5. Summary

This section has presented the conceptual framework to estimate the cost of capital of any financial asset. At the core of the considerations is the Capital Asset Pricing Model (CAPM), which describes the relation between the systematic risk and the average expected return of an asset as follows:

 

\(\mu_j = R_F + \beta_j \times (\mu_M - R_F)=R_F+\beta_j \times MRP \),

 

In this equation:

  • \(\mu_j\) is the average expected return on asset j. That's the discount rate that we are looking for.
     
  • \(R_F\) is the risk-free rate of return.
     
  • \(\beta_j\) is a measure of the systematic risk of asset j, namely the covariance of the asset return with the market return (\(\sigma_{Mj}\)), divided by the variance of the market return (\(\sigma_M^2\)):  \(\beta_j = \frac{\sigma_{Mj}}{\sigma_M^2}\).
     
  • MRP is the market risk premium, i.e., the difference between the expected return on the market portfolio (\(\mu_M\)) and the risk-free rate of return (\(R_F\)): \( MRP = \mu_M - R_F\).

  

The important takeaways are as follows:

  • The minimum return that investors expect to earn corresponds to the risk-free rate of return.
     
  • In addition to the risk-free rate of return, investors require a compensation for the riskiness of the asset. 
      
  • However, not the total risk of an asset (\(\sigma_j\)) is rewarded with a higher expected rate of return. The reason is that investors can diversify a part of that risk, the so-called diversifiable risk.
     
  • Because parts of the total risk can be diversified fairly easily, the total risk of an asset is an inadequate risk measure. 
     
  • Only the risk that cannot be diversified is rewarded with a higher expected return. This is the so-called systematic risk.
     
  • The most popular measure of systematic risk is the "beta" of the asset. 
     
  • To obtain the asset's risk premium, e multiply the beta of the asset with the market risk premium.

  

To estimate the cost of capital, we therefore need to know the following information:

  • Risk-free rate of return
  • Systematic risk of the asset
  • Market risk premium.

  

The next section will briefly discuss how to estimate these important parameters.