Download Economic Value of Stock Return Forecasts: An

Economic Value of Stock Return Forecasts:
An Assessment on Market Efficiency
and Forecasting Accuracy
Jing Tian
∗
Abstract
This article explores the economic values of forecasts of stock returns in
both emerging and developed stock markets for an investor in an emerging
country. The investor is assumed to allocate her assets between one developed
stock market, the domestic emerging stock market, and the local short-term
bond market, according to her forecasts of excess stock returns in the two
stock markets. She uses a recursive forecasting approach, and we assume that
she adjusts her forecasting models when new information is publicly available,
switching her asset portfolios across three assets according to a simple trading
rule. The mixed results of both positive and negative net economic benefits in
excess of returns under buy-and-hold strategies, obtained by the investor who
follows our forecasting rule, cannot be used to disprove the efficient market
hypothesis. This paper emphasizes the tight link between decision-making and
forecasting evaluation in a situation in which economic profit is an appropriate
measurement for forecast accuracy.
Keywords: stock return forecasts, emerging stock markets, efficient market hypothesis,
forecast evaluation, market timing, economic measurements.
JEL code: C22, C53, G11.
∗
Correspondence to: Jing Tian, School of Economics, College of Business and Economics,
The Australian National University, ACT, 0200, Australia. Phone: 61-2-61256126. Email:
[email protected]. The author is grateful for the insight comments from Heather Anderson, Farshid Vahid and Martin Richardson from School of Economics, ANU and Tom Smith from
School of Finance and Applied Statistics, ANU.
1
1
Introduction
The predictability of stock returns has been a major issue in empirical finance since Kendall
(1953) suggested that future short-term stock-exchange movement is almost impossible to
forecast without extraneous information. Associated with the random-walk movement of
stock prices observed in early works, the efficient market hypothesis (EMH) was based
on the idea that unlimited economic profits would be generated if one could successfully
predict stock returns constantly. Extended from the study of the evolution of returns
based on its own historical information, a large amount of literature recently focuses on
the predictability of stock returns based on state variables that can reveal the evolution
of financial markets and the macro economy. With the usage of U.S. and international
data, financial variables such as dividend yield, earning price ratio, different types of
interest rates and macroeconomic variables such as aggregate-wealth ratio, inflation rate,
and aggregate output are widely found to have predictive power for the variations of excess
stock returns1 .
However, the evidence of the predictability of stock returns shown in many of the
previous studies only comes from the statistical significance found by using developed
econometric techniques. To disprove EMH, those evidence from statistical tests is far less
than sufficient. Jensen (1978) gives a comprehensive definition of market efficiency as:
“A market is efficient with respect to information set Ωt if it is impossible to make economic
profits by trading on the basis of information set Ωt .”.
This definition points out that to examine the EMH, looking at the economic profits generated from trading in the markets based on an information set is a more appropriate
approach than the statistical significance. Therefore, in this paper, we discuss the predictability of stock returns in the perspective of the economic profits produced by the
forecasts.
We also consider that the purpose of forecasts of stock returns in the real world by
speculators is to earn economic returns. It follows that forecasting evaluation has to be
linked with realized economic profits from forecasts and investment decisions based on
those forecasts. However, in the academic literature, economic forecasting evaluation has
still been dominated by statistical measures of accuracy, rather than economic measurements. Hence in this paper, by exploring the economic profits of different investments
derived from different sets of forecasts, we demonstrate the importance of using economic
measures for evaluating forecasting techniques.
1
For example, Campbell and Thompson (2005), Campbell and Shiller (1988a), Fama and French
(1988), Hjalmarsson (2004), among others.
2
Only a few researchers have worked on the economic values of the predictable stock
returns. Breen et al. (1989) found that the negative relationship between nominal interest
rate and stock returns can be utilized by a fund manager to shift her portfolio between
market index of stocks in the New York Stock Exchange and treasury bills, earning returns worth an annual management fee. Pesaran and Timmermann (1995) show that the
predictability of S&P 500 stock returns can guide an investor to switch the asset holdings
between market portfolio and treasury bill, and exploit net profits over a buy-and-hold
strategy. An extended version based on this paper with the application on the UK stock
returns has also been done by Pesaran and Timmermann (2000). The investors, in these
papers, commonly switch their portfolios between one stock market portfolio and a shortterm treasury bill in their local developed markets, according to one set of forecasts on
excess stock returns in each period.
In this paper, we fit the structure of investors’ portfolio into a more realistic environment for modern investments. Since developing countries started financial liberalization
that enables capital to flow into and out of other countries, emerging markets have attracted both investors and academics. With the evidence of low correlations between
emerging countries’ stock returns and developed countries’ stock returns, one can expect
that participation in both markets would diversify the portfolio risk and increase the
chance of higher returns. Harvey (1995) and Bekaert and Urias (1996) find that portfolio
opportunities do significantly improve with adding emerging market assets. In the real
world, many fund managers are holding global equities for good investment performance.
Hence, it would be more realistic to assume that a profit-pursuing investor’s portfolio comprises a fixed income, stocks in developed markets and stocks in emerging markets. After
extending the components of asset holdings, the investor now operates two sets of forecasts
for excess returns of stocks in both emerging and developed markets. Instead of focusing
on one developed stock market, we address whether stocks returns from both emerging
and developed markets are predictable in terms of gaining net profits for investors.
This set-up also brings complication to investors’ decision-making process. The choice
of asset-holdings made by an investor does not only depend on whether she obtains positive
or negative forecasts of excess stock returns. If both forecasts of stock returns in emerging
and developed markets are positive, the investor needs to compare the magnitudes of two
sets of forecasts and decides the holdings on stocks. If we link the decision-making with
forecasting evaluation as suggested in Granger and Pesaran (2000), then the market timing
tests2 for the accuracy of forecasts are not sufficient for evaluating forecasts in this case.
