It is well argued that idiosyncratic risks are not desired and can be diversified away (Bodie et al 2007). While this knowledge dominates introduction to finance courses (subjects/modules), idiosyncratic risk is in other most circumstances the key to wealth.
Firm-specific and industry-specific characteristics are key to capture excess returns from CAPM expected return. For example, retail industry, food industry, metal industry etc. fluctuate to business cycles, and business cycles are not captured in CAPM.
Next, idiosyncratic volatility is useful for speculation purpose, especially when you do not have a concrete target on where to exit the investment. Volatile means holding through (or even shorting during) dip and exit during peaks. You earn steady income through dividends and small gains on stable stocks, but you make fortune on volatile-but-fundamentally good investments.
Treynor Black model for alpha specifies that on the Single Index Model
Active portfolio A should receive investment weight
where the rest of the portfolio should be invested in market index. This is one example in the academic world where idiosyncratic is, indeed, good.
Bodie Z, Kane A, Marcus A, 2007, ‘Investments’, McGraw-Hill, 2007
Treynor, J. L. and F. Black, 1973, ‘How to Use Security Analysis to Improve Portfolio Selection’, Journal of Business, January, pages 66–88
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