The Model of Valuation of the Price of Financial Assets or **Capital Asset Pricing Model** (known as model CAPM) is one of the most used tools in the financial area to determine the required rate of return for a certain asset.

In the conception of this model, three main economists worked simultaneously, but separately: **William Sharpe**, John Lintner and Jan Mossin, whose research was published in different specialized magazines between 1964 and 1966. The concern that attracted them to this topic was the development of explanatory and predictive models for the behavior of financial assets.

They had all been influenced by the **Harry Markowitz’s Portfolio Theory**, published in 1952 and reformulated in 1959. In it, **Markowitz** raises the advantages of diversifying investments in order to reduce risk. It should be noted that the idea of ”investment portfolio” had been raised in 1950 by James Tobin with a measure to predict the rise or fall of investment, a key issue in determining the level of employment and production, the “q” of Tobin. Markowitz captured the potentialities of this idea in financial models.

## Diversifying investments

The idea of diversifying investments implies distributing resources in various areas, such as: industry, construction, technologies, natural resources, R&D, health, etc. Markowitz called this portfolio or portfolio, and the thesis was that the better diversified that portfolio was, the better prepared it would be to face risks. The CAPM took a step further by seeking to maximize the return on each share and thereby obtain an even more profitable portfolio. About him **CAPM model** we speak today in our **Concepts of Economics**.

Markowitz’s portfolio model was deepened and enriched by the work of **Sharpe**: *Capital Asset Prices: A Theory of Market Equilibrium under Condition of Risk*, 1964; **Lintner**: *The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets*, 1965; and *Security Prices, Risk and Maximal Gains from Diversification*, 1965; and **Mossin**: *Equiibrium in a Capital Asset Market*, 1966.

Notably **Jack Treynor** wrote in 1961 a rather pioneering work: *Toward a Theory of the Market Value of Risky Assets*, but did not manage to publish. Sharpe, however, acknowledges in his work that he became aware of Treynor’s work. For this **important contribution to the development of the financial economy**, William Sharpe received the Nobel Prize in Economics (together with Harry Markowitz and Merton Miller) in 1990.

The model CAPM offers in a pleasant and intuitive way a simple way to predict the risk of an asset, separating them into **systematic risk and unsystematic risk**. Systematic risk refers to general economic uncertainty, the environment, the exogenous, what we cannot control. The unsystematic risk, on the other hand, is a specific risk of the company or of our economic sector. In other words, it is our own risk.

## Portfolio Theory Maximization

The Portfolio Theory (or Portfolio Theory) of Markowitz, established the benefits of diversification and formulated the line of the Capital Market. This line has a positive slope by **the direct relationship between risk and return** (the higher the risk, the higher the return). The point where the risk and return of an individual asset are located is always below the capital market line (shaded area of the graph). Investing in a single asset is inefficient. And the portfolio diversification proposed by Markowitz takes care of this shortcoming, although the portfolio return, as a whole, does not reach the optimum level.

That is the void that Sharpe’s proposal seeks to fill: maximize each of the assets separately to obtain the most profitable portfolio. That is, the CAPM it is located on the border of the Markowitz area (blue line) and maximizes at the tangent to the capital market line (red line) where leverage equals zero. That allows the CAPM **build the most optimal portfolio by determining with the greatest precision the investment percentages in each of the assets**. To determine this formula, the linear relationship between the returns of a given stock and the return that would have been obtained if it had been invested in the optimal market portfolio must be found. To do this, it introduces the parameter Beta (β), an index of the market risk component, which is the central protagonist of this model.

## Risk aversion

**For the construction of the Model CAPM the following assumptions are assumed:**

- investors are risk averse people
- Investors take care of the balance between the expected return and the associated variability to form their portfolios
- There are no frictions or failures in the market
- There is a risk-free rate at which investors can borrow or place funds
- There is no information asymmetry and investors are rational, which does not imply that all investors have the same conclusions about expected returns and standard deviations of feasible portfolios.

These assumptions were present in all three authors since they developed the model in the 1960s. Over time, some of these assumptions (3 and 5, especially) were considered irrelevant.

The CAPM It is used to determine the expected rate of return on an asset. At equilibrium, if added to a suitably diversified Investment Portfolio, it will be able to locate anywhere along the red line, known as the **Capital Market Line**. As in the Markowitz model, as the investor takes greater risk (shift to the right), he obtains a higher expected return. The CAPM take into account **the asset’s sensitivity to non-diversifiable risk**, known as market risk or systemic risk, represented by the symbol Beta (β), as well as the expected return of the market and the expected return of a theoretically risk-free asset.

**According to the graph:**

- E (ri) is the expected rate of return of capital on asset i.
- βim is the Beta (amount of risk with respect to the Market Portfolio)
- E (rm – rf) is the excess return of the market portfolio.
- (rm) Market performance.
- (rf) Return on a risk-free asset.

We must bear in mind that it is an unlevered Beta, which assumes that the company does not have debt in its capital structure, therefore **own financial risk is not incorporated**. If you want to incorporate it, you have to determine a leveraged Beta; therefore the expected return will be higher. In this case, the leveraged Beta allows the cost of capital to be calculated.

## The importance of the Beta factor

It is important to highlight the importance of Beta (which is measured along the horizontal axis). Beta is the non-diversifiable risk and it depends on the risk of that market. The markets of similar companies have similar risks, such as airlines, railways or oil companies. This Beta is calculated with a matrix and econometric analysis of variances and covariances. If the Beta is zero, our expected return will be only * Rf*, the value of the risk-free asset, which would be its minimum value: for example, the value of the United States Treasury Bonds.

As Beta begins to rise (shift to the right along the horizontal curve), the expected return also increases. When Beta equals 1, our expected return will equal the market return. This is the reason why **a very high Beta tends to amplify the response of the system**. If the Beta is 2, the portfolio return will increase much faster if the market rises, for example, by 10%; but it will also fall faster if the market takes a downturn. **A high Beta amplifies the trend, while a Beta less than 1 dampens it.**. In periods of economic boom, it is normal for investors to operate with a high Beta. In those of turbulence they look for a small Beta.

This is so because Betas greater than 1 indicate that the asset has a higher risk than the average for the entire market; while a Beta below 1 indicates a lower risk. In addition, an asset with a high Beta should be discounted at a higher rate, as a means of rewarding the investor for assuming the risk that the asset carries. This is based on the principle that investors, **the riskier the investment**, require higher returns.

Since the Beta reflects the market’s specific non-diversifiable risk sensitivity, the market as a whole has a Beta of 1. And since it is impossible to calculate the expected return of the entire market, indices, such as the S&P 500 or the Dow Jones.

The portfolio of a CAPM includes the **systemic risk assessment** (or non-diversifiable risk) and the valuation of diversifiable risk. Systemic risk is to which all assets in a market are exposed, while diversifiable risk is that intrinsic to each individual asset. This diversifiable risk can be reduced by adding assets to the portfolio that mitigate each other (it is rare that in normal periods all sectors go down in unison). However, the systemic risk cannot be diminished.

Within the scope of this model, a rational investor should not take any risk that is diversifiable, as only non-diversifiable risk is rewarded with a higher return. At CAPM The rate of return required for a certain asset is linked to the contribution that asset makes **to the general risk of a certain portfolio**.

As we can see, this is one of the most relevant research topics in financial economic theory, subject, by the way, to the ups and downs of ever-changing systemic risk factors. Under normal circumstances, **This model allows for impeccable analysis to estimate investment returns**. But I repeat: under normal circumstances. In another article I will try to delve into the determination of the Beta parameter and why it can become an epicenter of systemic instability.

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