Final answer:
The statement that in CAPM the ratio of the risk premiums on two assets is equal to the ratio of their betas is true. By comparing the CAPM equations for two different assets and their risk premiums, it's established that the common factors cancel out leaving the ratio of their betas.
Step-by-step explanation:
Using the Capital Asset Pricing Model (CAPM), we can indeed show that the ratio of the risk premiums on two assets is equal to the ratio of their betas (βs). The CAPM formula states that the expected return on an asset above the risk-free rate (its risk premium) is proportional to the market risk premium multiplied by its beta. The formula is given as:
Expected Return = Risk-Free Rate + β( Market Return - Risk-Free Rate)
For two assets, i and j, the CAPM can be written as:
E(Ri) = Rf + βi (E(Rm) - Rf)
E(Rj) = Rf + βj (E(Rm) - Rf)
Now, if we want to compare the risk premiums of these two assets, we subtract the risk-free rate from each equation:
Risk Premiumi = βi (E(Rm) - Rf)
Risk Premiumj = βj (E(Rm) - Rf)
By taking the ratio of these two risk premiums, we get:
Risk Premiumi / Risk Premiumj = [βi (E(Rm) - Rf)] / [βj (E(Rm) - Rf)]
Since the market return minus the risk-free rate is common to both, it cancels out, leaving us with:
Ratio of Risk Premiums = βi / βj
Conclusively, the statement is true.