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## What is the ‘Capital Market Line – CML’

The capital Market line (CML), in the 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.

## BREAKING DOWN ‘Capital Market Line – CML’

The capital market line (CML), in 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 which have 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 Capital Market Line Equation

The return on portfolio p, where R_{T} and σ_{T} are tangency portfolio T’s return and standard deviation, is the risk-free rate of return plus the trade-off between risk and return, (R_{T}– r_{f})/σ_{T} – also known as the Sharpe ratio – multiplied by the standard deviation of portfolio p.

## The Capital Market Line, the Capital Allocation Line and the Security Market Line

The CML is sometimes confused with the capital allocation line (CAL) and the security market line (SML). While the CAL is one of an infinite number of lines plotting the possible combinations of the risk free asset and a portfolio of risky assets – depending on investors’ return expectations — the CML is the specific instance where the risky portfolio is the market portfolio. The CML is the CAL with the highest Sharpe ratio (slope). The Sharpe ratio is the average return earned in excess of the risk-free rate per unit of volatility or total risk. The greater the value of the Sharpe ratio, the more attractive the risk-adjusted return.

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 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.

## History of the Capital Market Line

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.

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