## How do you Set-up a Beta Hedge of an Entire Portfolio?

### Example: Hedging a DAX portfolio (Depot)

 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 weightedMarket value 7,497,400

The portfolio with a current value of EUR 6,930,000 has a correlation of 0.85 to the DAX. The portfolio beta is 1.082.

### Hedge ratio

 Portfolio value x Portfolio beta = EUR 6,930,000 x 1,082 = 47,83 Index level x index multiplier 6,270 x EUR 25

48 DAX Futures contracts are sold at a price of 6,280 points.

This, of course, is merely an assumed price change for which the historical betas of the shares can only partially "predict" the future correctly.

 Share Old market value New market value Loss Allianz 1,720,000 1,479,200 240,800 BASF 1,160,000 1,032,400 127,600 Daimler 840,000 739,200 100,800 Deutsche Bank 990,000 841,500 148,500 Deutsche Telekom 900,000 837,000 63,000 SAP 1,320,000 1,235,520 84,480 Gesamt 6,930,000 6,164,820 765,180

Performance of the 48 sold DAX Futures contracts:

 DAX Future at sale: 6,280 DAX Future at present: 5,652

### Profit at possible close out:

6,280 points - 5,652 points = 628 points

628 points x EUR 25/point x 48 contracts = EUR 753,600

### Summary:

 Loss from the equity portfolio: EUR 765,180 Profits from futures contracts: EUR 753,600 Residual loss: EUR 11,580

The profits generated by the futures contracts offset most of the losses from the shares. However, as the portfolio that was hedged does not correlate entirely with the DAX, there still is a risk that uncorrelated price developments in individual issues cannot be fully compensated by the futures contracts - despite the adjustment based on the beta.