In a world where we are bombarded with scam advertisements claiming we can make 6 figures a month from the comfort of our living room, is it unreasonable to use mathematics to make a quick buck?

While not a multilevel marketing sales strategy, portfolio theory and the associated mathematics proposes a solution to creating easy, risk-free money. I do jest, but to make money you need some starting amount to invest. It’s what you do with this money that will decide your fate. Will you become a millionaire overnight? Unlikely, though portfolio theory suggests you can increase the likelihood of increasing your wealth steadily over time while minimising the chance of low returns.

My research investigated the robustness of investment portfolios constructed using portfolio theory. Robustness was defined to be maintaining a similar level of risk and meeting the target return. Portfolio construction means investing money into different stocks with the aim of increasing our capital by a certain amount. We also want to invest our money to minimise the chance of not reaching our desired monetary increase.

There are many ways of measuring the chance of not reaching a desired investment return, each being referred to as a ‘risk measure’. Example risk measures include variance, semi-variance, value at risk, tail value at risk and portfolio beta. Each ‘risk measure’ can be calculated to give an idea of how likely certain risks are to occur. An example being, if the worst 5% scenario were to happen, will I still achieve my desired monetary increase?

Thus, it is using these risk measures a person could choose how to invest their money and which stocks to invest in. Hypothetically they would be set up to achieve their financial goals and could just let their money do the work. However, my research suggests that this is not the case. The supposedly ‘optimised’ portfolios constructed to minimise their respective risk and achieve a targeted return failed to perform as expected. Thus, the portfolios were not ‘robust’.

The results show that minimising a specific risk on an investment portfolio using past returns has almost no ability to maintain similar risk levels or to meet the required return. This result is not surprising, though disappointing. It would be nice to find an easy, risk-free way of making good money.

From the findings of this research, it would be recommended to utilise more robust mathematical and financially sound methods to invest in the stock market. This would increase your chances of achieving your financial goals while minimising your exposure to risk.

Zachary Tindale
Curtin University

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