idiosyncratic vs market risk; what it cannot save you from
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Start studyingDiversification protects against the risk of being wrong about a single company. It does not protect against market-wide events that move most stocks in the same direction at the same time.
Each stock carries two layers of risk. The first layer is idiosyncratic: a fire at a factory, a fraud, a product recall, a failed drug trial. The second layer is systematic, the part of a stock's movement that is tied to the broad market rather than the firm itself, usually captured by a metric called beta.
When you add a holding that moves independently of the ones you already own, its bad days are not the same as your other holdings' bad days. Combined, the spikes partly cancel and the variance of the whole portfolio falls. The variance tied to the market, however, is shared by every stock you buy. Adding more stocks that all load on the same market does not remove that shared component, because removing it would require selling the market exposure entirely.
Suppose each stock has the same annual volatility and pairs of stocks correlate at around 0.3, a figure in the range of typical pairwise correlations on a broad index. The portfolio's variance per dollar invested then shrinks by a factor of about 1/N plus the correlation term. Plugging in numbers, going from one stock to twenty cuts that volatility to roughly 58% of the single-stock figure. Going from twenty to thirty shaves off only another percentage point or two. Beyond thirty, you are doing little more than adding trading costs and dilution.
Owning twenty stocks in one industry is one bet wearing twenty costumes. Sector concentrations often correlate at 0.7 or higher, so the idiosyncratic layer has already collapsed before you started. True diversification means different revenue drivers, different sensitivities to interest rates, and different geographic exposures, not a longer list.
The useful follow-up question to "how diversified are you?" is "diversified against which risk?"