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2007 Annual International CHRIE Conference & Exposition
145
Table 1
Foreign tourist arrivals in Taiwan by nationality market: 1996- 2005
Year
Japan
Hong
Kong
USA
Thailand
South
Korea
Singapore
Philippines
Malaysia
and
Indonesia
Europe
Others
Total foreign
tourist
arrivals
1996 918
(38.9%)
263
(11.1%)
290
(12.3%)
121
(5.1%)
127
(5.4%)
78
(3.3%)
112
(4.7%)
106
(4.5%)
152
(6.5%)
191
(8.1%)
2,358
(100%)
1997 906
(38.2%)
260
(10.9%)
304
(12.8%)
122
(5.1%)
99
(4.2%)
82
(3.4%)
119
(5.0%)
109
(4.6%)
159
(6.7%)
212
(8.9%)
2,372
(100%)
1998 827
(36.0%)
280
(12.2%)
309
(13.4%)
129
(5.6%)
63
(2.7%)
87
(3.8%)
126
(5.5%)
97
(4.2%)
160
(7.0%)
221
(9.6%)
2,299
(100%)
1999 826
(34.3%)
320
(13.3%)
318
(13.2%)
138
(5.7%)
76
(3.2%)
86
(3.6%)
123
(5.1%)
129
(5.4%)
162
(6.7%)
233
(9.7%)
2,411
(100%)
2000 916
(34.9%)
361
(13.8%)
360
(13.7%)
133
(5.1%)
84
(3.2%)
95
(3.6%)
84
(3.2%)
165
(6.3%)
161
(6.1%)
265
(10.1%)
2,624
(100%)
2001 971
(37.1%)
431
(16.5%)
339
(13.0%)
117
(4.5%)
83
(3.2%)
97
(3.7%)
69
(2.6%)
146
(5.6%)
148
(5.7%)
214
(8.2%)
2,615
(100%)
2002 986
(36.2%)
462
(17.0%)
354
(13.0%)
106
(3.9%)
80
(2.9%)
107
(3.9%)
74
(2.7%)
152
(5.6%)
147
(5.4%)
258
(9.5%)
2,726
(100%)
2003 657
(29.2%)
323
(14.4%)
273
(12.1%)
98
(4.4%)
93
(4.1%)
79
(3.5%)
80
(3.6%)
105
(4.7%)
119
(5.3%)
421
(18.7%)
2,248
(100%)
2004 887
(30.1%)
417
(14.1%)
383
(13.0%)
103
(3.5%)
148
(5.0%)
117
(4.0%)
87
(2.9%)
137
(4.6%)
165
(5.6%)
506
(17.2%)
2,950
(100%)
2005 1,124
(33.3%)
433
(12.8%)
391
(11.6%)
94
(2.8%)
183
(5.4%)
166
(4.9%)
92
(2.7%)
195
(5.8%)
172
(5.1%)
528
(15.6%)
3,378
(100%)
Total 9,019
(34.7%)
3,549
(13.7%)
3,319
(12.8%)
1,160
(4.5%)
1,035
(4.0%)
994
(3.8%)
967
(3.7%)
1,343
(5.2%)
1,546
(5.9%)
3,049
(11.7%)
25,981
(100%)
Note: 1. Numbers in parenthesis are mean market shares in the overall foreign tourist market. 2. Unit: Thousands
Table 2
Growth rate of foreign tourist arrivals (%)
Residency
Japan
Hong
Kong
USA
Thailand
South Korea
Singapore
Philippines
Malaysia
and
Indonesia
Europe
Others
Total foreign
tourist arrivals
1997
-1.35
-1.11
4.74
1.12 -21.81 4.35 7.05 2.17 4.49
11.23 0.59
1998 -8.71 7.80 1.57 5.26 -36.42 6.34 5.53 -10.75 0.59 4.26
-3.10
1999 -0.05
14.26
3.05 7.34 20.67 -1.35 -2.60 33.25 0.96 5.32
4.90
2000 10.90
12.97
13.13
-3.47 9.96 10.55 -31.64 27.59 -0.49 13.55
8.82
2001 5.99
19.17
-5.60
-12.59 -1.25 1.98 -17.80 -11.51 -8.24
-19.00 -0.36
2002 1.53 7.39
4.33
-9.12 -3.06 10.96 7.44 3.68 -0.62
20.24 4.28
2003 -33.37
-30.11
-22.94
-7.00 15.89 -26.67 7.76 -30.72
-19.06
63.25 -17.55
2004 35.04
29.06
40.30
4.78 59.43 48.42 8.72 30.29
38.79
20.30 31.25
2005 26.71 3.75 2.12
-9.24 23.24 42.19 5.83 42.45 4.58 4.36
14.50
Mean 4.08
7.02
4.52
-2.55 7.41 10.75
-1.08 9.60 2.33
13.72 4.81
Standard
deviation
19.81
16.50
16.69
7.38 27.77 22.62 14.23 24.91 15.53
21.98 13.31
FINANCIAL PORTFOLIO THEORY AND OBJECTIVE FUNCTION
To apply the portfolio theory to the foreign tourist market for Taiwan, we needed to divide the market into
primary submarkets. In this study, we examined ten individual markets (nationalities) including Japan, Hong Kong,
the USA, Thailand, South Korea, Singapore, the Philippines, Malaysia/Indonesia, Europe, and others (all other
countries). We further considered that the expected return and variance of any optimal solution in a portfolio model
depends on a combination of the above markets’ demands. To quantify the individual market demands, we
considered both the growth rates of arrivals from different countries and the numbers of tourist arrivals. We decided,
however, not to use the growth rates, because resultant mixes may not be practically meaningful solutions for
Taiwan. If growth rates are used, high growth rate of Singapore (e.g., 10.75 percent) is treated as higher return rather
2007 Annual International CHRIE Conference & Exposition
146
than the less high growth rate of Japan (e.g., 4.08 percent), which indicates that Singapore is a much more important
market than Japan, despite its small market size. In reality, however, Japan, which generates more arrivals (return),
should be treated more importantly. In other words, the optimal solutions are decided purely by the variance-
covariance combination of growth rate, assuming that the number of arrivals from countries is almost the same.
