不同類型共同基金報酬率與風險值之相關研究

(1)

國立

國立臺

臺

臺中教育大學數學教育學系碩士班碩士論文

中教育大學數學教育學系碩士班碩士論文

指

指導

導

導教

教

教授

授：

授

：

：許天維

：

許天維

許天維教授

許天維

教授

不同類型共同基金

報酬率與風險值之相關研究

研

研究

究

究生

生

生：

：

：王崇吉

：

王崇吉

王崇吉撰

撰

中

中華

華

華民

華

民

民國

國

國一

國

一百

一

百

百年

百

年

年七

七

七月

月

(2)

2009 1 2009 12 2010 σ=1.9326818 σ =1.5611789 σ=0.2787388 σ =2.3333778 σ=2.2569603。 1.0062 1.6677 0.5226 7.072 4.0603 0.721649

(3)

(4)

Abstract

Because there are some restrictions and shortcomings of the traditional index of fund performance, so, this study intends of estimate the volatility of BlackRock, Inc.’s five funds from the January of 2009 to the December of 2009 : BlackRock World Technology Fund, BlackRock World Energy Fund, BlackRock New Energy Fund, BlackRock World Mining Fund, BlackRock World Gold Fund by the interaction of the Bouchard-Mezard model, which was introduced by Feng-Rung Hu.

The purpose of this study is to analyze the volatility of the fund, and forecasts the net worth of the five funds. Then, this study will estimate the errors of the modeled net worth by Root Mean Squared Error (RMSE). Finally, this study analyzes the correlation between the different types of mutual fund and volatility by Pearson Correlation.

This study obtains the following empirical results.

(1)The volatility of BlackRock World Technology Fund is 1.9326818; BlackRock World Energy Fund 1.5611789; BlackRock New Energy

Fund .2787388; BlackRock World Mining Fund2.3333778; and BlackRock World Gold Fund 2.2569603

(2) The Root Mean Squared Error of BlackRock World Technology Fund is

1.0062; BlackRock World Energy Fund 1.6677; BlackRock New Energy Fund 0.5226; BlackRock World Mining Fund 7.072; and BlackRock World Gold Fund 4.0603.

(5)

(3)Pearson Correlation coefficient between the different types of mutual fund and volatility is 0.721649, reveals positive correlation.

From an analysis of the forecasts of the net worth, a distinctive difference can be found between some forecasted net worth and their actual worth.

Key words :Forecast of the fund’s net worth, Volatility, Bouchard-Mezard model.

(6)

... 1 ... 1 ... 3 ... 4 ... 5 ... 5 ... 8 ... 10 ... 13 ... 27 ... 27 ... 29 ... 34 ... 37 ... 37 ... 40 ... 41 ... 41 ... 42

(7)

3-1 σ_i ... 28

3-2 ... 35 3-3 2010 ... 45

(8)

3-1 2010 1 2010 12 ... 29 3-2 2010 1 2010 12 ... 30 3-3 2010 1 2010 12 ... 31 3-4 2010 1 2010 12 ... 32 3-5 2010 1 2010 12 ... 33 3-6 ... 36

(9)

(10)

1

Standard & Poor's Lipper

Sharpe Index

(11)

2

Sharpe Index

(2009) —

—

(12)

3

— (BlackRock, Inc.) — 2009 1 2009 12 (BlackRock, Inc.) — 2010 1 2010 12 (BlackRock, Inc.) —

(13)

4

(Sharpe Index) (Treynor

(14)

5

(econophysics) (polymer) (J.P.Bouchaud) (M.Mezard) 2000 t i X_i(t)

{

}

∑

= − + = n j i j i i i X t X t dt n J t dB t X t dX 1 ) ( ) ( ) ( ) ( ) ( σ

σ (volatility) B_i(t) Brownian motion

n J J=0 Black-Scholes — Black-Scholes J≠ 0

∑

{

}

= − n j i j t X t X n J 1 ) ( ) ( i i

(15)

