Past exam of the mathematics course of the University of Cambridge / 2004 / iii / Paper 35 / 1 / e

Solution

The expected return of the market portfolio is the weighted mean of the asset returns:

m_{M} = \frac{10 \cdot 13 + 17 \cdot 13 + 24 \cdot 12}{38} = \frac{639}{38} .

For its variance, use

Σ z = d

rather than expanding nine terms:

z^{T} Σ z = z^{T} d = \frac{7 \cdot 13 + 14 \cdot 13 + 21 \cdot 12}{11} = \frac{525}{11}, σ_{M}^{2} = \frac{525/11}{( 38/11 ) ^{2}} = \frac{5775}{3 8 ^{2}} .

Hence its return standard deviation is

σ_{M} = \frac{5 231}{38} .

Means and standard deviations here are both measured in percentage points, consistently with the given covariance matrix.

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