Estimation Risk Modeling in Optimal Portfolio Selection: An Empirical Study from Emerging Markets

Table 1

Descriptive Statistics of index returns. Three periods are explored, total period ranges from January 1995 to December 2008, the first subperiod ranges from January 1995 to December 2001, and the second subperiod ranges from January 2002 to December 2008. Numbers in parentheses are 𝑡-statistics.

(a)

Country

Alpha

Beta

Total period

First subperiod

Second subperiod

Total period

First subperiod

Second subperiod

Turkey

0.03344^∗∗∗

0.06640^∗∗∗

0.00389

1.04746^∗∗∗

1.24056^∗∗∗

0.95713^∗∗∗

(−3.15)

(−3.47)

(−0.43)

(−6.75)

(−4.48)

(−7.16)

Russian Federation

0.01905^∗∗∗

0.03654^∗∗∗

0.00372

1.37491^∗∗∗

1.64265^∗∗∗

1.14265^∗∗∗

(−2.39)

(−2.56)

(−0.54)

(−11.83)

(−7.95)

(−11.12)

Hungary

0.00953^∗

0.02532^∗

−0.00442

0.79591^∗∗∗

0.86536^∗∗∗

0.76185^∗∗∗

(−1.71)

(−1.71)

(−0.91)

(−9.82)

(−5.99)

(−10.56)

Mexico

0.00894^∗∗∗

0.01418^∗∗∗

0.00593^∗

0.69188^∗∗∗

0.80156^∗∗∗

0.58642^∗∗∗

(−2.51)

(−2.23)

(−1.82)

(−13.30)

(−8.70)

(−12.07)

Brazil

0.00892^∗∗∗

0.01287^∗∗

0.00643

0.88102^∗∗∗

0.98651^∗∗∗

0.80493^∗∗∗

(−2.29)

(−1.95)

(−1.52)

(−15.49)

(−10.31)

(−12.76)

China

0.00781

0.00479

0.00869

0.90282^∗∗∗

0.79943^∗∗∗

0.99837^∗∗∗

(−1.08)

(−0.37)

(−1.20)

(−8.52)

(−4.30)

(−9.22)

South; Africa

0.00648^∗∗∗

0.01084^∗∗∗

0.00366

0.67337^∗∗∗

0.74886^∗∗∗

0.59815^∗∗∗

(−2.09)

(−2.25)

(−0.92)

(−14.88)

(−10.73)

(−10.10)

India

0.00564

0.00055

0.00849

0.78962^∗∗∗

0.59681^∗∗∗

0.98873^∗∗∗

(−1.13)

(−0.07)

(−1.43)

(−10.80)

(−5.12)

(−11.13)

Poland

0.00526

0.01573

−0.00379

0.71096^∗∗∗

0.72058^∗∗∗

0.71894^∗∗∗

(−0.91)

(−1.50)

(−0.76)

(−8.45)

(−4.73)

(−9.67)

Indonesia

0.00494

0.00347

0.00586

0.78745^∗∗∗

0.75247^∗∗∗

0.81547^∗∗∗

(−0.82)

(−0.32)

(−1.01)

(−8.91)

(−4.74)

(−9.46)

Columbia

0.00493

−0.00724

0.01628^∗∗∗

0.43162^∗∗∗

0.33934^∗∗∗

0.51276^∗∗∗

(−1.04)

(−0.98)

(−2.74)

(−6.24)

(−3.18)

(−5.80)

Peru

0.00434

0.00131

0.0058

0.51444^∗∗∗

0.44296^∗∗∗

0.56970^∗∗∗

(−1.08)

(−0.21)

(−1.13)

(−8.76)

(−4.80)

(−7.47)

Pakistan

0.00359

−0.00085

0.00701

0.46288^∗∗∗

0.53493^∗∗∗

0.34748^∗∗∗

(−0.46)

(−0.07)

(−0.73)

(−4.06)

(−2.93)

(−2.43)

Argentina

0.0033

0.00885

0.00422

0.78993^∗∗∗

1.01402^∗∗∗

0.59031^∗∗∗

(−0.54)

(−0.85)

(−0.70)

(−8.82)

(−6.70)

(−6.58)

Chile

0.0001

−0.00123

0.00392

0.45985^∗∗∗

0.59743^∗∗∗

0.32677^∗∗∗

(−0.04)

(−0.29)

(−1.19)

(−11.38)

(−9.62)

(−6.63)

Malaysia

−0.00165

0.00279

−0.00245

0.66056^∗∗∗

0.90756^∗∗∗

0.44679^∗∗∗

(−0.34)

(−0.32)

(−0.78)

(−9.43)

(−7.14)

(−8.80)

Taiwan

−0.00254

0.00699

−0.01154^∗∗∗

0.83599^∗∗∗

1.00786^∗∗∗

0.69489^∗∗∗

(−0.59)

(−0.97)

(−2.64)

(−13.29)

(−9.67)

(−10.66)

