Analysis of a five-factor capital market model

TL;DR

This paper analyzes a five-factor capital market model, deriving exact simulation methods, extending the asset universe to inflation bonds, and exploring asset distribution dynamics and factor investing implications.

Contribution

It introduces an exact simulation approach for the five-factor model and extends the asset set to include inflation bonds with a new arbitrage-free BEI curve.

Findings

Exact simulation achieved via sampling from a seven-dimensional normal distribution

Derived arbitrage-free break-even inflation curve for inflation bonds

Analyzed distribution of stock index and Sharpe ratio in the model

Abstract

In this paper we analyse the five-factor capital market model of Munk et al.(2004). The model features a Vasicek interest rate model, an equity index with mean-reverting excess return and an index for realized inflation with mean-reverting expectation. The primary aim of the analysis is to facilitate so-called exact simulation from the model on a set of discrete time points. It turns out that this can be achieved by sampling from a (degenerate) seven-dimensional normal distribution. We derive the distributional results necessary and describe how to overcome the rank deficiency of the variance-covariance matrix in practice. The tradeable assets in the original model consist of cash, nominal bonds and stocks. We extend the investment universe to also include inflation bonds by deriving the arbitrage free break-even inflation (BEI) curve for a three-parameter specification of the two market prices of inflation risk. Finally, we provide a number of auxiliary results regarding the dynamics of constant-maturity nominal and inflation bond indices, the distribution of the stock index in nominal and real terms, and the distribution of the Sharpe ratio for individual assets and portfolios with an application to factor investing.