# Risk reduction and Diversification within Markowitz's Mean-Variance Model: Theoretical Revisit

**Authors:** Gilles Boevi Koumou  
**arXiv:** [1608.05024](https://arxiv.org/abs/1608.05024)  
**Date:** 2016-08-17  
**Summary page:** https://www.summarizepaper.com/en/paper/1608.05024v2/

## Key points

- Conventional wisdom of mean-variance (MV) portfolio theory assumes decreasing asymptotic relationship between risk and diversification
- Literature assumes equally-weighted or MV portfolio and measures diversification using portfolio size
- This paper fills the gap by examining impact of full information about asset expected return and risk on diversification within MV model
- Explores scenarios with and without risk-free rate availability
- Theoretical analysis of risk reduction and diversification within MV portfolio theory
- Findings contribute to understanding how investors can optimize portfolios with complete knowledge about asset return and risk, considering risky assets and risk-free asset.

## Summary

The conventional wisdom of mean-variance (MV) portfolio theory suggests that the relationship between risk and diversification follows a decreasing asymptotic function, where the asymptote represents the level of portfolio systematic risk or undiversifiable risk. However, this literature assumes that investors hold an equally-weighted or MV portfolio and measure diversification using portfolio size. These approaches are only optimal if asset returns distribution is exchangeable or if investors have no useful information about asset expected return and risk. Surprisingly, this question has never been addressed in current literature. This paper by Gilles Boevi Koumou aims to fill this gap by revisiting Markowitz's MV model and examining the impact of full information about asset expected return and risk on diversification. The author explores scenarios where both the risk-free rate is available and when it is not. By addressing these overlooked aspects, this research provides a theoretical analysis of risk reduction and diversification within MV portfolio theory. The findings from this study will contribute to a better understanding of how investors can optimize their portfolios when they have complete knowledge about asset expected return and risk, considering both risky assets and the role of the risk-free asset.