Capital Allocation Line - CAL

The capital allocation line (CAL), also known as the capital market link (CML), is a line created on a graph of all possible combinations of risk-free and risky assets. The graph displays to investors the return they might possibly earn by assuming a certain level of risk with their investment. The slope of the CAL is known as the reward-to-variability ratio.

The capital allocation line aids investors in choosing how much to invest in a risk-free asset and one or more risky assets. Asset allocation is the allotment of funds across different types of assets with varying expected risk and return levels, whereas capital allocation is the allotment of funds between risk-free assets, such as certain Treasury securities, and risky assets, such as equities.

An easy way to adjust the risk level of a portfolio is to adjust the amount invested in the risk-free asset. The entire set of investment opportunities includes every single combination of risk-free and risky assets. These combinations are plotted on a graph where the y-axis is expected return and the x-axis is the risk of the asset as measured by standard deviation.

The simplest example is a portfolio containing two assets: a risk-free Treasury bill and a stock. Assume that the expected return of the Treasury bill is 3% and its risk is 0%. Further, assume that the expected return of the stock is 10% and its standard deviation is 20%. The question that needs to be answered for any individual investor is how much to invest in each of these assets. The expected return (ER) of this portfolio is calculated as follows:

ER of portfolio = ER of risk-free asset x weight of risk-free asset + ER of risky asset x (1- weight of risk-free asset)

The calculation of risk for this portfolio is simple because the standard deviation of the Treasury bill is 0%. Thus, risk is calculated as:

Risk of portfolio = weight of risky asset x standard deviation of risky asset

In this example, if an investor were to invest 100% into the risk-free asset, the expected return would be 3% and the risk of the portfolio would be 0%. Likewise, investing 100% into the stock would give an investor an expected return of 10% and a portfolio risk of 20%. If the investor allocated 25% to the risk-free asset and 75% to the risky asset, the portfolio expected return and risk calculations would be:

ER of portfolio = (3% x 25%) + (10% * 75%) = 0.75% + 7.5% = 8.25%

Risk of portfolio = 75% * 20% = 15%

The slope of the CAL measures the trade-off between risk and return. A higher slope means that investors receive higher expected return in exchange for taking on more risk. The value of this calculation is known as the Sharpe ratio.