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## Table of Contents

List of Abbreviations

List of Figures

1 Introduction

2 Risk and Return in Financial Management

2.1 Important Definitions in the Context of Risk

2.2 Measuring Risk by Standard Deviation and Coefficient of Variation

2.3 Types of Risk that Business Firms Encounter

2.4 Methods of Risk Reduction

3 The Capital Asset Pricing Model (CAPM)

3.1 The Idea Behind – Basic Assumptions of the CAPM

3.2 The CAPM Formula

3.3 The Importance of CAPM in Firm Valuation - The CAPM Approach to Estimating the Cost of Internal Common Equity

4 Résumé

Appendix 1 Integral Total Management (ITM) Checklist

Bibliography V

## List of Abbreviations

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## List of Figures

Figure 1: Probability distribution of the return on Stock A and on Stock B

Figure 2: Formula for the Expected Rate of Return

Figure 3: Formula for the Variance

Figure 4: Formula for the Standard Deviation

Figure 5: Range of expected rates of return of stock A

Figure 6: Range of expected rates of return of stock B

Figure 7: Expected return and standard deviation of stock A and stock B

Figure 8: Formula for the Covariance and Correlation Coefficient

Figure 9: The standard deviation of a two-asset portfolio

Figure 10: Portfolio fluctuations and beta

Figure 11: Using CAPM to calculate required rates of return for investment projects

Figure 12: CAPM and the risk-return relationship

Figure 13: Relationship between beta and the expected rate of return

Figure 14: The flow of capital from equity investors to firms

## 1 Introduction

In everything you do, or don’t do, there is a chance that something will happen that you didn’t count on. Risk is the potential for unexpected things to happen.

Risk aversion is a common thing among almost all investors. Investors generally dislike uncertainty or risk and agree that a safe dollar is worth more than a risky one. Therefore, investors will have to be persuaded to take higher risk by the offer of higher returns. In this investment context, the additional compensation for taking on higher risk is a higher rate of return.

Every investment has a risk element: The investor will always not be certain whether the investment will be able to generate the required income. The degree of risk defers from industry to industry but also from company to company. It is not possible to eliminate the investment risk altogether but to reduce is. Nevertheless, often there remains a risky part. According to the degree of risk, the investor demands a corresponding rate of return that is, of course, higher than the rate of return of risk-free investments. Taking on a risk should be paid off.

The Capital Asset Pricing Model (CAPM) is an economic model for valuing stocks, securities, derivatives and/or assets by relating risk and expected rate of return. CAPM is based on the idea that investors demand additional expected return if they are asked to accept additional risk.

## 2 Risk and Return in Financial Management

### 2.1 Important Definitions in the Context of Risk

Business firms face risk in nearly everything they do. To assess risk is one of the most important tasks financial managers perform.^{1} To understand the different types of risk, their measuring, the ways to reduce or to compensate risk and at least the risk-return relationship explained by the Capital Asset Pricing Model (CAPM) the following three terms have to be defined:

-Risk

-Risk Aversion

-Risk-Return Relationship

If you go by car, there is always the risk of having an accident and getting injured. If you go by plane, there is always the risk of a crash leading to death. If you go jogging, there is the risk of tumbling and breaking a leg. And if you stay in bed to avoid such risks there is nevertheless the risk of getting coronary artery disease because of a lack of exercise. In everything you do – or you do not do – there is a chance that something will happen that you did not expect. As a result, *risk* is the potential for unexpected events to occur.^{2}

Most people try to avoid risks if it is possible - especially in financial setting. If people are faced with financial alternatives that are equal except for their degree of risk, most people will choose the less risky alternative.^{3} *Risk*

*aversion* is therefore the tendency to avoid additional risk.^{4} People being risk- averse will avoid risk if they can, unless they receive additional compensation for assuming that risk.^{5} “In finance, the added compensation is a higher expected rate of return.”^{6}

The *risk-return relationship* explains the relationship between risk and required rate of return.^{7} This relationship is a positive one because the more risk assumed, the higher the required rate of return most people will demand. Especially in the financial markets, where people invest for the future, they almost always seek to avoid risk unless they are adequately compensated. Risk aversion explains why risky junk bonds^{8} for example carry a higher market interest rate than essentially risk-free U.S. Treasury bonds^{9}.^{10}

### 2.2 Measuring Risk by Standard Deviation and Coefficient of Variation

Risk cannot be avoided entirely. That is the reason why firms must make sure that the anticipated return is sufficient to justify the degree of risk assumed.^{11} Firms must therefore able to answer the question “How risky is it?” To quantify the risk is difficult. “In business, risk measurement focuses on the degree of uncertainty present in a situation – the chance, or probability, of an unexpected outcome.”^{12} The lower the probability of an unexpected outcome, the lower the degree of risk and the other way around.

