The asset beta cannot possibly ever be greater than the equity beta. The equity beta includes the gearing risk, whereas the asset beta does not. If there is no gearing in the company then the equity beta will equal the asset beta; if there is gearing then the equity beta will be higher than the asset beta.
The asset beta formula enables you to calculate the equity beta if you know the asset beta (and vice versa).
The debt beta measures the riskiness of the debt. Unless told differently then when using the asset beta formula we assume it to be zero.
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