Philippines

−0.00256

−0.00183

−0.00085

0.63556^∗∗∗

0.85783^∗∗∗

0.41319^∗∗∗

(−0.55)

(−0.24)

(−0.16)

(−9.41)

(−7.87)

(−5.33)

Thailand

−0.00453

−0.00394

−0.00248

0.93898^∗∗∗

1.10057^∗∗∗

0.81091^∗∗∗

(−0.70)

(−0.34)

(−0.43)

(−9.98)

(−6.50)

(−9.55)

Country

F-Stat

Average return

Standard deviation

Total period

First subperiod

Second subperiod

Total period

First subperiod

Second subperiod

Total period

First subperiod

Second subperiod

Turkey

45.00^∗∗∗

20.07^∗∗∗

51.29^∗∗∗

3.35%

5.79%

0.98%

15.59%

19.34%

10.37%

Russian Federation

135.70^∗∗∗

63.23^∗∗∗

123.66^∗∗∗

1.92%

2.53%

1.08%

14.01%

17.20%

9.91%

Hungary

93.12^∗∗∗

35.99^∗∗∗

111.49^∗∗∗

0.96%

1.94%

0.03%

9.06%

10.83%

6.75%

Mexico

171.37^∗∗∗

75.67^∗∗∗

145.71^∗∗∗

0.90%

0.87%

0.96%

6.64%

8.00%

4.93%

Brazil

241.00^∗∗∗

106.19^∗∗∗

162.82^∗∗∗

0.90%

0.61%

1.14%

7.89%

9.08%

6.64%

China

69.44^∗∗∗

18.30^∗∗∗

85.04^∗∗∗

0.79%

−0.07%

1.49%

11.30%

12.93%

9.41%

South; Africa

213.13^∗∗∗

115.15^∗∗∗

102.03^∗∗∗

0.65%

0.57%

0.74%

6.14%

6.77%

5.40%

India

113.41^∗∗∗

26.21^∗∗∗

123.91^∗∗∗

0.57%

−0.35%

1.46%

8.48%

8.38%

8.57%

Poland

68.66^∗∗∗

22.42^∗∗∗

93.56^∗∗∗

0.53%

1.08%

0.07%

8.95%

10.75%

6.62%

Indonesia

75.96^∗∗∗

22.49^∗∗∗

89.44^∗∗∗

0.50%

−0.17%

1.09%

9.56%

11.21%

7.59%

Columbia

39.20^∗∗∗

10.12^∗∗∗

33.63^∗∗∗

0.50%

−0.96%

1.95%

6.84%

7.07%

6.39%

Peru

72.47^∗∗∗

23.05^∗∗∗

55.73^∗∗∗

0.44%

−0.17%

0.93%

6.31%

6.54%

6.02%

Pakistan

15.16^∗∗∗

8.59^∗∗∗

5.91^∗∗∗

0.36%

−0.45%

0.92%

10.63%

12.01%

9.01%

Argentina

81.50^∗∗∗

44.89

43.36

0.34%

0.19%

0.79%

9.65%

11.78%

6.75%

Chile

132.26

92.45^∗∗∗

43.97^∗∗∗

0.01%

−0.53%

0.60%

4.79%

5.67%

3.72%

Malaysia

92.46^∗∗∗

51.01^∗∗∗

77.43^∗∗∗

−0.16%

−0.34%

0.03%

7.72%

10.13%

4.31%

Taiwan

177.67^∗∗∗

93.60^∗∗∗

113.59^∗∗∗

−0.25%

0.01%

−0.72%

8.02%

9.54%

6.13%

Philippines

87.64^∗∗∗

62.00^∗∗∗

28.44^∗∗∗

−0.25%

−0.77%

0.17%

7.44%

9.03%

5.47%

Thailand

101.92^∗∗∗

42.22^∗∗∗

91.16^∗∗∗

−0.44%

−1.15%

0.26%

10.57%

13.05%

7.51%

∗, ∗∗, and ∗∗∗indicate significant at 10%, 5%, and 1%, respectively.

(b)

Country	Information ratio
	Total period	First subperiod	Second subperiod
Turkey	295.7651	181.6571	48.3165
Russian Federation	300.5328	179.6849	78.2327
Hungary	308.6629	255.3434	−188.4281
Mexico	703.1102	350.4998	557.6252
Brazil	587.5088	294.6973	358.7845
China	148.1109	28.7707	164.5916
South Africa	674.1654	467.1711	231.4469
India	224.6173	8.5055	239.0569
Poland	158.2308	142.5708	−152.1374
Indonesia	134.6862	28.8828	174.9011
Columbia	219.6666	−133.5755	462.2749
Peru	268.1393	32.2578	221.1845
Pakistan	58.9806	−5.3772	76.1875
Argentina	87.5264	81.0338	116.5557
Chile	13.5179	−66.9743	358.3304
Malaysia	−71.5389	36.3157	−210.6151
Taiwan	−136.7961	135.1681	−602.6266
Philippines	−119.5397	−32.4259	−31.299
Thailand	−109.0524	−28.7929	−76.1938