Difference Between SML And CML, Importance Of Minimum Variance Portfolios, And Relevance Of CAPM Equation

SML GRAPH

A graphical representation of the capital asset pricing model or CAPM is depicted by security market line (Atkinson, 2012). It shows the relationship between the risk and expected return associated with a security where risk is being measured by its beta coefficient. In a sense, it reflects the expected return if an investor possess a certain level of risk or shows the level of risk an investor might have to bear for any given expected return (Berry, 2009). The equation could be presented as :

E(R_i) = R_F + β_i × (E(R_M) – R_F)

Where E (R_i) = expected return of a security;

 R_F = risk-free rate;

β_i = security’s beta coefficient ;

And E (R_M) = expected market return.

SML GRAPH :

In the following graph, the x-axis represents the beta or the level of risk in a security while the y-axis shows us the return expected (Easton, 2010).  The following can be concluded from the graph :

• The return expected will be equal to the risk free rate of return at the zero beta of the security.
• The market risk premium (RP_M) is the slope of the security market line that shows us the difference between the return expected from the market and the risk free rate of return. Thus, the slope would get steeper with the increasing market risk and vice-versa (Elaine, 2015).
• If the coefficient of beta changes with time, the position of the security would also change on the security market line.
• The SML line would shift with respect to changes in the economical factors such as changes in inflation rate, unemployment rate, change in GDP, etc.

The problem with security market line is the same as it is with CAPM that It is based on same assumptions. Strong efficiency cannot characterize the real market conditions because different investors have different credibility grounds to borrow or lend money at a risk free rate of return and also differs with transaction costs (Girard, 2014). Thus, the stock, as shown in the graph, can be positioned above or below the SML as represented:

Stocks above the SML are undervalued because investors need a return higher than the CAPM assessment for a given beta or risk. However, in case of stocks below the SML, they are considered as overvalued which means that investors need a return lower than that assessed by the CAPM at a given level of risk (Holtzman, 2013).

The concept of capital market line is regarding graphical representation of the return expected from an entire portfolio composed of various possible equations between the risk free asset and market portfolio (Horngren, 2012). The term ‘market portfolio’ delivers the diversification that consists of systematic risk and the expected return which is equal to the return expected from the market as a whole. Generally, the formula for calculation of the expected return from a particular portfolio (E (Rc)) :

E (R_c) = y × E(R_M) + (1 – y) × R_F

where y =proportion of a market portfolio ;

 E(R_M) = expected return of a market portfolio ;

(1-y) = proportion of a risk-free asset; and

Capital Market Line (CML)

RF = risk-free rate.

The problem with CML is same as that of SML, that is, it has the same assumptions as that of CAPM. The taxes and transaction costs can be different for all the investors (Ittelson, 2009). It is an assumption that an investor can lend or borrow at a risk free rate of return. However, in reality, considering market conditions, the investors can lend at a lower rate than borrow that somewhat graphically represents in the following way :

Also, there is unequal information among investors and not all of them are rationale in nature or posses risk fear. The other risks such as inflation risk, currency risk etc is not considered. The risk free assets don’t exist in real market. Thus, in reality, CML isn’t a precise line but rather looks fuzzy more graphically (McLaney & Adril, 2016).

Both the concepts are the derived concepts from CAPM model. However, they do differ in a lot of ways. Capital market line represents the relationship between the expected returns and the level of risk of an entire portfolio comprising of various securities while security market line represents the relationship between the expected return and the level of risk of an individual security. In case of CML, the unit of measurement of risk is standard deviation while in case of SML, beta of the security is used for measuring the risk which in turn helps a potential investor find out the contribution of risk in the portfolio (Menifield, 2014).

Both being graphically represented, CML gives a picture of portfolios that are efficient while SML gives a picture of both efficient and non-efficient portfolios. Also, in case of CML, the y-axis shows the expected return while in case of SML, the same axis shows the return required from an individual security. The x-axis, in case of CML, shows us the level of risk or more precisely, standard deviation while in case of SML, it shows the beta or the level of risk associated with the individual security.

Where CML determines the market portfolio and risk free investments, SML measures all other security factors. Where one considers the portfolio with various securities and measures the returns or risks of the portfolio as a whole, the other one or SML measures the risk and return of the individual security contained in that same portfolio. Thus, SML helps in deciding the stock that should be a part of the portfolio while CML helps in deciding the most effecient portfolio among all possible combinations.

Minimum variance portfolios

Well, from an overall view, Capital Market Line is considered superior to Security Market Line.

