DCU researcher applies maths to the human behaviour of investing

Dr Andrea Meireles Rodrigues is using maths to analyse how investors make decisions, in the hope of optimising portfolios. She spoke to Claire O’Connell.

Humans tend not to excel at predicting the future precisely, which is why some of us win and some of us lose on the stock market. So choosing the best consumption and investment strategy is an important problem that we are faced with in our everyday lives. 

That’s according to Dr Andrea Meireles Rodrigues, who is using maths to better understand how human behaviour affects how we do or don’t invest. 

“When we are looking for the best investment strategy, one of the first questions to think about is about how people make decisions in the face of uncertainty,” said Meireles Rodrigues, a lecturer at Dublin City University (DCU)’s School of Mathematical Sciences.  

One of the most widely applied theories in optimal portfolio selection problems is ‘expected utility theory’, she explained: “It is used for modelling decisions in the face of risk. It assumes that people are fully rational and can assess perfectly how likely an event is, that people always prefer more to less and they are always risk averse in any scenario.”

Human behaviours

However, human behaviours don’t always match with the expected utility hypothesis. “For example, according to expected utility theory, each investor should invest at least a certain proportion of their wealth in stocks,” said Meireles Rodrigues. “But surveys show this is not the case; that a large percentage of households do not invest in stocks.”

At DCU, she is using maths to find optimal portfolios in an alternative framework where it is still assumed that our utility should be increasing, but which takes other behaviours into account too.

“This alternative theory suggests that our behaviour depends on whether we are gaining or losing – if we are gaining, we are risk averse; but when losing, we tend to become risk-seeking, we want to take chances, to play the game,” she explained. 

“It also says that when we evaluate an investment outcome, we compare it with a reference point rather than looking only at its absolute pay-off. And finally, it assumes that we are not really capable of objectively assessing the probabilities of events, that we distort their actual probabilities; for example, we tend to overweigh the probability of extreme rare events.”

While the work is still ‘very theoretical’, Meireles Rodrigues would be interested in possible real-life applications. “For now, the results obtained are interesting in that they seem to offer an alternative explanation for the observed phenomenon of limited market participation,” she said.

‘I always liked that you see maths everywhere and it is so rigorous and precise, it teaches you how to think and question everything’
^{– DR ANDREA MEIRELES RODRIGUES}

Solving the puzzle 

The mix of maths and human behavioural economics is fascinating, according to Meireles Rodrigues, who enjoyed maths in school.

“I always liked that you see maths everywhere and it is so rigorous and precise, it teaches you how to think and question everything,” she said. “You prove whether or not something is true.”

After studying maths in her native Lisbon, Portugal, she did a PhD at the University of Edinburgh. It was there that she started looking at applications of probability theory and stochastic processes in behavioural portfolio optimisation. She then got the opportunity to work in DCU as part of the financial mathematics research group.

One of the driving forces behind her research is her love of solving problems. “You can live with a research problem for a long time in your head,” said Meireles Rodrigues. “Sometimes it is frustrating, you can work on it for days and months and then one day, you have this idea where you solve a bit of the puzzle. And eventually, hopefully, you can complete the puzzle – it is so fulfilling.”

What then? “And then there is always another puzzle to solve.”