  A concept of martingale-fair index of return, consistent with Arbitrage Free
Pricing Theory, is introduced. An explicit formula for the average rate of
return of a group of investment/pension funds in a discrete time stochastic
model is derived and several properties of this index are shown. In particular,
it is proven to be martingale-fair, i.e. be a martingale provided the prices of
assets on the financial market form a vector martingale. The problem of merger
of the funds is treated in detail.
