Spoiler alert! if there is anyone who wants to save the answer to the question, what does the capital asset pricing model do? to the end of this article, then close your eyes or cover up the next paragraph or just quickly scroll down. Here it is:
The Capital Asset Pricing Model is a model used to determine the theoretical price and expected return of a stock taking into account the additional risk that the stock has above the risk of the rest of the market.
There are assumptions behind the statement above and looking into those assumptions gives a good understanding of what the Capital Asset Pricing Model, CAPM for short really does.
We should note that after the CAPM was introduced in 1961 it has drawn a lot of criticism and there have been refinements to the model. Nevertheless, and notwithstanding Nobel Prizes in Economics for some of those involved and in spite of the criticisms, the CAPM remains popular because of its ease of use and wide applicability.
Systematic risk, market risk, non-diversifiable risk, and idiosyncratic risk
That all sounds very complicated, but actually systematic risk, market risk and non-diversifiable risk are all the same thing or rather refer to the same component of the risk of a stock.
Let’s remember that risk is just a measure of the variability of the actual return we will receive from an investment with respect to the expected return from that investment. A high-risk investment has a high variability of return and a low-risk investment has a low variability of return.
The other risk component of a stock is the idiosyncratic risk of the stock. Unsurprisingly, the idiosyncratic risk is that part of risk specific to a stock that is not part of the market risk. Very simply this is what it would look like.
The systematic risk is risk that the whole market is subject to. So this would include risks of all the vagaries and things that go either right or wrong in the economy or with the weather or international trade for example. It is also non-diversifiable because it is part of the risk that you can’t get rid of by diversifying into other investments.
One of the variables that figure into the CAPM calculation is Beta. The Beta of a stock is the measure of how the stock price moves in relation to market price movements. This is easiest to see with a few examples.
- If the market rises or falls 1% and the stock price rises or falls 1% i.e. the stock price moves in step with the market then Beta of the stock is 1
- If the market rises or falls 1% and the stock price rises or falls 0.5% i.e. the stock price moves in the same direction as the market but by half as much, then the Beta of the stock is 0.5
- If the market rises or falls 1% and the stock price falls or rises 0.5% i.e. the stock price moves in the opposite direction as the market and by half as much, then the Beta of the stock is minus 0.5
- if the stock price movements have no correlation with market price movements, then the Beta of the stock is zero.
Many investors who have used Beta will know that it only works for small percentage movements in both market and stock prices. Once a price movement goes beyond a few percentage points, Beta no longer works, or rather even though a correlation of price movements may still be present it would not be expressed by a single static number.
Other variables and assumptions used by CAPM
The rate of return of a theoretical risk-free asset. The closest that comes to the return of a risk-free asset would be the return on a bond that pays back the principal and interest with absolute certainty even if the world went to hell in a handbasket. For practical purposes, a 10-year Treasury bond comes closest and can be used as a substitute.
The expected return of the market. For practical purposes, this is best represented by the average long-term return of the Standard and Poor’s 500 index.
Normal distribution of returns. The CAPM assumes that the rates of return of both the market and the stock statistically follow a normal distribution, with a mean value and an even deviation either side of that mean.
Zero transaction costs. The CAPM also assumes that diversification can be achieved with zero transaction costs to completely eliminate the idiosyncratic risk of the stock in question.
The outcome of the assumptions
The assumptions upon which the CAPM is built essentially mean that the appropriate theoretical price of a stock is determined by its Beta. So once we know the Beta of a stock, the expected market return, the expected return of a risk-free asset we would be in a position to determine the theoretical expected return of the stock and hence its theoretical price.
The Security Market Line
The CAPM assumes a linear relationship between its variables and is expressed as the Security Market Line as shown here.
So what this means is that the appropriate rate of return of a stock would be placed anywhere along the Security Market Line and that rate of return would determine the appropriate theoretical price for the stock. This also means that any stock whose Beta and rate of return place it above the Security Market Line would be currently underpriced and any stock under the Security Market Line would be currently over-priced.
The CAPM calculation
Here is the formula for the CAPM arranged to calculate the theoretically expected rate of return of an asset if its Beta is known. The variables are
Rs – is the expected rate of return of the stock
Rm – is the rate of return of the market
Rf – is the rate of return of the risk-free asset
Bs – is the Beta of the stock
We should note that to make the formula work, Rm, the expected rate of return of the market should be a historical average, usually, the long-term average return of the Standard and Poor’s 500 index, and Rf the rate of return of the risk-free asset should be a historical average of the 10-year Treasury bond. For it all to make sense all these rates of return should be annual.
Uses of the CAPM
The CAPM can also be used to calculate the expected return of a portfolio of stocks.
If you are curious about how financial derivatives pricing models, here is an article on the Black Scholes pricing model.
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