Investment Management: The Relevance of Portfolio Theory and Capital Asset Pricing Model

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Introduction

Background

Risks are essential repercussions of different investments. Treasury bills are considered safer than other investments. Treasury bills are those long term bond investments that offer investors assets whose prices rarely fluctuate. Low risk entails low returns. That is why treasury bills provide the lowest average return when compared to other investments in the stocks of large corporations. Investors have to pay for safety and earn less. In other words risk taking is directly related to higher earnings. In general, investors are risk averse. Risky investments offer higher expected returns than less risky investments to induce people to invest in them. Put differently risk and return go hand in hand. That is why based on historical performances the following facts have been drawn:

Treasury bills, the least risky of financial assets, earned the lowest average rate of return.
Common Stocks, the most risky of financial assets, earned the highest average annual rate of return.
Bonds, which occupy a middling position on the risk dimension, earned a middling average annual return.

It is found that most investors believe in diversification of their investments in order to distribute their risks as per their objectives of returns from such investments. They invest in a portfolio of assets as they do not want to put all their eggs in one basket. Hence what really matters to them is not the risk and return in isolation, but the risk and return of the portfolio as a whole.

Definitions

In order to appreciate the relevance of the portfolio theory and the CAPM, it is important to understand basic definitions of these concepts:

Portfolio theory A portfolio is a collection of securities. Portfolio theory is a formal analysis of the relationship between the rates of return on a portfolio of risky securities and the rates of return on the securities contained in that portfolio. The rate of return on a portfolio is random variable. The probability distribution that generates value for the rate of return on the portfolio is the compilation of the probability distribution that generates the rates of return on the securities contained in that portfolio.(James Bradfield, page 167). The theory is useful for an investor in decision making for allocation of funds in risky securities to create a portfolio that describes his or her preferences regarding combination of risk and expected returns.

Capital Asset Pricing Model (CAPM) It is believed that investments are largely influenced by the overall risks of those investments. The CAPM theory links risks and returns of the investments. Since the development of CAPM theory by William Sharpe, it has been analyzed and developed by many considering the diversifiable and non- diversifiable risks. Earlier the CAPM has only one systematic risk factor the risk of the overall movement of the market. The risk is referred to as market risk and the CAPM is given by the following formula:

E(_Ri)= R_f +²_i[E(R_M)- R_f]

Where:

E(R_M) = expected return on a market portfolio
²_i = measure of systematic risk of asset _i relative to market portfolio.

The expected return for an asset _iaccording to CAPM is equal risk free rate plus a risk premium. (Frank J. Fabozzi and Harry Markowitz, page 67).

Later the developers of CAPM theory linked diversifiable (unsystematic) risks and non- diversifiable (systematic) risks for all assets in the portfolio. Some management experts believed that CAPM is not true as it rules out active management and investment research. But as per Frank J. Fabozzi and Harry Markowitz even though the idea is not true it does not mean that the constructs introduced by the theory are not important. Constructs introduced in the development of theory include the notion of a market portfolio, systematic risk, diversifiable risks and beta.

Thesis Statement

The important thing is overall risk of the investors in the marketplace and the investors prefer portfolios instead of individual investments; and the basic theory that links risk and returns is the Capital Asset Pricing Model (CAPM) and helps to understand the basic risk- return tradeoffs involved in all types of financial decisions.(Lawrence J Gitman, page 246).

Main Body

Portfolio theory envisages that diversification reduce variability. Even a little diversification can provide a substantial reduction in variability. Basically diversification of investment ensures that movement of prices does not have a combined effect. Often a decline in the value of one asset is offset by the rise in the price of other asset. The risk that potentially be eliminated is unique risk. But there are other risks that cannot be avoided.

There are certain relationships between risk and returns that must be understood in order to appreciate the portfolio theory and relevance of CAPM:

Securities are risky as their returns are variable.
The most commonly used measure of risk or variability in finance is standard deviation. This is because the return on a portfolio is a weighted average of the returns of individual assets (Lawrence J Gitman, page 238). Suppose 47% of portfolio is invested in A expecting 17% return and the remainder is invested in B expected to provide 14% on investment. The expected return on portfolio is simply a weighted average of the expected return on the individual assets calculated as under: Expected portfolio return = (0.47 * 17) + (0.53 * 14) = 15.41%

It is important to note that when there are two assets in portfolio there are equal number of variances and covariances when we calculate standard deviation. When there are many assets in the portfolio, the number of covariances is larger than number of variances. Thus the variability of a well defined portfolio reflects mainly the covariances. Wise investors do not put all their eggs into just one basket: they reduce their risk by diversification. They are interested in the effect that each asset will have on the risk of their portfolio.