6 ) ( ) ( lim ) ( 1 t X t nX t Z _n j j i n i

∑

= ∞ > − = (2000) Z₁(t),Z₂(t),… ) ( limZ t Z _i n−>∞ =

∫

+ − − = ≤ z x _dx x C z Z P 0 1 1 e 1 ) ( µ µ 2 1 σ µ= + J

∫

∞ + − − = 0 1 1 e 1 1 dx x C x µ µ Z (power law) σ σ (2009) — σ consistent estimator

(16)

7 2009 — 0,1,2,3,…,N

( )

∑

= = _n t t i i X t X t Y 1 ) ( 2009 σ

( )

_            + − −

∑∑

= = = = N j n k k N j n k k j Y N n j Y N J 1 1 2 1 1 2 1 1 1 2 1 2 1 1 —

∑

= − + = n K i r i i i i X t X t dt n J t dB t X t dX 1 )} ( ) ( { ) ( ) ( ) ( σ (2009b) ri σ i σ1<σ2 <σ3 <…<σn r1 >r2 >r3…>rn i i σ

(17)

8 i σ } ) ) ( 1 ) ( 1 ( { 2 1 2 1 1

∑

= + − N k Yi k Y k nN J σ

mutual fund 1924 1940 1983 ( , 2000) 1.

(18)

9 2. 1. 2. 1. 2. 3.

(19)

10 1. 2. 3. 4. 5.

1924 1990

William Sharpe(1966) (Security Market

(20)

11

Treynor(1966) (Reward to

Volatility Ratio) Treynor Sharpe

Jensen(1968) Jensen CAPM 0 0 (Information Ratio) (Information Ratio)

(21)

12

(CAPM)

(2005)

1. Roll(1977)

(market proxy)

2. Lehmann and Modest(1987)

1.

2. Admati and Ross (1985) Dybvig and Ross (1985)

(22)

13

(2005) (market risk) (FASB) (SEC) (VAR)

(23)

14

(back test)

30

VAR RbVAR

(24)

15 β σ σ σ — (2006)

(25)

16

Dowd(1999) (Value at Risk)

Murray(1999) BRVaR(Benchmark- Relative Value at Risk)

Johnson Buetow Jensen (1999)

(26)

17

— —

(27)

18

Hell-White

(28)

19 Delta-Normal Dowd(1999) MSCI MSCI 39 1999 1 2001 12 156 1999 1 2000 12 104 2001

(29)

20

24

Delta-Normal

(30)

21

Delta-Normal

(2004)

(31)

22 90 1 92 12 36 96 80 16 88 1 92 12 60 80 0.2 0.3 (Artificial Neural Network) 911

(32)

23

(2001)

MVar

(33)

24 88 1 5 89 12 31 539 88 1 5 89 12 30 537 -MVaR MV – MVaR MV MVaR

(34)

25

MV

(35)

(36)

27 (BlackRock, Inc.) 2009 252 MATLAB —

(BlackRock, Inc.) 2009 1 12 (http://announce.fundclear.com.tw/MOPSFund Web /) Excel

{

}

∑

= − + = n k i k i i i i X t X t dt n J t dB t X t dX 1 ) ( ) ( ) ( ) ( ) ( σ

,

i=5

5 = i dB_i(t)=(B_i(t_j))n σ 0 0 2 0 1( )} ,{ ( )} , ,{ ( )} {B t _t_≥ B t _t_≥ _L B_n t _t_≥ n (Brownian Motion) J=1

(37)

28

Excel (BlackRock, Inc.)