2
See Henriksson and Merton (1981) and Pesaran and Timmermann (1992a).
3
A new test focusing on the correct relative size of predictions is required, and we expect
this test will be discussed in a later chapter in my thesis.
In this paper the investor is assumed to be located in Thailand. Her portfolio decision
will be made between Thai saving deposits, stocks in Thailand and stocks in the U.S..
Recursive investment decisions are simulated according to the predictions of excess stock
returns on both markets with a recursive forecasting rule. The investor faces model uncertainty in terms of the choices of predictors, the specifications of predictive models and
the best forecasts. Hence, at each particular time, based on the available information, the
investor needs to utilize model selection criteria to choose the preferred forecasting model
among all possible specifications. With the assumption that the investor is fully confident
in her forecasts of excess stock returns for the next month, she switches her 100% holdings
across three assets based on her forecasts. To see whether excess stock returns are predictable to generate economic profits, we compare the final wealth calculated according to
our portfolio decisions to the wealth based on some buy-and-hold strategies. Timmermann
and Granger (2004) argue that to invalidate the EMH transaction costs should be covered
by predictable patterns. Therefore, we consider transaction costs when making trading
decisions and computing economic returns of the investments.
The paper is organized as follows. Section 2 explains the investor’s prior choice of
the base set of regressors in the models for both markets, and provides a brief review
of relevant literatures. The trading and recursive modelling strategies are discussed in
Section 3. Section 4 describes the empirical results, followed by a brief conclusion in
Section 5.
2
The Base Set of Predictors
In this section, the choice of forecasting regressors that are considered by the investor is
discussed. Investors only choose candidates predictors that can be accessed ex ante, since
we attempt to undertake the exercise in “real time”. Based on her knowledge or prior
belief, as well as the public information available to her before the investment decision has
been made, the investor includes variables, which she believes to have certain power to
explain the variation of the excess stock returns in each stock market, into her base set.
Formal model selection criteria will help her choose specific variables among candidates
to forecast stock returns in each time. We focus on investor’s prior belief on the sets of
regressors to forecast excess stock returns of both emerging and developed markets in this
section. The second step of regressor-selection associated in the model specification will
4
be discussed in details in the next section.
It has been well documented that the predictability of stock returns can be identified
based on models constructed with lagged financial and macroeconomic variables. Among
financial variables, dividend yield is used as a popular proxy to the time-variance of expected stock returns. Fama and French (1988), for instance, estimate the portfolio returns
of different horizons to the NYSE index by using dividend yields. They find that the variances of long horizon expected returns can be substantially explained by dividend yields
due to the negative relationship between price-dividend ratios and expected returns with
discount rates. Campbell and Shiller (1988a) argue that if a stock is underpriced compared with its fundamental value such as dividend, returns tend to be high consequently.
Another so called price-ratio variable reported to predict stock returns is the earning yield
(see Campbell and Shiller (1988b) and Campbell and Shiller (1988a)). However, it should
be noted that recently a few papers have questioned the predicting power of these highly
persistent price-ratio variables by applying advanced econometrics techniques3 . Several
methodologies aiming at an appropriate correction on the bias caused by highly persistent
regressor have been proposed in some papers4 , but there is still no convincing evidence
on the predictive power of price-ratio variables. Overall, based on knowledge to these
literatures, the investor decides to count dividend yield and earning yield as potential
predictors to stock returns in both local emerging and foreign developed markets.
A few researchers have become interested in examining the relationship between trading volume and the future price changes. Ying (1966) finds a lead-lag pattern between
prices and volumes by looking at the S&P500 Composite Index and daily trading volume in the New York Stock Exchange, and suggests that dissociation from transaction
volumes when modelling stock price changes or vice versa is incomplete. Extending her
study, Gervais and Mingelgrin (2001) and Chordia and Swaminathan (2000) focus on individual stocks and address the influence of trading volumes on subsequent stock returns.
The intuition of predicting power of trading volume believed by the investor could be
that unusual transaction volumes might possibly attract investors’ attention and affect
investment decisions, resulting in the change of future stock prices.
Short-term interest rate is also expected to have a negative relationship with excess
stock returns and will be taken as another potential regressor. Predicting power from
short-term interest rates has been shown in many empirical works. For instance, Ang
and Bekaert (2001) uses a present value model with earning growth, payout ratios and
3
4
See Elliot and Stock (1994), Stambaugh (1999) and Nelson and Kim (1993).
See Goetzmann and Jorion (1993), Lewellen (2004), Campbell and Hamao (1992).
5
short rate as states variables to examine the predictability of stock returns. Working with
international data, they show that the short rate is the only robust predictor for short-run
stock returns.
There is also a belief that macroeconomic indicators have an impact on the movement
of stock prices. The investor chooses the change of narrow money supply in the base set of
predictors because she hypothesizes that the unexpected variations of the growth rate of
money supply will affect the stock holdings in investors portfolios, resulting in the changes
of stock prices. The negative relationship between inflation and stock returns has also
been studied extensively, which leads the investor to make the inflation rate as one of the
potential predictors.
If the variation of returns on emerging stock are explained only by local information,
the intuition is that the emerging stock market is segmented from the world markets
(Harvey, 1995). Under our assumption that the emerging stock market stock market is
imperfectly integrated with developed markets, variables that contain information from
the developed market might have predictive power for excess returns on the emerging
market. For example, Hjalmarsson (2004) examines the U.S. effect on international stock
returns and finds short-run predictive ability of the U.S. interest rates in many countries.
Therefore, the rate of U.S. 3-month treasury bill is one of the predictor candidates.
Another issue on the choice of regressors is the number of lags of the predictors.
