# Modern Portfolio Theory: CAPM and Related Concepts Explain and graphically depict how security market line (SML) is different from Capital Market Line (CML). Identify and discuss the importance of minimum variance portfolio? Why CAPM equation might be more relevant than other equations when calculation required rate of return. (2000 words)

Financial Management: Modern Portfolio Theory

CAPM and related concepts

Introduction

Financial Management is incomplete without reference to Modern Portfolio Theory and models such as CAPM. The following pages attempt to explain these key concepts and also explain minute differences and reasons for popularity.

Hence, the report discusses Capital Asset Pricing Model (CAPM) including the formula, assumptions, criticism and reasons for popularity of the same. CAPM has wide applications in the investment management field where it is used to select securities for a portfolio. Despite various criticisms, it has withstood the test of the time and continues to be a favourite to determine expected rate of return of a security due to the unique feature whereby the beta value representing systemic risk that cannot be diversified is considered.

This brings us to discussion regarding efficient portfolios where minimum variance portfolios are determined such that they provide an expected level of return at minimum possible level of risk through diversification of portfolio.

The discussion remains incomplete without reference to SML and CML and how they indicate different graphical information. While SML represents CAPM graphically, CML represent efficient portfolios and minimum variance portfolios graphically.

# Security Market Line versus Capital Market Line

The Security Market Line (SML) is a graphical representation of the CAPM formula as will be discussed in later stages of this report. Graphically, it is presented as follows: Source: Accaglobal.com

It can be seen that while y-axis represent expected rate of return for a security in the market, y-axis represent beta of the security value. Beta is a measure of systemic risk of the security. In other words, it represents the risk that cannot be diversified and cannot be rid of. The SML is also known as the Characteristic Line and indicates all the securities present in the market and their corresponding beta values or systemic risk contribution to the portfolio. The market risk premium of a security can be determined through the graph. If the security lies above the SML, it indicates that the security offers high premium and is currently undervalued. Hence, it should be included in the portfolio. Conversely, if the security lies below the SML, it means it offers lower premium and is overvalued and should be avoided in the portfolio.

SML is very important tool for analysis as it offers important information about various securities in one single graph. Further, it can be easily used to compare two or more securities and take decisions regarding the same.

In contrast, Capital Market Line (CML) is a graphical representation indicates trade-off between risk and return in efficient portfolios. Graphically, it is presented as follows: Source: Investopedia.com

It can be seen that while y-axis represents expected rate of return from the portfolio, x-axis represent risk or standard deviation value. Hence, the CML provides a view of efficient portfolios.

Hence, some of the major differences between SML and CML can be listed as follows:

1. The risk measure value is different in either case; while beta value is used for SML, standard deviation value of the portfolio is used for CML.
2. The y-axis values are different in either case; while expected return of a security is represented for SML, expected return of the portfolio is represented for CML. Hence, SML represents expected return of individual securities while CML represents the same for all efficient portfolios. Further, CML considers risk free rate of return also.
3. While SML provides a view of efficient and non-efficient portfolios, CML represents only efficient portfolios.
4.

# Importance of Minimum Variance Portfolios

## Diversification

The modern portfolio theory aims at minimizing risk related to an asset portfolio while maintaining same returns. The risk is also known as variance, standard deviation or volatility while the expected returns are also known as the mean return.

Hence, the main focus is on not putting all the eggs in one basket and rather diversifying which leads to lower risk. Hence, if person X invests \$1000 in one security A that entails risk of 8% and person Y invests \$1000 in two securities B and C both of which entail risk of 8%, person Y will have a risk lower than 8% only because he invested in two securities (assuming they are not perfectly correlated). Further, the risk can be lowered (or increased) by adjusting amount allocated to each security. This can be done by ensuring that the selected securities have low degree of correlation. In other words, when prices of one security increase (or decrease), the prices of the other security do not increase (or decrease) by the same magnitude or degree. This occurs due to the effect of diversification (Fabozzi et al., 2002)

## Mean-Variance Efficient Frontier

Theoretically, a portfolio of securities can be arrived at such that the risk is at minimum possible level for a given level of expected returns. Further, this portfolio is unique in nature such that no other combination of the securities can yield lower level of risk for the given level of expected returns. This unique portfolio is known as mean-variance efficient.

When all such mean-variance efficient unique portfolios are drawn graphically, a curve called efficient frontier is formed. A rational investor will invest only in the portfolios that lie on the efficient frontier. The logic is simple – these portfolios will entail minimum possible risk for the given level of expected returns. Hence, it makes sense to invest in these portfolios rather than investing in those that do not lie on efficient frontier because such portfolios will provide same level of expected return but will entail higher level of risk. Following graph depicts the efficient frontier concept (Haugen & Baker, 1991): Source: Haugen & Baker (1991)

From above, it is clear that efficient frontier represents efficient portfolios, that’s why the name. This frontier plays a very important role for those creating investment strategies. The technique is also known as Minimum Variance Portfolio (MVP) optimization and derives its roots within Modern Portfolio Theory by Markowitz (1952).