1.9326818 = σ σ } ) ) ( 1 ) ( 1 ( { 2 1 2 1 1

∑

= + − N k Yi k Y k nN J σ Excel 3-1 1.9326818 1.5611789 0.2787388 2.3333778 2.2569603

(38)

29

σ J =1 — (BlackRock, Inc.)2010 1 2010 12 (http://announce.fundclear.com.tw/ MOPSFundWeb/) 1.9326818 = σ 3-1 2010 1 2010 12 3-1

(39)

30 196 (RMSE) 1.0062 1.5611789 = σ 3-2 2010 1 2010 12 3-2 55 63 (RMSE) 1.6677

(40)

31 0.2787388 = σ 3-3 2010 1 2010 12 3-3 14 14 140 141 (RMSE) 0.5226

(41)

32 2.3333778 = σ 3-4 2010 1 2010 12 3-4 39 58 88 188 189 (RMSE) 7.072

(42)

33 2.2569603 = σ 3-5 2010 1 2010 12 3-5 9 110 111 208 (RMSE) 4.0603

(43)

34

(BlackRock, Inc.)

2010 1 2010 12

253 — Matlab

(Root Mean Squared Error , RMSE)

RMSE =

(

)

n E O n i i i 2 1

∑

= − i O E_i n

(44)

35 RMSE 1.0062 1.6677 0.5226 7.072 4.0603 3-2 3-2 Hu(2009a) — n i σ Yi

( )

) ( 1 t X t X t Y _n k k i i

∑

= = i X (Pearson Correlation)

(45)

36

∑

= n 1 = i 2 i 2 n 1 = i i i n 1 = i i ) Y -(Y ) X -X ( ) Y -)(Y X -X ( γ i Y X_i n 0.721649 Hu(2009b) Hu(2009b) 3-6

(46)

37

— (BlackRock , Inc.)2009 1 2009 12 2010 1 2010 12 (BlackRock, Inc.) 2009 1 2009 12

— 2009 1 2009 12 (BlackRock, Inc.) — Excel 2009 1 2009 12 σ =1.9326818 σ =1.5611789 σ =0.2787388 σ =2.3333778 σ =2.2569603

(47)

38

— 2010 1 2010 12

(Root Mean Squared Error , RMSE)

1.0062

1.6677 0.5226

7.072 4.0603

3-1 3-5 —

(48)

39

—

0.731865

(49)

40

5 > n 2010 1 2010 12 253

(50)

41 (2000) (2005) (2006) (1997) (2002) ─ (2004) (2000) (2010) Bouchaud-Mezard ─

(51)

42 (2005) (2004) (2005) (2002) -(2002) (2000)

Feng-Rung Hu (2009a): On the estimation of the power-law exponent in the mean-field Bouchaud-Mezard model, Physica A:Statistical Mechanics and its Applications, 387(18), 4605-4614.

Feng-Rung Hu (2009b): On the ratio processes induced from the mean-field Bouchaud-Mezard model. WSEAS Transactions on Mathematics, 7(6), 406-416.

(52)

43

Chu-Lin Huang(2004):Protfolio Optimization of Equity Mutual Fund with Fuzzy Return Rate and Risk

William Sharpe (1966):Mutual Fund Performance.Journal of Business 39 ,pp.119-138

Jack L. Treynor(1966): How to Rate Management of Investment Funds. Harvard Business Review 43, pp. 63-75.

Roll, Richard (1977): A critique of the asset pricing theory's tests Part I: On past and potential testability of the theory

Bruce N. Lehmann, David M. Modest(1987):Mutual Fund Performance Evaluation: A Comparison of Benchmarks and Benchmark Comparisons

Anat R. Admati and Stephen A. Ross(1985):Measuring Investment Performance in a Rational Expectations Equilibrium Model

Philip H. Dybvig and Stephen A. Ross(1985)Differential Information and Performance Measurement Using a Security Market Line

(53)

(54)

