Confounding the Return Notions Could Be Dangerous

In numerous finance publications, the term ‘return’ appears at first only as a necessary element for further research. Seemingly, it is so basic that it does not require a precise definition. However, the inappropriate use of ‘return’ has serious consequences. This chapter shows that confounding the return notions and inappropriate approximations lead to wrong results in portfolio optimisation. Using log-returns instead of ordinary (or simple) returns in a traditional Markowitz framework can feign arbitrage opportunities which are nonexistent in reality. Furthermore, this chapter highlights the huge numerical differences between key figures of log-return and ordinary returns. For instance, calculating the Sharpe ratio with log-returns can signalize a bad investment, whereas it is a really highly profitable investment.