Improved financial model set to change investment decisions

30 October 2006

A financial engineering paper that won the Best Paper Award at the recent International MultiConference of Engineers and Computers Scientists in Hong Kong is set to change understanding of one of the fundamentals of modern portfolio theory investment, the Capital Asset Pricing Model (CAPM).

The paper is authored by PhD candidate Nafees Hossain and his thesis supervisors, Professor Cas Troskie and Professor Renkuan Guo, of the Department of Statistical Sciences.

The CAPM influences how investors value securities and the theory, based on Nobel laureate Professor William Sharpe's multiple index mode. From its 1960s genesis as Sharpe's doctoral dissertation topic, his CAPM became a linchpin of modern investment.

Sharpe's model works on the assumption that security returns are related to each other solely through responses to one common factor. His theory was rooted in economist Harry Markowitz's seminal work on risk and return, one that presented a so-called efficient frontier of optimal investment. This advocated a diversified portfolio to reduce risk, but didn't adequately develop a practical means to assess how various portfolio holdings operate together.

"We believe that the empirical evidence and discoveries of our paper are of colossal importance and may be quite beneficial to the investment community," Hossain told Monday Paper.

The paper is a partial summary of Hossain's PhD research work, initiated by Troskie's theoretical preparation before his retirement, and is a collective effort.

"It is an excellent example that postgraduate students can generate high-quality publications during their study," said Guo.

Years ago, Markowitz had suggested that Sharpe investigate his Portfolio Theory as a thesis project. Sharpe did so, connecting a portfolio to a single risk factor, simplifying Markowitz's work and developing his "heretical notion" of investment risk and reward, one that became known as the Capital Asset Pricing Model.

The CAPM caused quite a stir among investment professionals in the 1960s, and in 1990 Sharpe's role in developing CAPM was recognised by the Nobel Prize committee. He shared the Nobel Memorial Prize in Economic Sciences that year with Markowitz and Merton Miller, a University of Chicago economist.

Hossain's paper, An Application of Principal Components Analysis to Portfolio Optimisation under the Sharpe Multiple Index Framework, is a step toward further refinement to Sharpe's theory, providing a more accurate risk-return structure in portfolio analysis - with significant potential to change the way investment decisions are made.

In statistics, principal components analysis is a technique for simplifying a dataset, by reducing multidimensional datasets to lower dimensions for analysis.

"The purpose of our paper is to investigate the behaviour of efficient frontiers under two developed index portfolio frameworks: the Sharpe Multiple Index (SMI) and the Improved Sharp Multiple Index (ISMI)," Hossain said.

Using their principal components they are able to illustrate a true risk and return structure for a portfolio of stocks on the Johannesburg Stock Exchange under the SMI and ISMI formulations.

Empirical results show that the Sharpe Multiple Index model gives an inaccurate risk structure of an investor's financial portfolio.

"The paper presented at the Hong Kong conference reveals and confirms a fundamental fact in financial market theory and practices: that existing Sharpe index models - single or multiple - can either underestimate of overestimate the portfolio efficient frontier. We used the principle component approach."

Their model reflects exactly what Markowitz's model was trying to do but is much easier to compute and gives a very accurate model of the risk return situation, a "huge improvement" on Sharpe's model and a boon for the investment community and their managers.

Without any doubt, these modelling developments are still assuming a linear world, however, just as Troskie says: "The differences between Sharpe's model and our own are small, but the benefits to investors will be huge. In investment it's very difficult to give a portfolio's risk return structure. The research work gives a very accurate risk-return structure of a portfolio."

Although the improved model has been developed according to the South African context, the authors say it can be applied to other stock exchanges, with similar results.

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