### Capital Asset Pricing Model (CAPM)

The Capital Asset Pricing Model (CAPM) provides a linear relationship between expected return for an asset and the beta. CAPM is graphically represented via the Security Market Line (SML). As opposed to the Capital Market Line (CML), where the X-axis was standard deviation, we’re now using beta – systematic risk – to approximate the expected return.

As with many financial models, it is reliant on a number of assumptions in order to simplify some of the complexity of the financial markets.

## CAPM Assumptions

As with many financial models, not all the complexities of the financial markets are accounted for. CAPM make the following assumptions:

#### Investors are risk-averse, utility-maximizing, rational individuals

This assumption does not require all investors to have the same degree of risk-aversion; it simply requires investors to be risk-averse as opposed to risk-neutral or risk-seeking. Investors are assumed to be rational if they correctly evaluate all available information to arrive at rational decisions. The rationality of investors has been called into question, as personal bias can result in irrational decision-making. However, this behavior does not affect the model outcome.

#### Markets are frictionless, including no transaction costs and no taxes

In addition to assuming no transaction costs, the model also assumes investors can borrow and lend at the risk-free rate. The transaction costs of many large institutions are negligible and many investors do not pay taxes. The practical inability to borrow or lend at the risk does not materially affect the CAPM results, but costs and restrictions on short-selling can introduce an upward bias on asset prices which does affect the CAPM conclusions.

#### Investors plan for the same, single holding period

The assumption of a single holding period is convenient as multi-period models become very difficult. There are shortcomings with the single-period assumption; however, it does not severely limit the applicability of the CAPM.

#### Investors have homogenous expectations or beliefs

This assumption assumes all investors analyze securities, in the same way using the same probability distributions and inputs for future cash flows. This then means that all asset valuations are identical and the same optimal portfolio of risky assets is generated – the market portfolio. This assumption can be relaxed as long as the generated optimal risky portfolios are not significantly different.

#### All investments are infinitely divisible

This assumes investors can hold fractions of assets and is convenient from a modeling perspective as it allows for continuous rather than discrete jump functions.

#### Investors are price takers

If investors are price takers, it means no one investor can influence prices by their trades. This assumption is generally true in practice.

## The Security Market Line (SML)

The Security Market Line (SML) is the graphical representation of the CAPM with beta reflecting systematic risk on the x-axis and expected return on the y-axis. The SML intersects the y-axis at the risk-free rate and the slope of the line is the market risk premium, Rm – Rf.

The SML is formulated as follows:

$$E(R_i) = R_f + β_i [E(R_m) – R_f]$$

Where $$β_i= \frac{ρ_{ i,m} σ_i } {σ_m}$$.

Although similar to the Capital Market Line (CML), the CML only applies to portfolios on the efficient frontier providing optimal combinations of risk and return, the SML applies to any security whether efficient or not. Total risk and systematic risk are equal for an efficient portfolio because the non-systematic risk has been diversified away.

## Question

Which statement does not identify assumptions of the capital asset pricing model?

A. Investors are price takers, investors are rational, and transaction costs are ignored.

B. Investors are risk-seeking, fractional ownership is possible, and investors are price takers.

C. Investors have the same holding period, investors value securities identically, and taxes can be ignored.

Solution

CAPM assumes all investors are risk-averse, utility-maximizing and rational individuals.

Explain the capital asset pricing model (CAPM), including its assumptions, and the security market line (SML)

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