45 3-3 2010 1 4 11.38 23.17 68.81 9.03 50.96 1 5 11.42 23.28 69.63 9.09 51.58 1 6 11.45 23.39 70.62 9.15 52.33 1 7 11.33 23.4 70.57 9.14 52.27 1 8 11.36 23.53 71.57 9.21 52.7 1 11 11.38 23.95 72.96 9.3 54.1 1 12 11.32 23.44 71.03 9.18 53.03 1 13 11.24 23.37 70.99 9.19 52.35 1 14 11.42 23.53 71.42 9.2 52.27 1 15 11.37 23.38 70.65 9.02 51.25 1 18 11.29 23.37 71.12 9 51.56 1 19 11.3 23.35 71.24 8.95 51.32 1 20 11.24 23.06 69.32 8.8 50.15 1 21 11.28 23.01 67.69 8.72 49.05 1 22 11 22.43 64.93 8.5 47.19 1 25 10.88 22.39 65.64 8.48 47.44 1 26 10.73 21.95 63.57 8.34 46.33 1 27 10.75 22 63.24 8.33 46.1 1 28 10.75 21.93 63.12 8.28 46.07 1 29 10.64 22.02 62.3 8.24 45.19 2 1 10.44 21.74 61.56 8.23 44.69 2 2 10.56 21.98 63.63 8.25 46.14 2 3 10.72 22.36 64.18 8.29 46.76 2 4 10.53 21.57 60.6 7.96 44.26 2 5 10.29 20.92 58.41 7.75 43.03 2 8 10.42 20.94 59.19 7.71 44.3

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46 2 9 10.46 21.28 60.97 7.83 44.94 2 10 10.57 21.31 61.14 7.82 45.3 2 11 10.46 21.35 61.1 7.76 45.56 2 12 10.49 21.49 61.34 7.72 45.83 2 15 10.58 21.72 62.31 7.79 46.47 2 16 10.68 22.07 63.3 7.84 47.28 2 17 10.82 22.3 64.96 7.95 48.32 2 18 10.82 22.27 64.78 7.98 48.08 2 19 10.77 22.17 64.05 7.91 47.04 2 22 10.85 22.29 65.13 7.98 47.52 2 23 10.8 21.97 64.15 7.91 46.82 2 24 10.76 21.86 63.12 7.81 45.88 2 25 10.6 21.36 61.21 7.65 44.98 2 26 10.7 21.74 62.74 7.66 46.3 3 1 10.84 21.99 63.67 7.72 46.75 3 2 11.02 22.32 64.93 7.82 48.22 3 3 11.02 22.45 66.52 7.96 49.42 3 4 10.99 22.53 66.63 7.98 49.29 3 5 11.11 22.61 67.58 8.01 49.69 3 8 11.21 22.76 68.59 8.05 49.77 3 9 11.2 22.69 67.61 7.99 49.06 3 10 11.29 22.73 68.13 8.03 49.13 3 11 11.31 22.86 67.06 7.99 48.14 3 12 11.4 23.14 68.71 8.07 49.2 3 15 11.27 22.71 67.48 8 48.28 3 16 11.39 22.92 68.44 8.01 49.22 3 17 11.57 23.24 69.77 8.09 49.8 3 18 11.55 23.05 69.36 8.08 49.8 3 19 11.46 22.58 67.88 7.97 48.95

(56)

47 3 22 11.57 22.41 67.25 7.95 48.27 3 23 11.56 22.61 68.66 8.03 48.77 3 24 11.61 22.61 68.29 8.01 47.78 3 25 11.65 22.54 68.24 8.09 47.37 3 26 11.65 22.29 68.01 8.08 47.14 3 29 11.68 22.51 68.99 8.13 47.93 3 30 11.71 22.73 70.39 8.13 48.26 3 31 11.65 22.83 70.1 8.09 48.3 4 1 11.8 23.26 72.27 8.19 50.03 4 6 11.83 23.82 73.38 8.17 50.86 4 7 11.86 23.66 73.38 8.27 51.49 4 8 11.74 23.26 72.05 8.16 51.55 4 9 11.84 23.82 73.82 8.29 52.48 4 12 11.9 23.78 73.65 8.34 52.41 4 13 11.93 23.6 72.63 8.33 51.32 4 14 12.09 23.64 73.45 8.36 51.75 4 15 12.17 23.94 73.49 8.39 51.95 4 16 12.12 23.68 72.17 8.36 51.05 4 19 12.01 23.31 70.2 8.2 49.92 4 20 12.08 23.78 71.33 8.3 50.89 4 21 12.22 23.9 70.43 8.28 50.73 4 22 12.08 23.49 68.85 8.13 50.09 4 23 12.27 23.82 69.92 8.28 50.72 4 26 12.33 24.15 71.25 8.33 51.59 4 27 12.25 23.85 69.8 8.25 51.16 4 28 12.01 23.39 67.93 8.04 51.04 4 29 12.05 23.68 68.83 8.17 52.11 4 30 12.13 23.25 68.13 8.26 52.61 5 3 12.03 23.27 67.44 8.22 52.24

