In this paper we investigate the relationship between portfolio returns and idiosyncratic risk for Australian stocks. We report that the portfolio with highest idiosyncratic volatility generates an average annual return of over 45%. We observe additionally that the outcome is consistent with an exponential growth process for stock prices. Further, consistent with Malkiel and Xu, we observe that a stock’s idiosyncratic volatility is inversely correlated with the size of the underlying firm. Thus, our model advances an interpretation of the Fama and French finding that portfolios of stocks of small firms offer superior risk-adjusted returns. Moreover, our findings challenge the portfolio theory of Markowitz (1959) and the asset-pricing model of Sharpe (1964).
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