When lawyers meet to settle a case, they usually start by estimating their chances of going to trial. They multiply that by the amount of money in play and come up with what usually becomes their opening bid.

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

Investors use a version of this logic when evaluating a potential investment. This is called the capital asset valuation model. This is how it works.

## What is the fixed asset pricing model?

Every investment carries a certain degree of risk. The stock you buy may fall. Real estate can lose value. Even a bank can shut down, forcing you to rely on the interest-free FDIC repayment.

The rate of return compensates you for it. The higher the risk, the higher the return expected by the investor. This is why you might want to get rich in exchange for a purchase from a start-up business, for example, because there is a good chance that you will lose your money completely. In contrast, securities issued by the US Treasury are virtually risk free and therefore offer a very low rate of return.

The Asset Valuation Model (CAPM) is the formula for calculating the rate of return you must accept on a risky asset before investing. The higher the risk, the more the asset must pay before it becomes a rational investment.

## Calculation of the fixed asset valuation model

The fixed asset valuation model asserts that for an investment to be rational, its rate of return must 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 US analysts use a 10-year Treasury bond as a risk-free benchmark. You can still put your money in this safe alternative, so for a riskier investment to be worth it, it has to pay more than the treasury bill.

The fixed asset valuation formula is as follows:

Ra = Rrf + (Ba x (Rm – Rrf))

Or:

â€¢ Ra = The expected rate of return on the security. This is the return that the security must offer for it to be a rational investment. If security offers less than that, then you had better put your money in risk-free security.

â€¢ Rrf = Risk-free rate of return. This is the rate of return of the risk-free alternative that you use as a benchmark. As noted above, most analysts use ten-year treasury bills as the standard risk-free rate of return.

â€¢ Ba = Security beta. It is a coefficient allowing to measure the degree of volatility (and therefore of risk) of a given investment. It is calculated as a proportion of the volatility of the specific investment relative to the volatility of its market. For example, if a stock on the New York Stock Exchange has a beta of 2, that means it is twice as volatile as the NYSE as a whole.

The beta is usually generated as part of a stock’s market information package on most major sources.

â€¢ Rm = Expected return from the market. This is the expected rate of return you would receive if you invested in a fund indexed to that market as a whole.

â€¢ (Rm – Rrf) = This is called the â€œmarket risk premiumâ€. It represents the additional return you would receive by investing in a particular market compared to investing in your safe alternative asset.

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

You first calculate your market risk premium. This will be how much more you would earn in the NYSE market as a whole compared to just putting your money in a 10 year treasury bill. 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 completely lose your money on that particular security.

Finally, you add to that the rate you might get by investing in a 10-year treasury bill. This risk-free rate of return is your minimum. The stock you choose must make at least that much money, otherwise you’d better go for Treasury Bond.

The end result is the rate of return your stock would need to make the investment risk worth it.

## Example of the fixed asset valuation model

Let’s see this in practice. Suppose you want to buy stocks in Grow Co. Our formula would use the following variables:

â€¢ Rrf = 2.53% (the yield on a 10-year Treasury bill at the time of writing)

â€¢ Beta = 1.5 (which means that the Grow Co. stock is 1.5 times more volatile than the S&P 500 index as a whole)

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

We would therefore do the following calculation:

â€¢ Ra = 0.0253 + (1.5 x (0.10 – 0.0253)) = 13.7%

You should expect a 13.7% return before the Grow Co. stock, based on its risk, is a wise investment.

## Systemic risk vs specific risk

There are two types of risks when investing. It is important to understand that the capital asset valuation model only considers one of them.

â€¢ Specific risk – This is the risk inherent in a specific security or security. It reflects trading decisions, weather conditions, consumer choices and any other aspect of the security’s performance that has to do with the specific asset and not the market as a whole.

â€¢ Systemic risk – It is the risk inherent in a market as a whole. It refers to anything that can affect all investments, rather than issues specific to an individual asset. Recessions, political decisions, regulations, tax changes and interest rates are all examples of systemic risk.

The fixed asset valuation model deals only with systemic risk. The beta used to assess the appropriate rate of return on an investment only takes into account the volatility of the investment relative to the market as a whole. The formula does not attempt to assess the risks specific to that particular asset.

Instead, investors typically try to correct a specific risk through diversification. By spreading your investments across a wide range of investments and investment categories, you can usually correct most of the risks that a single product can create.

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

## Criticisms of the fixed asset valuation model

For decades, investors and economists have questioned the CAPM.

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

Ultimately, concerns about the CAPM come from the same place. Critics of the model argue that it is too simplistic. The formula does not take into account all of the risks inherent in investing and does not adequately assess reasonable returns. A stock may have a relatively high beta relative to the market as a whole, for example, but that could just as easily mean that the market has been unusually calm that the stock is particularly risky.

If so, the CAPM might recommend an unrealistic rate of return before investing in what (in fact) is a solid 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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