(57)

48 5 4 11.9 22.84 64.03 8 51.06 5 5 11.62 22.25 62.01 7.7 49.43 5 6 11.6 22.2 62.7 7.72 50.36 5 7 11.14 21.3 60.6 7.41 50.21 5 10 11.53 21.94 64.13 7.75 50.69 5 11 11.47 21.72 63.19 7.64 52.51 5 12 11.64 22 64.37 7.76 54.46 5 14 11.35 21.41 62.4 7.58 53.7 5 17 11.26 21.21 61.53 7.52 53.37 5 18 11.34 21.45 61.85 7.63 52.83 5 19 11.1 20.77 58.58 7.36 50.52 5 20 10.79 19.97 55.37 7.07 48.48 5 21 10.68 19.81 56.57 7.06 47.86 5 25 10.37 19.11 55.04 6.74 47.62 5 26 10.76 20.11 58.54 7.02 50.01 5 27 10.81 20.5 59.69 7.06 50.5 5 28 10.96 20.64 60.73 7.21 50.92 5 31 10.87 20.48 60.4 7.16 50.98 6 1 10.82 19.94 59.73 7.06 51.31 6 2 10.78 19.59 59.21 7.02 50.71 6 3 11.1 20.42 60.92 7.23 51.61 6 4 11.02 20.3 58.61 7.06 50.14 6 7 10.8 19.9 56.94 6.91 49.75 6 8 10.5 19.35 56.15 6.73 50.89 6 9 10.59 19.92 58.39 6.84 51.87 6 10 10.74 20.16 60.02 6.98 52.16 6 11 10.83 20.34 60.09 7.06 52.32 6 14 11.03 20.7 61.47 7.2 52.96 6 15 11.09 20.77 61.75 7.3 52.81

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49 6 16 11.2 20.98 62.56 7.37 53.61 6 17 11.3 21.13 62.81 7.42 54.51 6 18 11.3 20.94 62.35 7.44 55.3 6 21 11.49 21.55 64.9 7.61 56.04 6 22 11.33 21.08 63.5 7.46 54.88 6 24 11 20.3 61.66 7.29 54.19 6 25 10.9 20.08 61.19 7.19 54.64 6 28 10.87 20.08 61.35 7.2 55.45 6 29 10.64 19.53 58.84 6.98 53.52 6 30 10.54 19.39 58.02 6.98 53.4 7 1 10.39 19.15 57.15 6.92 52.91 7 2 10.37 19.3 57.44 6.99 51.88 7 5 10.33 19.18 56.41 6.97 51.11 7 6 10.56 19.57 58.09 7.18 51.35 7 7 10.57 19.67 57.94 7.11 51.11 7 8 10.89 20.2 59.61 7.29 52.15 7 9 10.92 20.38 60.63 7.29 52.84 7 12 11.05 20.57 60.69 7.32 53.31 7 13 11.06 20.7 60.94 7.38 53.38 7 14 11.29 20.5 60.38 7.42 52.9 7 15 11.27 20.64 60.41 7.47 52.91 7 16 11.12 20.4 59.22 7.38 51.56 7 19 11.04 20.36 59.14 7.35 50.8 7 20 10.9 20.29 59.41 7.3 50.6 7 21 11.11 20.65 61.8 7.4 51.44 7 22 11.15 20.85 63.24 7.51 52.41 7 23 11.2 20.8 63.34 7.51 52.35 7 26 11.37 21.14 64.04 7.61 52.41 7 27 11.46 21.24 64.54 7.71 51.86

