Derivation of the Beta Risk Factor

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Presentation transcript:

Derivation of the Beta Risk Factor Calculate portfolio variance Split into market proportional variance and firm specific variance m: number of assets in portfolio M: ‘market’

Derivation of the Beta Risk Factor

Derivation of the Beta Risk Factor Split Firm specific covariance is assumed zero. Split the variances and covariances Market proportional Firm specific variance covariance variance covariance

Derivation of the Beta Risk Factor Firm specific covariance is assumed zero

Derivation of the Beta Risk Factor Systemic risk contribution only Portfolio covariance is a linear function of beta Systemic and non-systemic (firm specific) Contribution to variance for asset i

Derivation of the Beta Risk Factor Substitute into CAPM formula The two assumptions in the derivation are: A market proportional covariance matrix can be constructed and Covariances between firm specific risks are zero Return other than from taking market driven risk is captured by α which in the CAPM model is a normally distributed random variable with an expected value of zero

Portfolio Beta Derivation

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