To illustrate the rank correlation test, consider the data given in Table 11.2. The data pertain to the average annual return (E, %) and the standard deviation of annual return (o,, %) of 10 mutual funds.
The capital market line (CML) of portfolio theory postulates a linear relationship between expected return (E,) and risk (as measured by the standard deviation, o) of a portfolio as follows:
Using the data in Table 11.2, the preceding model was estimated and the residuals from this model were computed. Since the data relate to 10 mutual funds of differing sizes and investment goals, a priori one might expect heteroscedasticity. To test this hypothesis, we apply the rank correlation test. The necessary calculations are given in Table 11.2.
Applying formula (11.5.6), we obtain
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