We assume that the investor is interested in the most recent information. Hence, only
one lagged data will be considered for each variable. Based on the fact that monthly
macroeconomic data are released 1 month later than the financial data, the investor who
is collecting available public information from both countries at each time will use a
1-month lag for financial indicators and 2-month lag for macroeconomic indicators. To
summarize, the base set of regressor for predicting excess returns on emerging stock market
contains 1-lagged dividend yield, 1-lagged earning yield, 1-lagged trading volume, 1-lagged
short-term interest rate, 2-lagged inflation rate, 2-lagged change of money supply, 1-lagged
change of exchange rate and 1-lagged short-term interest rate in the developed country;
except for the last two series, the base set of regressors for modelling developed market
excess stock returns includes 6 variables from the developed country.
6
3
Trading and Modelling Strategy
3.1
Switching Portfolio Strategy
The investor’s portfolio simulation combined with a recursive modelling and forecasting
strategy in this paper extends the method proposed in Pesaran and Timmermann (1995)
and Pesaran and Timmermann (2000). With free access to foreign capital markets, local
investors in emerging market are able to take assets from foreign markets into account.
We assume that the investor has a logarithmic utility function. Then a multiple-period
decision problem with log-utility can be reduced to many independent single-period decision problems. To maximize her utility over all investment periods, the investor should
choose the optimal portfolio for each individual period. In other words, instead of binding
with one particular portfolio all the time, she might change her asset-holdings between
stocks in the local emerging market, stocks in a developed market and a local risk-free
asset over time.
At time t, the investor uses the published information on the variables discussed in
the above section, and tries to forecast both the excess emerging stock market returns
and the excess developed stock market returns over the local risk-free return in t + 1,
respectively. With two sets of forecasts at time t, the decision-making process becomes
more complicated. If the forecasts of the excess domestic stock returns is positive and
greater (less) than the forecasts of the excess foreign stock returns, the investor, who is
fully confident in her forecasts, will decide to invest 100% of her wealth in the emerging
stock market (developed stock market) in the next period; otherwise, she prefers the local
risk-free asset. The same exercise is repeated at time t + 1 when information has been
updated and forecasts for t + 2 are pursued.
Since the magnitudes of forecasts of excess returns in both markets over returns of the
local risk free asset might be different over time, the investment decisions determined by the
relative magnitudes of forecasts and the signs of forecasts will change over time. Therefore,
the optimal portfolio is switching across the emerging stock market, the developed stock
market and the risk-free asset in the emerging country.
3.2
Model Selection Criteria and Recursive Forecasting Strategy
With the portfolio-switching trading strategy as well as return and utility maximization
over time, the investor needs to operate feasible modelling and forecasting strategies for
7
the portfolio switches. The standard approach is to set up a predictive model of oneperiod-ahead returns by using historical information and calculate future returns with
that fixed model specification. Timmermann and Granger (2004) criticize some versions
of definition of market efficiency for ignoring investors’ uncertainty about specifying forecasting models. They also point out that choosing forecasting models is a difficult task
for investors in reality. Hence, this paper considers large uncertainties about model specification. We suppose that the investor does not know the true data generating process
for excess stock returns and that she also does not have a strong belief in one particular
model specification, although she conjectures that the variation of excess stock returns
could be linearly explained well by the variables from the base sets 5 . Therefore, by the
end of every period, she will carry on individual estimations based on the past information
and undertake one-period-ahead forecasts from a model that might be different from the
one she used in the last period.
When the true data generating process is not known by the investor, it is common
that the investor’s predictive models will be misspecified. In the case of misspecification,
forecasts based on the estimators with a limited memory will often perform better than the
forecasts based on estimators obtained with an expanding sample window (Giacomini and
White, 2006). As one of the typical methods used to produce limited-memory estimators,
rolling-window estimations with fixed sample size T will be utilized by the investor. When
new information comes and she moves to the next period, she discards the oldest data and
includes the newest data to reestimate and forecast the excess stock returns.
Statistical methods are often implemented to select the relevant variables that have
explanatory power in forecasting models. A simple approach could be a conventional
t-test on individual regressors. However, highly persistent and unit-root nonstationary
explanatory variables such as the dividend yield or short-term interest rate as regressors,
imply that conventional t-tests or F-tests might be invalid. Focusing on this persistency
issue, many recent papers have proposed “efficient” tests of the stock returns predictability
with “valid” inference ( see Campbell and Yogo (2003) and Lewellen (2004)). However,
the robustness of these tests is still under debate. In this paper, we avoid having to correct
inferences by undertaking an alternative approach to specify the predictive models.
We let i = 1, 2 represent the emerging stock market and the developed stock market,
respectively. With Ki potential predictors, there are 2Ki possible sets of combinations of
5
In Pesaran and Timmermann (2000), they distinguish possible regressors by three types. Every
model starts with all core variables in set A, allowing new variables introduced from set B and C
into the predictive model. In our paper, we simply assume that the investor chooses predicting
variables from the same set of regressors in every period.
8
regressor candidates. Therefore, at the end of each month t, the investor estimates 2Ki
linear models for the one-period-ahead excess stock returns, for both the emerging market
and the developed market, by using ordinary least squares(OLS). For each model j, we
have
0
j = 1, 2, 3, ..., 2Ki
ERi,t = βi,j Xi,t−l,j + ui,t,j ,
l = 1, 2.
(1)
where Xi,t−l,j is a (ki,j + 1) × 1 vector, consisting of a subset of kj lagged regressors in the
model for excess stock returns in the market i. The OLS estimators are derived as
0
0
0
βi,t,j = (Xi,t−l,j Xi,t−l,j ) Xi,t−l,j ERi,t
(2)
Formal statistical model selection criteria assist the investor to find the “best” specification across 2Ki different models at each time. There are many selection criteria, both
statistical and non-statistical, that have been developed and applied for model specifications in literatures. Our investor will adopt some representatives that can function in nonnested model comparisons. R̄2 , Akaike’s Information Criterion (AIC) (Akaike, 1974), and
Schwarz’s Bayesian Information Criterion (BIC) (Schwarz, 1978), incorporate a trade off
between goodness-of-fit and the extent of parsimony in models, and are common choices.
