Expected vs required return in valuation

Question

This is a rather simple question, so this is maybe not the right place, but...

I have done quite a bit of reading on predicting asset returns, i.e. determining return expectations. I have now started reading some fundamental literature on DCF valuation. For example, one might perform company valuation by doing as follows:

\begin{equation} EquityValue= \Sigma^T_t\frac{FTE_{t}}{(1+k^e_{t})^t} \end{equation}

where $FTE_i$ denotes the expected free cash flow to equity holders in period $t$, $k^e_t$ denotes the required rate of return on equity (of that firm) for the respective period $t$.

What I do not fully understand is: Usually textbooks will say that one estimates $k^e_t$ by means of the CAPM. In other words, required return on equity is assumed to be equal to the expected return on equity (derived via the CAPM). I am not trying to start a discussion on whether the CAPM is an appropriate model for deriving expected returns. What I do not get is: Why is the required return assumed to be equal to the expected return? What I expect and what I require are conceptually completely different to me.

Answer 1

Why is the required return assumed to be equal to the expected return?

Required return in a model depends on how you model agent's behavior and beliefs.

If you assume agents in a model consider CAPM the correct model of asset pricing, that is they all believe CAPM is the correct description of how returns should be related to market risk and opportunity cost of money, then no agent would accept return lower than the return given by CAPM. If the return would be lower they would simply not invest according to the model.

From economic perspective when CAPM is used to model agent's behavior, CAPM can be viewed as:

$$\underbrace{r_i}_{\text{required return}} = \underbrace{r_f}_{\text{compensation for impatience }} + \underbrace{b_i(r_m−r_f)}_{\text{compensation for risk}}.$$

If we introduce randomness into the model by making $r_i$ and $r_m-r_f$ random variable and people believe this is the correct model then this will also be return given by rational expectations (you can just take expectations of both sides).

Alternatively if we assume that CAPM is the 'correct' statistical model to model returns the we also can reinterpret the CAPM model as a regression model where you regress $r_i$ on $r_m-r_f$ making $r_i$ the expected return.

Answer 2

Expected and required have to be equal in equilibrium. These are market expectations and requirements, not yours, though (but we assume that everyone shares the same expectations). So if the market requires more than it expects, the demand for the stock will go down, taking the price with it, so that the return will grow – until the expected value matches the required one. And if the market expects more than it requires, the demand for the stock will go up, taking the price with it, so that the return will shrink – until the expected value matches the required one.