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# Capital Market Line – Definition

### Capital Market Line (CML) Definition

Capital market line (CML) is a graph representing portfolios’ expected return as well as combined risk. The line represents the premium risk an investor earns when he or she takes additional risk. There is diversification of market portfolio that carries systematic risks, and whose expected return equals that of the entire market return.

### A Little More on What is a Capital Market Line (CML)

A capital market line is a line that represents the rate of return for those efficient portfolios in the capital- asset pricing model. The variance of the rates is highly dependent on the level of risk as well as risk-free returns for a given portfolio. The CML will always show a positive linear relationship between portfolio betas and returns.

Rational investors always look forward to higher returns from riskier assets. And so, CML shows this in a graph. For a portfolio to be considered a Markowitz efficient, it should reflect the capital market line accurately. Generally, the capital market line’s slope represents the equilibrium market price risk’s calculation.

If an investor is able to define “the market” as his or her domestic stock market index, he or she can express the market’s expected returns as that index’s expected return. In most cases, risky assets with a well-diversified portfolio have zero unsystematic risks. Meaning, it has zero standard deviation. A good example of such an analysis is the US treasury securities. So, if an investor is able to borrow or lend at the risk-free rate, then he or she can create an asset allocation with;

• Risk-free assets
• The portfolio of the risky portfolio

### The equation for Capital Market Line

Where:

Rₚ = Portfolio return

rf = Risk-free rate

RT = Market return

⥀ₚ = Standard deviation of portfolio returns

σT  = Standard deviation of market returns

### The Capital Market Line vs. the Security Market Line

Most people confuse the security market line (SML) with the capital market line (CML). We derive the security line from the capital market line. CML shows a specific portfolio’s rates of return while the SML represents a market risk as well as given time’s return. It also shows individual assets’ expected returns.

CML represents the total risk, and its measurement is in the SML (beta or systematic risk). Fairly priced securities always plot on the SML and CML. Note that securities which generate higher results for a certain risk, are usually above the SML or CML, and are always underprice and vice versa.

### Capital Allocation Line (CAL) vs Capital Market Line (CML)

Capital allocation line typically represents the risk and portfolio returns, combining the risk-free rate, including any other portfolio on the efficient frontier. Both lines in the graphs represent capital allocation lines.

On the other hand, capital allocation line represents the risk-free asset’s mix, and portfolio D is superior to the risk- free asset’s CAL and portfolio B. It is referred to as a capital market line and the best means through which an investor can combine a portfolio of risky assets and the risk-free rate. The reason is that portfolio D gives a higher return at all risk levels. The capital market line is a precursor.

### Reference for “Capital Market Line – CML”

financialmanagementpro.com/capital-market-line-cml/

https://www.investopedia.com › Investing › Financial Analysis

https://en.wikipedia.org/wiki/Capital_market_line

financialmanagementpro.com/capital-market-line-cml/

www.bankpedia.org/index.php/en/89…/23151-capital-market-line-cml-encyclopedia

### Academic research on “Capital Market Line – CML”

The instantaneous capital market line, Nielsen, L. T., & Vassalou, M. (2006). The instantaneous capital market line. Economic Theory28(3), 651-664. We show that if the intercept and slope of the instantaneous capital market line are deterministic, then investors will not hold any hedge portfolios in the sense of Merton [9, 11]. They will choose portfolios that plot on the capital market line, and they will slide up and down the capital market line over time as their wealth and risk tolerance change. This result allows us to aggregate over investors and derive a single factor CAPM where the first and second moments of security returns may change stochastically over time and markets are potentially incomplete.

Portfolio selection with randomly time-varying moments: The role of the instantaneous capital market line, Nielsen, L. T., & Vassalou, M. (2002). Portfolio selection with randomly time-varying moments: The role of the instantaneous capital market line. Working Paper, Columbia University.