Bossaerts and Hillion (1999) investigate a wide range of the statistical model selection
criteria when predicting stock returns. They comment on the validity of the Fisher’s
Information Criterion (FIC) and the Predictive Information Criterion (PIC) even when
predictors are nonstationary. At time t, after estimating model j for excess stock returns
in both emerging and developed markets, the investor calculates
T − 1 ESSi,j
,
T − ki,j T SSi,j
(3)
2ki,j
ESSi,j
)+
,
T
T
(4)
ESSi,j
ki,j ln(T )
)+
,
T
T
(5)
2
R̄i,j
=1−
AICi,j = ln(
BICi,j = ln(
0
F ICi,j
|Xi,j Xi,j |(T − ki,j )
T
ESSi
= ESSi,j
+
ln(
),
T − ki,j
T − Ki
ESSi,j
(6)
0
P ICi,j = ESSi,j
|Xi,j Xi,j |(T − Ki )
ESSi
− ESSi +
ln(
).
T − Ki
ESSi
9
(7)
0
0
where we define T as the estimation window size; ESSi,j = (ERi − β̂i,j Xi,j ) (ERi −
0
β̂i,j Xi,j ); ESSi is the sum of squared residuals (ESS) from the “full” model including all
¯ i )0 (ERi − ER
¯ i ).
Ki regressors; T SSi,j = (ERi − ER
For model criterion R̄2 , the investor chooses the model that maximizes the criterion
function to forecast excess stock returns in the next period. For the other criteria, the
next period forecasting model is the one whose criterion is the minimum.
Apart from statistical criteria, the investor also considers the “Sign Criterion” (SC)
(Pesaran and Timmermann, 1995), that keeps track of the proportion of correct signs
predicted by the model over the sample up to time t. We follow the two-step procedure proposed in Pesaran and Timmermann (1995). Firstly, the investor computes the
proportion of correct signs forecasted from model i at time t, given by
i
SCt,j
=
1
T
t
X
ˆ i,τ,j ) + (1 − I(ERτ ))(1 − I(ER
ˆ i,τ,j ))]
[I(ERτ )I(ER
(8)
τ =t−T +1
In this equation, I(ERi,τ ) = 1 if the realized excess stock returns at time τ = t in the
ˆ i,τ,j , the forecast obtained from
market i is positive, and zero otherwise. Similarly, if ER
ˆ i,τ,j ) will be 1,
the model j at time τ = t for the market i, is greater than zero, then I(ER
and zero otherwise. The investor ranks the 2Kj SCs at each time t, and selects the model
that generates the highest SC. When more than one model achieves the highest SC, the
forecasting model for excess return at t + 1 chosen using R̄2j .
4
Empirical Results
4.1
Data
In this study, we choose Thailand as the emerging stock market, and the investor is
located there. In addition to local stocks, she would also like to invest in one of the most
influential global stock markets, the U.S. stock market. The 1-month deposit in her bank
in Thailand will be treated as her risk free asset6 . All the data used in this paper come
from Thomson Financial Datastream. They are measured in local currency Thai Baht on
the last trading day of each month from 1993(01) to 2006(05). For both stock markets, the
total market return index RI including a discrete quantity of dividend paid is defined as
t
, where Pt is the price and Dt is the dividend payment. The Thai deposit
RIt = RIt−1 PPt +D
t−1
6
Note that the short-term treasury bill normally appears in the financial literature as the risk
free asset. We use bank deposits, because Datastream only started recording Thai 3-month treasury
bill returns from 2000, but we believe that this is a reasonable choice.
10
saving interest rate tds is taken as the midpoint between the bid and offered rates. Since it
measures annual returns for deposit savings, we transform it into monthly returns by using
1 + tdst = (1 + T DSt )12 , where T DS is the monthly Thai deposit saving rate and it will be
the returns from the risk free asset for the investor. Therefore the excess stock return in
terms of Thai Baht at time t can be calculated as ERi,t = ln(RIi,t )−ln(RIi,t−1 )−T DSt−1 ,
where i = 1, 2 represents Thai and U.S stock markets 7 . T DSt−1 denotes the return that
the investor can obtain at the end of this month t if she has money in the Thai bank at
the end of month t − 1. Observing that the interest rate of Thailand deposit saving is very
invariant, we use the 1-month Bangkok interbank interest rate measured with the offered
rate as a potential predictor for excess returns on Thai stocks over the Thailand deposit
saving rate. The rate of return of 1-month Treasury Bill in U.S. is a possible predictor
in the U.S. model. In Datastream, the dividend yield is expressed as the anticipated
annualised dividends per share in the following 12 months over the current share price.
Similarly, the earning yield ratio is computed as the latest annualised earning rate per
share in the last 12 months divided by the share price. Turnover by volume, expressed
in the unit of 109 , shows the number of shares transacted. The inflation rates for each
country were computed as the percentage changes of the CPI (consumer and retail prices)
in this country. Narrow Money supply series (M1) are used to calculate the percentage
change in nominal money supply. The exchange rates between the U.S. dollar and Thai
Baht on the end of each month are also drawn from the Datastream.
In this paper, we define the excess stock returns as the stock returns measured in
Thai Baht over the short term Thailand deposit saving rate. This requires that all dollarmeasured variables in the U.S. predictive model have to be converted to Thai Baht by
utilizing exchange rate series before conducting estimation. Therefore, the forecast of
excess US stock returns in the next month is measured by Thai Baht, which is convenient
for the investor to compare the relative sizes of two forecasts and make a trading decision.
