On the martingale-fair index of return for investment funds

TL;DR

This paper introduces a martingale-fair index of return for investment funds, consistent with Arbitrage Free Pricing Theory, providing an explicit formula and analyzing properties including its martingale nature and merger implications.

Contribution

It presents a new index of return that is martingale-fair and derives an explicit formula within a discrete-time stochastic model, linking it to asset price martingales.

Findings

The index is proven to be martingale-fair.

Explicit formula for the average return is derived.

Analysis of fund merger effects on the index.

Abstract

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.