1. CHAPTER 05 RISK&RETURN

2. Formal Definition- RISK # The variability of returns from those that are expected. Or, # The chance that some unfavorable event will occur. Or, # The chance of financial loss, or the variability of returns associated with a given asset.

3. Types of Risk Total Security Risk = Total Security Risk = Nondiversifiable risk + Diversifiable risk Nondiversifiable risk + Diversifiable risk # Diversifiable Risk: # Diversifiable Risk: The portion of an asset’s risk that is attributable to firm-specific, random causes; can be eliminated through diversification. Also called unsystematic risk or company-specific risk. The portion of an asset’s risk that is attributable to firm-specific, random causes; can be eliminated through diversification. Also called unsystematic risk or company-specific risk.

4. Types of Risk # Nondiversifiable Risk: The relevant portion of an asset’s risk attributable to market factors that effect all firms; cannot be eliminated through diversification. Also called systematic risk or market risk. The relevant portion of an asset’s risk attributable to market factors that effect all firms; cannot be eliminated through diversification. Also called systematic risk or market risk. Diversification: Diversification: Spread your risk across a number of assets or investments in order to reducing total risk of investments. Spread your risk across a number of assets or investments in order to reducing total risk of investments.

5. Formal Definition- Return # The total gain or loss experienced on an investment over a given period of time; calculated by dividing the asset’s cash distributions during the period, plus change in value, and divide by its beginning-of-period investment value. Formula: Formula: K t = actual, expected or required rate of return during period t C t = cash flow received from the asset investment in the time period t-1 to t. P t = Price (value) of asset at time t P t-1 = price (value) of asset at time t-1 P t-1 = price (value) of asset at time t-1

6. Example1: Mr. Pleto, a financial analyst for Skyline Industry, wishes to estimate the rate of return for two similar risk investments, X and Y. Pleto’s research indicates that the immediate past returns will serve as reasonable estimates for future returns. A year earlier, investment X had a market value of Tk. 200,000, investment Y of Tk. 550,000. During the year, investment X generated cash flow of Tk. 15,000 and investment Y generated Tk. 68,000. The current market value of investment X and Y are Tk. 210,000 and Tk. 550,000 respectively. Example1: Mr. Pleto, a financial analyst for Skyline Industry, wishes to estimate the rate of return for two similar risk investments, X and Y. Pleto’s research indicates that the immediate past returns will serve as reasonable estimates for future returns. A year earlier, investment X had a market value of Tk. 200,000, investment Y of Tk. 550,000. During the year, investment X generated cash flow of Tk. 15,000 and investment Y generated Tk. 68,000. The current market value of investment X and Y are Tk. 210,000 and Tk. 550,000 respectively.  Calculate the expected rate of return on investment X and Y.  Which one should Pleto recommend? Why?

7. Risk Preference Risk Indifferent: The attitude toward risk in which no change in return would be required for an increase in risk. Risk Indifferent: The attitude toward risk in which no change in return would be required for an increase in risk. Risk-averse: The attitude toward risk in which an increased return would be required for an increase in risk. Risk-averse: The attitude toward risk in which an increased return would be required for an increase in risk. Risk-seeking: The attitude toward risk in which a decreased return would be accepted for an increase in risk. Risk-seeking: The attitude toward risk in which a decreased return would be accepted for an increase in risk.

8. Measuring Risk Probability Distribution: Probability Distribution: A listing of all possible outcomes or events with a probability (chance of occurrence) assigned to each outcome. A listing of all possible outcomes or events with a probability (chance of occurrence) assigned to each outcome. Outcome Probability Outcome Probability Rain 0.4 = 40% Rain 0.4 = 40% No Rain 0.6 = 60 No Rain 0.6 = 60 1.0 = 100% 1.0 = 100%

9. Measuring Risk Expected Return: Expected Return: The weighted average of possible returns, with the weights being the probabilities of occurrence. The weighted average of possible returns, with the weights being the probabilities of occurrence. Formula: Formula:Where, K j = return for the J th outcome Pr j = probability of occurrence of j th outcome n = number of outcomes considered

10. Measuring Risk There are three statistical tools used to measure the risk- Range, Standard Deviation, and Coefficient of Variation (CV): There are three statistical tools used to measure the risk- Range, Standard Deviation, and Coefficient of Variation (CV): Range: Measures the difference between the highest value of the return and its lowest value. Higher the range, higher will be the risk of an asset. Standard Deviation: The most common statistical indicator of an asset’s risk; it measures the dispersion around the expected value or the average value of squared deviations from mean. It is a measure of volatility. Formula:σ k = Formula:σ k = Higher the standard deviation greater the risk

11. Measuring Risk Coefficient of Variation (CV): Coefficient of Variation (CV): The ratio of the standard deviation of a distributing to the mean (expected return) of that distribution. It measures the risk per unit of return. The ratio of the standard deviation of a distributing to the mean (expected return) of that distribution. It measures the risk per unit of return. Formula: CV = σ/k Formula: CV = σ/k The higher the coefficient of variation, the greater will be risk. Example: 5-7, 5-10

12. Example The market and stock j have the following probability distribution: The market and stock j have the following probability distribution: Probability Km Kj Probability Km Kj 0.3 15% 20% 0.3 15% 20% 0.4 09 05 0.4 09 05 0.3 18 12 0.3 18 12 a. Calculate the expected rates of return for the market and stock j. b. Calculate the standard deviation for market and stock j. c. Calculate the coefficient of variation for the market and stock j.