Suppose the investor is standing at the end of 1997(12) and decides to trade. The
first estimations based on 5 years historical data from the end of 1993(01) to the end of
1997(12) will be done. With 8 regressors in the model for Thailand, she uses OLS to
estimate 28 = 256 models with different combinations of those 8 regressors at the end of
1997(12). The forecasting model will be chosen using one of the selection criteria, and this
will be followed by calculating one-step-ahead forecast of the excess returns in 1998(01)
on Thai stocks over Thai deposit rates. The same approach using the same selection
7
When i = 2, RI series will be converted from dollar measured series into Thai Baht measured
ones.
11
criterion will be applied to forecast excess returns in 1998(01) on U.S. stocks in terms of
Thai Baht over Thai deposit rate, except that there are 6 regressors in the model, resulting
in less OLS estimations. Given these forecasts, the investor rebalances her portfolio(if the
forecasts suggest that it will increase her wealth) and then she reconsiders her situation
at the end of 1998(01) when new data are published. She gets rid of the information in
1993(01) and adds new 1998(01) data, which keeps her estimation sample the same size.
The whole procedure of estimation, forecasting, and rebalancing repeats until the last
forecasts of excess stock returns in 2006(05) have been made and acted upon.
4.2
4.2.1
Predictability of Excess Stock Returns
Specifications of Forecasting Models
Table 1 shows the percentages of months for which each model selection criterion includes
each variable in the forecast model. From December 1996 to April 2006, the investor
needs to choose 2 forecasting models from 256 and 64 candidates for 1-month ahead
excess stock returns in Thai market and U.S. market, respectively. FIC and PIC generate
similar models for both excess Thai stock returns and U.S stock returns, and they are the
only two that consistently pick up some of the variables every month. BIC prefers the
least number of variables in the forecasting models, while the average number of variables
chosen by FIC and PIC are the most. R̄2 and SC not only choose similar average number
of regressors, but also share similar patterns in the choice of variables, particularly for the
forecasting models of the U.S. excess stock returns. It possibly results from applying R̄2
to achieve forecasting models for SC.
Regressors like the dividend yield and earning yield are often chosen for forecasting
both excess stock returns. Trading volume in Thailand is rarely chosen by any of the
criteria, while it is frequently selected in the forecasting models for the U.S. excess stock
returns. Similarly, R̄2 and AIC favour the inclusion of inflation in the models for Thai
excess returns more often than not, but they seldom choose it for the U.S. excess returns.
The differences between the predictors selected for the Thai and U.S. models may indicate
different features of information flows in emerging and developed stock markets. It can
also been seen that U.S. 3-month treasury bill rate has not been chosen regularly in the
U.S. forecasting model. The reason could be that we are interested in the forecasts of
excess U.S. stock returns over Thai deposit rate, which might be less related to the U.S.
short-term interest rate.
[Table 1]
12
4.2.2
Forecasts of Excess Stock Returns and Forecasting Evaluation
Forecasts of excess Thai stock returns and the U.S. stock returns based on the models
selected by alternative criterion are illustrated in Figure 1 and Figure 2, respectively. The
forecasts obtained from the model that include all regressors are also shown. The last
graphs on the right bottom are the realized excess returns from January 1998 to May 2006
on both markets. Most of the forecasts share the same pattern, except for those based
on models selected by BIC. In this case, flatter and smoother forecasts of excess returns
result from using less predictors in the forecasting models. FIC and PIC generate very
similar recursive forecasts for both excess returns as applying all regressors over the whole
sample periods, because except for volumes and earning yield, FIC and PIC constantly
choose the other predictors for every forecast.
[Figure 1]
[Figure 2]
The accuracy of forecasts is critical since our investor’s investment decisions are determined by her forecasts. According to our trading strategy based on recursive forecasts,
failures of forecasts will lead to the loss of money.
Measures of forecasting errors such as squared root of mean of squared errors (RMSE)
are often utilized to evaluate forecasting performance. Table 2 lists the RMSEs of forecasts
based on models chosen using various model selection criteria and the model that includes
all regressors. 1-month ahead forecasts based on the model selected by R̄2 are the least
accurate in terms of the magnitude of RMSE, while those based on BIC are the best. Also,
each model selection criterion performs differently when modelling excess returns on Thai
stocks and the U.S. stocks.
[Table 2]
To check the unbiasedness of forecasts, we regress the (recursive) forecasting errors
on a constant. T-statistics show whether the means of forecasting errors are statistically
equal to zero or not. In table 3, low t-statistics suggest that null hypothesis of zero mean of
forecasting errors cannot be rejected with 10% test level for any of the forecasts, regardless
of the underlying model selection criteria.
[Table 3]
13
However, conventional statistics based on the size of forecasting errors do not necessarily guide users to gain profits (Leitch and Tanner, 1991). Recent forecast evaluation
methods combine statistical and economic measures are now becoming popular. Since the
correct prediction of market direction can inform an investor whether to enter or leave the
market to gain or avoid losing money, the proportion of correct signs of excess stock returns
has been used as a measure for forecasting evaluations. Pesaran and Timmermann (1992b)
develop a formal nonparametric test on the correct predictions of signs. The standardized
test statistics (PT statistics) have a asymptotical standard normal distribution.
In table 4, it can be seen that forecasts in Thai markets based on models selected
by FIC, PIC are more accurate than others in terms of the ability to correctly predict
market directions. PT statistics are higher than the 10% critical value of a standard
normal distribution8 . Models with all regressors can also achieve the same sign forecasting
performance with FIC and PIC. However, models for Thai returns based on BIC predict
wrong signs in more than half periods, and the PT statistic is too low to reject the null
hypothesis of no predictive power. Because BIC chooses the least number of predictors
and generates flatter forecasts, we conjecture that BIC has a poor ability to predict sign
correctly on emerging stock markets that are well-known to have high volatilities.
