THE VALIDITY OF COMPOSITE RISK‐RETURN MEASURES WITHIN MUTUAL FUND SUBGROUPS*

Abstract

THE BASIC HYPOTHESIS tested in this study is that management objectives of a particular mutual fund, to a large extent, determine the risk and return structure of the fund's portfolio. Thus, if funds are grouped by objectives such as growth or income, it is expected that risk will be homogeneous within those mutual fund groups and adjustment for risk is then redundant. The main thrust of this research is to (1) test for homogeneity of risk within and between fund groups within and between time periods and (2) attempt to develop a new composite risk-return index for use in comparing the performance of funds with different objectives. Risk homogeneity was investigated for two risk proxies: the standard deviation of return (Sharpe) and the beta value (Treynor). Three time periods were investigated 1944-1953, 1954-1963 and 1964-1970. Mutual fund objectives were derived from Wiesenberger's publication and funds were classified into four groups: growth, growth-income, income and balanced funds. The results obtained from testing the standard deviations of return are: a) the hypothesis of a within-group homogeneous standard deviation of return is rejected during the 1944-1953 time period, but cannot be rejected during the 1954-1963 and 1964-1970 time periods; b) standard deviations of return are different between subgroups; c) standard deviations within fund groups have grown more similar over time; d) significant positive rank correlation over time occurs when fund types were mixed; however, the within group correlation between the ranks of the individual funds is not significant over time. The following results are obtained by testing the homogeneity of beta values: a) the beta coefficients of mutual fund subgroups do not significantly differ from the average beta coefficient. Income funds during one of the two time periods investigated for this fund type provide the only definite exception to this conclusion; b) all mutual fund groups combined display only one average beta value during the 1964-1970 time period; during the 1944-1953 period the growth and growth-income funds do not significantly differ from their average beta value. Thus, two distinct mutual fund groups can be formed (income funds are not investigated for that particular period); during the 1954-1963 time period four distinct fund groups evolve; c) a majority of the beta values for individual funds are stable over time, whereas stability of average beta values of fund groups over time is not found. The interpretation of the empirical tests of the risk proxies lend credence to the basic hypothesis that (1) homogeneous risk groups of funds with similar objectives do exist, and (2) it is preferable to assume that risk as measured by the above proxies is generally found to be heterogeneous for fund types with different objectives. The generally made assumption of stability of risk over time