  We consider a Black-Scholes market in which a number of stocks and an index
are traded. The simplified Capital Asset Pricing Model is the conjunction of
the usual Capital Asset Pricing Model, or CAPM, and the statement that the
appreciation rate of the index is equal to its squared volatility plus the
interest rate. (The mathematical statement of the conjunction is simpler than
that of the usual CAPM.) Our main result is that either we can outperform the
index or the simplified CAPM holds.
