Prize-linked savings (PLS) instruments implement the lottery-like component into the structure of traditional financial products. Following existing research based on both real and experimental data, such programs appeared highly successful in raising the overall savings rates within the given environments. PLS accounts seem to be treated by decision-makers as substitutes to ordinary lotteries, but this does not hold when comparing PLS with traditional interest-bearing savings products. This paper explains such empirical observations in a framework of portfolio selection problem. For that purpose, two models have been presented and used for deriving optimal portfolios in a presence of PLS, lottery and savings products. As shown in the analysis, the standard mean-variance model does not allow for a PLS instrument to be of optimum choice, whereas in the case of behavioural portfolio model allocating all disposable income to PLS can be in fact the best decision under certain individual conditions.