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Capital Asset Allocation Line (CAL), Capital Market Line (CML),and Portfolios of Risky and Risk-free Assets



Within the CFA Level 1 curriculum understanding portfolio risk and return is non-negotiable. And the foundational theory underpinnning this discussion for all three levels of the CFA program starts with understanding the Capital Asset Allocation Line (CAL) and its similarities and differences to the Capital Market Line (CML) and the Securities Market Line (SML).

As a Level 1 Candidate, cementing this knowledge and distinction will serve you well and allow you a deeper understanding of covariance, correlation, and risk/return trade-offs and measurements (such as the Sharpe Ratio).

With that context, let's dive into what you need to know.

The Capital Asset Allocation Line (CAL)

The capital asset allocation line (CAL) represents all of the possible combinations (weights) of a risk free asset and optimal risky-asset portfolios. 

It is the set of all possible efficient portfolios. The line begins at the intercept with the minimum return of the risk-free asset (and no risk) and runs to the point where the entire portfolio is invested in the risky portfolio.

Capital Asset Allocation Line - CFA Level 1

In other words, you put a certain percentage of your portfolio into risky assets (A) and the rest into a risk free asset (B). The expected return at a standard deviation of zero is the risk free rate (in the graph this is shown as 7%), and the slope of the CAL reflects the additional return per unit of risk.

Selecting an Optimal Portfolio on the Capital Asset Allocation Line (CAL)

As a CFA Level 1 Candidate you will almost certainly need to identify the optimal asset allocation for an investor given their unique preferences. 

Every investor has their own utility function representing their risk and return preferences (i.e. degree of risk aversion). These utility curves are upward sloping reflecting that more risk will only be taken in exchange for more return. The steeper the slope the more risk averse the investor. 

We can map these indifference curves against the capital asset allocation line (CAL), which is the set of all efficient portfolios. The point of tangency is the utility maximizing, or optimal portfolio (more detail for the CFA Level 3 context in this post).

Tangency Portfolio, Indifference Curves, CAL for the CFA 

Note the flatter a given investor’s indifference curve, the less risk averse they are, and the higher their expected return/risk will be at the point of tangency.

Combining a Risk-free Asset with a Portfolio of Risky Assets

We just established the capital asset allocation line as the line plotting the possible combinations of the risk free asset and a portfolio of risky assets.  If investors have different expectations of expected return they will each have a different CAL.

The capital market line (CML) is the specific instance where we define the risky portfolio as the market portfolio. In this case investors can combine the risky market portfolio and the risk-free asset portfolios in-line with their risk preferences to build superior risk-return portfolios.

Capital Market Line and Tangency - CFA Level 1 exam

Graphically, the CML shows expected portfolio return as a linear function of portfolio risk. The y-intercept is the risk free rate and the slope is the market risk premium. Any point up and to the left of the CML is not achievable.

With the CML we assume that every investor can both invest and borrow at the risk-free rate. If investors are borrowing that means they are investing in the market portfolio using margin and the weight of their risky portfolio will be > 100%.

Why does the risk-free asset allow us to build better risk-return portfolios?

Remember that the availability of a risk-free asset allows investors to build portfolios with superior risk-return properties. By combining a risk-free asset with a portfolio of risky assets, the overall risk and return can be adjusted to appeal to investors with various degrees of risk aversion.

Recall that correlation for a two asset portfolio is captured as:

Because a risk-free asset has zero standard deviation and zero correlation of returns with a risky portfolio, standard deviation of the combined portfolio can be captured by the following equation:

Systematic vs. Unsystematic Risk

This leads us to the final distinction between types of risk.

Generally speaking there are two major types of risk: systematic risk and unsystematic, or company-specific risk. 

Systematic risk is market-level risk (beta) that cannot be diversified away. It is caused by things like GDP growth and interest rate changes that affect the value of all risky securities. The higher a company’s beta the greater its systematic risk.

Unsystematic risk, or company-specific risk, is risk that can be diversified away in a portfolio (i.e. through diversification)

Adding the two together gives us total risk:  

Total risk = systematic risk + unsystematic risk

 

One of the assumptions of Modern Portfolio Theory (MPT) is that stock/portfolio returns depend on the level of systematic risk, NOT total risk. The riskiest stock does not necessarily have the highest expected return.

Put differently, diversification is free, and thus you will not be rewarded for taking on high levels of unsystematic risk. Instead one can achieve higher risk-adjusted returns through diversification. Studies show that a portfolio of less than 30 stocks can achieve 90% of the diversification effects.

CAPM vs. Systematic Risk

In the CFA Level 1 curriculum the CAPM model is first introduced the capital asset pricing model (CAPM) in the corporate finance section as a way to calculate the cost of equity. CAPM is a single-index pricing model which we often use to estimate a security’s returns given its Beta. In other words, the CAPM models the explicit tradeoff between beta (systematic risk) and expected return.

The formula for CAPM is:

rr+β (r− rf)

Where:
re = The required return on equity
rf = Risk−free rate
rm = The market return
β = The stock market beta
(rm−rf) = The Equity risk Premium (ERP)

As a next step to build off of this post I recommend you check out our full post on the CAPM Model and how it gets tested on the CFA Exam.