CAPITAL MARKET LINE CML: Definition, Formula and Examples

capital market line

The Capital Market Line (CML) is concerned with portfolios that properly balance risk and return. It is a graph that depicts the predicted return on a portfolio given a certain amount of risk. Read on to learn more about the capital market line formula with an example and how it relates with security market line.

What is a Capital Market Line?

A capital market line (CML) is a line that intersects returns on no-risk investments and market returns. The capital market line differs from the efficient frontier in that the capital market line includes no-risk investments. All portfolios that follow the capital market line are efficient.

The capital market line is used to assess the performance of a portfolio. Any point on the line below any other point on the line will provide lower returns but the same risk, and is thus not optimal.

The capital market line is a metric used to assess the performance of a portfolio. A capital market line, often known as a CML, is a graph used in asset pricing models to show rates of return in a market portfolio. The capital market line denotes the rates of return for efficient portfolios that are affected by the level of risk and the risk-free rate of return for a specific portfolio. CML is based on the idea that all investors have a market portfolio. The magnitude of risk is proportional to the expected reward.

How Capital Market Line (CML) Works

The CML is a subset of the Capital Allocation Line (CAL). The CAL displays an efficient frontier for a risky asset portfolio. A weighted percentage of risk-free assets is included in the CML. The risk-return expectation becomes linear as a result, but the CAL is a curved frontier.

The CML equation is as follows:

y E(RM) + (1 y) RF = E(Rc).

Capital Market Line Formula

E(Rc) = the portfolio’s expected return

E(RM) = the market portfolio’s expected return

RF = The risk-free rate of return

The line illustrates the risk premium that an investor receives while taking on greater risk.

There is market portfolio diversification that carries systematic risks and whose projected return equals the overall market return.

Most people mix up the security market line (SML) and the capital market line (CML) (CML). The security line is derived from the capital market line. The CML displays the rates of return for a specified portfolio, whereas the SML represents market risk as well as a set time return. It also displays the predicted returns on particular investments. The CML indicates overall risk and is measured in the SML (beta or systematic risk). Securities with reasonable prices always plot on the SML and CML. It is worth noting that stocks that offer larger returns for a given risk are usually above the SML or CML and are always underpriced, and vice versa.

The Formula for Capital Market Line

The Capital Market Line (CML) formula is as follows:

Rf + SDp * (ERm – Rf) /SDm = ERp

Capital Market Line Formula

where,

  • Portfolio Expected Return
  • The Risk-Free Rate
  • Portfolio Standard Deviation
  • The Market’s Expected Return
  • Market Standard Deviation

By entering the data into this equation, we can calculate the expected return for any amount of risk.

Capital Market Line Graph – Source: Assignment Point

Capital Market Line Example

Assume the current risk-free rate is 5% and the predicted market return is 18%. The market portfolio has a standard deviation of 10%.

Now consider two portfolios with varying Standard Deviations:

  • Portfolio A has a 5% return.
  • Portfolio B has a 15% return.

Using the Capital Market Line Formula, calculate

  • Portfolio A’s Expected Return Calculation

5% + 5% * (18% – 5%)/10%

= 11.5 percent ER(A)

  • Portfolio B’s Expected Return Calculation

5% + 15% (18% – 15%)/10%

= 24.5 percent ER(B)

The capital market line displays several asset combinations for a given Sharpe ratio. The predicted return rises as we raise the portfolio’s risk (as we move up the Capital Market Line). The same is true in reverse. However, the Sharpe ratio (excess return per unit of risk) remains constant.

What the CML Can Show You

In theory, portfolios that fall on the capital market line (CML) maximize the risk/return relationship, maximizing performance. The capital allocation line (CAL) represents an investor’s allocation of risk-free assets and riskier portfolios.

CML is a subset of CAL in which the risk portfolio is the market portfolio. As a result, the Sharpe ratio of the market portfolio is represented by the slope of the CML. In general, buy assets if the Sharpe ratio is greater than the CML and sell assets if the Sharpe ratio is less than the CML.

CML is distinct from the more widely used efficient frontier in that it incorporates risk-free investments. The intersection of CML and the efficient frontier would yield the most efficient portfolio, known as the tangency portfolio.

Harry Markowitz and James Tobin pioneered mean-variance analysis. Markowitz found the efficient frontier of optimal portfolios in 1952, and James Tobin introduced the risk-free rate into modern portfolio theory in 1958. In the 1960s, William Sharpe invented the CAPM, which earned him a Nobel Prize in 1990 along with Markowitz and Merton Miller.

Read Also: Capital Distributing: All You Need To Know

The CAPM is the line connecting the risk-free rate of return to the tangency point on the efficient frontier of optimal portfolios that offer the highest expected return for a given level of risk, or the lowest risk for a given level of expected return.

This line represents the portfolios with the best trade-off between expected returns and variance (risk). The best portfolio of risky assets, known as the market portfolio, is the tangency point. According to the assumptions of mean-variance analysis—that investors strive to maximize their anticipated return for a given level of variance risk, and that there is a risk-free rate of return—all investors will choose portfolios that are on the CML.

Finding the market portfolio and the best combination of that market portfolio and the risk-free asset are independent tasks, according to Tobin’s separation theorem. Depending on their risk tolerance, individual investors will either hold only the risk-free asset or a combination of the risk-free asset and the market portfolio.

