# CAPM – Capital Asset Pricing Model

The Capital Asset Pricing Model establishes the link between the expected return for an asset and systematic risk. The CAPM uses a simple mathematical formula. Although debunked and not widely used anymore, this pricing model is conceptually sound.

It provides an interesting take on the expected return of investment. At the same time, it uses variables, some of which make its own existence redundant.

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## What Is The CAPM Formula?

The formula that defines the CAPM is:

ERi = Rf+βi*(ERm-Rf)

## Understanding The CAPM

In the mentioned equation, ERi is the expected return of investment. This is the variable that we are looking to find through the mathematical exercise entailed by the formula.

- Rf is the risk-free rate. We define the Rf as the return on an investment with zero risk. Of course, Rf is a theoretical variable. In the CAPM equation, Rf is meant to account for the time value of money. The time value describes the earning potential of money over time.
- ERm is the market risk rate. This is higher than the Rf, because the risk involved in the Rf is zero. The ERm defines the return on a market-risk/theoretical market portfolio investment.
- In the CAPM equation, the ERm-Rf defines the market risk premium. It is logical: by subtracting the risk-free rate from the market risk rate, we get this difference, which is the premium.
- βi is where the formula takes an interesting twist. Called the “beta” of the investment, βi describes the amount of risk a particular investment adds to/subtracts from the risk carried by a market portfolio.

The beta can be more than one or less than one. It can even be negative. What do these value-ranges mean?

The intrinsic beta of the market is 1. If a stock has a beta of two, it means that historically, it went up 10% when the market climbed 5%, and dropped 10% when the market dropped 5%. Its historical volatility is twice that of the market.

When a stock climbs 5% as the market climbs 10%, and drops 5% when the market drops 10%, its volatility is half of the market’s. Its beta is thus 0.5.

Negative beta occurs when a stock is inversely correlated with the market. Such a stock would climb 10% as the market dropped 10% and it would drop 10% as the market climbed 10%. This example would imply a beta of -1. Such inversely-correlated assets are extremely valuable. They offer great avenues for diversification.

Knowing this, it is plain to see why the CAPM offers a conceptually sound evaluation of fair stock value.

## So Why Is The CAPM Obsolete/Redundant?

If it were possible to estimate the future return of a stock with high accuracy, we would not need the CAPM.

The beta is based on historical data. This is notoriously unreliable. Looking past that, the formula also ignores the fact that asset value-movements in both directions do not entail equal risk.

The risk-free rate tends to vary over time as well. The CAPM assumes however that it remains constant.

We can define the Rf in relation to the US Treasury bond interest rate. In this case, a change in the Treasury bond interest rate would alter the Rf as well.

We can only poorly approximate the market risk-rate through a major stock index. An ideal market-portfolio is theoretical. Such a theoretical entity does not offer a viable investment alternative to any stock. Using a major stock index as an alternative is an imperfect solution.

## CAPM Still Retains Utility

An investor can still use the CAPM to determine the performance of a portfolio compared to the market. The CAPM also offers a reasonable starting point for future expectations.