The Mathematics of Idiosyncratic Volatility and the Small Firm Effect : Australian Evidence

In the context of Australian stockmarkets, we examine the relationship between a stock's return performance, the stock idiosyncratic volatility, and the firm's market capitalization. The paper's main conclusions may be summarized as follows. The stocks of the smallest firms markedly outperform the largest capitalized stocks, and for such small capitalized stocks, those with greater idiosyncratic volatility have markedly superior returns. It appears that the relationship of higher returns with higher idiosyncratic volatility is consistent with the mathematics of idiosyncratic volatility. In which case, the small size effect may also be interpreted as the mathematical outcome of idiosyncratic volatility. The paper further examines the condition on which the higher returns reported for either small firm size or high idiosyncratic volatility are likely to be wealth-forming. Finally, we observe that the high performances of the stocks of the smallest firms are likely irrelevant to the class of firms that are of interest to the institutional investor