Capital Asset Pricing Model

The Capital Asset Pricing Model (CAPM) is an economic model for valuing stocks, securities, derivatives and/or assets by relating risk and expected return. CAPM is based on the idea that investors demand additional expected return (called the risk premium) if they are asked to accept additional risk. This model was originally developed in 1952 by Harry Markowitz and fine-tuned over a decade later by others, including William Sharpe.

A model that describes the relationship between risk and expected return and that is used in the pricing of risky securities.

(ra: expected return of security)

The general idea behind CAPM is that investors need to be compensated in two ways: time value of money and risk. The time value of money is represented by the risk-free (rf) rate in the formula and compensates the investors for placing money in any investment over a period of time. The other half of the formula represents risk and calculates the amount of compensation the investor needs for taking on additional risk. This is calculated by taking a risk measure (beta) that compares the returns of the asset to the market over a period of time and to the market premium (Rm-rf).
The CAPM says that the expected return of a security or a portfolio equals the rate on a risk-free security plus a risk premium. If this expected return does not meet or beat the required return, then the investment should not be undertaken. The security market line plots the results of the CAPM for all different risks (betas).

Using the CAPM model and the following assumptions, we can compute the expected return of a stock: if the risk-free rate is 3%, the beta (risk measure) of the stock is 2 and the expected market return over the period is 10%, the stock is expected to return 17% (3%+2(10%-3%)).

Beta measures the volatility of the security, relative to the asset class. The equation is saying that investors require higher levels of expected returns to compensate them for higher expected risk. You can think of the formula as predicting a security's behaviour as a function of beta: CAPM says that if you know a security's beta then you know the value of r that investors expect it to have.

One consequence is that CAPM implies that investing in individual stocks is pointless, because you can duplicate the reward and risk characteristics of any security just by using the right mix of cash with the appropriate asset class. This is why followers of MPT avoid stocks, and instead build portfolios out of low cost index funds.

Assumptions of CAPM

• All investors have rational expectations.
• There are no arbitrage opportunities.
• Returns are distributed normally.
• Fixed quantity of assets.
• Perfectly efficient capital markets.
• Investors are solely concerned with level and uncertainty of future wealth
• Separation of financial and production sectors.
• Thus, production plans are fixed.
• Risk-free rates exist with limitless borrowing capacity and universal access.
• The Risk-free borrowing and lending rates are equal.
• No inflation and no change in the level of interest rate exists.
• Perfect information, hence all investors have the same expectations about security returns for any given time period.

Shortcomings of CAPM

• The model assumes that asset returns are (jointly) normally distributed random variables. It is however frequently observed that returns in equity and other markets are not normally distributed. As a result, large swings (3 to 6 standard deviations from the mean) occur in the market more frequently than the normal distribution assumption would expect.
• The model assumes that the variance of returns is an adequate measurement of risk. This might be justified under the assumption of normally distributed returns, but for general return distributions other risk measures (like coherent risk measures) will likely reflect the investors' preferences more adequately.
• The model does not appear to adequately explain the variation in stock returns. Empirical studies show that low beta stocks may offer higher returns than the model would predict. Some data to this effect was presented as early as a 1969 conference in Buffalo, New York in a paper by Fischer Black, Michael Jensen, and Myron Scholes. Either that fact is itself rational (which saves the efficient markets hypothesis but makes CAPM wrong), or it is irrational (which saves CAPM, but makes EMH wrong - indeed, this possibility makes volatility arbitrage a strategy for reliably beating the market).
• The model assumes that given a certain expected return investors will prefer lower risk (lower variance) to higher risk and conversely given a certain level of risk will prefer higher returns to lower ones. It does not allow for investors who will accept lower returns for higher risk. Casino gamblers clearly pay for risk, and it is possible that some stock traders will pay for risk as well.
• The model assumes that all investors have access to the same information and agree about the risk and expected return of all assets. (Homogeneous expectations assumption)
• The model assumes that there are no taxes or transaction costs, although this assumption may be relaxed with more complicated versions of the model.
• The market portfolio consists of all assets in all markets, where each asset is weighted by its market capitalisation. This assumes no preference between markets and assets for individual investors, and that investors choose assets solely as a function of their risk-return profile. It also assumes that all assets are infinitely divisible as to the amount which may be held or transacted.
• The market portfolio should in theory include all types of assets that are held by anyone as an investment (including works of art, real estate, human capital...) In practise, such a market portfolio is unobservable and people usually substitute a stock index as a proxy for the true market portfolio. Unfortunately, it has been shown that this substitution is not innocuous and can lead to false inferences as to the validity of the CAPM, and it has been said that due to the inobservability of the true market portfolio, the CAPM might not be empirically testable. This was presented in greater depth in a paper by Richard Roll in 1977, and is generally referred to as Roll's Critique. Theories such as the Arbitrage Pricing Theory (APT) have since been formulated to circumvent this problem.
• Because CAPM prices a stock in terms of all stocks and bonds, it is really an arbitrage pricing model which throws no light on how a firm's beta gets determined.