Proceedings of Applied International Business Conference 2008
ASSET ALLOCATION DECISION MAKING: DO TIME AND BREAK MATTER?
Hooi Hooi Lean ψ and Ruhani Ali
Universiti Sains Malaysia, Malaysia
Abstract
The modern portfolio theory recommends that diversifying the security investments across different
classes of security or asset is a method to reduce the risk bared. However, the decided diversification
strategy is bounded to a specific investment horizon. The longer an investor holds risky assets, the
more he/she will benefit from what is often called as time diversification. The focus of this research is
to examine how the investment horizon affects investment allocation decision-making in Malaysia.
Proof of mean reversion from structural break models may suggest some scope of benefit from time
diversification in the stock market.
Keywords: Time diversification; Investment horizon; Structural break; Equity market.
JEL Classification Codes: G12 ; G14 ; G15.
1. Introduction
It is well known that in the asset allocation decision making theory, the concept of diversification refers
to how investors allocate their money between the risky and risk-free assets for maximizing their utility.
Applying the concept of diversification to time is called time diversification. If the time diversification
effect exists, equity returns are less risky over long time horizons than over short time horizons. Thus,
the conventional financial advisers will advise the investors to increase their equity exposure as their
investment horizons lengthen. However, time diversification has been a long standing debate between
practitioners and academics. Samuelson (1969) first argued strongly against the existence of time
diversification. Since then, other academics have also raised theoretical challenges to the notion of time
diversification.
On the other hand, empirical evidence has hardly supported their view. Most investment practitioners
subscribe to the time diversification principle, stating that portfolio risk declines as the investment
horizon lengthens (Jaggia and Thosar, 2000). Samuelson (1991) and Kritzman (1994) showed that the
time diversification principle can be justified if there is mean reversion in stock returns. Lo and
MacKinlay (1988) reported that returns under one year are positively autocorrelated, which indicates
mean aversion. Poterba and Summers (1988) also reported evidence of mean aversion in returns under
one year, as well as statistically significant mean reversion at longer horizons. Fabozzi et al. (2006)
defined time diversification as the ability to make long-term forecasts and documented that time
diversification is exhibited only by models.
Bodie (1995) reported that investors with a long-term perspective should invest more heavily in the
stock market for investment risk declines with time horizon. Hansson and Persson (2000) supported the
existence of time diversification. The weights for stocks in efficient portfolios are significantly higher
for long investment horizons that for a one-year horizon. Sanfilippo (2003) suggested that an investor
should avoid bonds in the long run due to the time diversification effect. Giannetti (2005) found that
investing in the stock market would be less risky in the long run. Guo and Darnell (2005) documented
that diversification through multiple periods is effective only when it is combined with diversification
across multiple assets. They were very confident that holding a well-diversified stock portfolio with 20
years or longer will almost always deliver positive returns.
ψ
Corresponding author. Hooi Hooi Lean. School of Social Sciences, Universiti Sains Malaysia, 11800
Penang, Malaysia. Corresponding author Email: [email protected]
Proceedings of Applied International Business Conference 2008
Jaggia and Thosar (2000) offered alternative explanation that individuals are more risk tolerant when
the investment horizon is long. People generally feel comfortable with allocating a larger proportion of
their portfolio to equities if their investment horizon is long. Perhaps the justification of this behavior
comes not from the fact that risk declines over time but rather that investors are subjectively more risktolerant given longer horizons (Jaggia and Thosar 2000, pp. 212). To date, the question still remains
wide open: Does time diversification exist? If so, what are the policy implications for asset allocation?
Most of studies on long-term stock returns focus in US market only and Jorion (2003) extended his
study to 30 stock markets. However, he mainly focus on the Western developed markets. The study on
East Asia markets is absent may be due to lack of long time series data in these markets.
This paper tests whether investment time horizon is applicable in diversifying asset investments in
Malaysia. Specifically, it is to study the characteristics of Malaysia’s equity returns over different
investment horizons. Moreover, we also examine the existence of structural break on the impact of time
diversification. Investors would like to understand whether they can utilize different investment time
horizons to diversify their asset investments in Malaysia effectively. Our research may offer some
practical implications for financial planners and other investment advisers.
