# Arbitrage Capital Asset Pricing Model

## Components of Capital Asset Pricing Model

The **capital asset pricing model** (CAPM) is an equilibrium pricing model. The **CAPM** measures how much a given asset's return is affected by the movement of the overall market. The S&P 500 is often the benchmark index used in the model. The first component of the CAPM is the beta or risk associated with the asset. Thus, the beta for a asset is calculated based on the asset's returns, Ri, relative to returns from the market, Rm:

The second component of the CAPM is the expected rate of return for an asset based on the beta coefficient and the risk free rate of return and the market wide risk premium. The reference point for the risk free rate in the U.S. is the return on a treasury bond.

For an example let us say that stock A has a beta (Bi = .5%), the risk free rate of return (Rf = 4%) and the expected rate of return for the market (Rm = 10%). You would calculate the expected rate of return for the asset as follows:

The graphical portrayal of the equilibrium trade-off between expected return and risk is the Security Market Line (SML). The Capital Asset Pricing Model displays the SML relative to the expected rate of return E(R) and the Beta (B).

## Example of an Arbitrage Technique utilizing the Capital Asset Pricing Model

As you can see in the above model, asset B's expected rate of return is greater than the Security Market Line and asset A is sitting on the SML. This is a sign that asset B is currently undervalued and asset A is appropriately priced. So, how can we hedge this position? Assuming that both assets have the same beta and asset B is cheaper than asset A by let's say 2%, we can buy asset B and use the proceeds to sell short asset A to hedge our position. This short entry will generate an initial net cash flow because the price of B is less than the price of A. This is inline with the fact that the expected rate of return for asset B is greater than that for asset A. This simple transaction will lock in 2% misevaluation of asset B as a risk less excess return. The excess return is hedged because each asset has the same beta. So, no matter which way the market moves, you have locked in a 2% gain utilizing the capital asset pricing model.