The overall portfolio risk and return rise as an investor travels up the CML. Risk-averse investors will choose portfolios that are close to the risk-free asset, choosing minimal volatility above higher returns. Less risk-averse investors will pick portfolios higher up on the CML, which have a higher expected return but more volatility. By borrowing funds at a risk-free rate, they can also invest more than 100% of their investable funds in the risky market portfolio, raising both the expected return and the risk over and beyond what the market portfolio provides.

Security Market Line vs. Capital Market Line

The capital market line CML is sometimes mixed up with the security market line (SML). The security market line SML is a descendant of the CML. The CML displays the rates of return for a specific portfolio, whereas the SML indicates the market’s risk and return at a given time and displays the predicted returns of individual assets. And, although the CML measures risk as the standard deviation of returns (total risk), the SML measures risk as systematic risk or beta.

Fairly priced securities will plot on the capital market line CML and the security market line SML. Securities that plot above the capital market line CML or security market line SML are underpriced and generate returns that are too high for the risk. Securities that plot below the CML or the SML generate returns that are insufficient for the risk and are overvalued.

What Is the Importance of the Capital Market Line?

In theory, portfolios that fall on the capital market line (CML) maximize the risk/return relationship, maximizing performance. As a result, the Sharpe ratio of the market portfolio equals the slope of the CML. In general, investors should try to acquire assets if the Sharpe ratio is greater than the CML and sell assets if the Sharpe ratio is less than the CML.

What Is the Relationship Between Capital Allocation Line (CAL) and CML?

The capital allocation line (CAL) represents an investor’s allocation of risk-free assets and riskier portfolios. CML is a subset of CAL in which the risk portfolio is the market portfolio. The overall portfolio risk and return rise as an investor travels up the CML. Risk-averse investors will choose portfolios that are close to the risk-free asset, choosing minimal volatility above higher returns. Less risk-averse investors will pick portfolios higher up on the CML, which have a higher expected return but more volatility.

Is CML the same as Efficient Frontier?

CML is distinct from the more widely used efficient frontier in that it incorporates risk-free investments. The efficient frontier is comprised of investment portfolios that provide the best projected return for a given degree of risk. The intersection of CML and the efficient frontier would yield the most efficient portfolio, known as the tangency portfolio.

Is CML the same as Security Market Line (SML)?

The CML is sometimes mixed up with the security market line (SML). The SML is a descendant of the CML. The CML displays the rates of return for a specific portfolio, whereas the SML indicates the market’s risk and return at a given time and displays the predicted returns of individual assets. And, although the CML measures risk as the standard deviation of returns (total risk), the SML measures risk as systematic risk or beta.

The Capital Market Theory

Capital Market Theory attempts to describe the behavior of capital markets through time by employing one of many mathematical models. The Capital Asset Pricing Model is the most widely utilized model in Capital Market Theory. The goal of Capital Market Theory is to price assets on the market. Investing Professionals or Investment Managers

Attempting to estimate market risk and future returns frequently employs multiple of the models under this idea.

Capital Market Theory Assumptions

Certain assumptions in Capital Market Theory hold true for the CML.

  • Frictionless Marketplaces – The theory is based on the assumption of the presence of frictionless markets. It is assumed that investors can perform market transactions smoothly and without incurring any additional charges. There are no transaction fees or taxes associated with such transactions.
  • There are no restrictions on short selling – Short selling is when you borrow securities and sell them with the anticipation that their price will fall. According to Capital Market Theory, there are no restrictions on how the funds earned from short selling can be used.
  • Rational Investors – The Capital Market Theory assumes that investors are rational and make decisions based on a risk-return analysis. It is assumed that investors are well-informed and make well-considered decisions.
  • Homogeneous Expectation – Investors in their portfolios have the same expectations for future returns. Given the portfolio model’s three basic inputs for calculating future returns, all investors will arrive at the same efficient frontier. Because the risk-free asset remains constant, the tangency point corresponding to the Market Portfolio will be the obvious choice for all investors.

Limitations

  • Assumptions – The concept of the Capital Market Line includes some assumptions. However, in practice, these assumptions are frequently violated. Markets, for example, are not frictionless. Certain charges are linked with the transactions. Furthermore, investors are not always reasonable. They frequently make decisions based on feelings and emotions.
  • Borrowing/Lending at Risk-Free Interest Rate – In theory, investors should be able to borrow and lend at the risk-free rate without restriction. In the actual world, however, investors typically borrow at a greater rate than they can lend. It raises a leveraged portfolio’s risk or standard deviation.

Conclusion

The Capital Market Line (CML) is founded on capital market theory and the capital asset price model. For a given Sharpe Ratio, it is a theoretical depiction of various combinations of a risk-free asset and a market portfolio. It outperforms the efficient frontier because it comprises solely of risky assets/market portfolios. This market portfolio is combined with this market portfolio by the CML. As we advance up the capital market line, the portfolio’s risk rises, as does the predicted return. The danger lowers as we proceed down the CML, as does the expected return. The CML formula can be used to calculate the expected return for any portfolio given its standard deviation.

Capital Market Line FAQs

What is difference between CML and SML?

The primary distinction between CML and SML is that CML defines your average rate of success or loss in market share, whereas SML determines the market risk you are taking with your investment. It denotes a point or degree beyond which you may be putting your shares in danger.

Why CML is a straight line?

The Sharpe-Lintner version of the Capital Asset Pricing Model has a straight Capital Market Line since everyone can borrow or lend any amount at the same risk-free rate.

What is the slope of the SML?

The security market line’s slope shows the market risk premium, or the excess return over the market return. The market risk premium compensates for the security’s added systematic risk.

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