and 1200.
3
http://www.hec.unil.ch/agoyal/
4
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
- 10 -
market returns. The negative coefficient indicates that the aggressive stock-selection
opportunity negatively results in future market returns. A potential reason is that when
investors capture this aggressive opportunity, they may overreact to it and then their
aggressive trading activities result in high market uncertainty and high illiquidity.
Moreover, explains the most variance of future market returns among
all 15 predictors supported by the highest in-sample R-squared 1.248%. Among 14
macroeconomic variables, only 5 predictors show a significant predictive impact on
stock market returns, including TBL, LTY, TMS, LTR, and INFL. These estimations
simply illustrate the powerful predictive role of in the predictability of
stock market returns.
Insert Table 2 about here
To further identify the unique predictive information of , Table 3
presents the in-sample results of bivariate models conducted by two regressors of
and one of the macro predictors. The results show that still
possesses significantly negative coefficients in all bivariate models, consistent with
the findings of the univariate model of . Moreover, these coefficients of
are very stable around -0.058 with little deviation, which directly
demonstrates the predictive information obtained from is independent of
that of the 14 macroeconomic variables. In addition, the bivariate model based on
and TBL has an in-sample R-squared of 2.151%, which is the highest
- 11 -
among all 14 bivariate models.
Overall, the in-sample results show has unique predictive information
in forecasting stock market returns.
Insert Table 3 about here
3.2. Out-of-sample performance
In Panel A of Table 4, we present the out-of-sample forecasting results. The
univariate predictive model based on has a significant and positive oos
2 of
0.890%, a positive CER gain of 2.494 and SR gain of 0.277, which are the highest
economic values among these univariate models. For the other predictors, only TBL
and LTY yield significant oos
2 . In Panel B, almost all of these bivariate models with
bring significant oos
2 values and positive economic values.
Comprehensively summarizing the results of Table 4, we find that introducing
improves the forecasting performance of predictive models.
Insert Table 4 about here
To test the independent predictive information of , we compare a
forecast combination of bivariate models with and a combination of
univariate models without . We have 4 forecasting combination models
- 12 -
(Zhang et al. 2020): Equal-weighted combination (EWC), trimmed mean combination
(TMC), and two combination models based on the discounted MSPE (DMSPE) of
Stock and Watson (2004), that is, DMSPE models with discount ratios of 1 and 0.9.
Table 5 presents the out-of-sample results for forecasting combinations. Across the
four combination methods, the forecasting combination of bivariate models with
show significantly positive oos
2 and positive economic values but the
forecasting combination of univariate models without does not.
In short, the unique predictive information obtained from is supported
from the out-of-sample perspective.
Insert Table 5 about here
4. Robustness check
4.1. Economic constraint
Campbell and Thompson (2008) document that many predictors in the literature
cannot beat the historical mean of returns. The CT truncation rule of Campbell and
Thompson (2008) limits the return forecasts to be greater than zero. We also apply the
CT truncation rule to our forecasts and further test the forecasting accuracy of the
model based on .
In Table 6, we report the oos
2 of the forecasts based on the CT truncation rule
for 15 univariate models and 14 bivariate models. The CT forecasts of the univariate
- 13 -
model based on obtain a significantly positive oos
2 of 1.587% which is
even higher than the oos
2 by the raw forecasts without truncation. Most of the
bivariate models have significant oos
2 excluding the model based on and
SVAR that still has improvement in forecasting performance beyond the univariate
model of SVAR. On the whole, applying the CT rule does not affect the significance
of the forecasting performance of but enhance the predictive accuracy.
Insert Table 6 about here
4.2. Trading cost
One may concern about the effect of transaction cost on the profits of investment
strategies. Following Anderson et al. (2012) and Byun et al. (2018), we examine the
impact of the transaction cost. Two trading cost ratios are considered: c = 0.1% (Byun
et al. 2018), and c = 0.2%. We report the economic values of portfolios in Table 7.
The results further shed light on the predictive performance of under the
actual situation with trading costs.
Insert Table 7 about here
- 14 -
5. Discussion
5.1. The potential economic channel for the predictive role of
The aggressive stock-selection opportunities capture investors' aggressive trading
behavior that may lead to excess trading volume or increase market volatility, then
affect market returns. To address this issue, we perform the following regressions:
SVAR = + ∑ 1 ⋅ SVAR−
1
=1 + + −1 + , (7)
= + ⋅ SVAR + , (8)
and
AVOL = + ∑ 1 ⋅ AVOL−
2
=1 + + −1 + , (9)
= + ⋅ AVOL + , (10)
where SVARt is short-term market volatility, AVOLt is the abnormal trading volume
of the S&P 500 index by the current trading volume divided by the average trading
volume over the past 12 months, and is the residual term. The lag terms are
determined by the AIC rule, specifically, 3 lags for SVAR and 1 lag for AVOL.