To measure risk, two statements form the basis:

-Higher risk projects require a higher rate of return.^{13}

-Higher required rates of return cause lower present values (PV):^{14} The following example justifies these statements:

By a given rate of return of 7% p. a., an input of 467.29 EUR is required to realise an output of 500 EUR after one year:

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Whereas by a given higher rate of return of 13% p. a. an input of 442.48 EUR is necessary to realise an output of 500 EUR:

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If an investor wishes to realise a higher return in an efficient market, than that investor must be exposed to more risk or uncertainty regarding the future return.^{15}

As future is uncertain, investors do not know what rate of return their investments will realise. Finance assumes that individuals base their decision on what they expect to happen. When evaluating potential investments in financial assets, these two dimensions of the decision making process are called expected return and risk.^{16} In statistics, *distributions* are used to describe the many values variables might have. For example a stock’s return on investment is a variable with many values. So the stock’s return on investment may be described by a distribution of the possible returns with different probabilities attached to each value. The probability distribution can be described by a graph, a table or a formula:

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**Figure 1: Probability distribution of the return on Stock A and on Stock B Source: See also Tolkmitt (2007), p. 42.**

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**Figure 2: Formula for the Expected Rate of Return Source: Tolkmitt (2007), p. 43.**

The mean of the distribution – the average of a set of values – is the most likely, or expected, rate of return.^{17} The expected rate of return can be calculated with the following formula:

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To quantify the expected rate of return of stock A and stock B (see figure 1) by using the above mentioned formula, results in the following two expected rates of return:

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The expected return on stock A varies between -5% and 20% (difference of 25%), whereas the expected return on stock B varies between -15% and 30% (difference of 45%). The narrowness of wideness of a distribution reflects the degree of uncertainty about the expected value of the variable in question (return). The relatively wide variation of stock B shows that there is more uncertainty about its return that about the return on stock A.

One way to measure risk is to compute the *standard deviation* (SD) of a variable’s distribution of possible values. “The standard deviation is a numeric indicator of how widely dispersed the possible values are around a mean.”^{18}

In fact, the more widely dispersed a distribution is, the larger the standard deviation and the greater the probability that the value of a variable will be greatly different than the expected value.^{19} As a result, the standard deviation indicates that an outcome different from what is expected will occur.

To quantify the degree of uncertainty, or risk, that is present, by calculating the standard deviation, the *variance* has to be calculated first as its square root is the standard deviation. The variance (VAR) of a probability distribution is one measure of statistical dispersion, averaging the squared distance of its possible values from the expected value:

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**Figure 3: Formula for the Variance Source: Tolkmitt (2007), p. 43.**

In case of the example of the rate of return of stock A and stock B (figure 1), the variance can be calculated as follows:

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As the standard deviation is the square root of the variance, the following formula exists:

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**Figure 4: Formula for the Standard Deviation Source: Tolkmitt (2007), p. 43.**

**[...]**

^{1} See Gallagher (2003), p. 162.

^{2} Ibid.

^{3} Ibid.

^{4} Ibid.

^{5} Ibid.

^{6} Gallagher (2003), p. 162.

^{7} See Gallagher (2003), p. 162.

^{8} Junk bonds are bonds with a lower than investment-grade ratings. Gallagher (2003), p. G-4.

^{9} Treasury bonds are securities issued by the federal government that make semi-annual coupon interest payments and pay the face value at maturity. Treasury bonds come in maturities of more than ten years. Gallagher (2003), p. G-7.

^{10} See Gallagher (2003), p. 162.

^{11} Ibid.p. 163.

^{12} Gallagher (2003), p. 163.

^{13} See Tolkmitt (2005), p. 41.

^{14} Ibid.

^{15} See Tolkmitt (2005), p. 41.

^{16} Ibid.

^{17} See Gallagher (2003), p. 163.

^{18} Gallagher (2003), p. 164.

^{19} See Gallagher (2003), p. 164.

- Quote paper
- Nadine Pahl (Author), 2007, Principles of the Capital Asset Pricing Model and the Importance in Firm Valuation, Munich, GRIN Verlag, https://www.grin.com/document/124630

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