The remainder of this paper is divided into three sections. In the next section, we present the data and
methodology of this study. In Section 3, we report the empirical results and finally, the conclusions will
be presented in Section 4.
2. Data and Methodology
The data used in this study is the weekly Kuala Lumpur Composite Index (KLCI). The sample period is
from January 1980 to December 2007 with a total observation of 1461. The Bank Negara Malaysia
Treasury Bills’ annual discount rates are used as the proxy for risk-free rate.
We first compute the log return over n-week horizon, Rn = ln (It / It-n) where, It = the index value on the
week t, and It-n = the index value for the n-week before It. We cover the holding week from 1 to 500
(equivalent to 10 years). Mean and standard deviation of each holding week’s return are then computed.
It is commonly assumed that the return’s mean and variance increase proportionally with the
investment time horizon. We consume the mean-variance optimization as a preliminary check for time
diversification. As average returns increase over time, it is more meaningful to compare risk with
appropriate normalization. In order to define time diversification, we follow Fabozzi et al. (2006) by
normalizing risk measures to the level of returns. If the ratio of risk to the expected returns decreases
with time, there is time diversification.
Consider two time horizons, T1 and T2 where T2 > T1. Let the expected returns at T1 and T2 as RT1 and
RT2 respectively; and the risk measures as SD1 and SD2 respectively. Time Diversification Index (TDI)
is represented by the equation below:
TDI =
SD1 RT1
SD2 RT2
If TDI > 1, then it is said that time diversification exist.
In finance, the unit root properties of stock prices have important practical implications for investors.
If stock prices are mean reverting it follows that the price level will return to its trend path over time
and that it might be possible to forecast future movements in stock prices based on past behavior, but if
stock prices follow a random walk process any shock to prices will be permanent. This means that
future returns cannot be predicted based on historical movements in stock prices and that volatility in
stock markets will increase in the long run without bound (Chaudhuri and Wu, 2003, 575-576).
Poterba and Summers (1988) and Fama and French (1988) documented that mean reversion in stock
market returns occurs during time horizon greater than one year. According to Madhusoodanan (1997),
the mean reversion is shown in a time series of a stock returns, in which if the series exhibit high return
in a period and revert back to low return in the following period or vice versa. If stock returns are
mean-reverting in the long run, risk is decreasing with the investment time horizon. Thus, it is
generally assumed that a mean-reverting process leads to time diversification (Giannetti, 2005; Fabozzi
et al., 2006).In addition, the existence of regime shifts and structural break will make returns uncertain
over long time horizons. Time diversification depends on the sequence of regimes.
833
Proceedings of Applied International Business Conference 2008
To further seek for proof of random walk theory in stock market returns with various time horizons, we
extend the existing theory by taking into account the structural breaks in the stock price returns. Proof
of mean reversion from structural break models may suggest some scope of benefit from time
diversification in the stock market.To examine whether the stock price returns in different holding
periods follow a random walk we use univariate Lagrange Multiplier (LM) unit root tests with one and
two structural breaks proposed by Lee and Strazicich (2004).
Univariate LM unit root tests with structural break
The LM unit root test can be explained using the following data generating process
(DGP): yt = δ ′Z t + et , et = β et −1 + ε t . Here, Z t consists of exogenous variables and ε t is an
error term with classical properties. Lee and Strazicich (2004) developed two versions of the LM unit
root test with one structural break. Using the nomenclature of Perron (1989), Model A is known as the
“crash” model, and allows for a one-time change in the intercept under the alternative hypothesis.
[
]
'
Model A can be described by Z t = 1, t , Dt , where Dt = 1 for t ≥ TB + 1, and zero otherwise; TB is
the date of the structural break, and δ' = ( δ1 , δ2 , δ3 ). Model C, the “crash-cum-growth” model, allows
for a shift in the intercept and a change in the trend slope under the alternative hypothesis and can be
[
]
'
described by Z t = 1, t , Dt , DTt , where DTt = t − TB for t ≥ TB + 1, and zero otherwise.