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50 7 28 11.42 21.12 63.98 7.66 50.92 7 29 11.33 21.21 64.58 7.68 51.4 7 30 11.11 20.91 63.41 7.5 51.18 8 2 11.31 21.47 65.79 7.69 52.42 8 3 11.37 21.65 66 7.68 52.4 8 4 11.38 21.91 66.3 7.72 53.16 8 5 11.39 21.88 66.4 7.72 53.08 8 6 11.37 21.84 66.85 7.78 53.72 8 9 11.29 21.77 66.24 7.78 53.27 8 10 11.15 21.46 64.72 7.67 52.74 8 11 10.9 21.1 63.32 7.47 52.82 8 12 10.71 20.8 62.17 7.35 52.47 8 13 10.75 20.99 62.99 7.39 52.88 8 16 10.71 20.65 62.9 7.31 52.91 8 17 10.82 20.97 63.97 7.51 53.48 8 18 10.88 20.93 63.81 7.43 53.44 8 19 10.9 20.86 64.05 7.39 54.23 8 20 10.78 20.43 62.07 7.18 53 8 23 10.87 20.63 63.02 7.27 53.67 8 24 10.59 20.07 60.21 7.03 52.15 8 25 10.48 19.81 59.22 6.94 52.22 8 26 10.63 20.13 61.13 7.11 54.01 8 27 10.47 19.95 60.55 7.05 53.74 8 30 10.64 20.39 62.13 7.17 54.79 8 31 10.43 20.07 61.87 7.05 55.36 9 1 10.62 20.52 63.96 7.24 55.97 9 2 10.75 20.78 64.94 7.35 56 9 3 10.99 21.21 66.41 7.44 56.41 9 6 11.02 21.12 65.91 7.44 56.65

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51 9 7 10.91 20.8 64.63 7.32 56.67 9 8 10.89 20.99 65.62 7.35 57.14 9 9 10.99 21.22 66.44 7.42 57.38 9 10 10.91 21.17 65.79 7.41 56.86 9 13 11.08 21.36 67.12 7.5 56.99 9 14 11.15 21.4 67.75 7.52 58.43 9 15 11.19 21.32 67.69 7.48 58.54 9 16 11.23 21.36 67.98 7.5 59.23 9 17 11.29 21.26 68.16 7.47 59.53 9 20 11.33 21.37 68.4 7.43 59.75 9 21 11.39 21.64 68.53 7.51 59.46 9 22 11.33 21.75 70.03 7.6 60.78 9 23 11.24 21.28 68.64 7.43 60.02 9 24 11.4 21.79 70.49 7.56 60.64 9 27 11.44 21.86 70.63 7.56 60.2 9 28 11.38 21.72 70.2 7.56 59.27 9 29 11.53 22.01 71.33 7.61 60.84 9 30 11.6 22.37 71.85 7.7 60.87 10 1 11.57 22.62 72.49 7.69 61.34 10 4 11.51 22.62 72.47 7.65 61.15 10 5 11.56 22.67 72.9 7.72 61.98 10 6 11.59 22.93 75.24 7.86 63.4 10 7 11.54 22.83 75.05 7.82 63.2 10 8 11.48 22.9 75.3 7.84 62.7 10 11 11.56 23.15 76.12 7.87 63.13 10 12 11.47 22.87 74.5 7.81 62.14 10 13 11.75 23.28 76.94 7.98 63.88 10 14 11.8 23.37 78.04 8.04 64.71 10 15 11.83 23.31 77.77 8.02 63.97

