Capital Allocation Line with Two Assets

Let’s assume that investor chooses to invest in a risky portfolio that lies on this efficient frontier. Let’s call it Ri.

The investor can combine the risky portfolio, Ri, with a risk-free asset Rf, to create a new portfolio, RP.

The risk-return profile of this combined portfolio of risk assets and risk-free asset will be as follows:

In the above equation, the risk (standard deviation) for the risk-free asset is 0. So, the equation will be reduced to the following:

We can create different portfolios with different weights for the risk-free asset and the risky portfolio. The following graph shows the risk-return of the portfolio by varying the weight from 0 to 100%. The line is called the Capital Allocation Line.

If 100% of the money is invested in the risk-free asset, then the return will be Rf at zero risk. If 100% money is invested in the risky portfolio, the investor will get expected returns of E(Ri) with a risk of σi.

Any portfolio can be created on this line by varying the proportion of funds invested in risk-free asset and risky asset.

The Capital Allocation Line (CAL) can be explained using the standard regression equation Y = MX + C, as follows:

Note that when you invest in a risk-free asset, you are actually lending money to the government. For this reason, any portfolio created between Rf and Ri is called a lending portfolio. An investor can earn returns higher than the risky portfolio by borrowing money at the risk-free rate and investing this money in the portfolio of risky assets. This is represented in the following chart:

Let’s say you borrow 25% at the risk-free rate. In that case w = -0.25 and 1-w = 1.25. The returns on the portfolio will be: