Doubling Times in Finance

Abstract

This dissertation proposes an alternative measure of performance, termed doubling time. Doubling time is defined as the time taken for an initial investment in an asset to double in value. This alternative performance metric has an intuitive appeal yet has received little attention in the academic literature to date. This thesis provides the foundations required for the use of doubling times in finance.The work begins by examining the problem of computing the expected doubling time from a sample of doubling times. Analytical formulae and a simulation are proposed as alternative approaches to estimating the expected doubling time. Using these methods,expected doubling times are computed for the Australian equity market, using both price and accumulation indices. Expected doubling times are also computed for bonds. The doubling time is then modelled as a first passage time problem. It is shown that if returns are normally distributed then the doubling times will be inverse Gaussian distributed. It is also shown that, regardless of the underlying distribution the returns follow, the simulated doubling time is very likely to be inverse Gaussian distributed. Following this, portfolio formation using doubling times is investigated. It is shown that minimising either the skewness, or the inverse shape parameter, of the doubling times inverse Gaussian distribution, result in points on the efficient frontier for returns that are identical to those obtained under the classical Markowitz framework. In this way a two parameter (mean and variance) portfolio optimisation problem is reduced to a one parameter problem (skewness or shape). Measurement errors can result in the ex-post performance of optimised portfolios being no better than naive equally weighted portfolios. This is sometimes referred to as the problem of error maximisation in portfolio formation. A doubling time transformation is used to reduce the problem of error maximisation, and the results indicate an improvement in the ex-post performance of the optimised portfolios.