We show the regression results in Table 8, and the risk channel is supported and
the trading channel is half successful. Specifically, both the contemporaneous and
lagged have a significant impact on SVAR. Moreover, the relation between
SVAR and market return over the same period is significant and negative which is
consistent with previous studies regarding the complex volatility-return relation, such
as Glosten et al. (1993), Bekaert and Wu (2000), and Jin (2017). These impact
directions are consistent, that is, the positive -SVAR predictive relation and
- 15 -
the negative SVAR-return contemporaneous relation result in the negative
-return predictive relation. From the market volatility perspective, the evidence
shows the potential transitive relationship among the three items of , market
volatility, and market returns.
For the trading activities channel, although the does significantly
increase market trading volume, the latter does not have a significant impact on
market returns over the same period.
In short, our evidence supports the risk channel for the predictive role of
, that is, the change in the aggressive stock-selection opportunities increases
future stock market volatility and then negatively impacts future market returns.
Insert Table 8 about here
5.2. Comparing stock-selection opportunity measurements: The
success of comes from its aggressive angle
One may concern whether the original SSO measurement of Jiang et al. (2021)
has a predictive role on stock market returns. In Table 9, our in-sample results show
the raw SSO cannot significantly affect market returns and the change of SSO
( ) has a weak significant and negative coefficient. Here we also report how
the ASSO affects the subsequent market returns, and we find the absence of a
significant coefficient for ASSO. The result indicates that , the detrended
- 16 -
measurement, is more suitable and sensitive to predicting market returns than the raw
form of ASSO. Comparing the results between and , we find that
the aggressive stock-selection opportunities in the market have stronger predictive
information for market returns rather than the moderate stock-selection opportunities
(e.g. SSO).
Furthermore, our is constructed by the information of positive alphas
and idiosyncratic volatilities (residual volatilities) of individual stocks. A direct
conjecture to one is that the predictive information could be due to the idiosyncratic
volatilities of stocks. In Jiang et al. (2021), the average of idiosyncratic volatilities
( ) of individual stocks also could be suitable as a proxy for stock-selection
opportunities. We also examine the impacts of and the change form
on future market returns. Our results show there are no significant coefficients and
small in-sample R-squared values close to zero for these two measurements. In short,
we demonstrate the unique predictive role of by excluding the potential
predictive power of the average of positive alphas and the average of idiosyncratic
volatilities.
Insert Table 9 about here
6. Conclusion
We define a measurement of aggressive stock-selection opportunity (ASSO) and
- 17 -
find that the change of aggressive stock-selection opportunity ( ) has powerful
and unique predictive information for stock market returns. Compared with the
original measure of stock-selection opportunity (SSO) by the average positive alphas
in Jiang et al. (2021), our ASSO is the average of the positive alphas plus the
idiosyncratic volatilities of cross-sectional individual stocks. Our empirical evidence
in the US stock market supports the unique role of in predicting stock
market returns. Moreover, the predictive impact of is not due to the
individual predictive impacts of the average of positive alphas and the average of
idiosyncratic volatilities. This indicates the effectiveness of the distinctive definition
in . Our study is helpful for investors to improve their trading strategies and
portfolio management. In our future work, we will further study the stock-selection
issues, such as the impact of stock-selection risk on stock market returns, and how
investors trade-off between stock-selection risk and opportunity.
Conflict of Interest
We declare that there is not conflict of interest.
- 18 -
References
1) Anderson, R.M., Bianchi, S.W., Goldberg, L.R., 2012. Will My Risk Parity
Strategy Outperform? Financial Analysts Journal 68, 75-93
2) Baker, S.R., Bloom, N., Davis, S.J., 2016. Measuring economic policy
uncertainty. Quarterly Journal of Economics 131, 1593-1636
3) Bekaert, G., Wu, G., 2000. Asymmetric Volatility and Risk in Equity Markets.