The LM unit root test statistic is obtained from the following regression:
∆yt = δ ′∆Z t + φS t −1 + µ t
where S t = y t − ψˆ x − Z t δˆ t , t = 2 ,...,T ;
ψ̂ x
δ̂
are coefficients in the regression of
∆yt on ∆Z t ;
is given by y t − Z t δ ; and y1 and Z1 represent the first observations of y t and Z t respectively.
The LM test statistic is given by: τ
= t-statistic for testing the unit root null hypothesis that φ = 0 .
The location of the structural break (TB ) is determined by selecting all possible break points for the
minimum t-statistic as follows:
ln f τ% ( λi ) = ln f τ% ( λ ) , where λ = TB T .
λ
The search is carried out over the trimming region (0.15T, 0.85T), where T is sample size. To select the
lag length, we use the same procedure as described above. After determining the optimal lag length at
each combination of breakpoints, we determined the breaks where the endogenous two-break LM t-test
statistic is at a minimum. Critical values for the one break case are tabulated in Lee and Strazicich
(2004).
3. Empirical Results and Discussion
Figure 1 shows that both the mean and standard deviation of returns have upward trend. The mean
return is increasing with the holding periods while the standard deviation fluctuates a little between the
holding weeks of 20 to 400. After the 400 holding weeks, the standard deviation is decreasing. In
addition, the degree of increase is more for the mean return than the volatility especially after the 100week. Thus, there is the possibility of convergence as the holding period gets longer. This is an early
indication that the KLCI log returns do not follow the normal distribution and are not independently
and identically distributed. According to Fabozzi et al. (2006), if returns are independent and
identically distributed (IID) in long time series, the return should be very close to the theoretical
average return.
834
Proceedings of Applied International Business Conference 2008
Figure 1: Term Structure of Return and Volatility
0.
7
0.
6
0.
5
0.
4
0.
3
0.
2
0.
1
0
1
3
5
7
9
1
1
2
0
4
0
6
0
8
0
10
15
0
0
holding
week
20
0
Mean
25
0
30
0
35
0
40
0
42
0
44
0
46
0
48
0
50
0
Std.Dev.
The observations also indicate it is not advisable to pursue investment in KLCI for a time horizon of 20-250 weeks,
unless for reasons other than the risk perceived by the volatility results. From the observation, it is more advisable
to pursue investment in KLCI with time horizon greater than 400-week where the volatility is decreasing while the
mean return is still increasing.
Figure 2: Risk-Return Trade-off
0.5
0.45
0.4
returns
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
volatility
Figure 2 shows the risk-return trade-off pattern. This is a plot of returns versus volatilities, guiding by the time
horizon. The graph shows that the relationship between return and volatility is in positive correlation. The pattern
seems to suggest a bounded pattern after 440 weeks, and hence, the KLCI may exhibit mean reversion pattern. The
investment horizon of 440 weeks (about 8 years) could be considered as turning point in the risk-return trade-off.
Figure 3: Term Structure of Normalized Risk Ratio and Time Diversification Index
30
1.5
25
1.4
1.3
15
1.2
10
TDI
ratio
20
1.1
5
0
1
1
3
5
7
9
11
20
40
60
80
100
150
200
250
300
350
400
420
440
460
480
holding w eeks
ratio
TDI
Figure 3 shows the normalized risk ratio and TDI. The ratio is decreasing overtime and the TDI is above one for all
holding periods indicating time diversification exists. Both measures after normalized to the returns clearly show
that time diversification exists in the Malaysian equity market.