The risk of a security can be split into parts : unique risk and market risk

Unique risk is caused by factors specific to the asset that generate volatility, for example, a change of management within a company. This type of volatility is unique to the assets, or unsystematic. (Bruce J Feible, page 191). It is seen risks those are unique in nature emerge from firm factors that are very specific in nature. Such a situation can be created say by a new industrial policy of the state affecting a particular business. Events of this nature primarily affect the particular entity and they do not have a general effect on all entities in the industry. That is why unique risks are also called diversifiable risk or unsystematic risk.

On the other hand market risks are general in nature. These risks affect firms in an industry to a greater or lesser degree. Investors cannot avoid the effect of such risks. Even diversification of investment of a portfolio may not change the effects of such risks. Hence it is referred to as systematic risk or non- diversifiable risk. Systematic risk factors are reflected in the market returns, therefore, we can isolate the influence of systematic factors on an individual asset by observing market returns. (Bruce J Feible, page 191). Therefore the risk of a well diversified portfolio depends on the market risk of the assets included in that portfolio.

The contribution of a security to a fully diversified portfolio is measured by its beta. The beta coefficient is a relative measure of non- diversifiable risk. It is an index to the degree of movement of an assets return in response to a change in the market return. An assets historical returns are used in finding the assets beta coefficient. The market return is the return on the market portfolio of all traded securities.(Lawrence J Gitman, page 247)

For calculating the beta of a security, the following market model is employed: R_jt = ±_j + ²_j R_Mt + e_j

Where:

R_jt = return of security _j in period _t
± = intercept term alpha
²_j = regression coefficient beta
R_Mt = return on market portfolio in period _t
e_j= random error term

Stocks with betas greater than 1.0 tend to amplify the overall movements of the market. Stocks with beta between 0 and 1.0 tend to move in the same direction as the market, but not so far. Of course, the market is the portfolio of all stocks, and that is why the average stock has a beta of 1.0

If an asset does have an element of market risk, CAPM states that it should earn a risk premium proportnate to the amount of market risk reflected in the asset. If the underlying market itself has a degree of return uncertainty, we assume that the market return will be higher than the risk free return. This is the excess market return. To derive the incremental excess return, we lever the excess market return up or down by the degree of market risk exposure inherent in the asset. (Bruce J Feible, page 192).

Conclusion

It is observed that diversification reduces risks and therefore make sense for investors. If an investor is diversified in accord with the theory, then CAPM indicates that the percentage of returns that is due to the market should be 100 per cent. As a result, effective diversification under CAPM should provide investors with investment returns that are consistent with market returns. (John Mauldin, Page 93). The variability of stocks representing unique risk may be mitigated by introducing diversification of investment portfolio, but such diversification cannot eliminate market risk. Beta measures the amount that investors expect stock price to change. A stock with beta greater than 1 is unusually sensitive to market movements, whereas a stock with a beta below 1 is unusually insensitive to market movements. The standard deviation of a well diversified portfolio is proportional to its beta.

Limitations

CAPM is not testable. The market portfolio is theoretical and not really observable, so we cannot test the relation between expected return on an asset and the expected return of the market to see if relation specified in CAPM holds.(Frank J Fabozzi and Pamela P Peterson, page 299). Only unique risks are dealt with by CAPM and market risks are not at all addressed. Moreover CAPM assumes that risk can be encapsulated in a single figure (beta).(John Ogilvie, page 185). Critics argue that it is not necessarily reasonable to measure risk purely in terms of variance of portfolio returns (Peter J Booth, page 97). In fact CAPM is considered in both its standard form and with distribution parameter extensions an incomplete model of asset pricing(Robert R Trippi and Jae K Lee, page 38).

Recommendations

Risk is best judged in portfolio context. Part of the uncertainty about a securitys return is diversified when security is grouped with others in a portfolio. There is no doubt that diversification is a good thing for investors. This does not imply that firms should diversify. Corporate diversification is redundant if investors can diversify on their own account. Though it lacks realism and is difficult to apply, the CAPM makes some sense regarding the role of diversification and the type of risks we need to consider in investment decisions. (Frank J Fabozzi and Pamela P Peterson, page 299).

References

James Bradfield, Introduction to the economics of financial markets, Oxford University Press S, 2007, page 167.

Frank J. Fabozzi and Harry Markowitz, The theory and practice of investment management, John Wiley & Sons, 2002, page 67).

Lawrence J Gitman, Principles of Managerial Finance, Pearson Education, 2006, page 246.

Bruce J Feible, Investment Performance Measurement, John Wiley and Sons, 2003, page 191.

John Mauldin, Just One Thing: Twelve of the worlds best investors reveal with one strategy, John Wiley and Sons, 2005, Page 93.

John Ogilvie, CIMA Learning System 2007 Management Accounting Financial Strategy, Elsevier, page 185.

Peter J Booth, Modern Actuarial Theory and practice, Part I, CRC, 1998, page 97.

Robert R Trippi and Jae K Lee, Artificial Intelligence in finance & investing state of art, Irwin Professional Book Team, 1996, page 38.

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