The Review of Financial Studies 13, 1-42
4) Bollerslev, T., Marrone, J., Xu, L., Zhou, H., 2014. Stock return predictability and
variance risk premia: Statistical inference and international evidence. Journal of
Financial and Quantitative Analysis 49, 633-661
5) Byun, S.J., Frijns, B., Roh, T.Y., 2018. A comprehensive look at the return
predictability of variance risk premia. Journal of Futures Markets 38, 425-445
6) Campbell, J.Y., Thompson, S.B., 2008. Predicting excess stock returns out of
sample: Can anything beat the historical average? Review of Financial Studies 21,
1509-1531
7) Campbell, J.Y., Vuolteenaho, T., 2004. Bad beta, good beta. American Economic
Review 94, 1249-1275
8) Chen, J., Jiang, F.W., Tong, G.S., 2017. Economic policy uncertainty in China
and stock market expected returns. Accounting and Finance 57, 1265-1286
9) Clark, T.E., West, K.D., 2007. Approximately normal tests for equal predictive
accuracy in nested models. Journal of Econometrics 138, 291-311
10) Dai, Z.F., Zhou, H.T., Kang, J., Wen, F.H., 2021. The skewness of oil price
returns and equity premium predictability. Energy Economics 94
11) Glosten, L.R., Jagannathan, R., Runkle, D.E., 1993. On the Relation between the
Expected Value and the Volatility of the Nominal Excess Return on Stocks. The
Journal of Finance 48, 1779-1801
12) Goyal, A., Welch, I., 2003. Predicting the equity premium with dividend ratios.
Management Science 49, 639-654
13) Guo, H., 2006. Time-varying risk premia and the cross section of stock returns.
- 19 -
Journal of Banking & Finance 30, 2087-2107
14) He, M.X., Zhang, Y.J., Wen, D.Y., Wang, Y.D., 2021. Forecasting crude oil prices:
A scaled PCA approach. Energy Economics 97
15) Jiang, G.J., Zaynutdinova, G.R., Zhang, H., 2021. Stock-selection timing. Journal
of Banking & Finance 125, 106089
16) Jin, X., 2017. Time-varying return-volatility relation in international stock
markets. International Review of Economics & Finance 51, 157-173
17) Lewellen, J., 2004. Predicting returns with financial ratios. Journal of Financial
Economics 74, 209-235
18) Liu, L., Ma, F., Wang, Y.D., 2015. Forecasting excess stock returns with crude oil
market data. Energy Economics 48, 316-324
19) Neely, C.J., Rapach, D.E., Tu, J., Zhou, G.F., 2014. Forecasting the Equity Risk
Premium: The Role of Technical Indicators. Management Science 60, 1772-1791
20) Newey, W.K., West, K.D., 1987. A Simple, Positive Semi-definite,
Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.
Econometrica 55, 703-708
21) Rapach, D.E., Strauss, J.K., Zhou, G., 2010. Out-of-sample equity premium
prediction: Combination forecasts and links to the real economy. Review of
Financial Studies 23, 821-862
22) Stock, J.H., Watson, M.W., 2004. Combination forecasts of output growth in a
seven-country data set. Journal of Forecasting 23, 405-430
23) Wang, X., 2020. Frequency dynamics of volatility spillovers among crude oil and
international stock markets: The role of the interest rate. Energy Economics 91,
104900
24) Wang, Y., Diao, X., Pan, Z., Wu, C., 2019a. Heterogeneous beliefs and aggregate
market volatility revisited: New evidence from China. Pacific-Basin Finance
Journal 55, 127-141
25) Wang, Y.D., Ma, F., Wei, Y., Wu, C.F., 2016. Forecasting realized volatility in a
changing world: A dynamic model averaging approach. Journal of Banking &
Finance 64, 136-149
- 20 -
26) Wang, Y.D., Pan, Z.Y., Liu, L., Wu, C.F., 2019b. Oil price increases and the
predictability of equity premium. Journal of Banking & Finance 102, 43-58
27) Welch, I., Goyal, A., 2008. A comprehensive look at the empirical performance of
equity premium prediction. Review of Financial Studies 21, 1455-1508
28) Zhang, Y., Ma, F., Liao, Y., 2020. Forecasting global equity market volatilities.