Thus, using the growth rates may lead to erroneous solutions for Taiwan. Therefore, the study decided to use the
number of arrivals to Taiwan for individual countries (markets). The weight of each individual market within the
portfolio also will play an important role in determining the overall arrivals. First of all, the expected return (mean
arrivals) of a portfolio comprising
n
markets is the weighted average of the expected return of each market in the
portfolio:
( )
( )
∑
=
=
n
i
i
i
p
r
E
w
r
E
1
,
(1)
, where
( )
p
r
E
: the expected return of the portfolio,
w
i
: the proportion of market
i
in the portfolio,
( )
i
r
E
: the
expected return on market
i
,
n
: the number of markets in the portfolio.
Second, the variance of returns of the portfolio depends on the variance and covariance of markets in the
portfolio. For the case of a two-market portfolio, the variance of the portfolio returns can be expressed as:
( )
(
)
2
1
2
1
2
2
2
2
2
1
2
1
2
,
2
r
r
Cov
w
w
w
w
r
Var
p
p
+
+
=
=
σ
σ
σ
,
(2)
, where
( )
p
r
Var
: the variance of returns of the portfolio,
2
i
σ
: the variance of returns of market
i
,
(
)
2
1
,
r
r
Cov
: the
covariance of returns between markets 1 and 2, which measures the extend to which returns of markets 1 and 2
move together,
(
)
2
1
12
2
1
,
σ
σ
ρ
=
r
r
Cov
,
12
ρ
: the correlation coefficient between returns of markets 1 and 2,
1
w
and
2
w
: the weights of markets 1 and 2 respectively, where
0
1
≥
w
and
0
2
≥
w
and
1
2
1
=
+
w
w
.
When
(
)
0
,
2
1
=
r
r
Cov
, returns of markets 1 and 2 are uncorrelated. It is obvious that the variance of the portfolio
returns would be:
( )
2
2
2
2
2
1
2
1
σ
σ
w
w
r
Var
p
+
=
.
(3)
Since
1
0
1
≤
≤
w
and
1
0
2
≤
≤
w
, thus
1
2
1
w
w
≤
and
2
2
2
w
w
≤
. Accordingly, the variance of returns of the
portfolio would be less than the weighted sum of the variances of the individual markets. When
(
)
1
,
2
1
<
r
r
Cov
,
then the variance of the portfolio will be less than the weighted sum of the individual markets. Apparently, if the
arrivals from different markets are negatively correlated, the benefits (reduction in portfolio variance) from
diversification will be greater. When
(
)
1
,
2
1
−
=
r
r
Cov
(perfectly negative correlation), the portfolio variance will
fall to zero.
To find all possible efficient portfolios, we need to calculate the expected arrivals and variance of each
market and the pair-wise covariance between markets. After we computed the expected arrivals and the
variance/covariance matrix, the problem is reduced to the optimization of a quadratic function subject to constraints.
The variance and expected returns of individual efficient portfolios can be calculated based on the following model:
Objective function: Min
( )
j
i
n
i
n
i
n
i
j
j
j
i
i
i
r
r
Cov
w
w
w
,
1
1
,
1
2
2
∑
∑ ∑
=
=
≠
=
+
σ
,
(4)
Subject to:
∑
=
=
n
i
i
w
1
1
(5)
( )
( )
p
n
i
i
i
r
E
r
E
w
=
∑
=
1
(6)
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