Capital Asset Pricing Model

In 1952, Harry Markowitz laid the foundations that govern the risk-profitability relation while studying investment portfolio development. According to these studies, before choosing subject investment assets, we should first know which is the mathematical expectancy of each of them and also their standard variance or deviation, and once this results are known, then make a decision.

For example, we have to choose between two assets “A” and “B”; “A” has a 20% mathematical expectancy and “B” has a 10%, then, according to Markowitz, the investors, while being rational subjects that seek to maximize their money’s yield, will choose stock “A”. Similarly, between two stocks with the same mathematical expectancy but with a different standard deviation, investors preferred the one with lower risk, since while they are looking for more profitability, they will avoid risk by choosing the lowest possible standard deviation.

However, if we have to choose between two “X” and “Z” assets, where “X” has a mathematical expectancy of 20% with a 10% standard deviation and stock “Z” has a 35% mathematical expectancy and a 22% standard deviation, the investor will choose the risk level he or she is willing to assume, in a merely subjective and personal choice.

As an anecdote, to illustrate how personal the decision of choosing a portfolio asset components, let me tell you that during the peak of stock markets in the mid nineties, I presented a client with an option to invest in good quality stock, with earnings that could easily go over 100% per year but with medium risk levels, and stock of prime rate stocks (blue chips), with slightly lower mathematical expectancies (in comparison) and also lower risks.

We are talking about times when the market sentiment was bull market, stock market investments were in vogue and it was only 30% of this person’s total patrimony (the rest was invested in fixed rent, term accounts and “investment degree” bonds). Curiously, he preferred exclusively blue chip stocks, apologizing for not being able to endure higher risks.

Once the profitability and standard deviation information is known, we trace “indifference curves” according to our risk aversion, and we define profitability levels expected for each investment.

In the following chart we show three profitability levels for a same risk degree (a, b, c); note that the lower curves have lower yield expectancy. Put in another way, for a specific yield level, we can choose up to three risk degrees (c, o, e), and the asset choice depends on each investor. 

However, when choosing assets that can be part of an investment portfolio, we don’t necessarily have to choose a stock and discard the rest; quite on the contrary, different assets are incorporated through diversification, which reduce the total risk in a portfolio.

Following that train of thought, Markowitz names “efficient portfolios” the area within which we find possible earning-risk combinations for the chosen asset basket. So within this area, we will find, for each asset, the estimated profitability level with its respective risk level.

The AB line, known as the “efficient portfolio line”, gives us the maximum expected profitability level possible for the assumed risk degree.

Subsequently, with the evolution the Markowitz model went through and its use in more sophisticated formulas (where loan portfolios are included – to an asset rate “sans risk” – and debt profits, in which we borrow the money at the asset rate “sans risk”), the efficient portfolio line turns into a straight line called “Stock market line”.

When H. Markowitz developed the portfolio selection method which minimizes risk according to the return expectation on each asset, and called it “Capital Asset Pricing Model” (CAPM), and assumed that there is a base asset considered by every investor as “sans risk” (which is really the asset with the lowest possible risk in the market, since by principle there is no investment with “zero” risk), which are the US Treasury bonds.  

Since it is the asset “sans risk”, its beta equals zero (b= 0).