For the forecasts of the U.S. excess returns, the proportion of correct signs predicted
is generally less than that from the forecasting models for Thai returns. We expect this
weaker forecasting performance since the predictions of the U.S. excess stock returns measured in Thai Baht implicitly contain investors’ forecasts on the exchange rate growth. In
contrast to the Thai case, forecasting models of the U.S. returns selected by BIC can predict correct signs more often than the other model selection criteria, and give the highest
PT statistic.
Overall, the forecasting performance of models selected by each criterion is not the
same for an emerging market and a developed market, and this results from distinct
features in each market. On average, FIC beats the other criteria and gives more accurate
forecasts in terms of signs, while AIC provides the worst forecasts. Market timing tests
generally show that the forecasting models have poor ability to predict correct signs.9
[Table 4]
8
We are using one-tail test here since rejection of null hypothesis with high positive PT statistics
means forecasts and realized value are dependent in terms of the same signs.
9
Note that the market timing tests have weak power when the sample size is small.
14
4.3
Economic Returns under the Switching Portfolio Trading Strategy
In this section, we compute the final wealth of the investor who fully switches her assetholdings between stocks in Thailand, stocks in U.S. and deposits in Thailand, according
to her recursive forecasts over 101 months. Note that to apply this trading strategy, we
need to assume that the investor has absolute faith in her forecasts and bears risks from
stock markets and foreign exchange markets. Aiming at maximizing returns of assets and
utility in every month, the investor’s optimal portfolio will be switched between markets.
Transaction costs are associated with frequent trading, and they erode the returns
of assets for the investor as well as change her investment decisions. Therefore, it is
important to take account of transaction costs when computing the investor’s final wealth
and utilizing economic profits to judge the EMH. We suppose that there are three types
of transaction costs in stock markets: zero, 0.5% and 1% of the total value of stocks.
However, depositing or withdrawing money from banks does not cost the investor any
transaction fees. The efficient market hypothesis will be rejected if economic returns net
transaction costs can be gained under this comprehensive trading and forecasting strategy.
To show whether the forecasts generate net profits under the investor’s switching-portfolio
strategy, we need to compare this net profit with those under some buy-and-hold strategies
that do not require any forecast of stock returns.
Table 5 reports the cumulative wealth measured in Thai Baht by the end of May 2006
under a portfolio-switching strategy and some buy-and-hold strategies. We assume that
the investor has 100 Thai Baht as the initial endowment. Recursive forecasting models
are chosen based on six alternative model selection criteria or all predictors. Under a buyand-hold strategy, benchmark wealth is obtained if the investor either deposits money,
buys the U.S. stocks or buys Thai stocks at the end of December 1997. In addition, an
equal weight of three assets portfolio is constructed at the end of December 1997 and rolls
until the end of the sample period.
With no transaction costs, the final wealth under various model selection criteria with a
switching portfolio strategy exceeds all buy-and-hold investments. If the investor follows
the “Sign Criterion” to choose forecasting models, she earns more returns than other
criteria. Predictions under BIC are the most inferior ones in terms of the average return
to the investor. The “All regressors” forecasts beat the model selection criteria, providing
above 200% returns to the investor after 101 months.
Increasing transaction costs to 0.5% on both the U.S. and Thai stock markets, we
expect that the final wealth will be reduced when the portfolio is rebalanced often. Con-
15
sidering that transaction costs have to be paid twice if the investor moves from one stock
market to another, she might not switch her portfolio very frequently. From table 5, it
can be seen that predictions under BIC do not necessarily generate more profit than the
passive portfolio strategies. R̄2 outperforms the other model selection criteria and the “all
regressors” rule. Under the high transaction cost scenario, the investor can still earn more
profits with switching portfolios based on R̄2 , AIC, SC and all regressors. However, forecasting models FIC, PIC and BIC based strategies are inferior to most of the buy-and-hold
strategies.
[Table 5]
It is interesting to see the difference between statistical and pure economic measures
when we evaluate forecasts accuracy. FIC and PIC are the best two criteria in that they can
provide correct sign predictions in two markets for more than half of the time. However,
they produce less money than other selection criteria and cannot outperform buy-andhold strategies with high transaction costs. The difference between the statistical and
economic measures can also be found when using AIC. Average sign predictions under
AIC are correct for less than 50% of the time; but the average returns generated when
AIC facilitates the switching-portfolio strategy exceed all passive investments and some
of the model selection criteria. Market timing tests generally display no forecasting power
of the models to predict correct signs, but net economic profits in excess of returns from
buy-and-hold strategies can still be generated based on those forecasts.
We have looked at the investor’s decision and the corresponding benefit or loss from
trading in each month. With the comparison of forecasts and realized excess returns,
we see that the investor can still possibly earn positive profit in a month even though
the sign of her forecast is incorrect in that month. In this case, it is the correct relative
size of two forecasts that drives the investor to move to the higher-return market. For
example, the investor forecasts of excess return of Thai and the U.S. stocks in December
1998 under BIC are 0.0326 and 0.0417, respectively; while the realized values are -0.0204
and 0.0748. The investor chooses to stay in the U.S. stock market because her forecast
for the excess returns of U.S. stocks is higher. Excess returns realized in December 1998
prove her correct trading decision. This investment increases her wealth by 0.163 U.S.
dollars (about 6 Thai Baht according to the exchange rate in that month) at the end of
the month. On the other hand, if both of the forecasts are accurate in terms of market
timing, the correct investment decision for making more money or avoiding loss will be
guided by these forecasts. Therefore, the market timing test helps us to evaluate forecasts,
16
but cannot determine the results of the assessment if the target of forecasting is to produce
money.
