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How is the Portfolio Beta Determined?

The portfolio beta is determined by multiplying the market values of each share in the portfolio with their betas (for example 250-day beta). The result is a risk-weighted portfolio value. This value is then divided by the actual value of the portfolio.

The hedger should never forget, that all betas and correlations are historical numbers. The share prices may well fluctuate differently in future.

Example: Beta of a DAX portfolio

 

Share Quantity Price (EUR) Market value
(price x quantity)
Beta Risk weighted value
(Market value x beta)
Allianz 20,000 86 1,720,000 1.33 2,287,600
BASF 20,000 58 1,160,000 1.08 1,252,800
Daimler 20,000 42 840,000 1.20 1,008,000
Deutsche Bank 30,000 33 990,000 1.48 1,465,200
Deutsche Telekom 100,000 9 900,000 0.71 639,000
SAP 30,000 44 1,320,000 0.64 844,800
Market value: 6,930,000 Risk weighted
market value
7,497,400

 

Please note: The portfolio illustrated here has adequate correlation (0.85) to the DAX. You can find correlations and betas for single shares under the following link for free: dax-indices.com.

A portfolio's correlation to the index can, for instance, be measured over a historical period of time by comparing the development of the unchanged portfolio to that of the index every day.

 

Portfolio beta  =  Risk-weighted market value  =  EUR 7,497,400  =  1.167
------------------------ ------------------------
Market value EUR 803,000

 

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