: : : 3 :2004 6 30 39 67,, 2005 1 1 2006 12 31,,, ( Evans and Archer) (Latane and Young) (Markowitz) :,,, :?,?,,,, 2006 12 31, 321, 8564161,53 1623150, 18196 % ; 268 6941110, 81104 %, 50 %,,2006,,,2006, ( ) 52, 52 48, ( ) 32, 26 3,( ),, :shaoanhuang @sdu. edu. cn ;, ( ), :250100, :weiqian @mail. sdu. edu. cn (:04JZD0007) 2006 2007 1 16, 52 118
2007 12,, :, ;,,?, : (1), ; (2),,,, ; (3),,, :,;; ;,,,,(Markowitz,1952) 1959 (,,2000),,, 20 60, ( Evans and Archer,1968) 1958 1967 470,,,60 1 60 2 60 40,, 40,, 8, (0105 ),; 10,,,, : (Fisher and Lorie,1970), ; (Wagner and Lau, 1971), ;, (Johnson and Shannon, 1974),,,,, ( Elton and Gruber,1977),, :,N,,, (Mao,1970),Lintner (1965),,, 119
: : (1 - ) [ ((1 -,0 << 1,N = ) + ) 2 ], [1 - ((1 - ) + ) 2 ], (Brennan,1975),,, : N = ( ) ( R m ) X ( E( R m ) - r),, r ; X ; ; F 2 F(1 + r) ;( ) ;( R m ) ; E ( R m ), :, :(1996) (1998) ;(2000) ;(2001),,,,,, ; (2003),,,: (1),,; (2), 11,,,, ;,,, 2005 1 1 2006 12 31,, ;,2005 2006,, 2004 12 31, 6, 2004 6 30 ( 39 67 ),, 2006 12 31,, 2007 6 30 13 120
2007 12 2005 1 1 2006 12 31 98 21, 31 (1),,, (Fama, 1976,p. 31), (2003) 1997 2000,, (2) i t : R i, t = ln P i, t + D i, t P i, t - 1,, i,p i, t i t ; i,p i, t i t ; D i, t i t i T : gr i i T : i = = 1 T T R i, t t = 1 T ( R i, t - gr i ) 2 t = 1 T - 1 (3) t : R P, t = ln 1 N, T : gr P T : P = (4) Sharpe N i = 1 + D i, t P i, t P i, t - 1 = 1 T T R P, t t = 1 T ( R P, t - gr P ) 2 t = 1 T - 1, N n Sharpe : S P, n, R P 4. (1) = R P - R f, R f P,,,, R f = 1 T T {[1 + i t, n (1 - r) ] 1Π52-1}, i t, n n t t = 1, r R f 0101105 % 121
: :,N,12n n,n, : ( N ) 1, ; N - 1 1, 2, ; N - 2 1, 3, ;, n 1 n, 1000,1000 1 1000 2 1000 n,, (2), 8,,, 8, 100, : 8,,1 ; 9 16, 8 1, 8, 2 ; 17 24, 8 2, 8, 3 ;, 100,,1000 1 1000 2 1000 100,,,39 67 106,,, 35, 60,100 : 1. 12 3 12 3,,, 2. matlab710,( ), 122
2007 12 4,,,,,, 1 5, (9125 %) ; 5 10, (1164 %) ; 10 15, ( 0149 %) ;,, 31257 %, 1 5, 5121 % ; 5 10, 1 2 3 0174 % ;,,21535 % 4 - ( 1000),, 123
: : t,,1 %5 %, 18 22, 26 37, 67 73, 5, 1 %, 11140 %, 6122 %, 13104 % 5 t p, 6,,,, 4 6,,,,, 31 Sharpe, Lintner (1965),, CAPM, Treynor (1965), Sharpe (1966) Jensen (1968), Treynor Jensen,, Sharpe Sharpe 7, : t t = gx - gyπs, s x y ( Efficient Market Hypothesis) Fama (1970),,,(CAPM APT ),20 80,90,,,,,,, 124 1Πn + 1Πm,, gx gy ( x y), n m
2007 12 6 - (1) Sharpe,Sharpe, 7,,Sharpe 22,Sharpe ; 28,Sharpe ; 73,, Sharpe,, 22,28, 73, (2) Sharpe,,3,Sharpe,,,, 73 41 7 sharpe,,: (1) : 125
: : Y i = + 1 N i (1), N i ( N i = 1,2,,12) ; Y i (2) (Latane and Young) : (3) : 1 Y i = + 1 N i (2) Y i = + 1 N i (3) t R 2 R 2 312446 302317 33 (1000 1 014557 91127 33 019961 019959 311586 537176 ) 33 2 1 014687 27147 33 019581 019568 35,,, (2) 3 1 (1) (3), (3) 2 (1),, (1) (3) 3 1, 2 (2003),(1) (3) (2) 51 3 1015160 199716 33 311363 128105 33 215306 1339211 33 011769 154121 33 215064 1312102 33 011620 23169 33 614029 655112 33 019218 155138 33 216263 730419 33 014169 148128 33 215819 104515 33 013552 32176 33 618934 505916 33 212353 218123 33 019980 019979 019976 019975 019063 019046 019976 019976 019956 019955 019163 019155 019979 019979 :t 1 %,5 % 106,,8 9 : (1),, ; (2),,,Sharpe 10,,,Sharpe, 126 60 100
2007 12,,, 8-9 - 10 sharpe 127