(61)

52 10 18 11.89 23.33 76.98 8.03 62.93 10 19 11.7 22.95 74.66 7.91 60.8 10 20 11.76 22.95 75.28 7.91 60.88 10 21 11.89 23.22 76.87 7.97 61.56 10 22 11.89 23.17 75.5 7.93 60.3 10 25 12.1 23.58 77.86 8.05 62.2 10 26 11.96 23.27 76.61 7.92 61.49 10 27 12 23.12 75.64 7.9 60.75 10 28 12.06 23.28 76.48 7.94 61.46 10 29 12.04 23.17 76.43 7.87 62.29 11 2 12.1 23.53 78.3 7.89 63.15 11 3 12.17 23.61 78.32 7.92 63.16 11 4 12.41 24.31 81.84 8.09 65.71 11 5 12.41 24.56 83.61 8.05 67.27 11 8 12.38 24.49 82.56 8 66.35 11 9 12.49 24.86 84.68 8.06 69.1 11 10 12.25 24.41 81.56 7.88 66.01 11 11 12.08 24.66 82.75 7.83 66.8 11 12 12.12 24.68 82.86 7.83 67.02 11 15 12.06 24.51 81.54 7.74 65.62 11 16 11.98 23.96 78.98 7.64 63.81 11 17 11.9 23.83 78.29 7.54 63.33 11 18 12.09 24.34 80.24 7.67 64.71 11 19 12.1 24.22 79.33 7.66 63.94 11 22 12.26 24.51 80.16 7.67 64.71 11 23 12.09 24.04 78.24 7.52 64.47 11 24 12.22 24.31 78.74 7.55 64.53 11 25 12.31 24.47 79.48 7.58 64.7 11 26 12.25 24.28 78.32 7.53 63.78

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53 11 29 12.1 23.91 76.57 7.37 62.77 11 30 12.08 24.05 76.56 7.35 63.26 12 1 12.34 24.67 78.88 7.48 64.19 12 2 12.51 25.07 80.98 7.55 65.74 12 3 12.74 25.34 82.51 7.67 67.07 12 6 12.79 25.54 83.46 7.67 67.93 12 7 12.88 25.78 85 7.78 68.56 12 8 12.84 25.52 84.13 7.7 67.24 12 9 12.89 25.44 83.6 7.68 66.65 12 10 12.87 25.48 83.12 7.74 65.8 12 13 12.93 25.79 84.96 7.81 67.02 12 14 12.93 25.78 84.75 7.78 67.02 12 15 12.84 25.64 84.73 7.78 67.11 12 16 12.77 25.36 83.13 7.67 65.54 12 17 12.94 25.59 83.47 7.7 65.31 12 20 12.93 25.76 84.26 7.69 65.9 12 21 13.08 25.89 85 7.73 65.82 12 22 13.08 26.11 85.33 7.73 65.91 12 23 13.1 26.23 85.24 7.73 65.6 12 27 12.94 26.21 85.37 7.69 65.68 12 28 13.03 26.32 85.59 7.69 66.25 12 29 13.01 26.41 85.93 7.73 66.82 12 30 13.04 26.67 87.12 7.8 67.29 12 31 12.99 26.62 86.7 7.8 67.44

不同類型共同基金報酬率與風險值之相關研究

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國立

國立

國立臺

臺

臺

臺中教育大學數學教育學系碩士班碩士論文

中教育大學數學教育學系碩士班碩士論文

中教育大學數學教育學系碩士班碩士論文

中教育大學數學教育學系碩士班碩士論文

指

指

指

指 導

導

導

導 教

教

教

教 授

授：

授

授

：

：許天維

：

許天維

許天維 教授

許天維

教授

教授

教授

不同類型共同基金

不同類型共同基金

不同類型共同基金

不同類型共同基金

報酬率與風險值之相關研究

報酬率與風險值之相關研究

報酬率與風險值之相關研究

報酬率與風險值之相關研究

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