Calculate Risk-adjusted Returns Using Beta
The risk-adjusted return of a portfolio or an asset can be calculated using the Capital Asset Pricing Model.
Using this model, we calculate the expected return on the asset commensurate with the risk in the asset. The asset’s beta is used as the measure of risk, which indicates how much more or less volatile the asset is compared to the whole market.
The returns are calculated using the following formula:
E(R) = Rf +β*(Rm –Rf)
- Rm is the market return
- Rf is the risk-free rate
- β is the asset’s beta
In the above formula, the risk-free rate can be observed from the yields of long-term bonds such as 10-year bond.
The beta, or systematic risk of the asset, is given by the following formula:
β = r*sA/sM
r is the correlation coefficient between the rate of return on the risky asset and the rate of return on the market portfolio; sA is the standard deviation of the rate of return on the risky asset. sM is the standard deviation of the rate of return on the market portfolio.