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1 : : : 3 : ,, ,,, ( Evans and Archer) (Latane and Young) (Markowitz) :,,, :?,?,,,, , 321, , , % ; , %, 50 %,,2006,,,2006, ( ) 52, 52 48, ( ) 32, 26 3,( ),, edu. cn ;, ( ), :250100, sdu. edu. cn (:04JZD0007) ,

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3 : : (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,,,, ;,,, ,, ;, ,, , 6, ( ),, ,,

4 , 31 (1),,, (Fama, 1976,p. 31), (2003) ,, (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 % 121

5 : :,N,12n n,n, : ( N ) 1, ; N - 1 1, 2, ; N - 2 1, 3, ;, n 1 n, 1000, n,, (2), 8,,, 8, 100, : 8,,1 ; 9 16, 8 1, 8, 2 ; 17 24, 8 2, 8, 3 ;, 100,, ,,, ,,, 35, 60,100 : ,,, 2. matlab710,( ), 122

6 ,,,,,, 1 5, (9125 %) ; 5 10, (1164 %) ; 10 15, ( 0149 %) ;,, %, 1 5, 5121 % ; 5 10, % ;,,21535 % 4 - ( 1000),, 123

7 : : t,,1 %5 %, 18 22, 26 37, 67 73, 5, 1 %, %, 6122 %, % 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

8 (1) Sharpe,Sharpe, 7,,Sharpe 22,Sharpe ; 28,Sharpe ; 73,, Sharpe,, 22,28, 73, (2) Sharpe,,3,Sharpe,,,, sharpe,,: (1) : 125

9 : : 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) 3 1 (1) (3), (3) 2 (1),, (1) (3) 3 1, 2 (2003),(1) (3) (2) :t 1 %,5 % 106,,8 9 : (1),, ; (2),,,Sharpe 10,,,Sharpe,

10 ,,, sharpe 127

11 : :,, : (1),,,1 %5 %, 18 22, 26 37, ;,22, 28, 73, (2),, Sharpe,,3, Sharpe,, 73 (3),,,, Sharpe,,, (4),,,,,, ,,,15 %20 %, ;,,,: ;,,2001 :,5,2000 :,,2000 :Markowitz, 1 128

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 Elton, E.J., and M.J. Gruber, 1977,Risk Reduction and Portfolio Size : An Analytical Solution, Journal of Business, Vol. 50, pp Evans, J.L, and S. H. Archer, 1968,Diversification and the Reduction of Dispersion : An Empirical Analysis, Journal of Finance, Vol. 23, pp 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 Jensen, M. C., 1968,The Performance of Mutual Funds in the Period , Journal of Finance, Vol. 23, pp Johnson, K. H., and D. S. Shannon, 1974,A Note on Diversification and the Reduction of Dispersion, Journal of Financial Economics, Vol. 1, pp Lintner, J., 1965,Security Prices, Risk, and Maximal Gains from Diversification, Journal of Finance, Vol. 20, pp Mao, James C. T., 1970,Essentials of Portfolio Diversification Strategy, Journal of Finance, Vol. 25, pp Markowitz, Harry M., 1952,Portfolio Selection, Journal of Finance, Vol. 7, pp Sharpe, W. F., 1966,Mutual Fund Performance, Journal of Business, Vol. 39, pp Terynor, J.L., 1965,How to Rate Management Investment Funds, Harvard Business Review, Vol. 43, pp Wagner, W. H., and S. C. Lau, 1971,The Effect of Diversification on Risk, Financial Analysts Journal, Vol. 26, pp 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, 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

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