Theory of portfolios: New considerations on classic models and the Capital Market Line, Rambaud, S. C., Pérez, J. G., Granero, M. A. S., & Segovia, J. E. T. (2005). Theory of portfolios: New considerations on classic models and the Capital Market Line. European journal of operational research163(1), 276-283.

An algorithm for deriving the capital market line, Alexander, G. J. (1977). An algorithm for deriving the capital market line. Management Science23(11), 1183-1186. This paper examines the problem of deriving the tangent (or market) portfolio from a given set of risky assets and a specified risk-free borrowing and lending rate. Deriving the tangent portfolio involves solving a mathematical programming problem which can be specified as the minimization of a quadratic objective function with linear constraints. The complementary pivot algorithm has previously been shown to be capable of deriving the optimal solution to certain quadratic programming problems, subject to a nonnegativity constraint. This paper demonstrates that the algorithm can be used to derive the tangent portfolio and that the nonnegativity constraint does not pose any serious handicap. Furthermore, it is shown that the algorithm can efficiently solve large-scale problems of this nature.

Capital Market Line Based on Efficient Frontier of Portfolio with Borrowing and Lending Rate, Lee, M. C., & Su, L. E. (2014). Capital Market Line Based on Efficient Frontier of Portfolio with Borrowing and Lending Rate. Universal Journal of Accounting and Finance2(4), 69-76. Capital Asset Pricing Model (CAPM) is a general equilibrium model. It not only allows improved understanding of market behavior, but also practical benefits. However, there exists a risk-free asset in the assumption of the CAPM. Investors are able to borrow and lend freely at the rate may not be a valid representation of the working of the marketplace. Therefore, in this paper, it studies that the efficient frontier of portfolio in different borrowing and lending rate. This paper solves the highly difficult problem by matrix operation method. It first denotes the efficient frontier of Markowitz model with the matrix expression of portfolio. Then it denotes the capital market line (CML) with the matrix expression too. It is easy to calculate by using Excel function. The aim of this study is to develop the mean- variance analysis theory with regard to market portfolio and provide algorithmic tools for calculating the efficient market portfolio. Then explain that the portfolio frontier is hyperbola in mean-standard deviation space. It constructs CML in order to get more returns than that of efficient frontier if risk-free securities are included in the portfolio. A proposed step for CML on efficient frontier of portfolio with borrowing and lending rate is presented. Under these tools, it is easy calculation SML and CML by using Excel function. An example show that proposed method is correct and effective, and can improve the capability of the mean-variance portfolio efficiency frontier model.

A Simple Derivation of the Capital Asset Pricing Model from the Capital Market Line, Deeley, C. (2012). A Simple Derivation of the Capital Asset Pricing Model from the Capital Market Line. Available at SSRN 2132332. This paper demonstrates a simple way of deriving both the Capital Asset Pricing Model (CAPM) and a capital asset’s beta value from the Capital Market Line (CML). The CML model is extended to include a series of isocorrelation curves along which the returns of any portfolio can be plotted according to its total risk and the degree to which its return correlates to that of the market. This approach is simpler than methods currently available in the relevant literature and may be useful for teaching purposes.

The efficient frontier and the capital market line: the case of the Swiss stock market index, Martins, I. A. (2017). The efficient frontier and the capital market line: the case of the Swiss stock market index(Doctoral dissertation, Instituto Superior de Economia e Gestão). The subprime-crisis, which arguably led investors to lose their confidence in banks, in the market, and in the US economy, had international consequences in all indices and markets. In order to analyze the consequences of a crisis in one of the most developed countries of Europe, this project studies the case of Switzerland ? a country usually perceived as neutral and almost immune to crises – in particular it assesses the changes present in the Stock Market. The analysis is divided into two equal periods of time from January 1, 2001 to December 31, 2008 and from January 1, 2009 to December 31, 2016 firstly, and then the study focuses on shorter sub-periods around the crisis, to analyze the impact in more detail.