: :,, : (1),,,1 %5 %, 18 22, 26 37, 67 73 ;,22, 28, 73, (2),, Sharpe,,3, Sharpe,, 73 (3),,,, Sharpe,,, (4),,,,,, 39 2006,,,15 %20 %, ;,,,: ;,,2001 :,5,2000 :,,2000 :Markowitz, 1 128
2007 12,1996 :, 10,1998 :, 4,2003 :, Brennan, H.J., 1975,The Optimal Number of Securities in a Risky Asset Portfolio When There Are Fixed Costs of Transacting : Theory and Some Empirical Results, Journal of Financial and Quantitative Analysis, Vol. 10, pp. 483 496. Elton, E.J., and M.J. Gruber, 1977,Risk Reduction and Portfolio Size : An Analytical Solution, Journal of Business, Vol. 50, pp. 415 437. Evans, J.L, and S. H. Archer, 1968,Diversification and the Reduction of Dispersion : An Empirical Analysis, Journal of Finance, Vol. 23, pp. 761 767. 417. Fama, E. F., 1970,Efficient Capital Markets :A Review of Theory and Empirical Work, Journal of Finance, Vol. 25 (May), pp. 383 Fama,E. F.,1976,Foundations of Finance :Portfolio Decision and Security Prices,New York :Basic Books Inc. Fisher, L., and J. H. Lorie, 1970,Some Studies of Variability of Returns on Investments in Common Stocks, Journal of Business, Vol. 43, pp. 99 134. Jensen, M. C., 1968,The Performance of Mutual Funds in the Period 1945 1964, Journal of Finance, Vol. 23, pp. 389 416. Johnson, K. H., and D. S. Shannon, 1974,A Note on Diversification and the Reduction of Dispersion, Journal of Financial Economics, Vol. 1, pp. 365 372. Lintner, J., 1965,Security Prices, Risk, and Maximal Gains from Diversification, Journal of Finance, Vol. 20, pp. 587 615. Mao, James C. T., 1970,Essentials of Portfolio Diversification Strategy, Journal of Finance, Vol. 25, pp. 1109 1121. Markowitz, Harry M., 1952,Portfolio Selection, Journal of Finance, Vol. 7, pp. 77 91. Sharpe, W. F., 1966,Mutual Fund Performance, Journal of Business, Vol. 39, pp. 119 138. Terynor, J.L., 1965,How to Rate Management Investment Funds, Harvard Business Review, Vol. 43, pp. 63 113. Wagner, W. H., and S. C. Lau, 1971,The Effect of Diversification on Risk, Financial Analysts Journal, Vol. 26, pp. 48 53. The Optimum Number of Funds Held by Institutional Investors : An Empirical Analysis Based on Chinese Data Huang Shaoan and Wei Qian (Center for Economic Research,Shandong University) Abstract :This paper selects 39 close2end funds and 67 open2end funds as samples which have been established before June 30 th, 2004. We choose the weekly ration of return as the index. According to the data from January 1 st, 2005 to December 31 th, 2006, we examine the relations between the risk and return of the portfolio and the number of funds involved in portfolio. Then, we study the problem of optimum number of funds from only considering the factor of risk and from comprehensive consideration of risks and returns respectively. We also comparatively examine which one is better between the portfolio which have different investment style funds and those which is chosen randomly in equal. At last, we use data to examine three different optimum number models : Evans and Archer s, Latane and Young s and Markowitz s. Key Words :Securities Investment Fund ; Optimum Number of Funds ; Portfolio Risk ; Portfolio Return JEL Classification : G110, G290, G310 ( : ) ( : ) 129