One way to value a cashflow is to first calculate the expected return from CAPM, and then use the expected return to discount the future cashflows.
The problem here is that the expected return from CAPM is an average $\mathrm{E}[R]$, and therefore, by Jensen's inequality:
$$\mathrm{E}\left[\frac{1}{R}\right] \ge \frac{1}{\mathrm{E}[R]}$$
Then I wonder why people use $\frac{1}{\mathrm{E}[R]}$ to discount cashflows.
To clarify, I will use an example.Let's assume there is only one cashflow of \$100 a year from now I want to value. According to CAPM, the expected return is $$ \bar{R}_a = R_f + \beta_a (\bar{R}_m - R_f) $$
Note that the return $R$ is defined as $R=\frac{S_{t+1}}{S_t}$.
Now the problem here is that $\bar{R}_a$ represents an average return of the following year. The actual return $R_a$ is a random variable that is not known right now. In other words, $\bar{R}_a=\mathrm{E}[R_a]$, but $R_a$ is random, and will realize different values in different alternative universes.
However, what I usually see is that we value the \$100 cashflow a year from now as $$\frac{100}{\bar{R}_a}=\frac{100}{\mathrm{E}[R_a]} $$
But shouldn't it be valued as $$\mathrm{E} \left [ \frac{100}{R_a} \right] $$?
But according to Jensen's inequality: $$\mathrm{E} \left [ \frac{100}{R_a} \right] \ge \frac{100}{\mathrm{E}[R_a]} $$