樂透股的風險與報酬關係

Abstract

本研究以西元1999年至 2021年臺灣上市櫃公司為研究樣本，欲找出在臺灣的樂透股中是否存在著風險與報酬的反向關係。實證結果顯示，在只控制兩項變數的投資組合二次排序分組方法中，每一種風險指標下，樂透股組別均無看到風險與報酬有顯著的反向關係；但使用Fama and MacBeth (1973)迴歸來控制其它可能影響變數，包括偏態係數、規模、帳市值比、過去報酬表現及週轉率等，則發現在使用月報酬標準差、個別風險及公司成立年數倒數作為風險指標時，平均而言，樂透股在風險越高的情況下，報酬顯著越低。因此本研究認為在一部份的風險指標衡量下，臺灣的樂透股並非如傳統金融理論所描述的高風險、高報酬，反而存在著高風險、低報酬，這樣的風險與報酬反向關係。

Using the data of listed firms in Taiwan from 1999 to 2021. This paper tries to find out whether lottery-like stocks have negative relation between risk and return. In the method of double-sorting portfolio, the portfolio of lottery-like stocks doesn’t have significant negative relation between risk and return in terms of every risk measure. However, this paper performs Fama and MacBeth (1973) regressions, which can conveniently control for additional variables such as skewness, firm size, book-to-market, past returns and turnover. It is found that when using monthly return standard deviation, idiosyncratic risk, and reciprocal of firm age as risk measure, high-risk lottery-like stocks have significantly lower returns on average. So, this paper concludes that, in certain risk measure, high-risk lottery-like stocks in Taiwan are not with high-return as described by traditional financial theories but rather high-risk with low-return. It shows that there are inverse relation between risk and return.