## Importance of Minimum Variance Portfolios

Creation of Minimum Variance Portfolios involves allocation of weights to various securities in the portfolio such that minimum possible level of risk is achieved. Many research studies in the past have proved that using Minimum Variance Portfolio optimization technique helps to attain similar expected returns as the weighted indices although with a standard deviation which is almost 30% lower than that of respective indices. The following figure presents the process of portfolio optimization (Clarke, Silva, and Thorley, 2006): Source: Clarke, Silva, and Thorley (2006)

Hence, the use of Minimum Variance Portfolio technique is very popular for creation of equity strategies, investment fund strategies and similar usages. In fact, since the past decade, many investment funds market their funds by stating that the fund uses Minimum Variance Portfolio optimization strategy for their fund (Keefe, 2008).

# CAPM for Required Rate of Return

As seen above, the process of portfolio optimization, in fact, the entire ‘Theory of Modern Portfolio’ rests on a pillar called expected returns. Since the Minimum Variance Portfolio

Hence, it is very important to estimate the expected returns correctly and accurately as far as possible. However, this condition itself poses a big challenge.

Many techniques are available to estimate expected rate of return but most of them yield results which are not accurate and reliable. The large errors in estimation make these techniques redundant or not very useful for the purpose of portfolio optimization.

One of the techniques traditionally used for estimating expected returns is Capital Asset Pricing Model or popularly known as ‘CAPM’.

## CAPM

CAPM is an important financial management concept that was developed by economists John Lintner, Jack Treynor, William Sharpe etc. It is an extension of Markowitz’s diversification theory. It represents linear relationship between required rate of return and systemic risk involved and this relationship is represented in the following equation: E(ri) = Rf + βi (E(rm) – Rf), where (Watson & Head, 2016)

• E(ri) is the required rate of return on the asset,
• Rf is the risk free rate of return,
• βis the beta value for the asset,
• E(rm) is the average market return,

Hence, effectively, CAPM considers equity risk premium, that is rate of return of the asset that is in excess of the average return provided by the market. Further, this equity risk premium is adjusted for the systematic risk present by considering the beta value. Beta value is nothing but the correlation of the asset with the market. Further, the risk free rate of return is added to arrive at the expected rate of return. Risk free rate of return is nothing but the rate of return available on short term securities, most popularly the treasury bills (Investopedia, 2018).

## Assumptions & Criticism of CAPM

Once the assumptions of CAPM are discussed, the criticism itself will become quite clear. The following are the main assumptions used for CAPM (Watson & Head, 2016):

1. The model assumes that the unsystematic risk can be completely eliminated through diversification in the portfolio. It also assumes that the investor holds diversified portfolio.
2. In order to get comparable data for risk free rate of return, average rate of return in the market and beta value, the CAPM model assumes single-period horizon for all transactions. Typically, one year period is utilized for calculating all the inputs, although this period can be changed basis requirement.
3. The model assumes that all investors have access and knowledge of the risk free rate of return available in the market and that they will borrow or lend in risk free it. This rate can be arrived at graphically through intersection of the security market line and y-axis, as depicted below: Source: Accaglobal.com

1. The CAPM model also assumes perfect capital market, that is, there are no transaction costs or taxes and that all the information available is correct and can be plotted easily. Further, all of this information is easily accessible to the investors.

Looking at the above assumptions, it is clear that while these assumptions may be necessary to create a theoretical framework and a model, they are definitely not something that will be available in real world market scenario where there are many hurdles such as, taxes, transaction cost, availability of information to investors, free trading of investments, etc. Another assumption of investor holding a diversified portfolio is difficult to envisage in the real world environment as it is not necessary that every investor will want to replicate the entire market in the asset portfolio held by him. Another major criticism is that not every investor can borrow and lend money at the risk free rate of return in the real world. The rate of lending and borrowing differ, especially so for individual investors where rate of borrowing is much higher than the risk free rate of return in the market.

## Importance of CAPM

Despite all the criticism, CAPM remains one of the most popular and widely used methods for calculating the expected rate of return. Many methods were used instead of CAPM, however, CAPM still remains a favourite.

In fact, the utilization of CAPM in the investment management industry and corporate finance world has become quire advanced and sophisticated. Further, it is used parallel with other techniques and methods such that the results can be validated and outliers can be identified and rectified.

CAPM remains popular as it accounts for only systemic risk that cannot be diversified and also provides the information in a standard and clear format. Further, in past 50 years, CAPM has been subjected to frequent empirical testing and it has withstood the results. The method is also widely used to calculate cost of equity as it accounts for systemic risk. Hence, it is superior to the dividend growth model also. Hence, CAPM remains a favourite with the financial managers.

# Conclusion

The above pages discussed some of the most widely used financial management concepts, such as CAPM, diversification, efficient portfolios, SML and CML.

These make the pillars of financial management and investment management world where they hold prime importance in taking investment related decisions.

Despite various criticisms, they stand the test due to frequent empirical testing that proves that they in fact, assist in taking investment related decisions. Further, the tools have become advanced and sophisticated so as to minimise estimation error and are used in tandem with other tools also.