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In particular lets consider a zero-beta asset $i$ (in the CAPM sense). Let

  1. $R_f$ be the risk free rate

    $R_f$ be the risk free rate

  2. $R_i$ the return on the asset $i$

    $R_i$ the return on the asset $i$

  3. $R_m$ the return on the market portfolio

    $R_m$ the return on the market portfolio

  4. $\beta=\frac{Cov(R_i,R_m)}{Var(R_m)}$

    $\beta=\frac{Cov(R_i,R_m)}{Var(R_m)}$

  5. $E_P (E_Q)$ 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 $P=Q$?

In particular lets consider a zero-beta asset $i$ (in the CAPM sense). Let

  1. $R_f$ be the risk free rate
  2. $R_i$ the return on the asset $i$
  3. $R_m$ the return on the market portfolio
  4. $\beta=\frac{Cov(R_i,R_m)}{Var(R_m)}$
  5. $E_P (E_Q)$ 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 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 $P=Q$?

In particular lets consider a zero-beta asset $i$ (in the CAPM sense). Let

  1. $R_f$ be the risk free rate

  2. $R_i$ the return on the asset $i$

  3. $R_m$ the return on the market portfolio

  4. $\beta=\frac{Cov(R_i,R_m)}{Var(R_m)}$

  5. $E_P (E_Q)$ 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 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 $P=Q$?

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Jesus
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Can the historical probability be the same as the risk neutral probability measure?

In particular lets consider a zero-beta asset $i$ (in the CAPM sense). Let

  1. $R_f$ be the risk free rate
  2. $R_i$ the return on the asset $i$
  3. $R_m$ the return on the market portfolio
  4. $\beta=\frac{Cov(R_i,R_m)}{Var(R_m)}$
  5. $E_P (E_Q)$ 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 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 $P=Q$?