# All about Capital Market Line Theory

When you invest in mutual funds, a fund manager manages the portfolios of stocks, debt instruments, or a combination of both. In other words, it is a form of portfolio managementthat involves a plethora of formulae, concepts, calculations, and portfolio management theories. One such theory is the Capital market theory which explains the movement of capital markets over certain periods using mathematical models and is also largely used to price assets in the market. There are many facets to this theory, one of which is the capital market line or CML. This article will explain the basics of the capital market line and how it is used in portfolio management.

## What Is the Capital Market Line (CML)?

Capital Market Line is a theoretical concept expressed in a graph representing portfolios that optimally combine risk and return. In terms of risk, it includes both the risk-free rate and the risk of the market portfolio and hence is considered better than the Efficiency Frontier, which only considers risky assets. CML’s slope is called the Sharpe ratio of the market portfolio, a financial measure used to determine the portfolio’s risk-adjusted return. On a graph, when the CML and the Efficient Frontier intersect, this particular point results in the most efficient portfolio and is called the point of tangency. When you move up the CML, the portfolio’s risk increases, asdoes the return expectation. Similarly, moving down the CML will result in a decrease in risk and, subsequently, a decrease in return expectations.

Calculation and Formula of the Capital Market Line (CML)

The Capital Market Line formula is expressed as follows:

ERp = Rf +SDp * (ERm –Rf) / SDm

Where,

ERp = Expected return of the portfolio

Rf = Risk-free rate

SDp = Standard deviation of the portfolio

ERm = Expected return from the market

SDm = Standard deviation of the market

Here’s an example to illustrate the above formula:

Assume that the current risk-free rate is 8%, the expected return from the market is 15%, and the market portfolio's standard deviation is 10%.

Furthermore, consider portfolios A and B, each with a different standard deviation. Thus,

SDp of A = 10%

SDp of B = 15%

Then applying the Capital Line Market formula for both portfolios, the expected return from each would work out as follows:

Expected Return of Portfolio A = 8% + 10% *(15%-8%)/10% = 15%

Expected return of Portfolio B = 8% + 15% *(15%-8%)/10% = 18.5%

## Capital Market Line vs Security Market Line

Capital Market Line and Security Market Line (SML) are not necessarily the same; the SML is derived from the CML. While the CML indicates a particular portfolio's risk and rates of return, the SML represents the expected returns of individual assets. Further, for CML, standard deviation forms the measure of risk, while for SML, the risk is measured by beta.

Thus, when you place both the CML and SML together, fairly priced securities will find a place on both the SML and the CML. Securities that place above the CML or the SML indicate that they are generating higher returns when compared to the given risk and are, therefore, underpriced. If the securities are placed below the CML or the SML, it means that they are generating lower returns than the given measure of risk and are thus overpriced. In other words, one can consider buying assets if the Sharpe ratio is coming to be above the Capital Market Line and selling if the Sharpe ratio is coming to be below the Capital Market Line.

Mathematical theories tend to give a broader understanding of how the markets work, even if the reality can often differ from a perfect model. The Capital Market Line is one of many toolsportfolio managers use to determine the expected returns from various portfolios. However, it must be noted that the CML is a theoretical concept, and while it can give an idea of the expected returns for a given level of risk, the formula is based on certain assumptions which might not hold water in the real world.

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