# Market Efficiency and Growth Optimal Portfolio

## TL;DR

This paper demonstrates that when stocks are measured in units of the growth optimal portfolio, their expected returns are zero, supporting an efficient market hypothesis and proposing a hierarchically weighted index as an improved proxy.

## Contribution

It introduces the hierarchically weighted index (HWI) as a superior proxy for the growth optimal portfolio and provides empirical evidence for the efficient market property in this context.

## Key findings

- Equities denominated in units of the GP have zero expected returns.
- The HWI closely approximates the GP and outperforms traditional indices.
- The efficient market property remains robust when using the HWI as a proxy.

## Abstract

The paper predicts an Efficient Market Property for the equity market, where stocks, when denominated in units of the growth optimal portfolio (GP), have zero instantaneous expected returns. Well-diversified equity portfolios are shown to approximate the GP, which explains the well-observed good performance of equally weighted portfolios. The proposed hierarchically weighted index (HWI) is shown to be an even better proxy of the GP. It sets weights equal within industrial and geographical groupings of stocks. When using the HWI as proxy of the GP the Efficient Market Property cannot be easily rejected and appears to be very robust.