This conclusion results from the decision-making rule in our paper. The investor’s
trading decision is determined not only by the signs of the forecasts of excess stock returns,
but also the relative magnitudes of two positive forecasts for two markets. Hence, without
the consideration of decision-making aspects, simply applying statistical measures for point
forecasts or directional forecasts are not appropriate. This idea matches the argument in
Granger and Pesaran (2000).
5
Conclusion
This paper assesses the economic significance of the forecasts of stock returns in both
emerging and developed stock markets, and it addresses the importance of using economic
measurement for forecasting evaluations from the perspective of an investor in an emerging country who is maximizing her asset returns on her local risky assets, foreign risky
assets and a risk free asset. Extending previous literatures, we construct a more realistic
and complex portfolio with three assets, a more complicating investment decision-making
process, a recursive modelling strategy with a fixed estimation window size, and a forecasting strategy with the usage of model selection criteria. The investor is facing modelling
uncertainties, so every month she is looking for the best forecasting models for excess
returns of stocks in both markets according to various model selection criteria. Under the
assumption that the investor is 100% confident in her forecasts, she enters or gets out of
markets with her full funds.
The economic profits generated from predictions are mixed across model selection
criteria. Although there is evidence that some forecasts do not produce more returns than
buy-and-hold strategies, the investor who chooses forecasting models with all regressors,
or models based on R̄2 , AIC, SC can earn more returns net transaction costs than passive
investment strategies. Therefore, whether economic profits in excess of profits from buyand-hold strategies can be obtained from forecasts of excess returns in both emerging and
developed markets depends on the choice of model selection criteria for the best forecasting
models in each month. Even if R̄2 outperforms over 101 months, this result is found ex
post and it is not clear that the investor trusts this criterion ex ante. Therefore, the judge
of EMH is inconclusive.
The statistical measurements of forecasting accuracy show little predictability of stock
returns in both markets, and doubtless this results from larger volatilities in emerging
17
markets and uncertainties from exchange markets when predicting Thai Baht-measured
U.S. excess stock returns. However, a 100% economic profit can still be generated by “poor
forecasts” with the switching-portfolio trading strategy. After tracking down the forecasting performance and the realized benefits or loss from an investment in every month, we
find that according to our decision-making rule, good forecasts do not necessarily require
a high proportion of correct sign predictions. Although the signs of forecasts of excess
returns are opposite to the real, as long as the relative size of two sets of forecasts are
correct as the realized ones, it is still possible that positive returns can be earned if the
investor realizes her investment decisions. Two critical points follow this finding. Firstly,
it is essential to use decision theory for forecast evaluation, even though most of the literature and forecasting textbooks are still applying conventional statistical accuracy measures
of point forecasts for every forecasting target. Secondly, since comparing magnitudes of
forecasts of future returns for different assets is a common process when investors decide
their portfolio weights of asset holdings, a new test for measuring relative-size-accuracy
of forecasts should be developed. With the insufficiency of relevant statistical measures
for forecasting evaluation, an economic approach of comparing final wealth from trading
decisions based on different sets of forecasts seems to be important.
This paper can be extended in the following directions. The current forecasting models
can be improved in the way of extending the base set of predictors, using nonlinear model
specifications and identifying structural breaks. Moreover, if the investor finds that her
forecasting models gives her opposite values to the actual excess returns in the first several
months, then her confidence in the model selection criterion that has been used previously
should be reduced. Therefore, it would be more interesting to see how the investor learns
or reacts to the failure of her forecasts in real time when she invests.
18
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21
Figure 1: Forecasts of excess returns on the Thai stock market based on alternative
model selection criteria and the realized excess returns
.4
.4
.3
R2
.3
.2
.2
.1
.1
.0
.0
-.1
-.1
-.2
-.2
-.3
-.3
-.4
-.4
1998 1999 2000 2001 2002 2003 2004 2005
1998 1999 2000 2001 2002 2003 2004 2005
.4
.3
.4
.3
BIC
.2
.2
.1
.1
.0
.0
-.1
-.1
-.2
-.2
-.3
-.3
-.4
1998 1999 2000 2001 2002 2003 2004 2005
.4
.4
.3
PIC
.2
.2
.1
.1
.0
.0
-.1
-.1
-.2
-.2
-.3
-.3
-.4
SC
-.4
1998 1999 2000 2001 2002 2003 2004 2005
1998 1999 2000 2001 2002 2003 2004 2005
.4
.4
.3
FIC
-.4
1998 1999 2000 2001 2002 2003 2004 2005
.3
AIC
.3
All Regressors
.2
.2
.1
.1
.0
.0
-.1
-.1
-.2
-.2
-.3
-.3
Realized Excess Stock Returns
-.4
-.4
1998 1999 2000 2001 2002 2003 2004 2005
1998 1999 2000 2001 2002 2003 2004 2005
22
Figure 2: Forecasts of excess returns on the U.S. stock market based on alternative
model selection criteria and the realized excess returns
.4
.4
.3
.3
R2
AIC
.2
.2
.1
.0
.1
-.1
.0
-.2
-.1
-.3
-.4
-.2
1998 1999 2000 2001 2002 2003 2004 2005
1998 1999 2000 2001 2002 2003 2004 2005
.4
.3
.4
BIC
.3
.2
.2
.1
.1
.0
.0
-.1
-.1
-.2
-.2
-.3
-.3
-.4
-.4
1998 1999 2000 2001 2002 2003 2004 2005
1998 1999 2000 2001 2002 2003 2004 2005
.4
.3
.4
.3
PIC
.2
.2
.1
.1
.0
.0
-.1
-.1
-.2
-.2
-.3
-.3
-.4
SC
-.4
1998 1999 2000 2001 2002 2003 2004 2005
1998 1999 2000 2001 2002 2003 2004 2005
.4
.4
.3
FIC
.3
All Regressors
.2
.2
.1
.1
.0
.0
-.1
-.1
-.2
-.2
-.3
-.3
Realized Excess Stock Returns
-.4
-.4
1998 1999 2000 2001 2002 2003 2004 2005
1998 1999 2000 2001 2002 2003 2004 2005
23
Table 1: Percentage of months when each variable is included in the forecasting
model for both countries a
Panel A: Excess stock returns in Thailand
Model selection criterion
Predictor
R̄2
AIC
BIC
FIC
PIC
SC
Dividend yield
63.4
46.5
26.7
100
100
72.3
Earning yield
81.2
71.3
15.8
100
100
42.6
Volume
13.9
5.9
1.0
3.0
3.0
33.7
1-month interbank interest rate
48.5
29.7
12.9
100
100
40.6
Inflation rate
76.2
60.4
19.8
100
100
46.5
Rate of change in Thai money supply
35.6
29.7
16.8
100
100
79.2
Rate of change in exchange rate to U.S. dollars
31.7
16.8
2.0
100
100
58.4
U.S. 3-month treasury bill rate
53.5
35.6
8.9
100
100
47.5
Average number of predictors included
4.0
3.0
1.0
7.0
7.0
4.2
Panel B: Excess stock returns in the U.S.
