When lawyers meet to settle a lawsuit they typically begin by estimating their chances at trial. They multiply that by the amount of money at stake and come up with what typically becomes their opening offer.

So, a lawyer who wants \$100,000 in damages and thinks she has an 80% chance of winning in court would probably take \$80,000 to settle the lawsuit (100,000 x 0.80).

Investors use a version of this logic when they price out a potential investment. It's called the capital asset pricing model. Here's how it works.

## What Is the Capital Asset Pricing Model?

Every investment comes with a certain degree of risk. The stock you purchase might fall through. A piece of property might lose value. Even a bank might go out of business, forcing you to rely on interest-free reimbursement from the FDIC.

Rate of return compensates you for this. The higher the risk, the higher the return an investor expects. This is why you might want to get rich in exchange for buying into a startup company, for example, because there is a significant chance that you'll lose your money completely. By contrast, securities issued by the United States Treasury have virtually no risk whatsoever and, as a result, give a very low rate of return.

The capital asset pricing model (CAPM) is the formula for calculating the rate of return you should accept in a risky asset before investing. The higher the risk, the more the asset has to pay out before it becomes a rational investment.

## Calculating the Capital Asset Pricing Model

The capital asset pricing model asserts that for an investment to be rational, its rate of return has to be the sum of a generic risk-free return plus a premium based on the risk profile of that particular asset.

Essentially, this formula says that you should approach every investment by comparing it to a completely safe alternative. Most analysts in the U.S. use a 10-year Treasury bond as the risk-free benchmark. You could always put your money in this safe alternative, so for a riskier investment to be worthwhile it has to pay more than the Treasury bond would.

The formula for capital asset pricing is as follows:

Ra = Rrf + (Ba x (Rm - Rrf))

Where:

Ra = The expected rate of return on the security. This is the return that the security has to offer for it to be a rational investment. If the security offers less than this, then you're better off putting your money in the risk-free security.

Rrf = Risk-free rate of return. This is the rate of return on the risk-free alternative that you're using as a benchmark. As noted above, most analysts use the ten year Treasury bond as the standard risk free rate of return.

Ba = Beta on the security. This is a coefficient used to measure the degree of volatility (and therefore risk) involved in a given investment. It is calculated as a proportion of the specific investment's volatility compared to the volatility of its market. For example, if a stock on the New York Stock Exchange has a beta of 2, this means that it is twice as volatile as the NYSE overall.

Beta is typically generated as part of a security's market information package on most mainstream sources.

Rm = Expected return of the market. This is the expected rate of return you would receive if you invested in a fund indexed to that market overall.

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(Rm - Rrf) = This is known as the "market risk premium." It represents the additional return you would receive by investing in a particular market as compared to investing in your safe alternative asset.

So, let's break down the formula conceptually for an investment on the New York Stock Exchange.

First you calculate your market risk premium. This will be how much more you would make on the NYSE market overall compared with simply putting your money into a 10-year Treasury bond. This is your compensation for not keeping your money safe.

Then you multiply that by the beta of your particular investment. This adjusts the additional compensation to reflect the risk that you might lose your money altogether on this particular stock.

Finally, you add onto this the rate you could get by investing in a 10-year Treasury bond. This risk-free rate of return is your minimum. The stock you've picked has to return at least that much money, otherwise you're better off choosing the Treasury bond.

The final result is the rate of return your stock would need in order for it to be worth the risk of investing.

## Example of the Capital Asset Pricing Model

Let's look at this in practice. Say you want to buy stock in Grow Co. Our formula would use the following variables:

• Rrf = 2.53% (the yield on a 10-year Treasury bond at time of writing)

• Beta = 1.5 (meaning that Grow Co.'s stock is 1.5 times as volatile as the S&P 500 index overall)

• Rm = 10% (the average rate of return for the S&P 500 index, a typical benchmark for CAPM calculations with a stock purchase)

We would therefore run the following calculation:

• Ra = 0.0253 + (1.5 x (0.10 - 0.0253)) = 13.7%

You would need to expect a return of 13.7% before Grow Co.'s stock, based on its risk, would be a rational investment.

## Systemic vs. Specific Risk

There are two types of risk when making an investment. It's important to understand that the capital asset pricing model only accounts for one of them.

Specific Risk - This is the risk inherent to a specific stock or security. It reflects business decisions, weather patterns, consumer choices and any other aspect of the security's return that has to do with the specific asset and not the market overall.

Systemic Risk - This is the risk inherent to a market overall. It refers to anything that can affect all investments, rather than issues specific to an individual asset. Recessions, political decisions, regulation, tax changes and interest rates are all examples of systemic risk.

The capital asset pricing model deals only with systemic risk. The beta used in pricing an investment's appropriate rate of return looks only at the investment's volatility compared to the market overall. The formula does not attempt to price for the risks particular to that given asset.

Instead, investors typically try to correct for specific risk through diversification. By spreading your investments across a broad range of investments and investment classes, you can typically correct for most risks that a single product might create.

When considering the CAPM, it's important to remember this. The model only helps you to assess risk in the context of the overall market, nothing more.

## Criticisms of the Capital Asset Pricing Model

For decades investors and economists have questioned the CAPM.

One of the most important advantages to the CAPM is its clarity. This formula creates a simple, easily applied target for risk management. For any given investment, unless you can expect a return of Ra, the product is not worth purchasing.

Ultimately, the concerns about the CAPM come from the same place. Critics of the model argue that it is too simplistic. The formula doesn't capture all of the risks inherent to investing, nor does it adequately assess reasonable returns. A stock might have a relatively high beta compared to the market over all, for example, but that could just as easily mean that the market has been unusually quiet as that the stock is particularly risky.

If that's the case, the CAPM might recommend an unrealistically high rate of return before investing in what (in fact) is a sound asset.

For investors, the CAPM creates a useful tool that allows them to quickly analyze and quantify their choices. It is an essential part of modern investing, and one that anyone interested in the market should understand.

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