In particular lets consider a zero-beta asset $i$ (in the CAPM sense). Let
- $R_f$ be the risk free rate
$R_f$ be the risk free rate
- $R_i$ the return on the asset $i$
$R_i$ the return on the asset $i$
- $R_m$ the return on the market portfolio
$R_m$ the return on the market portfolio
- $\beta=\frac{Cov(R_i,R_m)}{Var(R_m)}$
$\beta=\frac{Cov(R_i,R_m)}{Var(R_m)}$
- $E_P (E_Q)$ the expectation under $P$ the historical probability ($Q$ the risk neutral probability)
$E_P (E_Q)$ the expectation under $P$ the historical probability ($Q$ the risk neutral probability)
By the martingale properties the follwoing identity holds: $E_Q[R_i]=R_f$
By the martingale properties the follwoing identity holds: $E_Q[R_i]=R_f$
By the CAPM the following holds:
$E_P[R_i]=R_f+\beta E_P[R_m-R_f]= E_Q[R_i]+\beta E_P[R_m-R_f]$
If we assume $\beta=0$, then $E_P[R_i]=E_Q[R_i]$
My question is: does $E_P[R_i]=E_Q[R_i]$ imply $P=Q$?