835
Proceedings of Applied International Business Conference 2008
Table 1: LS Model A
Holding Period (weeks)
TB
k
1
7/13/1994
6
2
7/29/1998
8
3
10/28/1998
8
4
7/22/1998
8
5
8/19/1998
8
6
10/7/1998
8
7
5/6/1998
8
8
10/21/1998
8
9
10/21/1998
8
10
10/21/1998
8
11
10/21/1998
8
12
10/21/1998
8
20
11/11/1998
8
30
2/4/1998
8
40
2/11/1998
8
50
11/12/1986
8
60
9/3/1986
7
70
6/25/1986
8
80
4/16/1986
8
90
2/19/1986
8
100
1/8/1986
8
125
6/5/1985
8
150
1/26/1994
8
175
6/20/1984
8
200
2/9/1994
8
225
7/28/1993
8
250
1/26/1994
7
275
9/2/1992
7
300
3/11/1992
8
325
8/28/1991
8
350
4/17/1991
7
375
10/3/1990
7
400
4/11/1990
7
410
1/31/1990
7
420
11/22/1989
8
St-1
1
***
Bt
***
-0.7648
(-12.4291)
-0.3041***
(-8.9895 )
-0.2816***
(-11.2314)
-0.1902***
(-9.1352)
-0.2033***
(-11.2890)
-0.1309***
(-9.0991)
-0.1008***
(-7.9878)
-0.0860***
(-7.2945)
-0.1493***
(-12.1840)
-0.1442***
(-12.1314)
-0.1251***
(-11.1029)
-0.1122***
(-10.7489)
-0.0611***
(-8.2705)
-0.0324***
(-5.7205)
-0.0247***
(-4.8595)
-0.0200***
(-4.5881)
-0.0160**
(-4.0297)
-0.0157**
(-4.1747)
-0.0142**
(-3.8473)
-0.0155**
(-3.9549)
-0.0131*
(-3.3511)
-0.0149**
(-3.7877)
-0.0122
(-3.1272)
-0.0108
(-2.9868)
-0.0099
(-2.9204)
-0.0092
(-2.7657)
-0.0076
(-2.4442)
-0.0073
(-2.3303)
-0.0085
(-2.6102)
-0.0050
(-1.8973)
-0.0053
(-1.9930)
-0.0066
(-2.2033)
-0.0161
(-10.1341)
-0.0064***
(-5.1977)
-0.0040***
(-3.6713)
-0.0107***
(-6.7991)
-0.0111***
(-7.5347)
-0.0102***
(-6.4902)
-0.0067***
(-4.7909)
-0.0057***
(-4.2370)
-0.0143***
(-8.3521)
-0.0091***
(-6.1689)
-0.0058***
(-4.1976)
-0.0058***
(-4.1943)
-0.0060***
(-4.0838)
-0.0050***
(-3.2593)
-0.0056***
(-3.2594)
-0.0077***
(-3.7187)
-0.0094***
(-3.5823)
-0.0104***
(-3.7967)
-0.0093***
(-3.3899)
-0.0065***
(-3.0843)
-0.0064***
(-2.7515)
-0.0055***
(-2.7395)
-0.0030*
(-1.7078)
-0.0057**
(-2.4170)
-0.0038*
(-1.9089)
-0.0040*
(-1.8551)
-0.0027
(-1.3231)
-0.0019
(-0.9975)
-0.0015
(-0.8496)
0.0007
(0.4541)
-0.0002
(-0.0902)
-0.0010
(-0.6122)
0.0077
(0.2161)
0.0074
(0.1948)
0.1306***
(3.3076)
-0.0576
(-1.4463)
0.0081
(0.1911)
0.1519***
(3.5569)
0.0348
(0.8135)
0.1133***
(2.6644)
0.1210**
(2.5169)
0.0949*
(1.9086)
0.1159**
(2.3495)
0.0800
(1.6244)
0.1599***
(3.2577)
0.1982***
(3.9705)
0.1198**
(2.3824)
0.1718***
(3.4247)
0.2228***
(4.2626)
0.2354***
(4.5472)
0.1831***
(3.6276)
0.1782***
(3.4642)
0.1748***
(3.3628)
0.2067***
(4.0560)
-0.1342***
(-2.6193)
0.1674***
(3.1876)
-0.1219**
(-2.2902)
-0.1753***
(-3.3381)
-0.1680***
(-3.1375)
-0.1516***
(-2.8378)
-0.1301**
(-2.3618)
-0.1936***
(-3.7708)
-0.1408***
(-2.6425)
-0.1264**
(-2.3846)
-0.0069
(-2.2500)
-0.0058
(-1.9767)
-0.0053
-0.0010
(-0.6019)
0.0012
(0.7263)
0.0001
-0.1212**
(-2.2910)
-0.1742***
(-3.3085)
-0.1432***
836
Proceedings of Applied International Business Conference 2008
430
10/28/1987
8
440
6/14/1989
8
450
4/5/1989
8
460
12/27/1989
7
470
1/31/1990
8
480
10/28/1987
8
490
10/28/1987
8
500