13. Portfolio Risk and Returns Portfolio: A portfolio consists of individual stocks where the objective is to maximize the returns it generates. Portfolio: A portfolio consists of individual stocks where the objective is to maximize the returns it generates. Portfolio Return: Is the weighted average of the expected returns on the individual stocks in the portfolio, with the weights being the fraction of the total portfolio invested in each stock. Portfolio Return: Is the weighted average of the expected returns on the individual stocks in the portfolio, with the weights being the fraction of the total portfolio invested in each stock. Formula K p = sum W j K j, j=1 to n

14. Portfolio Risk and Returns Portfolio Risk: It is calculated by using correlation coefficient, r. The relationship between two variables is called correlation, and the coefficient which measures the degree of the relationship between the variables is called the correlation coefficient. Its value moves from -1 to +1, where, -1 denotes perfectly negative correlation and +1 measures perfectly positive correlation. Portfolio Risk: It is calculated by using correlation coefficient, r. The relationship between two variables is called correlation, and the coefficient which measures the degree of the relationship between the variables is called the correlation coefficient. Its value moves from -1 to +1, where, -1 denotes perfectly negative correlation and +1 measures perfectly positive correlation.

15. Use of Correlation Coefficient: Diversification Diversification refers to use of multiple stocks which are negatively (or lower positively) correlated to reduce the risk to near zero or as low as possible. Diversification refers to use of multiple stocks which are negatively (or lower positively) correlated to reduce the risk to near zero or as low as possible. DO NOT PUT ALL OF YOUR EGGS IN THE SAME BASKET DO NOT PUT ALL OF YOUR EGGS IN THE SAME BASKET –Uncorrelated stocks are those which has near zero correlation coefficient. –Use of perfectly negative correlated stock will result in zero risk. It is impossible to have perfectly negative correlation. –Most of the assets are less than perfectly correlated and addition of assets to a portfolio will lower and lower the risk.

16. Relationship between Risk and Returns (CAPM) The Capital asset Pricing Model (CAPM) measures the link between the non-diversifiable risk and return for all assets. The Capital asset Pricing Model (CAPM) measures the link between the non-diversifiable risk and return for all assets. Beta measures the extent to which the return on a given stock move with the stock market. If the historical returns on the market are plotted on the X axis and the similar returns of the individual stocks are plotted on the Y axis, the slope of the line is called the beta coefficient or beta in short. Beta measures the extent to which the return on a given stock move with the stock market. If the historical returns on the market are plotted on the X axis and the similar returns of the individual stocks are plotted on the Y axis, the slope of the line is called the beta coefficient or beta in short.

17. Relationship between Risk and Returns (CAPM) Beta can also be calculated using the following formula Beta can also be calculated using the following formula B j = The ratio between Cov (return on asset j and the return on the market) and the variance of the return on the market portfolio. If the value of beta is greater than 1, it shows above average market risk, if equal to 1, average market risk and, if less than 1, it shows below average market risk. If the value of beta is greater than 1, it shows above average market risk, if equal to 1, average market risk and, if less than 1, it shows below average market risk.

18. Relationship between Risk and Returns (CAPM) SML: k j = K RF + (K M – K RF )b j SML: k j = K RF + (K M – K RF )b j Where, Kj is the required return on stock j Krf is risk free rate of return govt treasury bond. Km is the rerun on the market portfolio bj is the beta coefficient of stock j. Figure of SML P.240

19. Questions Define risk. According to the preference of risk investors are divided into three types explain. Define risk. According to the preference of risk investors are divided into three types explain. Compare between standard deviation and coefficient of variation as measurement of risk. Compare between standard deviation and coefficient of variation as measurement of risk. What is a port folio? How portfolio risk and returns are calculated? What is a port folio? How portfolio risk and returns are calculated? Define correlation coefficient. What does it’s value mean? Define correlation coefficient. What does it’s value mean? Explain the types of risk. What type of risk CAPM try to explain? Explain the types of risk. What type of risk CAPM try to explain? Define the following terms: CAPM, beta and SML. Use graph to explain. Define the following terms: CAPM, beta and SML. Use graph to explain.