# Standard deviation of the S&P Composite Index: Can it be 20.3%?

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How could the S&P Composite Index have a standard deviation of 20.3% if the historical standard deviation of common stocks has been 20.5% and the small company stocks have been 33.3%. I do not quite understand this, can you explain this?

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#### Solution Preview

Because the formula of Variance is

Vp = W1^2 * V1 + W2^2 * V2 + 2W1*W2*Cov(1,2)

If Cov(1,2) < SQRT(V1*v2),

W1^2 * V1 + W2^2 * ...

#### Solution Summary

With the formulas and calculations, the solution solves the answer to the problem.

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