The capital asset pricing model (CAPM) provides linear relationship between return and beta coefficient.

The equation for expected return E(R_i) is as follows:

\[ E(R_i)=R_f+β_i × [E(R_m)-R_f] \]It shows that the expected return on an asset is a function of its systematic risk as measured by beta coefficient. Hence, two assets with same beta must earn the same expected return.

## Assumptions of the CAPM

CAPM is founded on certain assumptions, most of which are constraining:

- Investors are risk-averse, utility-maximizing, rational individuals. It means that investors prefer less risk over more and more wealth over less. It doesn’t mean that all investors must reach the same conclusion but that they all process information rationally. Recent research calls into question the assumption of rationality.
- Markets are frictionless which means that (a) all sorts of trades including short-selling is allowed, (b) lending and borrowing at the risk-free rate is possible, (c) there are no transaction costs and (d) there are no taxes. While these assumptions may not be met in all situations, they do not affect the general conclusions of CAPM. However, a restriction on short-selling may create an upward bias on prices.
- Investors plan for same single holding period. Even though this assumption does not reflect investor learning or that an investor might be willing to sustain a loss in the short-run to gain in the long-run, this assumption does not severely limit applicability of CAPM.

Investors have homogeneous expectations or beliefs: This means that all investors use the same inputs in their decisions, the same decision-making processes and reach the same conclusions. However, CAPM still works if this assumption is relaxed. - All investments are infinitely divisible. This allows the model to employ continuous functions. It has an inconsequential impact on the conclusions of the model.
- Investors are price takers. It assumes that since there are many investors and no investor is large enough, security prices would not be affected by investor trades.

Despite these assumptions, the CAPM provides a reasonable benchmark for initial return estimates.

## The security market line

The security market line (SML) is a graph of the CAPM which plots the expected return on y-axis and systematic risk (represented by beta) on the x-axis. Its y-intercept equals the risk-free rate and its slope equals the market risk premium.

While the capital market line (CML) applies only to portfolios on the efficient frontier, the SML applies to all assets. SML can be used to work out the expected return on an asset.

When we have a portfolio of securities, its beta equals the weighted average of the individual betas and the expected return can be calculated by using the portfolio beta in the CAPM equation.

CAPM can be used to estimate expected return for capital budgeting, determine benchmark return for performance appraisal, security selection, etc. For example, CAPM can be used to work out the hurdle rate for capital budgeting projects. Such an application uses a measure of project risk.

## Limitations of the CAPM

The CAPM is subject to theoretical and practical limitations.

### Theoretical limitations

- It prices only systematic risk or beta risk which makes it restrictive and inflexible.
- It does not consider multi-period implications. Hence, it cannot capture factors that vary over time and span several periods.

### Practical limitations

- CAPM defines a true market portfolio as including assets, financial and nonfinancial. Since many assets are not investable, CAPM-defined market portfolio cannot be created. This is why CAPM cannot be tested.
- Due to a lack of true market portfolio, different practitioners use different proxies for the market portfolio which causes them to generate different return estimates for the same asset, which is a violation of one of the assumptions of CAPM.
- A long history of returns is needed to estimate beta but this might not be an accurate representation of the current or future systematic risk of the stock. Beta estimates also vary due to differences in return frequency (for example, weekly versus monthly). Hence, different beta estimates may result in different return estimates.
- Empirical studies suggest that the CAPM is a poor predictor of returns.
- The assumption that there is homogeneity in investor expectations does not hold in reality.