Risk Measurements - Business Finance - ثاني ثانوي

6.4 Risk Measurements Key Terms Standard deviation Beta coefficient Capital asset pricing model (CAPM) As stated earlier, there are a number of factors that can impact the risks faced by firms and by extension, their management and investors. In Chapter 4, there was also a discussion of the Efficient Market Hypothesis (EMH). Under this hypothesis, the value of a firm reflects all the information. including risk information, that exists in the marketplace. For an investor, there are several indicators to assess risk developed in the finance field. This includes standard deviations of asset prices and beta coefficients. Link te dijital lesson www.den.edu.18 6.4a The Standard Deviation as a Measure of Risk As stated earlier, risk is concerned with the uncertainty that the realized return will not equal the expected return. One measure of risk, the standard deviation, emphasizes the extent to which the return differs from the average or expected return. An alternative measure of risk, a beta coefficient, is an index of the return on an asset relative to the return on a portfolio of assets (for example, the return on a stock relative to the retur on a stock index). The standard deviation measures the dispersion around an average value. As applied to investments, it considers an average return and the extent to which individual returns deviate from the average If there is very little difference between the average return and the individual returns, the dispersion will be small. If there is a large difference between the average return and the individual returns, the dispersion will be large. Typically, the larger this dispersion, the greater the risk associated with the investment. This measurement is perhaps best illustrated by a simple example. Consider the returns on two stocks over a period of five years: Standard deviation A measure of dispersion around an average value, a measure of sk وزارة التعليم CHAPTER & Risk and Its Measurements 239

Return Year Return Stock T Return Stock 2 T 2 13.5% 11% 14.5% 13% 3 15% 15% 4 15.5% 17% 5 16.5% 19% 15% 15% FIGURE 4.2 Distribution of Two Stacks Average return The average return over the five years is the same for both stocks, 15%, but annual returns differ. Stock 1's individual returns were close to the average return. The worst year generated a 13.5% return while the best year generated a 16.5% return. None of the individual returns deviated from the average by more than 1.5%. Stock 2's individual returns differ from the average return, ranging from a low of 11% to a high of 19%. With the exception of year 3, all the returns deviate from the average by 2%. Dispersion can be measured by the standard deviation. The standard deviation measures the tendency of the individual returns to cluster around the average return, it may be used as a measure of risk. The larger the dispersion, the greater the standard deviation and the larger the risk associated with the particular investment. The standard deviation is easily calculated using a computer program. Frequency of Occurrence of Security Returns Returt Pul 240lyBusiness Finance Even though both stocks achieved the same average return, an investor needs to evaluate these changes in determining the risk of investing in specific stocks. Figure 6.2 above shows that Stock 1 has not varied greatly over five years while Stock 2 shows a larger standard deviation. .

6.4b Beta Coefficients A beta coefficient is a measure of the systematic risk associated with a particular asset. While the concept may be applied to any asset, the usual explanation employs common stock. A beta coefficient is an index of risk that quantifies the responsiveness of a stock's return to changes in the return on the market. Since a beta coefficient measures a stock's return relative to the return on the market, it measures the systematic risk associated with investing in these stocks. EXAMPLE 1. A beta coefficient of 1 means that the stock's return moves exactly with an index of the market as a whole. A 10% increase in the market produces a 10% increase in the return on the specific stock. Correspondingly, a 10% decline in the market results in a 10% decline in the return on the stock. 2. A beta coefficient of less than 1 implies that the return on the stock tends to fluctuate less than the market as a whole. A coefficient of 0.7 indicates that the stock's return will rise only 7% as a result of a 10% increase in the market, but will fall by only 7% when the market declines by 10%. 3. A beta coefficient of more than 1 implies that the return on the stock tends to fluctuate more than the market as a whole. A coefficient of 1.2 means that the return on the stock will rise by 12% if the market increases by 10%, but the return on the stock will decline by 12% when the market declines by 10%. Set coefficient A measure of systemic risk; an index of the risk of a stock's return relative to changes in the return on the market The greater the beta coefficient, the more market (systematic) risk is associated with the individual stock. High beta coefficients may indicate higher returns during rising markets, but they also indicate greater losses during declining markets. The converse is true for stocks with low beta coefficients, which should underperform the market during periods of rising stock prices but outperform the market as a whole during periods of declining prices. Such stocks are referred to as "defensive stocks." وزارة التصليدر CHAPTER & Risk and Its Measurements 241

