CAPM as a Model for the Cost of Equity

# Why is the use of CAPM justified for estimating the cost of equity?


# Why is the use of CAPM justified for estimating the cost of equity?












For an investor in a stock, stock returns are how they are paid for providing their capital. Why is the measure of performance for how capital is utilized by a company tied to the return they generate on the projects they invest in?

## Answer by Matthew Gunn (score 3)

https://quant.stackexchange.com/a/83982

Let $f_t(X)$ be a function that gives the market equilibrium expected rate of return for the next $t$ months given company specific variables $X_i$. That is, in equilibrium, the expected return of the company is:

$$ \operatorname{E}[R_{i,{0 \rightarrow t }} \mid X_{i,{0 \rightarrow t }}] = f_t(X_{i,{0 \rightarrow t }}) $$

This is the expected return investors demand.

The idea in financial economics is that exected return function $f_t$ is determined by macroeconomic processes and is some function of exposure to macroeconomic risk.

- The CAPM is a particular theory that implies $f_t(\beta_{it}) = r_{ft} + \beta_{it}(\operatorname{E}[R_{m, t}]-r_{ft})$, the expected return is a function of the risk free rate, the stock's regression beta with respect to the market, and the expected market return. In the CAPM, there is only one source of risk of hedging concern to investors: the market return itself.

Note also that:

- The CAPM is an EMPIRICAL FAILURE. It does not work. It is will known in finance that it empirically does NOT work.

- There are other models of market equilibrium besides the CAPM.

- For example, some models that are better connected to empirical reality are the Fama-French 3 factor or 5 factor model, or other various multi-factor models.

- Note also that all of these factor models that appear to work better have poor grounding in theory. Some models that have better grounding in theory (e.g. consumption based asset pricing) have problems matching the data. What generates expected returns isn't a solved question.

- Market betas are estimated poorly for an individual company. Even if you had a good model of market equilibrium returns, application to a specific company is problematic.

Back to your original question, the broad theoretical idea is that a company's stock has some expected return where needs to match the market rate of return for a company's return with those particular risk characteristics.

## Answer by D Stanley (score 2)

https://quant.stackexchange.com/a/83981

If you invest in a company, you expect the value of that investment to grow over time (otherwise you'd be better off putting the money in the bank and earning interest). Since there are lots of companies available to invest in, you have to have a reasonable measure of how much your investment in a company will grow over time. You also have to consider other investments of similar risk, and choose the ones that are expected to get the highest return (taking risk into account). So you have a minimum expected return on the equity you buy.

Looking at it from the company's perspective, how much return should you expect to get for a new project that must be financed? You have to raise the funds through some combination of debt (borrowing) or selling equity, so the return that the project should be expected to generate must be greater then the cost of the funds raised to finance the project.

CAPM is one model used to measure the "cost of equity" - it is not the only way. CAPM measures future returns based on past returns, comparing how risky the stock has been compared to the overall market, and assuming that samne riskiness going forward. There may be other models that more accurately predict future performance.