A manager hedges a specific stock portfolio by selling index futures. A fundamental limitation of this hedge is that:
Because no market index (and hence no index future) exactly matches a given stock portfolio, the manager is cross-hedging: the index is related but not identical to the portfolio, and the portfolio's volatility may not perfectly match the index's, leaving residual (basis) risk.
Index hedges are approximate, not exact; the imperfect match is precisely why beta and the hedge ratio matter.
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