CAPM. VaR Value at Risk. VaR. RAROC Risk-Adjusted Return on Capital

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1 C RAM 3002 C RAROC Rsk-Adjusted Return on Captal C C RAM Rsk-Adjusted erformance Measure C RAM RAM Bootstrap RAM C RAROC RAM Bootstrap F830.9 A CAM 2 CAM 3 Value at Rsk RAROC Rsk-Adjusted Return on Captal 200 RAROC RAROC RAM Rsk-Adjusted erformance Measure Sharpe

2 RAM= / 200 Artzner et al C Condtonal Value-at-Rsk C RAM 2 3 C C RAM RAM C. C RAM x x X y y Y x y ( f xy, ) f ( xy, ) ξ ψ ( x, ξ) = p ( y) dy () f x, y ξ 0, ( x) mn { R: ( x, ) } ξ = ξ ψ ξ (2) ( ) (, ) C C x = f ( x, y) ( x) f x y p y dy (3) φ ξ C C C 2 3 C C 2 2

3 3 C RI C.2 RAM = RI ξ (4) C = RI φ (5) RI ~ N ( µ, σ ) c = 2 erf (2 ) 2 d = { 2π exp[ erf (2 )] ( ) } 2 x 2 t erf ( x) = e dt 0 π ξ = µ + c σ (6) C 2 φ = µ + d σ (7) erf 95% ( x ) d > 0 d > c > ( ) c ( > ) > 0 x µ = = µ + c( σ ) + c ( σ / µ ) C ( ) = + d ( σ / µ ) σ σ > j j C C < ( 2 ) > j ( 2 ) > j µ µ C 2 j 2 j C ( ) > C.3 C 4 C 2 C 95% 95% 97.5% 99% n d = k k 2 k d = 0 d = d = n 3

4 D 48 D = k k (8) = 2 D D ξ C Rockafellar T ( x, ) ( ) T f ( x, y) + φ ξ = ξ + ξ (9) RAM RAM ~ C Bootstrap Bootstrap Bootstrap Bookstaber & McDonld B-M IID B-M Bootstrap RI ξ φ 4

5 ˆ j RIˆ ˆ = RIj ˆ 000 ˆ ξ = ξj ˆ 000 ˆ φ = φj ˆ C j k ˆD ˆ j= j= j= Bootstrap 2 2 ˆ C j ˆ j ˆ k ˆD RIˆ ˆ ξ ˆ φ 2 RIˆ ˆ ξ ˆ φ ˆ C ˆ j j ˆ k ˆD 2 2 RIˆ ˆ ξ ˆ φ ˆ C ˆ j j ˆ k ˆD Bootstrap Kolmogorov-Smnov % Shapro-Wlk % 0.05 C C C C C C C -C 99%-97.5% 99%-95% 97.5%-95% 99%-97.5% 99%-95% 97.5%-95% 99% 97.5% 95% D Bootstrap

6 2 RIˆ ˆ ξ ˆ φ ˆ j ˆ C j RI ˆ ˆ ξ ˆ φ ˆ j ˆ C j RIˆ ˆ ξ ˆ φ ˆ j ˆ C j % 8.6% 3.9% 4.5% 3 95% C 3 Bootstrap 95% 99%-97.5% %-95% %-95% %-97.5% C 99%-95% %-95% % C 97.5% % C C 99.9% 7.5% 97.5% 7.84% 95% 25.67% 95% C 47.2% 7.8% C 6

7 C C % 97.50% 95% C 3 C RAROC C C Bootstrap C C 2 C RAM C []Artzner, Delbaen F, Eber J M, Heath D. Coherent measures of rsk[j]. Mathematcal Fnance, 999(9): [2]Bookstaber R M, J B McDonald. A General Dstrbuton for Descrbng Securty rce Returns[J]. Journal of Busness, 987(7): [3]Ippolto, Rchard A. On Studes of Mutual Fund erformance, [J]. Fnancal Analysts Journal, 993(-2): [4]Katerna Smons. Rsk-Adjusted erformance of Mutual Funds[J]. New England Economc Revew, 998(9-0): [5]Kent Danel, Mark Grnblatt, Sherdan Ttman, Russ Wermers. Measurng Mutual Fund erformance wth Characterstc-Based Benchmarks[J]. The Journal of Fnance, 997(7-8):

8 [6]Kevn Dowd. Adjustng for Rsk: An Improved Sharpe Rato[J]. Internatonal Revew of Economcs and Fnance 2000(3): [7]Lehmann B, D Modest. Mutual Fund erformance Evaluaton: A Comparson of Benchmarks and Benchmark Comparsons[J]. The Journal of Fnance, 987(2): [8]Mark Grnblatt, Sherdan Ttman. ortfolo erformance Evaluaton: Old Issues and New Insghts[J]. The Revew of Fnacal Studes, 989(2): [9]Rockafellar R T, S Uryasev. Condtonal Value-at-Rsk for General Loss Dstrbutons[J]. Journal of Bankng and Fnance, 2002(7): [0]Zhwu Chen, eter J Knez. ortfolo erformance Measurement: Theory and Applcaton[J]. The Revew of Fnancal Studes, 996(8): [][ ]. hlppe Joron. Fnancal Rsk Manager Handbook [M]., 2004: [2],. C [J]., 2004(8): [3]. [EB]., 2, RAM to Fund erformance Evaluaton: Usng C and Usng Fang Y, Zhang Yshan (Busness School of Jln Unversty, Jln Changchun 3002, Chna) Abstract: The paper ntroduces C nto RAROC (Rsk-Adjusted Return on Captal) to evaluate mutual fund performance. And t compares the results of RAROC by usng C and usng. It can learn from that, n the condton of normal dstrbuton, both the RAM (Rsk-Adjusted erformance Measure) by usng C and that by usng are suffcent, relant and effectve, and the two measures are equvalent. But the RAM by usng C s more suffcent, more conservatve and more relant than that by usng n the condton of abnormal dstrbuton. What s more, we do emprcal study wth bootstrap and ndcate that the concluson have great value on general RAM. Key words: C RAROC RAM. Bootstrap

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