The aim of this research is to analyze stock prices that are undervalued (cheap) and overvalued (expensive) from the intrinsic value obtained when compared with the prices formed on the stock market, to analyze the optimal portfolio of shares resulting from the formation of LQ-45 shares, to analyze the large proportion of funds in each each stock that forms an optimal portfolio of LQ-45 shares, analyzing the expected level of return from the risk of the portfolio formed of LQ-45 shares. The results of the analysis show that there are 20 (twenty) sample companies that are undervalued and to analyze the stock portfolio using the Single Index Model approach, which can form an optimal portfolio, namely ICBP (Indofood CBP Sukses Makmur Tbk.) shares of 0.7739 (77.39). %), BBRI (Bank Rakyat Indonesia (Persero)) Tbk., amounting to 0.2154 (21.54%) and SMGR (Semen Indonesia (Persero) Tbk) amounting to 0.0107 (1.07%). The results of this research show that there is investor rationality in selecting shares and forming an optimal portfolio using a single index model on the Indonesia Stock Exchange for LQ45 shares for the period February 2018 - January 2020.
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