tailieunhanh - Encyclopedia of Finance Part 12

Chapter 21 A NOTE ON THE RELATIONSHIP AMONG THE PORTFOLIO PERFORMANCE INDICES UNDER RANK TRANSFORMATION. Abstract This paper analytically determines the conditions under which four commonly utilized portfolio measures (the Sharpe index, the Treynor index, the Jensen alpha, and the Adjusted Jensen’s alpha) will be similar and different. | Chapter 21 A NOTE ON THE RELATIONSHIP AMONG THE PORTFOLIO PERFORMANCE INDICES UNDER RANK TRANSFORMATION KEN HUNG National Dong Hwa University Taiwan CHIN-WEI YANG Clarion University USA DWIGHT B. MEANS Jr. Consultant USA Abstract This paper analytically determines the conditions under which four commonly utilized portfolio measures the Sharpe index the Treynor index the Jensen alpha and the Adjusted Jensen s alpha will be similar and different. If the single index CAPM model is appropriate we prove theoretically that well-diversified portfolios must have similar rankings for the Treynor Sharpe indices and Adjusted Jensen s alpha ranking. The Jensen alpha rankings will coincide if and only if the portfolios have similar betas. For multi-index CAPM models however the Jensen alpha will not give the same ranking as the Treynor index even for portfolios of large size and similar betas. Furthermore the adjusted Jensen s alpha ranking will not be identical to the Treynor index ranking. Keywords Sharpe index Treynor index Jensen alpha Adjusted Jensen alpha CAPM multiindex CAPM performance measures rank correlation ranking rank transformation . Introduction Measurement of a portfolio s performance is of extreme importance to investment managers. That is if a portfolio s risk-adjusted rate of return exceeds or is below that of a randomly chosen portfolio it may be said that it outperforms or underperforms the market. The risk-return relation can be dated back to Tobin 1958 Markowitz 1959 Sharpe 1964 Lintner 1965 and Mossin 1966 . Evaluation measures are attributed to Treynor 1965 Sharpe 1966 and Jensen 1968 1969 . Empirical studies of these indices can be found in the work by Friend and Blume 1970 Black et al. 1972 Klemkosky 1973 Fama and MacBeth 1974 and Kim 1978 . For instance the rank correlation between the Sharpe and Treynor indices was found by Sharpe 1966 to be . Reilly 1986 found the rank correlation to be 1 between the Treynor and Sharpe indices .