*The Business Professor*, updated September 23, 2019, last accessed August 5, 2020, https://thebusinessprofessor.com/lesson/capital-market-line-definition/.

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### Capital Market Line (CML) Definition

Capital market line (CML) is a graph representing a portfolio’s expected return based upon a given level of risk.

On the horizontal axis is the portfolio standard deviation. On the vertical axis is the expected rate of return.

σL = Standard deviation of L portfolio

σM = Standard deviation of market returns

σR = Standard deviation of R Portfolio

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

The CML is a special version of the Capital Allocation Line (CAL). The CAL demonstrates an efficient frontier for a portfolio of risky assets. The CML integrates a weighted percentage of risk-free assets. This makes the risk-return expectation linear, whereas the CAL is a curved frontier.

The equation for the CML is:

E(R_{c}) = y × E(R_{M}) + (1 – y) × R_{F}

E(R_{c}) = the expected return of the portfolio

E(R_{M}) = the expected return of the market portfolio

R_{F} = the risk-free rate of return.

The line represents the risk premium that an investor earns when he or she takes on additional risk. There is diversification of market portfolio that carries systematic risks, and whose expected return equals that of the entire market return.

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.

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

The instantaneous **capital market line**, **Nielsen, L. T., & Vassalou, M. (2006). The instantaneous capital market line. ***Economic Theory***, ***28***(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 research***, ***163***(1), 276-283.**

An algorithm for deriving the **capital market line**, **Alexander, G. J. (1977). An algorithm for deriving the capital market line. ***Management Science***, ***23***(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 Finance***, ***2***(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.