# Capital allocation line (CAL)

The asset allocation line, better known by its name in English, capital allocation line (CAL), is the graphic representation of all possible combinations of risk and return given an investment portfolio made up of risk-free assets and assets with risk. It should be noted in this definition that when we refer to risky assets we are talking about shares as a general rule. Portfolio returns are defined as the mathematical expectation of portfolio returns. In addition, portfolio risk is also defined as the standard deviation of portfolio returns.

The CAL line will be, as we will see later, an ascending straight line. This is because investors will only take higher risk if they are offered a higher expected return. Under this approach, the phrase arises: "the higher the risk, the higher the profitability."

## The Capital Allocation Line (CAL) graphically

Let’s imagine the following example to better understand how the Capital Allocation Line works and see it graphically:

• We have a portfolio composed of risk-free assets and a portfolio of stocks.
• The risk-free asset gives a return of 2% and a risk of 0%.
• The equity portfolio has a return of 10% and a risk of 8%.

Graphically the Capital Allocation Line would look like: • We would reach point A on the graph if we invested 100% of our capital in the risk-free asset. In other words, we would have a 2% return and a 0% risk.
• We would reach point B on the graph if we invested 100% of our capital in the stock portfolio. Where we would have a return of 10% and a risk of 8%.

Therefore, investing 100% of the capital in either of the two assets, marks the extreme points of the line. And therefore, we will place ourselves at a point between points A and B when we diversify between both assets. Let’s imagine that we start from a portfolio that invests 100% of the capital in the risk-free asset. Well, as we invest in the stock portfolio, the more we will move up the line. Let’s see this next.

## Continuing with the example …

Starting from the same data from the previous example, we are going to see how the CAL line will go up. Let’s imagine the following:

We initially invested 100% of the capital in the risk-free asset. Therefore, we will have a return of 2% and a risk of 0% (point A of the previous graph). Now we change the investment and invest 75% in the risk-free asset and 25% in the equity portfolio. What is now my profitability and risk?

Portfolio return = (75% * 2%) + (25% * 10%) = 4%

Portfolio risk = (75% * 0%) + (25% * 8%) = 2%

And as you can see we will be at a point on the line above point A. And we will move up the line as we invest more in the stock portfolio. The limit being to invest 100% in the stock portfolio. The point where an investor can be found will essentially depend on their degree of risk aversion.