This note studies the behavior of an index I_t which is assumed to be a
tradable security, to satisfy the BSM model dI_t/I_t = \mu dt + \sigma dW_t,
and to be efficient in the following sense: we do not expect a prespecified
trading strategy whose value is almost surely always nonnegative to outperform
the index greatly. The efficiency of the index imposes severe restrictions on
its growth rate; in particular, for a long investment horizon we should have
\mu\approx r+\sigma^2, where r is the interest rate. This provides another
partial solution to the equity premium puzzle. All our mathematical results are
extremely simple.