The Capital Market Line (CML) represents portfolios that optimally combine risk and return. This theoretical concept depicts all the portfolios that effectively merge the risk-free rate of return and the market portfolio containing risky assets. Under the Capital Asset Pricing Model (CAPM), all investors aim to position themselves along the capital market line by borrowing or lending at the risk-free rate, maximizing returns for a given level of risk.

### Key Takeaways

**Optimal Portfolio Combination**: The CML showcases portfolios that effectively balance risk and return.**Special Case of CAL**: The CML is a specific instance of the Capital Allocation Line (CAL) where the risk portfolio includes the market portfolio, thus its slope represents the market portfolio’s Sharpe ratio.**Tangency Portfolio**: The intersection of the CML and the efficient frontier yields the most efficient portfolio, known as the tangency portfolio.**Investment Strategy**: Generally, buy assets if their Sharpe ratio is above the CML and sell if it is below.

### Formula and Calculation

To calculate the Capital Market Line (CML):

```
Rp = rf + \\frac {RT - rf}{\\sigma_T} \\sigma_p
\\text{where:}
Rp = \\text{Portfolio Return}
rf = \\text{Risk-Free Rate}
RT = \\text{Market Return}
\\sigma_T = \\text{Standard Deviation of Market Returns}
\\sigma_p = \\text{Standard Deviation of Portfolio Returns}
```

### Insight from the CML

Portfolios plotted on the CML theoretically optimize the risk/return relationship, hence maximizing performance. The Capital Allocation Line (CAL) encompasses risk-free assets along with risky portfolios for investors.

The CML differs from the popular efficient frontier by including risk-free investments. The intercept point where the CML meets the efficient frontier gives the tangency portfolio\u2014the most optimal. Pioneers like Harry Markowitz and James Tobin introduced key concepts leading to modern portfolio theory, leading to William Sharpe\u2019s development of the CAPM. The CML represents the line connecting the risk-free rate with the highest returning portfolio at an optimal risk level.

Under mean-variance analysis assumptions, all investors are expected to pick portfolios situated on the CML, logically separating the problems of finding the market portfolio and its best risk-free asset combination per Tobin’s separation theorem.

Moving along the CML showcases an increase in both risk and returns. Investors with high-risk aversion will prefer portfolios closer to the risk-free asset, while those less risk-averse opt for portfolios higher up on the CML for more returns at the trade-off of increased risk.

### Capital Market Line vs. Security Market Line

Although sometimes confused with the Security Market Line (SML), which shows rates of return for individual assets considering market risk, the CML focuses on specific portfolios. The SML illustrates market risk and return at a certain point, using beta as the risk metric, whereas the CML uses standard deviation.

Fairly priced securities align with both the CML and SML. Securities plotted above or below these lines indicate underpricing or overpricing, respectively.

**Related Terms:** Capital Allocation Line, Efficient Frontier, Security Market Line, Risk-Free Rate, Market Portfolio.

### References

- The Nobel Prize. “This Year’s Laureates are Pioneers in the Theory of Financial Economics and Corporate Finance”.