I am currently looking through some actuarial study materials (CM2, formerly CT8) in which models of asset returns are being discussed. One such model is the market model (A.K.A The single-index model), which is defined to be of the form $$ R_i = \alpha_i + \beta_i R_M + \varepsilon_i $$ where
- $R_i$ is the return on asset $i$ (being modelled)
- $R_M$ is the return of the market
- $\alpha_i$ and $\beta_i$ are constants (to be found through regression analysis)
- $\varepsilon_i$ is a random variable representing the return from asset $i$ that is independent of market returns.
Within this context, it goes on to say that only the systematic risk, measured by $\beta_i$ should be expected to be rewarded by increased returns since this risk is non-diversifiable).
Can anyone explain why the unsystematic risk (i.e. the variance of $\varepsilon_i$) would not be expected to be rewarded with greater returns?
For example, suppose you have two companies within the same industry. If one company is a long-standing big player (HSBC, say) and another is a smaller up-and-coming company (Monzo) then although they would likely be correlated with the same underlying index, you would expect a greater return on the smaller player due to the greater market risk associated with it.