6/1/1988
8
(-1.8791)
-0.0051
(-1.9530)
-0.0066
(-2.2268)
-0.0064
(-2.1721)
-0.0041
(-1.6049)
-0.0046
(-1.7308)
-0.0046
(-1.8186)
-0.0048
(-1.8128)
-0.0057
(-1.8367)
(0.0546)
0.0001
(0.0629)
-0.0004
(-0.2210)
-0.0007
(-0.4331)
-0.0006
(-0.3133)
-0.0008
(-0.4506)
-0.0015
(-0.7190)
-0.0019
(-0.8262)
-0.0019
(-0.8931)
(-2.7183)
-0.1528***
(-2.9248)
-0.1403***
(-2.6736)
-0.1800***
(-3.4479)
-0.0823
(-1.5661)
-0.1129**
(-2.1861)
-0.1718***
(-3.2160)
-0.1481***
(-2.7860)
-0.1528***
(-2.9088)
Notes: Critical values for the LM test at 10%, 5% and 1% significant levels = -3.211, -3.566, -4.239.
Critical values for other coefficients based on standard t distribution = 1.645, 1.96, 2.576.
* ** ***
( ) denote statistical significance at the 10%, 5% and 1% levels respectively.
Table 2: LS Model C
TB
k
St-1
1
Bt
Dt
10/9/1985
6
2
4/30/1986
8
3
4/23/1986
8
4
3/5/1986
8
5
1/9/1985
8
6
11/11/1987
8
7
5/28/1986
8
8
6/4/1986
8
9
5/28/1986
8
10
3/19/1986
8
11
6/25/1986
8
-0.7648***
(-12.5176)
-0.3950***
(-10.4342)
-0.3206***
(-11.9660)
-0.2003***
(-9.3541)
-0.2078***
(-11.4851)
-0.1592***
(-10.1380)
-0.1310***
(-9.1073)
-0.1061***
(-8.0729)
-0.1726***
(-13.1549)
-0.1548***
(-12.5734)
-0.1281***
(-11.2076)
-0.0040*
(-1.9329)
-0.0164***
(-6.2729)
-0.0088***
(-3.8479)
-0.0099***
(-3.9980)
-0.0094***
(-3.4495)
-0.0210***
(-7.1540)
-0.0213***
(-6.4038)
-0.0116***
(-4.2744)
-0.0290***
(-8.4691)
-0.0132***
(-4.5156)
-0.0079***
(-2.8574)
0.0563
(1.5754)
-0.0391
(-1.0344)
-0.0220
(-0.5683)
-0.0155
(-0.3892)
0.0307
(0.7395)
-0.1149***
(-2.6420)
-0.0806*
(-1.8919)
0.0047
(0.1124)
-0.0689
(-1.4584)
0.0119
(0.2461)
0.0543
(1.1078)
-0.0175***
(-6.4755)
0.0181***
(6.1670)
0.0111***
(4.2505)
0.0039
(1.5282)
0.0019
(0.6727)
0.0156***
(5.4072)
0.0204***
(5.8472)
0.0119***
(3.9596)
0.0215***
(6.3434)
0.0102***
(3.2094)
0.0056*
(1.7964)
12
3/5/1986
8
20
1/29/1986
8
30
1/22/1986
8
40
2/12/1986
8
50
2/5/1986
8
60
2/5/1986
7
70
12/25/1985
8
80
4/16/1986
8
90
11/6/1985
8
100
8/7/1985
8
125
2/1/1995
8
150
4/6/1994
8
175
3/19/1986
8
-0.1172***
(-10.9534)
-0.0653***
(-8.5019)
-0.0387***
(-6.2102)
-0.0275**
(-5.1475)
-0.0231**
(-4.8750)
-0.0196**
(-4.3779)
-0.0196**
(-4.5651)
-0.0159
(-4.1319)
-0.0163
(-4.0142)
-0.0141
(-3.4322)
-0.0147
(-3.7748)
-0.0132
(-3.2979)
-0.0114
-0.0038***
(-1.3806)
-0.0097***
(-3.2146)
-0.0098***
(-3.1253)
-0.0100***
(-2.9540)
-0.0113***
(-3.1786)
-0.0137***
(-3.3085)
-0.0159***
(-3.6114)
-0.0110***
(-2.9926)
-0.0090**
(-2.4466)
-0.0089**
(-2.2448)
-0.0018
(-0.9777)
-0.0008
(-0.4052)
-0.0083*
0.1568***
(3.2488)
0.0276
(0.5599)
0.0640
(1.3015)
-0.0538
(-1.0778)
0.0014
(0.0292)
0.0508
(0.9958)
0.0120
(0.2356)
0.1856***
(3.6780)
0.0714
(1.4238)
0.0590
(1.1708)
-0.0724
(-1.4403)
-0.0610
(-1.1990)
-0.0553
-0.0020
(-0.6627)
0.0053*
(1.6492)
0.0084**
(2.4842)
0.0074**
(2.1274)
0.0067**
(1.9736)
0.0073**
(2.0217)
0.0089**
(2.3760)
0.0057*
(1.7113)