" Capital wat ming model ICAPMI A method of calculating the relationship between systematic risk and the expected return on assets; particularly stock 242Business Finance П 6.4c The Capital Asset Pricing Model and an Investment's Required Return The development of beta coefficients and a theory of risk reduction through diversification are exceedingly important to the process of asset valuation. The capital asset pricing modal or CAPM is one method used to determine that required return. The CAPM specifies the relationship between risk and return that is used either to value or to judge an asset's expected return (valuation expresses an asset's present worth in monetary units such as SAR, an asset's return is expressed in percentages). If an asset's value exceeds its cost, or if an asset's expected return exceeds the required return, the asset is purchased by the investors. Either method produces the same decision, since the only difference is the units of measure. The CAPM builds on the proposition that additional risk requires a higher return. This return has two components: (1) what may be earned on a risk-free asset, such as a high-quality government bond, and (2) a premium for bearing risk. For an investor, why should they purchase a risky security when they can purchase a risk-free security unless the risky security pays a higher rate of return? Since unsystematic risk is reduced through diversification, a stock's risk premium is the additional return required to bear the undiversifiable, systematic risk associated with the stock. This risk-adjusted required return (k) is expressed in Equation 6.2 below: k = risk-free rate + risk premium The risk premium is composed of two components: (1) the additional return that investing in securities in general offers above the risk-free rate and (2) the volatility of the particular security relative to the market as a whole, as measured by the security's beta coefficient. The additional return is measured by the difference between the expected return on the market (rm) and the risk-free rate (r). This differential (r) is the risk premium that is required to induce the individual to purchase risky assets. To induce the investor to purchase a particular stock, the risk premium associated with the market must be adjusted by the market risk associated with the individual security. This risk adjustment uses the stock's beta coefficient, which indicates the stock's volatility relative to the market. The risk adjustment is achieved by multiplying the security's beta coefficient by the difference

between the expected return on the market and the risk-free rate. Thus, the risk premium for the individual stock is expressed in Equation 6.3 below: Risk premium (r-r) x beta EXAMPLE The calculation steps of the risk-adjusted return of two stocks, Stock A and Stock B is shown below. Risk-free rate (r.) 4.303% Market return (r.) 9% Stock A beta 1 Stock B beta 1.31 Risk-adjusted required retum K-it,+ beta ir,,-t.) Stock A Stock B k=0.04303+(-0.04303) * 1 -0.04303+(-0.04303) x 1.31 k=0.04303 + (0.09 -0.04303) XT k=0.04303 + (0.09 -0.04303) x 1.31 k=0.04303+(0,04697) x 1 k-0.04303+0,04697 k=0.09 or 9% k-0.04303 (0.04697) * 1.31 x k=0.04303+0.0615307 k-0.1045607 or 10,46% As a result, the risk-adjusted required return for Stock A is 9% which is the same as the expected market return. This makes sense since the beta for Stock A is 1, or the risk is the same as the market return. Stock B has a higher beta indicating a more volatile stock, so the risk-adjusted required retum is higher at 10.46%. As a result, a stock with the higher beta coefficient has the higher required return because it is riskier. وزارة الصليد CHAPTER Risk and Its Measurements 243

N 244Business Finance 2921-185 You Try It Assume you are analyzing a risk-adjusted required return for a stack. You have determined the risk-free rate is 4.35%. The expected market rerum is 12%. Determine the expected risk-adjusted required return for this stock if: a. Company A beta coefficient is 0.8% b. Company B beta coefficent is 1.21. What does this tell you about the stock? Exercises Choose the correct answer. 1. The standard deviation measures an asset's expected return. True/False 2. To measure risk, the capital asset pricing model uses: a. bela coefficient. b. an asset's standard deviation. c. the volatility of an asset's cash flows. d. the term during which the asset is held.