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An equally weighted basket

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A basket holds $25$ names in equal weights. Each name has return variance $0.04$ , and every pair has correlation $0.25$ . What is the variance of the basket's return? Give an exact decimal.

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Hint

Split the matrix into its diagonal and the rest.

Solution

The covariance of a pair is $0.25 \times 0.04 = 0.01$ .
The variance is $\frac{0.04}{25} + \frac{24}{25} \times 0.01 = 0.0112$ .

Answer: $0.0112$

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