A potential investor would always think in a way of having maximum returns at minimum possible risk. A investor prefers constructing his portfolio with stocks /securities that could give more returns at a lesser risk because the level of risk gets reduced in comparison to risk associated with stock individually (Parrino, 2013). This structured model of the portfolio is called minimum portfolio variance. This strategy is more like ‘not only having the cake, but eating the cake too’.

Minimum portfolio variance is a portfolio composed of stocks that are combined to reduce the volatility of the price changes in the overall portfolio. Volatility is defined as a measurement of a security’s movements in price and is a substitute for the term ‘variance’ in the investment world. The more is the volatility, the more is the market risk. So reducing risks means reducing the movement upwards and downwards.

For constructing such portfolio model, a person is needed to take up investments with low volatility or combine such volatile investments that have a low correlation with each other. The latter one is more used for minimum portfolio variance. Investments with low correlation mean those investments that are performing in a different way provided the market conditions remain same and there is a constant economic environment (Penman, 2012). This is considered as a common example of diversification. A diversified portfolio is the minimum portfolio variance.

Let’s understand this through an example. Let us combine a bond mutual fund and a stock mutual fund. When the prices of stocks rises, the prices of bond may fall negatively and vice versa. This is because often the two securities do not move in opposite directions but when it comes to performance, they have a low correlation with each other. This portfolio helps an investor to mix high risky securities and enjoying sufficient returns without having much high risk.

The capital asset pricing model (CAPM) is the method adopted to describe the relationship between the risk an investor will bear after investing in a financial instrument and the expected return. According to it, the return expected from a security is equal to risk premium and a risk free return where risk premium is based on the beta of the instrument. We should understand that the risk premium is the difference between returns on a stock and the risk free return. Risk free return can be defined as the return associated with an investment that assures you certain percentage of return at zero risk (Piper, 2015). This return is more like the minimum requirement or expectation of an investor from the securities he has invested in. The return in excess of this risk free return that an investment is expected to provide is called risk premium. Risk premium is like an appreciation in terms of returns that compensates an investor who takes the risk of investment compared to the investments that are risk free. The beta is the measurement of risk a security possesses which is changed by the variations in the price levels in relation to the overall market. In other words, it calculates the sensitivity of a stock towards the market risk. If the beta equals to one, the return expected from a security would be equal to average market return. If the beta is negative that means the security is perfectly negatively correlated with the market.

Relevance of CAPM equation

CAPM can be calculated using following formula :

Ra = Rrf + [Ba x (Rm – Rrf)]

Where Ra = return expected from a security

Rrf = Risk Free Return

Ba = beta of the security

Rm = expected return on market.

We should know that risk premium is the difference between expected return on market and risk free return (Rm – Rrf). We use this formula to calculate the return expected from an investment or a security. It bases its formula on the assumption of systematic risk which is also called non-diversifiable risk or market risk and that’s what is compensated by risk premium (Robinson, 2014). After all, investors have an expectation of higher returns for possessing the additional risk on a security. The CAPM is mainly used in the sector of finance by professionals like investment bankers, accountants and financial analysts. The weighted average cost of capital (WACC) makes the maximum use of CAPM as it helps in the calculation of the cost of equity.

Capital Asset Price Model has always been a popular theory since past 40 years. CAPM, being a widely used concept in the field of finance industry, is criticized on the grounds that it shows an idealistic world more than the reality world. The reasons for such drawbacks are :

• The risk free rate is a volatile rate that changes frequently and that is why, clear stable results cannot be derived by using this rate.
• The assumption of lending and borrowing at a risk free rate is a myth while in reality; the investors might not be able to borrow at the same rate as the US Government might borrow.
• The method of tracing the beta is a challenging job and therefore, in case of an inaccurate beta, the outcomes couldn’t be as reliable as per expectations (Siciliano, 2015).

However, we still believe in using of CAPM over other formulas despite its several drawbacks.

• The consideration of systematic risk is a realistic approach by which investors having diversified portfolios can essentially eliminate the unsystematic risk.
• A frequent research and several tests are being made or applied to prove the concept that has been just theoretically calculated to depict the relation between systematic risk and required return.
• It is considered superior in comparison to dividend growth model (DGM) while calculating the cost of equity as it considers the systematic risk a company can take in relation to the stock market as a whole.
• In case of investment appraisal, CAPM allows the use of various discount rates making itself a better approach than weighted average rate of return.

There would always be criticisms for every conceptual theory. However, it has been observed that CAPM stands well against all the drawbacks despite the fact that a number of attacks are being made recently (Taillard, 2013). However, till the time a new theory comes up that presents itself better than CAPM model, the said concept would be used widely in the financial industry.

References

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