Hedging and Leveraging: Principal Portfolios of the Capital Asset Pricing Model

TL;DR

This paper analyzes the principal portfolios within the CAPM framework, revealing their hedging and leveraging properties, and providing insights into the structure of returns and volatility in large asset sets.

Contribution

It offers an explicit solution for principal portfolios in CAPM, highlighting universal properties and the impact of leveraging on risk and return.

Findings

Identification of a market-aligned portfolio and N-1 market-orthogonal portfolios

Market-orthogonal portfolios are market neutral and highly leveraged

Results enhance understanding of return-volatility dynamics in CAPM

Abstract

The principal portfolios of the standard Capital Asset Pricing Model (CAPM) are analyzed and found to have remarkable hedging and leveraging properties. Principal portfolios implement a recasting of any correlated asset set of N risky securities into an equivalent but uncorrelated set when short sales are allowed. While a determination of principal portfolios in general requires a detailed knowledge of the covariance matrix for the asset set, the rather simple structure of CAPM permits an accurate solution for any reasonably large asset set that reveals interesting universal properties. Thus for an asset set of size N, we find a market-aligned portfolio, corresponding to the market portfolio of CAPM, as well as N-1 market-orthogonal portfolios which are market neutral and strongly leveraged. These results provide new insight into the return-volatility structure of CAPM, and demonstrate the effect of unbridled leveraging on volatility.