Model selection criterion
Predictor
R̄2
AIC
BIC
FIC
PIC
SC
Dividend yield
59.4
46.5
29.7
100
100
57.4
Earning yield
79.2
57.4
31.7
52.5
98.0
80.2
Volume
82.2
61.4
38.6
26.7
27.7
84.2
U.S. 3-month treasury bill rate
34.7
14.9
6.9
100
100
37.6
Inflation rate
35.6
5.0
2.0
100
100
33.7
Rate of change in U.S. money supply
23.8
1.0
0.0
100
100
23.8
Average number of predictors included
3.1
1.9
1.1
4.8
5.3
3.2
a
Model selection criteria are recursively used to choose the forecasting models for excess stock
returns on both Thailand and U.S. markets over the Thailand deposit saving rate. The
figures in this table show the percentages of months when each variable is chosen by the
particular model selection criterion to forecast the next month excess returns. Predictors in
Panel B have been converted to Thai Baht measured variables.
24
Table 2: Out-of-sample performance (RMSE) of forecasting models based
on alternative model selection criteria from 1998(01) to 2006(05)a
Selection criterion
Thai excess stock returns
The U.S. excess stock returns
R̄2
0.140
0.066
AIC
0.133
0.059
BIC
0.122
0.054
FIC
0.139
0.064
PIC
0.139
0.067
SC
0.127
0.066
All regressors
0.144
0.065
a
RMSE is computed based on 1-month ahead recursive forecasts under alternative
model selection criteria and the model that includes all regressors.
Table 3: Estimation of mean of recursive forecasting errors
Thai
Selection Criterion
The U.S.
Coefficient
T-stats
Coefficient
T-stats
R̄2
-0.0189
-1.3654
0.0027
0.4101
AIC
-0.0170
-1.2860
-0.0059
-1.0002
BIC
-0.0003
-0.0216
-0.0063
-1.1898
FIC
-0.0147
-1.0631
-0.0098
-1.5475
PIC
-0.0147
-1.0631
-0.0086
-1.2900
SC
-0.0154
-1.2206
0.0019
0.2845
All regressors
-0.0207
-1.4488
0.0030
0.4649
a
The means of forecasting errors under alternative model selection
criterion have been estimated. We regress forecasting errors on a
constant. Null hypothesis of zero means cannot be rejected for all
forecasting errors at 10% test level.
25
a
Table 4: Predictive accuracy of excess return forecasts from 1998(01)
to 2006(05) a
Proportion of correct signs (%)
PT statistics
Selection criterion
Thai
The U.S.
Averageb
Thai
The U.S.
R̄2
52.5
47.5
50.0
0.035
-0.521
AIC
50.5
48.5
49.5
-0.354
-0.471
BIC
47.5
53.5
50.5
-0.558
0.815
FIC
58.4
51.5
55.0
1.350c
-0.012
-0.251
PIC
58.4
50.5
54.5
1.350c
SC
53.5
47.5
50.5
0.236
-0.581
All regressors
58.4
49.5
54.0
1.350b
-0.046
a
This table shows the proportion of correctly predicted signs over 101 months
and PT statistics developed by Pesaran and Timmermann (1992). At the
end of each month, the investor makes her investment decision based on the
sign and the magnitudes of 1-month ahead excess return forecasts in two
markets.
b
This is the simple average of the proportions of correctly predicted signs of
Thai and U.S. excess stock returns using each model selection criterion.
c
PT statistics show statistical significance of market timing at 10% test level.
26
Table 5: Performance of the switching-portfolio strategy and other buy-and-hold trading strategies a
Portfolio-switching under
alternative model selection
Final Wealth (Thai Baht)
criterion and other
Zero
Low
High
trading strategies
transaction cost
transaction cost
transaction cost
Portfolio-
R̄2
260.9
263.4
213.2
switching
AIC
224.9
189.9
155.3
strategy
BIC
159.1
117.3
102.7
FIC
205.7
158.7
114.1
PIC
206.0
151.4
114.1
SC
292.5
221.2
161.5
All regressors
338.5
247.4
185.3
Buy-and-
Thai stocks
125.6
124.3
123.1
hold
The U.S. stocks
107.9
106.9
105.8
strategies
Thailand bank deposit
119.8
119.8
119.8
Equal investments
117.8
117.0
116.2
a
The final wealth is the cumulative wealth that the investor owns at the end of May 2006, with
an initial endowment of 100 Thai Baht at the end of December 1997. Portfolios of each month
are switching among three assets according to the recursive excess return forecasts of Thai and
the U.S. stocks. Three different transaction costs of stocks are applied. The low transaction cost
rate is set at the rate of 0.5%, and the high transaction cost rate is set at 1%.
27