That low risk asset will earn high return, contrary to the traditional financial theory, is called low risk anomaly. Frazzini and Pedersen (2014) proposed a betting against beta (BAB) factor. To construct a BAB portfolio, all securities in an asset class are first ranked in ascending order on the basis of their estimated beta followed by buying a low beta portfolio and selling a high beta portfolio with a zero portfolio beta. This thesis explores whether the stocks listed on the Taiwan Stock Exchange have low risk anomaly and whether the BAB portfolio can generate excess returns. The empirical results in the thesis show that low risk anomaly exists for the stocks listed on the Taiwan Stock Exchange (TSE) and that the BAB portfolio generates excess returns.