0.0035
(1.0354)
0.0042
(1.1654)
-0.0015
(-0.5419)
-0.0032
(-1.0640)
0.0021
Holding
(weeks)
1
Period
837
Proceedings of Applied International Business Conference 2008
200
7/2/1986
8
225
12/16/1992
8
250
8/26/1992
7
275
4/22/1992
7
300
10/30/1991
8
325
11/20/1991
8
350
10/17/1990
7
375
4/25/1990
7
400
10/18/1989
7
410
11/1/1989
7
420
6/14/1989
8
430
3/8/1989
8
440
10/19/1988
8
450
12/14/1988
8
460
10/5/1988
7
470
10/5/1988
8
480
10/28/1987
8
490
10/28/1987
8
500
10/28/1987
8
(-3.0079)
-0.0108
(-3.0453)
-0.0099
(-2.9039)
-0.0106
(-2.8754)
-0.0106
(-2.8300)
-0.0124
(-3.1983)
-0.0136
(-3.2583)
-0.0145
(-3.2964)
-0.0107
(-2.8191)
-0.0097
(-2.7057)
-0.0105
(-2.6677)
-0.0111
(-2.7600)
-0.0118
(-2.9395)
-0.0112
(-2.9098)
-0.0123
(-3.0662)
-0.0114
(-2.6759)
-0.0122
(-2.8473)
-0.0139
(-3.3035)
-0.0157
(-3.4092)
-0.0172
(-3.2987)
(-1.9131)
-0.0068*
(-1.7795)
-0.0025
(-1.1154)
-0.0011
(-0.5064)
0.0002
(0.0895)
0.0006
(0.2751)
0.0067
(2.5013)
0.0033
(1.4490)
0.0014
(0.6039)
0.0008
(0.3474)
0.0049
(1.7982)
0.0032
(1.3238)
0.0028
(1.1979)
0.0008
(0.3358)
0.0017
(0.6918)
0.0019
(0.7991)
0.0026
(1.0535)
-0.0014
(-0.4738)
-0.0025
(-0.8263)
-0.0024
(-0.8163)
(-1.0663)
0.1326**
(2.5244)
-0.0770
(-1.4761)
-0.0316
(-0.5936)
-0.0842
(-1.5896)
-0.0684
(-1.2590)
-0.0354
(-0.6849)
-0.1329**
(-2.5327)
-0.0322
(-0.6141)
-0.0553
(-1.0590)
-0.0488
(-0.9264)
-0.0376
(-0.7257)
-0.0185
(-0.3618)
-0.0594
(-1.1394)
-0.0619
(-1.1888)
-0.0873*
(-1.6874)
-0.0672
(-1.2950)
-0.1603***
(-3.0065)
-0.1341**
(-2.5260)
-0.1087**
(-2.0344)
(0.5837)
0.0008
(0.2311)
-0.0031
(-0.9819)
-0.0065*
(-1.7296)
-0.0064*
(-1.6760)
-0.0081**
(-2.0604)
-0.0133***
(-2.6243)
-0.0143***
(-2.7868)
-0.0083**
(-1.9975)
-0.0069*
(-1.8620)
-0.0095**
(-2.1339)
-0.0112**
(-2.3835)
-0.0126***
(-2.6398)
-0.0106**
(-2.5434)
-0.0115**
(-2.5683)
-0.0125**
(-2.4108)
-0.0125**
(-2.4031)
-0.0163***
(-3.1926)
-0.0175***
(-3.2849)
-0.0162***
(-3.1372)
Critical values
location of break, λ
0.1
0.2
0.3
0.4
0.5
1% significant level
-5.11 -5.07 -5.15 -5.05 -5.11
5% significant level
-4.50 -4.47 -4.45 -4.50 -4.51
10% significant level -4.21 -4.20 -4.18 -4.18 -4.17
Notes: The critical values are symmetric around λ and (1-λ). * (**) *** denote statistical significance at the 10%, 5% and 1% levels
respectively.
Tables 1 and 2 report the LM unit root test with one break in the intercept and trend (Models A and C).
We find strong evidence of mean reversion for the holding periods from 1 week to 125 weeks with
Model A and from 1 week to 70 weeks with Model C. However, we are unable to reject the random
walk hypothesis for the holding period more than 125 and 70 weeks with the Model A and C
respectively. Hence, we conclude that the investors in Bursa Malaysia may not benefit from time
diversification in particular with the holding period more than 70 weeks. Our result contradicts to Lo