International Journal of Forecasting 36, 1454-1475
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Tables and Figures
Table 1. Descriptive statistics
Variables Mean. Std Skewness Kurtosis
0.325% 4.295% -0.452 1.826
0.112% 22.197% 0.394 3.417
DP 2.863% 1.161% 0.664 -0.340
DY 2.880% 1.166% 0.668 -0.329
EP 6.229% 2.704% 1.093 0.835
DE -3.366% 1.789% -0.669 1.373
SVAR 0.225% 0.509% 10.134 124.375
BM 0.477 0.263 0.887 -0.205
NTIS 0.888% 1.996% -0.507 -0.048
TBL 4.505% 3.263% 0.649 0.631
LTY 6.285% 2.878% 0.499 0.008
TMS -1.780% 1.470% 0.263 -0.288
LTR 0.614% 2.988% 0.411 2.328
DFY 1.025% 0.443% 1.733 4.388
DFR 0.025% 1.532% -0.680 7.377
INFL 0.316% 0.359% -0.039 3.066
Notes: is the market returns excessed the risk-free interest. The sample period spans from
1963-09 to 2021-12 with 700 observations.
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Table 2. Univariate models: +1 = + ·x + +1
Model t-stat
2( )
-0.058** -2.513 1.248
DP -0.002 -0.100 0.002
DY -0.001 -0.044 0.000
EP -0.004 -0.163 0.005
DE 0.004 0.177 0.007
SVAR -0.011 -0.234 0.042
BM -0.017 -0.768 0.108
NTIS -0.022 -0.932 0.179
TBL -0.049** -2.446 0.920
LTY -0.038* -1.894 0.556
TMS -0.034* -1.706 0.448
LTR 0.047** 2.244 0.825
DFY 0.020 0.732 0.147
DFR 0.024 0.777 0.223
INFL -0.043* -1.875 0.699
Notes: The sample period spans from 1963-09 to 2021-12 with 700 observations.
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Table 3. Bivariate models: +1 = + · + · + +1
Model t-stat t-stat
2( )
& -0.058** -2.515 -0.003 -0.118 1.250
& -0.058** -2.515 -0.001 -0.068 1.249
& -0.058** -2.510 -0.003 -0.151 1.252
& -0.057** -2.507 0.004 0.150 1.253
& -0.059*** -2.958 0.006 0.133 1.260
& -0.058** -2.520 -0.017 -0.789 1.360
& -0.058** -2.513 -0.022 -0.990 1.437
& -0.057** -2.498 -0.049** -2.450 2.151
& -0.058** -2.540 -0.039* -1.920 1.811
& -0.057** -2.450 -0.033* -1.659 1.657
& -0.058** -2.550 0.047** 2.267 2.089
& -0.057** -2.474 0.018 0.676 1.375
& -0.056** -2.506 0.019 0.615 1.385
& -0.057** -2.487 -0.043* -1.888 1.942
Notes: T The sample period spans from 1963-09 to 2021-12 with 700 observations.
- 24 -
Table 4. Out-of-sample results
Model R
2 ( ) CER gain SR gain
Panel A. Univariate models: +1 = + ∙ + +1
0.890** 2.494 0.277
DP -0.790 -0.334 -0.076
DY -0.818 -0.279 -0.069
EP -0.297 0.119 0.015
DE -0.259 -0.065 -0.007
SVAR -3.884 -0.110 -0.014
BM -0.365 -0.669 -0.026
NTIS -0.695 -1.667 -0.049
TBL 0.540** -0.006 0.099
LTY 0.521** 0.372 0.087
TMS -0.989 -2.652 -0.121
LTR -0.709 -0.551 0.026
DFY -1.018 -1.953 -0.207
DFR -0.487 0.932 0.131
INFL -0.116 0.231 0.104
Panel A. Bivariate models: +1 = + · + · + +1
& 0.128* 1.492 0.184
& 0.077* 1.379 0.172
& 0.600** 1.884 0.220
& 0.631** 1.989 0.228
& -3.170 1.594 0.191
& 0.557** 2.365 0.260
& 0.201** 2.022 0.227
& 1.405*** 3.925 0.369
& 1.423*** 3.545 0.354
& -0.152** 0.623 0.132
& 0.320** 1.581 0.191
& -0.119* 1.800 0.210
& 0.251* 2.316 0.261
& 0.713*** 3.599 0.346
Notes: The significance of the out-of-sample R
2 is based on Clark & West's (2007)
MSFE-adjusted statistic. The sample period spans from 1963-09 to 2021-12 with 700 observations.
The out-of-sample period is from 1983-09 to 2021-12.
