The capital market line (CML) represents portfolios that optimally combine risk and return. Capital asset pricing model (CAPM), depicts the trade-off between risk and return for efficient portfolios. It is a theoretical concept that represents all the portfolios that optimally combine the risk-free rate of return and the market portfolio of risky assets. Under CAPM, all investors will choose a position on the capital market line, in equilibrium, by borrowing or lending at the risk-free rate, since this maximizes return for a given level of risk.
How can the answer be improved?
Portfolios that fall on the capital market line (CML), in theory, optimize the risk/return relationship, thereby maximizing performance. The capital allocation line (CAL) makes up the allotment of risk-free assets and risky portfolio for an investor. CML is a special case of the CAL where the risk portfolio is the market portfolio. Thus, the slope of the CML is the sharpe ratio of the market portfolio. As a generalization, buy assets if the sharpe ratio is above the CML and sell if the sharpe ratio is below the CML.
CML differs from the more popular efficient frontier in that it includes risk-free investments. The intercept point of CML and efficient frontier would result in the most efficient portfolio, called the tangency portfolio.
The CAPM, is the line that connects the risk-free rate of return with the tangency point on the efficient frontier of optimal portfolios that offer the highest expected return for a defined level of risk, or the lowest risk for a given level of expected return. The portfolios with the best trade-off between expected returns and variance (risk) lie on this line. The tangency point is the optimal portfolio of risky assets, known as the market portfolio. Under the assumptions of mean-variance analysis – that investors seek to maximize their expected return for a given amount of variance risk, and that there is a risk-free rate of return – all investors will select portfolios which lie on the CML.
According to Tobin's separation theorem, finding the market portfolio and the best combination of that market portfolio and the risk-free asset are separate problems. Individual investors will either hold just the risk-free asset or some combination of the risk-free asset and the market portfolio, depending on their risk-aversion. As an investor moves up the CML, the overall portfolio risk and return increases. Risk averse investors will select portfolios close to the risk-free asset, preferring low variance to higher returns. Less risk averse investors will prefer portfolios higher up on the CML, with a higher expected return, but more variance. By borrowing funds at the risk-free rate, they can also invest more than 100% of their investable funds in the risky market portfolio, increasing both the expected return and the risk beyond that offered by the market portfolio.
The CML is sometimes confused with the security market line (SML). The SML is derived from the CML. While the CML shows the rates of return for a specific portfolio, the SML represents the market’s risk and return at a given time, and shows the expected returns of individual assets. And while the measure of risk in the CML is the standard deviation of returns (total risk), the risk measure in the SML is systematic risk, or beta. Securities that are fairly priced will plot on the CML and the SML. Securities that plot above the CML or the SML are generating returns that are too high for the given risk and are underpriced. Securities that plot below CML or the SML are generating returns that are too low for the given risk and are overpriced.
Mean-variance analysis was pioneered by Harry Markowitz and James Tobin. The efficient frontier of optimal portfolios was identified by Markowitz in 1952, and James Tobin included the risk-free rate to modern portfolio theory in 1958. William Sharpe then developed the CAPM in the 1960s, and won a Nobel prize for his work in 1990, along with Markowitz and Merton Miller.
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) 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.
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.
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).
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.
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.
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%.
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:
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.
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:
re = rf +β (rm − 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.