and MacKinlay (1988) and Poterba and Summers (1988) but consistent with Jorion (2003) who found
no evidence of mean reversion for long-term returns with the variance ratio tests. This is because the
US markets are different from the emerging markets like Malaysia.
We now briefly discuss the location of the break in each of the two models. In the results for Model A,
reported in Table 1, the break in the intercept is statistically significant for most of the holding weeks.
In Model C reported in Table 2, the break in the intercept is statistically significant for 10 out of 43
holding periods only. The break in slope is statistically significant for most of the holding weeks except
10 holding periods. In Model A, the break date for holding weeks shorter than 1 year is associated with
the Ringgit pegged regime, while the structural break occurs at the time of the world recession and oil
crisis in the late 80s for other holding weeks. In Model C, almost all significant structural breaks occur
at the time of the world recession and oil crisis in the late 80s.
838
Proceedings of Applied International Business Conference 2008
4. Conclusion
This paper is an empirical study to examine the evidence of time diversification in the Malaysia equity
market. Based only on the risk-return trade-off analysis, it is only sufficient to conclude that there is
possibility that mean reversion is present in the equity market. Based on the conventional meanvariance optimization, we found a turning point at eight years holding period. However, with the
normalized risk ratio and TDI as proposed by Fabozzi et al. (2006), there is strong evidence that time
diversification exists in the Malaysia equity market. However, by taking control of structural break in
the return series, we could not find any evidence of time diversification in the Malaysia equity market
for the period of 1980 to 2007. This may be due to the structural break changing the persistency of
stock prices. The impact of economic shocks is permanent to the stock prices in Malaysia. Sanfilippo
(2003) suggested that investment objectives must be pinpointed clearly since they determine an
investment’s holding period. The common stocks previously considered inherently risky, may be
considered low risk in the long run if they are held in portfolios with other financial assets such as
Treasury bills. Furthermore, Guo and Darnell (2005) argued that time diversification is not a substitute
for cross-asset diversification. Hence, it will be a good suggestion to an investor with a combination of
asset and time diversification. However, one would to re-allocate the investment decision when there is
a structural break.
Acknowledgement
This research is fully supported by the Fundamental Research Grant Scheme, Ministry of Higher
Education Malaysia Grant No. 203/PMGT/671090.
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