- 25 -
Table 5. Forecast combination results
2 ( ) CER gain SR gain
Panel A. The combination of univariate models without A
U-EWC 0.000 -0.717 -0.067
U-TMC 0.014 -1.077 -0.093
U-DMSPE (1) 0.007 -0.743 -0.069
U-DMSPE (0.9) 0.013 -0.725 -0.067
Panel B. The combination of bivariate models with A
B-EWC 0.836** 2.691 0.290
B-TMC 0.890** 2.721 0.291
B-DMSPE (1) 0.838** 2.704 0.291
B-DMSPE (0.9) 0.837** 2.690 0.289
Notes: The significance of the out-of-sample R
2 is based on Clark & West's (2007)
MSFE-adjusted statistic. The sample period spans from 1963-09 to 2021-12 with 700 observations.
The out-of-sample period is from 1983-09 to 2021-12.
- 26 -
Table 6. Robustness checks: Forecasts based on the CT truncation rule
Univariate models R
2 ( ) Bivariate models R
2 ( )
1.587***
DP -0.231 & 1.174**
DY -0.241 & 1.103**
EP 0.014 & 1.465***
DE 0.004 & 1.463***
SVAR -1.450 & -0.470
BM 0.058 & 1.491***
NTIS -0.306 & 1.211***
TBL 0.714** & 1.661***
LTY 0.706** & 1.894***
TMS -0.813 & 0.373**
LTR -0.128 & 1.023**
DFY -0.400 & 0.894**
DFR -0.035 & 1.112**
INFL -0.104 & 1.273***
Notes: The significance of the out-of-sample R
2 is based on Clark & West's (2007)
MSFE-adjusted statistic. The sample period spans from 1963-09 to 2021-12 with 700 observations.
The out-of-sample period is from 1983-09 to 2021-12.
- 27 -
Table 7. Robustness checks: Trading cost
Models c = 0.1% c = 0.2%
CER gain SR gain CER gain SR gain
1.979 0.229 1.463 0.180
DP -0.333 -0.077 -0.332 -0.077
DY -0.279 -0.070 -0.279 -0.071
EP 0.117 0.015 0.115 0.014
DE -0.068 -0.008 -0.071 -0.008
SVAR -0.177 -0.024 -0.245 -0.033
BM -0.692 -0.027 -0.714 -0.028
NTIS -1.721 -0.052 -1.775 -0.055
TBL -0.044 0.097 -0.082 0.096
LTY 0.353 0.086 0.335 0.086
TMS -2.744 -0.127 -2.836 -0.133
LTR -0.961 -0.005 -1.373 -0.036
DFY -1.975 -0.209 -1.996 -0.211
DFR 0.751 0.106 0.568 0.082
INFL -0.072 0.084 -0.375 0.064
& 1.094 0.143 0.695 0.102
& 0.983 0.131 0.585 0.090
& 1.398 0.173 0.910 0.126
& 1.472 0.180 0.954 0.131
& 1.096 0.144 0.596 0.096
& 1.858 0.215 1.348 0.169
& 1.522 0.190 1.021 0.154
& 3.323 0.325 2.720 0.281
& 3.015 0.311 2.483 0.267
& 0.048 0.093 -0.529 0.053
& 0.992 0.145 0.400 0.099
& 1.357 0.169 0.912 0.127
& 1.808 0.213 1.298 0.164
& 2.977 0.300 2.352 0.253
Notes: The sample period spans from 1963-09 to 2021-12. The out-of-sample period is from
1983-09 to 2021-12.
- 28 -
Table 8. Discussion results: The economic channel for the predictive role of
Intercept 0.039** 0.225*** 0.039** 1.055***
t-stat (2.127) (14.611) (1.981) (267.471)
-0.157***
t-stat (-6.186)
−1 0.154**
t-stat (2.556)
−2 0.085***
t-stat (3.024)
−3 0.051***
t-stat (3.358)
0.024
t-stat (0.840)
−1 0.102***
t-stat (22.916)
0.222*** 0.071***
t-stat (2.735) (11.525)
−1 0.118** 0.012**
t-stat (2.423) (2.248)
2( ) 9.251 32.835 0.226 52.768
Notes: The sample period spans from 1963-09 to 2021-12.
- 29 -
Table 9. The predictive role of other related stock-selection opportunity variables
Univariate models t-stat
2( )
-0.033 -1.575 0.410
-0.001 -0.021 0.000
-0.027 -1.013 0.270
-0.034* -1.831 0.448
-0.014 -0.480 0.076
-0.058** -2.513 1.248
Notes: The sample period spans from 1963-09 to 2021-12 with 700 observations.
- 30 -
Figure 1. Stock market excess returns and the change of aggressive stock-selection opportunity
