The Capital Asset Pricing Model or CAPM, is a model that is used in corporate finance to evaluate the expected return of capital assets based on their systematic risk. Systematic risk is the risk of a firm that contributes to the overall market portfolio- a portfolio that contains a weighted average of all capital assets. Non-systematic risk is, therefore, risk that comes from asset specific or industry specific sources. Most theorists in the area of corporate finance believe that you can eliminate almost all non-systematic (asset-specific) risk and be left with only systematic (market driven risk) by diversifying in around thirty assets. Eg shares, properties etc. CAPM prices assets on the basis that this non-systematic risk has been diversified away- that is, there is no compensation for bearing non-systematic risk by way of a higher expected return.

The equation for CAPM is as follows:

CAPM: E(ri) = rf + Bi(E(rm) - rf )

Where:

E(ri) is the expected annual return as a percentage on asset i rf is the risk free rate of return (usually measured by treasury yields, since governments are highly unlikely to default on their bonds). Bi is the Beta of asset i. E(rm) is the expected return of the market portfolio.

So what is Beta? Beta is a measure of the extent to which an asset’s expected return can be expected to change given some change in the market portfolio. Hence, the market portfolio is defined as having a Beta of 1. Betas higher than one are riskier than the market portfolio. For example, if the market portfolio expected return increases by 10% and an asset j has a Beta of 1.5, then we would EXPECT j’s expected return to increase by 15%. In other words, assets with high Beta are expected to magnify movements in the market portfolio. Conversely, returns on assets with low Beta are expected to move more conservatively than the market portfolio.

Beta of an asset i is defined as follows:

Bi = (Covariance(E(rm), E(ri)))/(Variance of Market)2

We see from the equation for the CAPM, that a higher Beta will increase Bi(E(rm) - rf ), known as the asset’s risk premium. A higher risk premium will give a higher overall expected return for the asset. So, since Beta is a measure of an asset’s contribution to the overall market risk or systematic risk, then investors are compensated by bearing high systematic risk with a higher expected return.

An Example: Treasury bonds have an expected return of 6%, but their Beta is virtually zero, ie close to no risk. A biotechnology stock might be extremely volatile and have a Beta of 2. This means we expect its return to change two-fold of however the market portfolio’s return changes. If the market risk premium (E(rm) - rf) is ten percent, then we would expect a return on this asset of 6% + 2*(10%) = 26%. A much higher return than the treasury bonds to compensate the holder of the asset for the riskiness of its return.

If it is priced at any expected return below this then we say that the stock is overvalued and if it is priced at an expected return above this, then we say it is undervalued. Market forces should act to correct any considerable mis-evaluation. eg "bargain hunting" in the stock market. That is, the price will move either upward or downward to decrease or increase expected return until it correctly compensates holders of the asset for its risk.

Much of the work on CAPM was done in the 1960s by Sharpe and Lintner. Subsequent testing of the CAPM to determine its relevance in real world corporate finance has found it to be useful, but flawed. The primary criticism of the model is based around the difficulty of acquiring and measuring a market portfolio. Roll’s Critique (1976) stated that the market portfolio, the central element of CAPM is impossible to study since it contains a weighted amount of each and every capital asset in the world – shares, property, machinery etc. The closest that we can come to such an index is perhaps the Morgan Stanley Capital Index, but clearly this is a far cry from the true market portfolio.

Nevertheless, CAPM and Beta are fundamental tools of much financial analysis and will be used widely until a more testable model is developed 1.

1. Bishop. (1999). Corporate Finance.

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