## Capital Market Line (CML) Definition

The Capital Market Line is a graphical representation of all the portfolios that optimally combine risk and return. CML is a theoretical concept that gives optimal combinations of a risk-free asset and the market portfolio. The CML is superior to Efficient Frontier in the sense that it combines the risky assets with the risk-free asset.

- The slope of the Capital Market Line(CML) is the Sharpe RatioSharpe RatioSharpe Ratio, also known as Sharpe Measure, is a financial metric used to describe the investors’ excess return for the additional volatility experienced to hold a risky asset. You can calculate it by, Sharpe Ratio = {(Average Investment Rate of Return – Risk-Free Rate)/Standard Deviation of Investment Return} read more of the market portfolio.
- The efficient frontierEfficient FrontierThe efficient frontier, also known as the portfolio frontier, is a collection of ideal or optimal portfolios that are expected to provide the highest return for the minimum level of risk. This frontier is formed by plotting the expected return on the y-axis and the standard deviation on the x-axis.read more represents combinations of risky assets.
- If we draw a line from the risk-free rate of return, which is tangential to the efficient frontier, we get the Capital Market Line. The point of tangency is the most efficient portfolio.
- Moving up the CML will increase the risk of the portfolio, and moving down will decrease the risk. Subsequently, the return expectationReturn ExpectationThe Expected Return formula is determined by applying all the Investments portfolio weights with their respective returns and doing the total of results. Expected return = (p1 * r1) + (p2 * r2) + ………… + (pn * rn), where, pi = Probability of each return and ri = Rate of return with probability. read more will also increase or decrease, respectively.

All investors will choose the same market portfolio, given a specific mix of assets and the associated risk with them.

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For eg:

Source: Capital Market Line (wallstreetmojo.com)

### Capital Market Line Formula

The Capital Market Line (CML) formula can be written as follows:

**ER _{p} = R_{f} + SD_{p} * (ER_{m} – R_{f}) /SD_{m}**

where,

- Expected Return of Portfolio
- Risk-Free RateRisk-Free RateA risk-free rate is the minimum rate of return expected on investment with zero risks by the investor. It is the government bonds of well-developed countries, either US treasury bonds or German government bonds. Although, it does not exist because every investment has a certain amount of risk.read more
- Standard Deviation of PortfolioStandard Deviation Of PortfolioPortfolio standard deviation refers to the portfolio volatility calculated based on three essential factors: the standard deviation of each of the assets present in the total portfolio, the respective weight of that individual asset, and the correlation between each pair of assets of the portfolio.read more
- Expected Return of the Market
- Standard Deviation of Market

We can find the expected return for any level of risk by plugging the numbers into this equation.

### Example of the Capital Market Line

**Suppose that the current risk-free rate is 5%, and the expected market return is 18%. The standard deviation of the market portfolio is 10%. **

Now let’s take two portfolios, with different Standard Deviations:

- Portfolio A = 5%
- Portfolio B = 15%

Using the Capital Market Line Formula,

**Calculation of Expected Return of Portfolio A**

- = 5% +5%* (18%-5%)/10%
**ER(A) = 11.5%**

**Calculation of Expected Return of Portfolio B**

- = 5% +15% (18%-5%)/10%
**ER(B) = 24.5%**

As we increase the risk in the portfolio (moving up along the Capital Market Line), the expected return increases. The same is true vice-versa. But the excess return per unit of risk, which is the Sharpe ratio, remains the same. It means that the capital market line represents different combinations of assets for a specific Sharpe ratio.

### Capital Market Theory

Capital Market Theory tries to explain the movement of the Capital Markets over time using one of the many mathematical models. The most commonly used model in the Capital Market Theory is the Capital Asset Pricing ModelCapital Asset Pricing ModelThe Capital Asset Pricing Model (CAPM) defines the expected return from a portfolio of various securities with varying degrees of risk. It also considers the volatility of a particular security in relation to the market.read more.

Capital Market Theory seeks to price the assets in the market. Investors or Investment Managers who are trying to measure the risk and future returns in the market often employ several of the models under this theory.

### Assumptions of the Capital Market Theory

There are certain assumptions in the Capital Market Theory, which hold true for the CML also.

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Source: Capital Market Line (wallstreetmojo.com)

**Frictionless Markets –**The theory assumes the existence of frictionless markets. This means that there are no transaction costs or taxes applicable to such transactions. It assumes that investors can smoothly conduct transactions in the market without incurring any additional costs.**No Limits on Short Selling**– Short selling is when you borrow securities and sell them with an expectation of the securities’ price going down. Capital Market Theory assumes that there are no limits on the usage of the funds received from short sellingShort SellingShort Selling is a trading strategy designed to make quick gains by speculating on the falling prices of financial security. It is done by borrowing the security from a broker and selling it in the market and thereafter repurchasing the security once the prices have fallen.read more.**Rational Investors –**The Capital Market Theory assumes that investors are rational, and they take a decision after assessing risk-return. It assumes that the investors are informed and make decisions after careful analysis.**Homogenous Expectation –**Investors have the same expectations of future returns in their portfolio. Given the 3 basic inputs of the portfolio model for calculating future returns, all investors will come up with the same efficient frontier. Since the risk-free asset remains the same, the tangency point, which represents the Market Portfolio, will be the obvious choice of all investors.

### Limitations

**Assumptions**– There are certain assumptions that exist within the concept of Capital Market Line. However, these assumptions are often violated in the real world. For example, the markets are not frictionless. There are certain costs associated with the transactions. Also, investors are usually not rational. They often make decisions based on sentiments and emotions.**Borrowing/Lending at Risk-Free Rate**– Theoretically, it is supposed that investors can borrow and lend without any limits at the risk-free rate. However, in the real world, investors usually borrow at a higher rate than the rate at which they are able to lend. This increases the risk or standard deviation of a leveraged portfolio.

### Conclusion

The Capital Market Line (CML) draws its basis from the capital market theory as well as the capital asset pricing model. It is a theoretical representation of different combinations of a risk-free asset and a market portfolio for a given Sharpe Ratio. As we move up along the capital market line, the risk in the portfolio increases, and so does the expected return. If we move down along the CML, the risk decreases as does the expected return. It is superior to the efficient frontier because the ef only consists of risky assets/market portfolio. The CML combines this market portfolio with this market portfolio. We can use the CML formula to find the expected return for any portfolio given its standard deviation.

The assumption for the CML is based on the assumptions of the capital market theory. But these assumptions often don’t hold true in the real world. The Capital Market Line is often used by analysts to derive the amount of return that investors would expect to take a certain amount of risk in the portfolio.

### Recommended Articles

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