In an experiment, we systematically tested the risk tolerance for trading stock shares that vary in the initial price of the shares. Persons inexperienced with the stock market had to set the selling points for 60 stocks in the case of (a) decreasing or (b) rising prices. First, a stronger risk aversion for falling compared to rising prices was obtained. Second, the experiment revealed a dramatic increase in risk tolerance the lower the buying prices of the stocks were; nearly perfectly following a power function (Pearson-R’s>.93). Furthermore, it seemed very difficult for persons to grasp the consequences of share price neglect, namely that the initial share price has a significant impact on the readiness to take higher risks, whether in a positive or negative direction. Therefore, we are also referring to it as a “hidden risk tolerance”. This paper offers insights into irrational decision making in trading stocks. It allows the formation of estimates regarding trading volume and share price potential on the basis of the initial share price. Furthermore, it provides clues for the consequent reduction of risk-seeking behavior.